PSPL Model Classes

PSPL Photometry + Astrometry, with Parallax

class model.PSPL_PhotAstrom_Par_Param1(*args, **kwargs)

Bases: ModelClassABC, PSPL_PhotAstrom, PSPL_Parallax, PSPL_PhotAstromParam1

Physical parameterization (i.e. mL instead of tE)

PSPL model for astrometry and photometry - physical parameterization.

A Point Source Point Lens model for microlensing. This model uses a parameterization that depends on only physical quantities such as the lens mass and positions and proper motions of both the lens and source.

Note the attributes, RA (raL) and Dec (decL) are required if you are calculating a model with parallax.

Attributes:

mL: float

Mass of the lens (Msun)

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in Solar System barycentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

beta: float

Angular distance between the lens and source on the plane of the sky (mas). Can be

• positive (u0_amp > 0 when u0_hat[0] < 0) or

• negative (u0_amp < 0 when u0_hat[0] > 0).

dL: float

Distance from the observer to the lens (pc)

dL_dS: float

Ratio of Distance from the obersver to the lens to Distance from the observer to the source

xS0_E: float

RA Source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_N: float

Dec source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muL_E: float

RA Lens proper motion (mas/yr)

muL_N: float

Dec Lens proper motion (mas/yr)

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Dec Source proper motion (mas/yr)

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str or list[str], optional

The observers location for each photometric dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing.
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

centroidnumpy array, dtype=float, shape = [len(t), 2]

The flux-weighted centroid of all lensed images from the source and any luminous lenses.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the astrometry for the foreground lens at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLarray_like, dtype=float, shape = [len(t), 2]

Position of the lens on the sky (arcsec).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_Par_Param2(*args, **kwargs)

Bases: ModelClassABC, PSPL_PhotAstrom, PSPL_Parallax, PSPL_PhotAstromParam2

Microlensing params with mag_src

PSPL model for photometry and astrometry – photom-like parameterization

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in Solar System barycentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time (days).

thetaE: float

The size of the Einstein radius in (mas).

piS: float

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_E: float

The microlensing parallax in the East direction in units of thetaE

piE_N: float

The microlensing parallax in the North direction in units of thetaE

xS0_E: float

RA Source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_N: float

Dec source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Source proper motion (mas/yr)

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str or list[str], optional

The observers location for each photometric dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing.
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

centroidnumpy array, dtype=float, shape = [len(t), 2]

The flux-weighted centroid of all lensed images from the source and any luminous lenses.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the astrometry for the foreground lens at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLarray_like, dtype=float, shape = [len(t), 2]

Position of the lens on the sky (arcsec).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_Par_Param3(*args, **kwargs)

Bases: ModelClassABC, PSPL_PhotAstrom, PSPL_Parallax, PSPL_PhotAstromParam3

Microlensing params with mag_base and log10_thetaE

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky. It is the same as PSPL_PhotAstromParam4 except it fits for log10(thetaE) instead of thetaE.

Attributes:

t0float

Time of photometric peak, as seen from Earth (MJD.DDD)

u0_ampfloat

Angular distance between the source and the GEOMETRIC center of the lenses on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tEfloat

Einstein crossing time (days).

log10_thetaEfloat

The size of the Einstein radius in (mas).

piSfloat

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_Efloat

The microlensing parallax in the East direction in units of thetaE

piE_Nfloat

The microlensing parallax in the North direction in units of thetaE

xS0_Efloat

R.A. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_Nfloat

Dec. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_Efloat

RA Source proper motion (mas/yr)

muS_Nfloat

Dec Source proper motion (mas/yr)

b_sffnumpy array or list

The ratio of the source flux to the total (source + neighbors + lenses). One for each filter.

\(b_sff = f_S / (f_S + f_L + f_N)\).

This must be passed in as a list or array, with one entry for each photometric filter.

mag_basenumpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing.
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

centroidnumpy array, dtype=float, shape = [len(t), 2]

The flux-weighted centroid of all lensed images from the source and any luminous lenses.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the astrometry for the foreground lens at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLarray_like, dtype=float, shape = [len(t), 2]

Position of the lens on the sky (arcsec).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_Par_Param4(*args, **kwargs)

Bases: ModelClassABC, PSPL_PhotAstrom, PSPL_Parallax, PSPL_PhotAstromParam4

Microlensing params with mag_base

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky. It is the same as PSPL_PhotAstromParam2 except it fits for baseline instead of source magnitude.

Parameters:

t0float

Time of photometric peak, as seen from Earth (MJD.DDD)

u0_ampfloat

Angular distance between the source and the GEOMETRIC center of the lenses on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tEfloat

Einstein crossing time (days).

thetaE:

The size of the Einstein radius in (mas).

piSfloat

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_Efloat

The microlensing parallax in the East direction in units of thetaE

piE_Nfloat

The microlensing parallax in the North direction in units of thetaE

xS0_Efloat

R.A. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_Nfloat

Dec. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_Efloat

RA Source proper motion (mas/yr)

muS_Nfloat

Dec Source proper motion (mas/yr)

b_sffnumpy array or list

The ratio of the source flux to the total (source + neighbors + lenses). One for each filter.

\(b_sff = f_S / (f_S + f_L + f_N)\).

This must be passed in as a list or array, with one entry for each photometric filter.

mag_basenumpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing.
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

centroidnumpy array, dtype=float, shape = [len(t), 2]

The flux-weighted centroid of all lensed images from the source and any luminous lenses.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the astrometry for the foreground lens at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLarray_like, dtype=float, shape = [len(t), 2]

Position of the lens on the sky (arcsec).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_Par_Param5(*args, **kwargs)

Bases: ModelClassABC, PSPL_PhotAstrom, PSPL_Parallax, PSPL_PhotAstromParam5

Microlensing params with mag_base and piE_E and piE_E/piE_N

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky. It fits for piEN/piEE and piEE, instead of piEE and piEN.

Attributes:

t0float

Time of photometric peak, as seen from Earth (MJD.DDD)

u0_ampfloat

Angular distance between the source and the lens on the plane of the sky at closest approach in units of thetaE. Can

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tEfloat

Einstein crossing time (days).

log10_thetaEfloat

The size of the Einstein radius in (mas).

piSfloat

Amplitude of the parallax (1AU/dS) of the source. (mas)

piEN_piEEfloat

Ratio of piE_N to piE_E.

piE_Efloat

The microlensing parallax in the East direction in units of thetaE

xS0_Efloat

R.A. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_Nfloat

Dec. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_Efloat

RA Source proper motion (mas/yr)

muS_Nfloat

Dec Source proper motion (mas/yr)

b_sffnumpy array or list

The ratio of the source flux to the total (source + neighbors + lenses). One for each filter.

\(b_sff = f_S / (f_S + f_L + f_N)\).

This must be passed in as a list or array, with one entry for each photometric filter.

mag_basenumpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing.
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

centroidnumpy array, dtype=float, shape = [len(t), 2]

The flux-weighted centroid of all lensed images from the source and any luminous lenses.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the astrometry for the foreground lens at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLarray_like, dtype=float, shape = [len(t), 2]

Position of the lens on the sky (arcsec).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

PSPL Photometry + Astrometry, no Parallax

class model.PSPL_PhotAstrom_noPar_Param1(*args, **kwargs)

Bases: ModelClassABC, PSPL_PhotAstrom, PSPL_noParallax, PSPL_PhotAstromParam1

Physical parameterization (i.e. mL instead of tE)

PSPL model for astrometry and photometry - physical parameterization.

A Point Source Point Lens model for microlensing. This model uses a parameterization that depends on only physical quantities such as the lens mass and positions and proper motions of both the lens and source.

Note the attributes, RA (raL) and Dec (decL) are required if you are calculating a model with parallax.

Attributes:

mL: float

Mass of the lens (Msun)

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in Solar System barycentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

beta: float

Angular distance between the lens and source on the plane of the sky (mas). Can be

• positive (u0_amp > 0 when u0_hat[0] < 0) or

• negative (u0_amp < 0 when u0_hat[0] > 0).

dL: float

Distance from the observer to the lens (pc)

dL_dS: float

Ratio of Distance from the obersver to the lens to Distance from the observer to the source

xS0_E: float

RA Source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_N: float

Dec source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muL_E: float

RA Lens proper motion (mas/yr)

muL_N: float

Dec Lens proper motion (mas/yr)

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Dec Source proper motion (mas/yr)

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str or list[str], optional

The observers location for each photometric dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Not supported on this object.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing.
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_lens_astrometry(t[, filt_idx])	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Not supported on this object.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

centroidnumpy array, dtype=float, shape = [len(t), 2]

The flux-weighted centroid of all lensed images from the source and any luminous lenses.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_lens_astrometry(t, filt_idx=0)

Get the astrometry for the foreground lens at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLarray_like, dtype=float, shape = [len(t), 2]

Position of the lens on the sky (arcsec).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_noPar_Param2(*args, **kwargs)

Bases: ModelClassABC, PSPL_PhotAstrom, PSPL_noParallax, PSPL_PhotAstromParam2

Microlensing params with mag_src

PSPL model for photometry and astrometry – photom-like parameterization

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in Solar System barycentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time (days).

thetaE: float

The size of the Einstein radius in (mas).

piS: float

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_E: float

The microlensing parallax in the East direction in units of thetaE

piE_N: float

The microlensing parallax in the North direction in units of thetaE

xS0_E: float

RA Source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_N: float

Dec source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Source proper motion (mas/yr)

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str or list[str], optional

The observers location for each photometric dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Not supported on this object.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing.
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_lens_astrometry(t[, filt_idx])	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Not supported on this object.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

centroidnumpy array, dtype=float, shape = [len(t), 2]

The flux-weighted centroid of all lensed images from the source and any luminous lenses.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_lens_astrometry(t, filt_idx=0)

Get the astrometry for the foreground lens at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLarray_like, dtype=float, shape = [len(t), 2]

Position of the lens on the sky (arcsec).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_noPar_Param3(*args, **kwargs)

Bases: ModelClassABC, PSPL_PhotAstrom, PSPL_noParallax, PSPL_PhotAstromParam3

Microlensing params with mag_base and log10_thetaE

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky. It is the same as PSPL_PhotAstromParam4 except it fits for log10(thetaE) instead of thetaE.

Attributes:

t0float

Time of photometric peak, as seen from Earth (MJD.DDD)

u0_ampfloat

Angular distance between the source and the GEOMETRIC center of the lenses on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tEfloat

Einstein crossing time (days).

log10_thetaEfloat

The size of the Einstein radius in (mas).

piSfloat

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_Efloat

The microlensing parallax in the East direction in units of thetaE

piE_Nfloat

The microlensing parallax in the North direction in units of thetaE

xS0_Efloat

R.A. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_Nfloat

Dec. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_Efloat

RA Source proper motion (mas/yr)

muS_Nfloat

Dec Source proper motion (mas/yr)

b_sffnumpy array or list

The ratio of the source flux to the total (source + neighbors + lenses). One for each filter.

\(b_sff = f_S / (f_S + f_L + f_N)\).

This must be passed in as a list or array, with one entry for each photometric filter.

mag_basenumpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Not supported on this object.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing.
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_lens_astrometry(t[, filt_idx])	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Not supported on this object.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

centroidnumpy array, dtype=float, shape = [len(t), 2]

The flux-weighted centroid of all lensed images from the source and any luminous lenses.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_lens_astrometry(t, filt_idx=0)

Get the astrometry for the foreground lens at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLarray_like, dtype=float, shape = [len(t), 2]

Position of the lens on the sky (arcsec).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_noPar_Param4(*args, **kwargs)

Bases: ModelClassABC, PSPL_PhotAstrom, PSPL_noParallax, PSPL_PhotAstromParam4

Microlensing params with mag_base

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky. It is the same as PSPL_PhotAstromParam2 except it fits for baseline instead of source magnitude.

Parameters:

t0float

Time of photometric peak, as seen from Earth (MJD.DDD)

u0_ampfloat

Angular distance between the source and the GEOMETRIC center of the lenses on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tEfloat

Einstein crossing time (days).

thetaE:

The size of the Einstein radius in (mas).

piSfloat

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_Efloat

The microlensing parallax in the East direction in units of thetaE

piE_Nfloat

The microlensing parallax in the North direction in units of thetaE

xS0_Efloat

R.A. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_Nfloat

Dec. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_Efloat

RA Source proper motion (mas/yr)

muS_Nfloat

Dec Source proper motion (mas/yr)

b_sffnumpy array or list

The ratio of the source flux to the total (source + neighbors + lenses). One for each filter.

\(b_sff = f_S / (f_S + f_L + f_N)\).

This must be passed in as a list or array, with one entry for each photometric filter.

mag_basenumpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Not supported on this object.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing.
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_lens_astrometry(t[, filt_idx])	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Not supported on this object.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

centroidnumpy array, dtype=float, shape = [len(t), 2]

The flux-weighted centroid of all lensed images from the source and any luminous lenses.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_lens_astrometry(t, filt_idx=0)

Get the astrometry for the foreground lens at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLarray_like, dtype=float, shape = [len(t), 2]

Position of the lens on the sky (arcsec).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

PSPL Photometry + Astrometry, Geocentric-Projected Frame

class model.PSPL_PhotAstrom_Par_Param4_geoproj(*args, **kwargs)

Bases: ModelClassABC, PSPL_Parallax, PSPL_PhotAstrom, PSPL_PhotAstromParam4_geoproj

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky. It is the same as PSPL_PhotAstromParam2 except it fits for baseline instead of source magnitude.

Parameters:

t0float

Time of photometric peak, as seen from Earth (MJD.DDD)

u0_ampfloat

Angular distance between the source and the GEOMETRIC center of the lenses on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tEfloat

Einstein crossing time (days).

thetaE:

The size of the Einstein radius in (mas).

piSfloat

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_Efloat

The microlensing parallax in the East direction in units of thetaE

piE_Nfloat

The microlensing parallax in the North direction in units of thetaE

xS0_Efloat

R.A. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_Nfloat

Dec. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_Efloat

RA Source proper motion (mas/yr)

muS_Nfloat

Dec Source proper motion (mas/yr)

b_sffnumpy array or list

The ratio of the source flux to the total (source + neighbors + lenses). One for each filter.

\(b_sff = f_S / (f_S + f_L + f_N)\).

This must be passed in as a list or array, with one entry for each photometric filter.

mag_basenumpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing.
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

centroidnumpy array, dtype=float, shape = [len(t), 2]

The flux-weighted centroid of all lensed images from the source and any luminous lenses.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the astrometry for the foreground lens at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLarray_like, dtype=float, shape = [len(t), 2]

Position of the lens on the sky (arcsec).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

PSPL Photometry Only, with Parallax

class model.PSPL_Phot_Par_Param1(*args, **kwargs)

Bases: ModelClassABC, PSPL_Phot, PSPL_Parallax, PSPL_PhotParam1

PSPL model for photometry only.

Point-source point-lens model for microlensing events with photometry only.

Note the attributes, RA (raL) and Dec (decL) are required if you are calculating a model with parallax.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in Solar System barycentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_{sff} = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str, optional

The observers location for each photometric dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Position of the observed (unresolved) source position in Einstein radii.
get_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source+lens if the lens didn't exist.
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the lens astrometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Position of the observed source position in Einstein radii.
get_source_astrometry_unlensed(t[, filt_idx])	Get the unlensed astrometry of the source.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x, y, xerr, yerr[, ...])	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Position of the observed (unresolved) source position in Einstein radii.

Parameters:

t: array_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t.

get_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source+lens if the lens didn’t exist. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the lens astrometry. In photometry-only coordinates, lens is at the origin.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLnumpy array, shape=[len(t), 2]

Position of the lens on sky, in Einstein radius units. Always zero.

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Position of the observed source position in Einstein radii.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the unlensed astrometry of the source. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii (i.e. vec{u})

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x, y, xerr, yerr, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_Phot_Par_Param2(*args, **kwargs)

Bases: ModelClassABC, PSPL_Phot, PSPL_Parallax, PSPL_PhotParam2

Point source point lens model for microlensing photometry only. This model includes the relative proper motion between the lens and the source. Parameters are reduced with the use of piRel (rather than dL and dS) and muRel (rather than muL and muS). Same as PSPL_PhotParam1, except fits for mag_base instead of mag_src.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in Solar System barycentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be positive (u0_amp > 0 when u0_hat[0] > 0) or negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_base: numpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Position of the observed (unresolved) source position in Einstein radii.
get_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source+lens if the lens didn't exist.
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the lens astrometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Position of the observed source position in Einstein radii.
get_source_astrometry_unlensed(t[, filt_idx])	Get the unlensed astrometry of the source.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x, y, xerr, yerr[, ...])	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Position of the observed (unresolved) source position in Einstein radii.

Parameters:

t: array_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t.

get_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source+lens if the lens didn’t exist. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the lens astrometry. In photometry-only coordinates, lens is at the origin.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLnumpy array, shape=[len(t), 2]

Position of the lens on sky, in Einstein radius units. Always zero.

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Position of the observed source position in Einstein radii.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the unlensed astrometry of the source. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii (i.e. vec{u})

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x, y, xerr, yerr, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_Phot_Par_Param3(*args, **kwargs)

Bases: ModelClassABC, PSPL_Phot, PSPL_Parallax, PSPL_PhotParam3

Point source point lens model for microlensing photometry only. Utilizes angle of muRel instead of piEE and pEN. Also fits in log(piE) and log(tE).

Attributes:

t0: float

Heliocentric time of closest approach (u0) between source and lens in MJD (MJD.DDD)

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be positive (u0_amp > 0 when u0_hat[0] > 0) or negative (u0_amp < 0 when u0_hat[0] < 0).

log_tE: float

Einstein crossing time in days.

log_piEfloat

The log of the microlensing parallax amplitude.

phi_muRelfloat

The angle of the muRel vector, in degrees. Angle is measured in degrees East of North (counter-clockwise on the sky from North).

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_base: numpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Position of the observed (unresolved) source position in Einstein radii.
get_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source+lens if the lens didn't exist.
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the lens astrometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Position of the observed source position in Einstein radii.
get_source_astrometry_unlensed(t[, filt_idx])	Get the unlensed astrometry of the source.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x, y, xerr, yerr[, ...])	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Position of the observed (unresolved) source position in Einstein radii.

Parameters:

t: array_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t.

get_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source+lens if the lens didn’t exist. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the lens astrometry. In photometry-only coordinates, lens is at the origin.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLnumpy array, shape=[len(t), 2]

Position of the lens on sky, in Einstein radius units. Always zero.

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Position of the observed source position in Einstein radii.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the unlensed astrometry of the source. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii (i.e. vec{u})

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x, y, xerr, yerr, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

PSPL Photometry Only, no Parallax

class model.PSPL_Phot_noPar_Param1(*args, **kwargs)

Bases: ModelClassABC, PSPL_Phot, PSPL_noParallax, PSPL_PhotParam1

Microlensing params with mag_src

PSPL model for photometry only.

Point-source point-lens model for microlensing events with photometry only.

Note the attributes, RA (raL) and Dec (decL) are required if you are calculating a model with parallax.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in Solar System barycentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_{sff} = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str, optional

The observers location for each photometric dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Not supported on this object.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Position of the observed (unresolved) source position in Einstein radii.
get_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source+lens if the lens didn't exist.
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_lens_astrometry(t[, filt_idx])	Get the lens astrometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Position of the observed source position in Einstein radii.
get_source_astrometry_unlensed(t[, filt_idx])	Get the unlensed astrometry of the source.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x, y, xerr, yerr[, ...])	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Not supported on this object.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Position of the observed (unresolved) source position in Einstein radii.

Parameters:

t: array_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t.

get_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source+lens if the lens didn’t exist. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_lens_astrometry(t, filt_idx=0)

Get the lens astrometry. In photometry-only coordinates, lens is at the origin.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLnumpy array, shape=[len(t), 2]

Position of the lens on sky, in Einstein radius units. Always zero.

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Position of the observed source position in Einstein radii.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the unlensed astrometry of the source. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii (i.e. vec{u})

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x, y, xerr, yerr, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_Phot_noPar_Param2(*args, **kwargs)

Bases: ModelClassABC, PSPL_Phot, PSPL_noParallax, PSPL_PhotParam2

Microlensing params with mag_base

Point source point lens model for microlensing photometry only. This model includes the relative proper motion between the lens and the source. Parameters are reduced with the use of piRel (rather than dL and dS) and muRel (rather than muL and muS). Same as PSPL_PhotParam1, except fits for mag_base instead of mag_src.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in Solar System barycentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be positive (u0_amp > 0 when u0_hat[0] > 0) or negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_base: numpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Not supported on this object.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Position of the observed (unresolved) source position in Einstein radii.
get_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source+lens if the lens didn't exist.
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_lens_astrometry(t[, filt_idx])	Get the lens astrometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Position of the observed source position in Einstein radii.
get_source_astrometry_unlensed(t[, filt_idx])	Get the unlensed astrometry of the source.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x, y, xerr, yerr[, ...])	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Not supported on this object.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Position of the observed (unresolved) source position in Einstein radii.

Parameters:

t: array_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t.

get_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source+lens if the lens didn’t exist. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_lens_astrometry(t, filt_idx=0)

Get the lens astrometry. In photometry-only coordinates, lens is at the origin.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLnumpy array, shape=[len(t), 2]

Position of the lens on sky, in Einstein radius units. Always zero.

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Position of the observed source position in Einstein radii.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the unlensed astrometry of the source. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii (i.e. vec{u})

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x, y, xerr, yerr, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_Phot_noPar_Param3(*args, **kwargs)

Bases: ModelClassABC, PSPL_Phot, PSPL_noParallax, PSPL_PhotParam3

Microlensing params with mag_base, log_tE, log_piE, and phi_muRel

Point source point lens model for microlensing photometry only. Utilizes angle of muRel instead of piEE and pEN. Also fits in log(piE) and log(tE).

Attributes:

t0: float

Heliocentric time of closest approach (u0) between source and lens in MJD (MJD.DDD)

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be positive (u0_amp > 0 when u0_hat[0] > 0) or negative (u0_amp < 0 when u0_hat[0] < 0).

log_tE: float

Einstein crossing time in days.

log_piEfloat

The log of the microlensing parallax amplitude.

phi_muRelfloat

The angle of the muRel vector, in degrees. Angle is measured in degrees East of North (counter-clockwise on the sky from North).

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_base: numpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Not supported on this object.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Position of the observed (unresolved) source position in Einstein radii.
get_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source+lens if the lens didn't exist.
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_lens_astrometry(t[, filt_idx])	Get the lens astrometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Position of the observed source position in Einstein radii.
get_source_astrometry_unlensed(t[, filt_idx])	Get the unlensed astrometry of the source.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x, y, xerr, yerr[, ...])	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Not supported on this object.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Position of the observed (unresolved) source position in Einstein radii.

Parameters:

t: array_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t.

get_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source+lens if the lens didn’t exist. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_lens_astrometry(t, filt_idx=0)

Get the lens astrometry. In photometry-only coordinates, lens is at the origin.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLnumpy array, shape=[len(t), 2]

Position of the lens on sky, in Einstein radius units. Always zero.

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Position of the observed source position in Einstein radii.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the unlensed astrometry of the source. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii (i.e. vec{u})

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x, y, xerr, yerr, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

PSPL Photometry Only, Geocentric-Projected Frame

class model.PSPL_Phot_Par_Param1_geoproj(*args, **kwargs)

Bases: ModelClassABC, PSPL_Parallax, PSPL_Phot, PSPL_PhotParam1_geoproj

PSPL model for photometry only.

Point-source point-lens model for microlensing events with photometry only.

Note the attributes, RA (raL) and Dec (decL) are required if you are calculating a model with parallax.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in Solar System barycentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_{sff} = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str, optional

The observers location for each photometric dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Position of the observed (unresolved) source position in Einstein radii.
get_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source+lens if the lens didn't exist.
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the lens astrometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Position of the observed source position in Einstein radii.
get_source_astrometry_unlensed(t[, filt_idx])	Get the unlensed astrometry of the source.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x, y, xerr, yerr[, ...])	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Position of the observed (unresolved) source position in Einstein radii.

Parameters:

t: array_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t.

get_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source+lens if the lens didn’t exist. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the lens astrometry. In photometry-only coordinates, lens is at the origin.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLnumpy array, shape=[len(t), 2]

Position of the lens on sky, in Einstein radius units. Always zero.

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Position of the observed source position in Einstein radii.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the unlensed astrometry of the source. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii (i.e. vec{u})

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x, y, xerr, yerr, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

PSPL Astrometry Only, with Parallax

class model.PSPL_Astrom_Par_Param4(*args, **kwargs)

Bases: ModelClassABC, PSPL_Astrom, PSPL_Parallax, PSPL_AstromParam4

Microlensing params with mag_base

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky. It is the same as PSPL_PhotAstromParam2 except it fits for baseline instead of source magnitude.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in Solar System barycentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time (days).

thetaE: float

The size of the Einstein radius in (mas).

piS: float

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_E: float

The microlensing parallax in the East direction in units of thetaE

piE_N: float

The microlensing parallax in the North direction in units of thetaE

xS0_E: float

RA Source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_N: float

Dec source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Dec Source proper motion (mas/yr)

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing.
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

centroidnumpy array, dtype=float, shape = [len(t), 2]

The flux-weighted centroid of all lensed images from the source and any luminous lenses.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the astrometry for the foreground lens at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLarray_like, dtype=float, shape = [len(t), 2]

Position of the lens on the sky (arcsec).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_Astrom_Par_Param3(*args, **kwargs)

Bases: ModelClassABC, PSPL_Astrom, PSPL_Parallax, PSPL_AstromParam3

Microlensing params with mag_base and log10_thetaE

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky. It is the same as PSPL_PhotAstromParam3 except it fits only astrometry, no photometry.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in Solar System barycentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time (days).

log10_thetaE: float

The log of the Einstein radius log10(thetaE/mas).

piS: float

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_E: float

The microlensing parallax in the East direction in units of thetaE

piE_N: float

The microlensing parallax in the North direction in units of thetaE

xS0_E: float

RA Source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_N: float

Dec source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Dec Source proper motion (mas/yr)

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing.
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

centroidnumpy array, dtype=float, shape = [len(t), 2]

The flux-weighted centroid of all lensed images from the source and any luminous lenses.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the astrometry for the foreground lens at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLarray_like, dtype=float, shape = [len(t), 2]

Position of the lens on the sky (arcsec).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

PSPL Photometry Only, with GP

class model.PSPL_Phot_Par_GP_Param1(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_Phot, PSPL_Parallax, PSPL_GP_PhotParam1

PSPL model for photometry only.

Point-source point-lens model for microlensing events with photometry only.

Note the attributes, RA (raL) and Dec (decL) are required if you are calculating a model with parallax.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in Solar System barycentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_{sff} = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str, optional

The observers location for each photometric dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Position of the observed (unresolved) source position in Einstein radii.
get_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source+lens if the lens didn't exist.
get_celerite_gp_object(mag_err_obs[, filt_idx])	Returns a celerite GP object that is used for all GP operations
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the lens astrometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Position of the observed source position in Einstein radii.
get_source_astrometry_unlensed(t[, filt_idx])	Get the unlensed astrometry of the source.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x, y, xerr, yerr[, ...])	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Position of the observed (unresolved) source position in Einstein radii.

Parameters:

t: array_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t.

get_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source+lens if the lens didn’t exist. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

get_celerite_gp_object(mag_err_obs, filt_idx=0)

Returns a celerite GP object that is used for all GP operations

Parameters:

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. The mean of mag_err_obs is inputted into the jitter term of the kernel if ‘gp_log_jit_sigma’ is not a parameter.

filt_idxinteger

An integer indicating which photometric data set should be used for the GP.

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Returns:

gpa celerite GP object

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the lens astrometry. In photometry-only coordinates, lens is at the origin.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLnumpy array, shape=[len(t), 2]

Position of the lens on sky, in Einstein radius units. Always zero.

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_photometry_with_gp(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Parameters:

tarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t. This is the “predictive mean” of the GP.

mag_model_stdarray_like

Standard deviation of the magnitude of the unresolved microlensing event at t. This comes from the diagonal (the varainces) of the “predictive covariance” of the GP.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Position of the observed source position in Einstein radii.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the unlensed astrometry of the source. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii (i.e. vec{u})

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x, y, xerr, yerr, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_idx] = True.

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_Phot_Par_GP_Param2(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_Phot, PSPL_Parallax, PSPL_GP_PhotParam2

Point source point lens model for microlensing photometry only. This model includes the relative proper motion between the lens and the source. Parameters are reduced with the use of piRel (rather than dL and dS) and muRel (rather than muL and muS). Same as PSPL_PhotParam1, except fits for mag_base instead of mag_src.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in Solar System barycentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be positive (u0_amp > 0 when u0_hat[0] > 0) or negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_base: numpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Position of the observed (unresolved) source position in Einstein radii.
get_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source+lens if the lens didn't exist.
get_celerite_gp_object(mag_err_obs[, filt_idx])	Returns a celerite GP object that is used for all GP operations
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the lens astrometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Position of the observed source position in Einstein radii.
get_source_astrometry_unlensed(t[, filt_idx])	Get the unlensed astrometry of the source.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x, y, xerr, yerr[, ...])	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Position of the observed (unresolved) source position in Einstein radii.

Parameters:

t: array_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t.

get_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source+lens if the lens didn’t exist. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

get_celerite_gp_object(mag_err_obs, filt_idx=0)

Returns a celerite GP object that is used for all GP operations

Parameters:

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. The mean of mag_err_obs is inputted into the jitter term of the kernel if ‘gp_log_jit_sigma’ is not a parameter.

filt_idxinteger

An integer indicating which photometric data set should be used for the GP.

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Returns:

gpa celerite GP object

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the lens astrometry. In photometry-only coordinates, lens is at the origin.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLnumpy array, shape=[len(t), 2]

Position of the lens on sky, in Einstein radius units. Always zero.

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_photometry_with_gp(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Parameters:

tarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t. This is the “predictive mean” of the GP.

mag_model_stdarray_like

Standard deviation of the magnitude of the unresolved microlensing event at t. This comes from the diagonal (the varainces) of the “predictive covariance” of the GP.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Position of the observed source position in Einstein radii.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the unlensed astrometry of the source. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii (i.e. vec{u})

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x, y, xerr, yerr, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_idx] = True.

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_Phot_Par_GP_Param3(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_Phot, PSPL_Parallax, PSPL_GP_PhotParam3

Point source point lens model for microlensing photometry only. Utilizes angle of muRel instead of piEE and pEN. Also fits in log(piE) and log(tE).

Attributes:

t0: float

Heliocentric time of closest approach (u0) between source and lens in MJD (MJD.DDD)

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be positive (u0_amp > 0 when u0_hat[0] > 0) or negative (u0_amp < 0 when u0_hat[0] < 0).

log_tE: float

Einstein crossing time in days.

log_piEfloat

The log of the microlensing parallax amplitude.

phi_muRelfloat

The angle of the muRel vector, in degrees. Angle is measured in degrees East of North (counter-clockwise on the sky from North).

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_base: numpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Position of the observed (unresolved) source position in Einstein radii.
get_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source+lens if the lens didn't exist.
get_celerite_gp_object(mag_err_obs[, filt_idx])	Returns a celerite GP object that is used for all GP operations
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the lens astrometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Position of the observed source position in Einstein radii.
get_source_astrometry_unlensed(t[, filt_idx])	Get the unlensed astrometry of the source.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x, y, xerr, yerr[, ...])	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Position of the observed (unresolved) source position in Einstein radii.

Parameters:

t: array_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t.

get_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source+lens if the lens didn’t exist. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

get_celerite_gp_object(mag_err_obs, filt_idx=0)

Returns a celerite GP object that is used for all GP operations

Parameters:

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. The mean of mag_err_obs is inputted into the jitter term of the kernel if ‘gp_log_jit_sigma’ is not a parameter.

filt_idxinteger

An integer indicating which photometric data set should be used for the GP.

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Returns:

gpa celerite GP object

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the lens astrometry. In photometry-only coordinates, lens is at the origin.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLnumpy array, shape=[len(t), 2]

Position of the lens on sky, in Einstein radius units. Always zero.

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_photometry_with_gp(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Parameters:

tarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t. This is the “predictive mean” of the GP.

mag_model_stdarray_like

Standard deviation of the magnitude of the unresolved microlensing event at t. This comes from the diagonal (the varainces) of the “predictive covariance” of the GP.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Position of the observed source position in Einstein radii.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the unlensed astrometry of the source. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii (i.e. vec{u})

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x, y, xerr, yerr, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_idx] = True.

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_Phot_Par_GP_Param1_2(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_Phot, PSPL_Parallax, PSPL_GP_PhotParam1_2

PSPL model for photometry only.

Point-source point-lens model for microlensing events with photometry only.

Note the attributes, RA (raL) and Dec (decL) are required if you are calculating a model with parallax.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in Solar System barycentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_{sff} = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str, optional

The observers location for each photometric dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Position of the observed (unresolved) source position in Einstein radii.
get_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source+lens if the lens didn't exist.
get_celerite_gp_object(mag_err_obs[, filt_idx])	Returns a celerite GP object that is used for all GP operations
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the lens astrometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Position of the observed source position in Einstein radii.
get_source_astrometry_unlensed(t[, filt_idx])	Get the unlensed astrometry of the source.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x, y, xerr, yerr[, ...])	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Position of the observed (unresolved) source position in Einstein radii.

Parameters:

t: array_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t.

get_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source+lens if the lens didn’t exist. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

get_celerite_gp_object(mag_err_obs, filt_idx=0)

Returns a celerite GP object that is used for all GP operations

Parameters:

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. The mean of mag_err_obs is inputted into the jitter term of the kernel if ‘gp_log_jit_sigma’ is not a parameter.

filt_idxinteger

An integer indicating which photometric data set should be used for the GP.

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Returns:

gpa celerite GP object

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the lens astrometry. In photometry-only coordinates, lens is at the origin.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLnumpy array, shape=[len(t), 2]

Position of the lens on sky, in Einstein radius units. Always zero.

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_photometry_with_gp(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Parameters:

tarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t. This is the “predictive mean” of the GP.

mag_model_stdarray_like

Standard deviation of the magnitude of the unresolved microlensing event at t. This comes from the diagonal (the varainces) of the “predictive covariance” of the GP.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Position of the observed source position in Einstein radii.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the unlensed astrometry of the source. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii (i.e. vec{u})

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x, y, xerr, yerr, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_idx] = True.

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_Phot_Par_GP_Param2_2(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_Phot, PSPL_Parallax, PSPL_GP_PhotParam2_2

Point source point lens model for microlensing photometry only. This model includes the relative proper motion between the lens and the source. Parameters are reduced with the use of piRel (rather than dL and dS) and muRel (rather than muL and muS). Same as PSPL_PhotParam1, except fits for mag_base instead of mag_src.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in Solar System barycentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be positive (u0_amp > 0 when u0_hat[0] > 0) or negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_base: numpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Position of the observed (unresolved) source position in Einstein radii.
get_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source+lens if the lens didn't exist.
get_celerite_gp_object(mag_err_obs[, filt_idx])	Returns a celerite GP object that is used for all GP operations
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the lens astrometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Position of the observed source position in Einstein radii.
get_source_astrometry_unlensed(t[, filt_idx])	Get the unlensed astrometry of the source.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x, y, xerr, yerr[, ...])	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Position of the observed (unresolved) source position in Einstein radii.

Parameters:

t: array_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t.

get_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source+lens if the lens didn’t exist. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

get_celerite_gp_object(mag_err_obs, filt_idx=0)

Returns a celerite GP object that is used for all GP operations

Parameters:

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. The mean of mag_err_obs is inputted into the jitter term of the kernel if ‘gp_log_jit_sigma’ is not a parameter.

filt_idxinteger

An integer indicating which photometric data set should be used for the GP.

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Returns:

gpa celerite GP object

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the lens astrometry. In photometry-only coordinates, lens is at the origin.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLnumpy array, shape=[len(t), 2]

Position of the lens on sky, in Einstein radius units. Always zero.

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_photometry_with_gp(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Parameters:

tarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t. This is the “predictive mean” of the GP.

mag_model_stdarray_like

Standard deviation of the magnitude of the unresolved microlensing event at t. This comes from the diagonal (the varainces) of the “predictive covariance” of the GP.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Position of the observed source position in Einstein radii.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the unlensed astrometry of the source. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii (i.e. vec{u})

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x, y, xerr, yerr, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_idx] = True.

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_Phot_Par_GP_Param2_3(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_Phot, PSPL_Parallax, PSPL_GP_PhotParam2_3

Point source point lens model for microlensing photometry only. This model includes the relative proper motion between the lens and the source. Parameters are reduced with the use of piRel (rather than dL and dS) and muRel (rather than muL and muS). Same as PSPL_PhotParam1, except fits for mag_base instead of mag_src.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in Solar System barycentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be positive (u0_amp > 0 when u0_hat[0] > 0) or negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_base: numpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Position of the observed (unresolved) source position in Einstein radii.
get_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source+lens if the lens didn't exist.
get_celerite_gp_object(mag_err_obs[, filt_idx])	Returns a celerite GP object that is used for all GP operations
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the lens astrometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Position of the observed source position in Einstein radii.
get_source_astrometry_unlensed(t[, filt_idx])	Get the unlensed astrometry of the source.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x, y, xerr, yerr[, ...])	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Position of the observed (unresolved) source position in Einstein radii.

Parameters:

t: array_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t.

get_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source+lens if the lens didn’t exist. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

get_celerite_gp_object(mag_err_obs, filt_idx=0)

Returns a celerite GP object that is used for all GP operations

Parameters:

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. The mean of mag_err_obs is inputted into the jitter term of the kernel if ‘gp_log_jit_sigma’ is not a parameter.

filt_idxinteger

An integer indicating which photometric data set should be used for the GP.

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Returns:

gpa celerite GP object

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the lens astrometry. In photometry-only coordinates, lens is at the origin.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLnumpy array, shape=[len(t), 2]

Position of the lens on sky, in Einstein radius units. Always zero.

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_photometry_with_gp(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Parameters:

tarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t. This is the “predictive mean” of the GP.

mag_model_stdarray_like

Standard deviation of the magnitude of the unresolved microlensing event at t. This comes from the diagonal (the varainces) of the “predictive covariance” of the GP.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Position of the observed source position in Einstein radii.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the unlensed astrometry of the source. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii (i.e. vec{u})

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x, y, xerr, yerr, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_idx] = True.

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_Phot_Par_GP_Param2_4(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_Phot, PSPL_Parallax, PSPL_GP_PhotParam2_4

Point source point lens model for microlensing photometry only. This model includes the relative proper motion between the lens and the source. Parameters are reduced with the use of piRel (rather than dL and dS) and muRel (rather than muL and muS). Same as PSPL_PhotParam1, except fits for mag_base instead of mag_src.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in Solar System barycentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be positive (u0_amp > 0 when u0_hat[0] > 0) or negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_base: numpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Position of the observed (unresolved) source position in Einstein radii.
get_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source+lens if the lens didn't exist.
get_celerite_gp_object(mag_err_obs[, filt_idx])	Returns a celerite GP object that is used for all GP operations
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the lens astrometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Position of the observed source position in Einstein radii.
get_source_astrometry_unlensed(t[, filt_idx])	Get the unlensed astrometry of the source.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x, y, xerr, yerr[, ...])	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Position of the observed (unresolved) source position in Einstein radii.

Parameters:

t: array_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t.

get_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source+lens if the lens didn’t exist. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

get_celerite_gp_object(mag_err_obs, filt_idx=0)

Returns a celerite GP object that is used for all GP operations

Parameters:

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. The mean of mag_err_obs is inputted into the jitter term of the kernel if ‘gp_log_jit_sigma’ is not a parameter.

filt_idxinteger

An integer indicating which photometric data set should be used for the GP.

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Returns:

gpa celerite GP object

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the lens astrometry. In photometry-only coordinates, lens is at the origin.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLnumpy array, shape=[len(t), 2]

Position of the lens on sky, in Einstein radius units. Always zero.

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_photometry_with_gp(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Parameters:

tarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t. This is the “predictive mean” of the GP.

mag_model_stdarray_like

Standard deviation of the magnitude of the unresolved microlensing event at t. This comes from the diagonal (the varainces) of the “predictive covariance” of the GP.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Position of the observed source position in Einstein radii.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the unlensed astrometry of the source. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii (i.e. vec{u})

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x, y, xerr, yerr, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_idx] = True.

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_Phot_Par_GP_Param2_5(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_Phot, PSPL_Parallax, PSPL_GP_PhotParam2_5

Point source point lens model for microlensing photometry only. This model includes the relative proper motion between the lens and the source. Parameters are reduced with the use of piRel (rather than dL and dS) and muRel (rather than muL and muS). Same as PSPL_PhotParam1, except fits for mag_base instead of mag_src.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in Solar System barycentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be positive (u0_amp > 0 when u0_hat[0] > 0) or negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_base: numpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Position of the observed (unresolved) source position in Einstein radii.
get_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source+lens if the lens didn't exist.
get_celerite_gp_object(mag_err_obs[, filt_idx])	Returns a celerite GP object that is used for all GP operations
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the lens astrometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Position of the observed source position in Einstein radii.
get_source_astrometry_unlensed(t[, filt_idx])	Get the unlensed astrometry of the source.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x, y, xerr, yerr[, ...])	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Position of the observed (unresolved) source position in Einstein radii.

Parameters:

t: array_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t.

get_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source+lens if the lens didn’t exist. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

get_celerite_gp_object(mag_err_obs, filt_idx=0)

Returns a celerite GP object that is used for all GP operations

Parameters:

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. The mean of mag_err_obs is inputted into the jitter term of the kernel if ‘gp_log_jit_sigma’ is not a parameter.

filt_idxinteger

An integer indicating which photometric data set should be used for the GP.

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Returns:

gpa celerite GP object

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the lens astrometry. In photometry-only coordinates, lens is at the origin.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLnumpy array, shape=[len(t), 2]

Position of the lens on sky, in Einstein radius units. Always zero.

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_photometry_with_gp(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Parameters:

tarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t. This is the “predictive mean” of the GP.

mag_model_stdarray_like

Standard deviation of the magnitude of the unresolved microlensing event at t. This comes from the diagonal (the varainces) of the “predictive covariance” of the GP.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Position of the observed source position in Einstein radii.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the unlensed astrometry of the source. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii (i.e. vec{u})

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x, y, xerr, yerr, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_idx] = True.

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_Phot_Par_GPnoJitter_Param2_2(*args, **kwargs)

Bases: ModelClassABC, PSPL_GPnoJitter, PSPL_Phot, PSPL_Parallax, PSPL_GP_PhotParam2_2

Point source point lens model for microlensing photometry only. This model includes the relative proper motion between the lens and the source. Parameters are reduced with the use of piRel (rather than dL and dS) and muRel (rather than muL and muS). Same as PSPL_PhotParam1, except fits for mag_base instead of mag_src.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in Solar System barycentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be positive (u0_amp > 0 when u0_hat[0] > 0) or negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_base: numpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Position of the observed (unresolved) source position in Einstein radii.
get_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source+lens if the lens didn't exist.
get_celerite_gp_object([filt_idx])	Returns a celerite GP object that is used for all GP operations
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the lens astrometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Position of the observed source position in Einstein radii.
get_source_astrometry_unlensed(t[, filt_idx])	Get the unlensed astrometry of the source.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x, y, xerr, yerr[, ...])	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Position of the observed (unresolved) source position in Einstein radii.

Parameters:

t: array_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t.

get_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source+lens if the lens didn’t exist. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

get_celerite_gp_object(filt_idx=0)

Returns a celerite GP object that is used for all GP operations

Parameters:

filt_idxinteger

An integer indicating which photometric data set should be used for the GP.

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Returns:

gpa celerite GP object

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the lens astrometry. In photometry-only coordinates, lens is at the origin.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLnumpy array, shape=[len(t), 2]

Position of the lens on sky, in Einstein radius units. Always zero.

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_photometry_with_gp(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Parameters:

tarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t. This is the “predictive mean” of the GP.

mag_model_stdarray_like

Standard deviation of the magnitude of the unresolved microlensing event at t. This comes from the diagonal (the varainces) of the “predictive covariance” of the GP.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Position of the observed source position in Einstein radii.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the unlensed astrometry of the source. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii (i.e. vec{u})

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x, y, xerr, yerr, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

The GP will only be used for filters where use_gp_phot[filt_idx] = True.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_Phot_Par_GPnoJitter_Param2_3(*args, **kwargs)

Bases: ModelClassABC, PSPL_GPnoJitter, PSPL_Phot, PSPL_Parallax, PSPL_GP_PhotParam2_3

Point source point lens model for microlensing photometry only. This model includes the relative proper motion between the lens and the source. Parameters are reduced with the use of piRel (rather than dL and dS) and muRel (rather than muL and muS). Same as PSPL_PhotParam1, except fits for mag_base instead of mag_src.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in Solar System barycentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be positive (u0_amp > 0 when u0_hat[0] > 0) or negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_base: numpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Position of the observed (unresolved) source position in Einstein radii.
get_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source+lens if the lens didn't exist.
get_celerite_gp_object([filt_idx])	Returns a celerite GP object that is used for all GP operations
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the lens astrometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Position of the observed source position in Einstein radii.
get_source_astrometry_unlensed(t[, filt_idx])	Get the unlensed astrometry of the source.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x, y, xerr, yerr[, ...])	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Position of the observed (unresolved) source position in Einstein radii.

Parameters:

t: array_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t.

get_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source+lens if the lens didn’t exist. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

get_celerite_gp_object(filt_idx=0)

Returns a celerite GP object that is used for all GP operations

Parameters:

filt_idxinteger

An integer indicating which photometric data set should be used for the GP.

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Returns:

gpa celerite GP object

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the lens astrometry. In photometry-only coordinates, lens is at the origin.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLnumpy array, shape=[len(t), 2]

Position of the lens on sky, in Einstein radius units. Always zero.

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_photometry_with_gp(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Parameters:

tarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t. This is the “predictive mean” of the GP.

mag_model_stdarray_like

Standard deviation of the magnitude of the unresolved microlensing event at t. This comes from the diagonal (the varainces) of the “predictive covariance” of the GP.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Position of the observed source position in Einstein radii.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the unlensed astrometry of the source. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii (i.e. vec{u})

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x, y, xerr, yerr, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

The GP will only be used for filters where use_gp_phot[filt_idx] = True.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_Phot_noPar_GP_Param1(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_Phot, PSPL_noParallax, PSPL_GP_PhotParam1

PSPL model for photometry only.

Point-source point-lens model for microlensing events with photometry only.

Note the attributes, RA (raL) and Dec (decL) are required if you are calculating a model with parallax.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in Solar System barycentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_{sff} = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str, optional

The observers location for each photometric dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Not supported on this object.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Position of the observed (unresolved) source position in Einstein radii.
get_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source+lens if the lens didn't exist.
get_celerite_gp_object(mag_err_obs[, filt_idx])	Returns a celerite GP object that is used for all GP operations
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_lens_astrometry(t[, filt_idx])	Get the lens astrometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Position of the observed source position in Einstein radii.
get_source_astrometry_unlensed(t[, filt_idx])	Get the unlensed astrometry of the source.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x, y, xerr, yerr[, ...])	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Not supported on this object.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Position of the observed (unresolved) source position in Einstein radii.

Parameters:

t: array_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t.

get_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source+lens if the lens didn’t exist. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

get_celerite_gp_object(mag_err_obs, filt_idx=0)

Returns a celerite GP object that is used for all GP operations

Parameters:

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. The mean of mag_err_obs is inputted into the jitter term of the kernel if ‘gp_log_jit_sigma’ is not a parameter.

filt_idxinteger

An integer indicating which photometric data set should be used for the GP.

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Returns:

gpa celerite GP object

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_lens_astrometry(t, filt_idx=0)

Get the lens astrometry. In photometry-only coordinates, lens is at the origin.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLnumpy array, shape=[len(t), 2]

Position of the lens on sky, in Einstein radius units. Always zero.

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_photometry_with_gp(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Parameters:

tarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t. This is the “predictive mean” of the GP.

mag_model_stdarray_like

Standard deviation of the magnitude of the unresolved microlensing event at t. This comes from the diagonal (the varainces) of the “predictive covariance” of the GP.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Position of the observed source position in Einstein radii.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the unlensed astrometry of the source. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii (i.e. vec{u})

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x, y, xerr, yerr, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_idx] = True.

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_Phot_noPar_GP_Param2(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_Phot, PSPL_noParallax, PSPL_GP_PhotParam2

Point source point lens model for microlensing photometry only. This model includes the relative proper motion between the lens and the source. Parameters are reduced with the use of piRel (rather than dL and dS) and muRel (rather than muL and muS). Same as PSPL_PhotParam1, except fits for mag_base instead of mag_src.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in Solar System barycentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. It can be positive (u0_amp > 0 when u0_hat[0] > 0) or negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time in days.

piE_E: float

The microlensing parallax in the East direction in units of thetaE.

piE_N: float

The microlensing parallax in the North direction in units of thetaE

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_base: numpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Not supported on this object.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Position of the observed (unresolved) source position in Einstein radii.
get_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source+lens if the lens didn't exist.
get_celerite_gp_object(mag_err_obs[, filt_idx])	Returns a celerite GP object that is used for all GP operations
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_lens_astrometry(t[, filt_idx])	Get the lens astrometry.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Position of the observed source position in Einstein radii.
get_source_astrometry_unlensed(t[, filt_idx])	Get the unlensed astrometry of the source.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x, y, xerr, yerr[, ...])	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Not supported on this object.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Position of the observed (unresolved) source position in Einstein radii.

Parameters:

t: array_like

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t.

get_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source+lens if the lens didn’t exist. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

get_celerite_gp_object(mag_err_obs, filt_idx=0)

Returns a celerite GP object that is used for all GP operations

Parameters:

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. The mean of mag_err_obs is inputted into the jitter term of the kernel if ‘gp_log_jit_sigma’ is not a parameter.

filt_idxinteger

An integer indicating which photometric data set should be used for the GP.

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Returns:

gpa celerite GP object

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_lens_astrometry(t, filt_idx=0)

Get the lens astrometry. In photometry-only coordinates, lens is at the origin.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLnumpy array, shape=[len(t), 2]

Position of the lens on sky, in Einstein radius units. Always zero.

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_photometry_with_gp(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Parameters:

tarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t. This is the “predictive mean” of the GP.

mag_model_stdarray_like

Standard deviation of the magnitude of the unresolved microlensing event at t. This comes from the diagonal (the varainces) of the “predictive covariance” of the GP.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Position of the observed source position in Einstein radii.

Parameters:

tarray_like, shape = [N_times]

Array of times to model.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the unlensed astrometry of the source. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii (i.e. vec{u})

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x, y, xerr, yerr, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_idx] = True.

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

PSPL Photometry + Astrometry, with GP

class model.PSPL_PhotAstrom_Par_GP_Param1(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_PhotAstrom, PSPL_Parallax, PSPL_GP_PhotAstromParam1

PSPL model for astrometry and photometry - physical parameterization.

A Point Source Point Lens model for microlensing. This model uses a parameterization that depends on only physical quantities such as the lens mass and positions and proper motions of both the lens and source.

Note the attributes, RA (raL) and Dec (decL) are required if you are calculating a model with parallax.

Attributes:

mL: float

Mass of the lens (Msun)

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in Solar System barycentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

beta: float

Angular distance between the lens and source on the plane of the sky (mas). Can be

• positive (u0_amp > 0 when u0_hat[0] < 0) or

• negative (u0_amp < 0 when u0_hat[0] > 0).

dL: float

Distance from the observer to the lens (pc)

dL_dS: float

Ratio of Distance from the obersver to the lens to Distance from the observer to the source

xS0_E: float

RA Source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_N: float

Dec source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muL_E: float

RA Lens proper motion (mas/yr)

muL_N: float

Dec Lens proper motion (mas/yr)

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Dec Source proper motion (mas/yr)

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str or list[str], optional

The observers location for each photometric dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing.
get_celerite_gp_object(mag_err_obs[, filt_idx])	Returns a celerite GP object that is used for all GP operations
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

centroidnumpy array, dtype=float, shape = [len(t), 2]

The flux-weighted centroid of all lensed images from the source and any luminous lenses.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_celerite_gp_object(mag_err_obs, filt_idx=0)

Returns a celerite GP object that is used for all GP operations

Parameters:

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. The mean of mag_err_obs is inputted into the jitter term of the kernel if ‘gp_log_jit_sigma’ is not a parameter.

filt_idxinteger

An integer indicating which photometric data set should be used for the GP.

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Returns:

gpa celerite GP object

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the astrometry for the foreground lens at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLarray_like, dtype=float, shape = [len(t), 2]

Position of the lens on the sky (arcsec).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_photometry_with_gp(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Parameters:

tarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t. This is the “predictive mean” of the GP.

mag_model_stdarray_like

Standard deviation of the magnitude of the unresolved microlensing event at t. This comes from the diagonal (the varainces) of the “predictive covariance” of the GP.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_idx] = True.

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_Par_GP_Param2(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_PhotAstrom, PSPL_Parallax, PSPL_GP_PhotAstromParam2

PSPL model for photometry and astrometry – photom-like parameterization

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in Solar System barycentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time (days).

thetaE: float

The size of the Einstein radius in (mas).

piS: float

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_E: float

The microlensing parallax in the East direction in units of thetaE

piE_N: float

The microlensing parallax in the North direction in units of thetaE

xS0_E: float

RA Source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_N: float

Dec source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Source proper motion (mas/yr)

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str or list[str], optional

The observers location for each photometric dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing.
get_celerite_gp_object(mag_err_obs[, filt_idx])	Returns a celerite GP object that is used for all GP operations
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

centroidnumpy array, dtype=float, shape = [len(t), 2]

The flux-weighted centroid of all lensed images from the source and any luminous lenses.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_celerite_gp_object(mag_err_obs, filt_idx=0)

Returns a celerite GP object that is used for all GP operations

Parameters:

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. The mean of mag_err_obs is inputted into the jitter term of the kernel if ‘gp_log_jit_sigma’ is not a parameter.

filt_idxinteger

An integer indicating which photometric data set should be used for the GP.

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Returns:

gpa celerite GP object

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the astrometry for the foreground lens at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLarray_like, dtype=float, shape = [len(t), 2]

Position of the lens on the sky (arcsec).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_photometry_with_gp(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Parameters:

tarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t. This is the “predictive mean” of the GP.

mag_model_stdarray_like

Standard deviation of the magnitude of the unresolved microlensing event at t. This comes from the diagonal (the varainces) of the “predictive covariance” of the GP.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_idx] = True.

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_Par_GP_Param3(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_PhotAstrom, PSPL_Parallax, PSPL_GP_PhotAstromParam3

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky. It is the same as PSPL_PhotAstromParam4 except it fits for log10(thetaE) instead of thetaE.

Attributes:

t0float

Time of photometric peak, as seen from Earth (MJD.DDD)

u0_ampfloat

Angular distance between the source and the GEOMETRIC center of the lenses on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tEfloat

Einstein crossing time (days).

log10_thetaEfloat

The size of the Einstein radius in (mas).

piSfloat

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_Efloat

The microlensing parallax in the East direction in units of thetaE

piE_Nfloat

The microlensing parallax in the North direction in units of thetaE

xS0_Efloat

R.A. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_Nfloat

Dec. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_Efloat

RA Source proper motion (mas/yr)

muS_Nfloat

Dec Source proper motion (mas/yr)

b_sffnumpy array or list

The ratio of the source flux to the total (source + neighbors + lenses). One for each filter.

\(b_sff = f_S / (f_S + f_L + f_N)\).

This must be passed in as a list or array, with one entry for each photometric filter.

mag_basenumpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing.
get_celerite_gp_object(mag_err_obs[, filt_idx])	Returns a celerite GP object that is used for all GP operations
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

centroidnumpy array, dtype=float, shape = [len(t), 2]

The flux-weighted centroid of all lensed images from the source and any luminous lenses.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_celerite_gp_object(mag_err_obs, filt_idx=0)

Returns a celerite GP object that is used for all GP operations

Parameters:

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. The mean of mag_err_obs is inputted into the jitter term of the kernel if ‘gp_log_jit_sigma’ is not a parameter.

filt_idxinteger

An integer indicating which photometric data set should be used for the GP.

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Returns:

gpa celerite GP object

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the astrometry for the foreground lens at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLarray_like, dtype=float, shape = [len(t), 2]

Position of the lens on the sky (arcsec).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_photometry_with_gp(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Parameters:

tarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t. This is the “predictive mean” of the GP.

mag_model_stdarray_like

Standard deviation of the magnitude of the unresolved microlensing event at t. This comes from the diagonal (the varainces) of the “predictive covariance” of the GP.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_idx] = True.

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_Par_GP_Param4(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_PhotAstrom, PSPL_Parallax, PSPL_GP_PhotAstromParam4

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky. It is the same as PSPL_PhotAstromParam2 except it fits for baseline instead of source magnitude.

Parameters:

t0float

Time of photometric peak, as seen from Earth (MJD.DDD)

u0_ampfloat

Angular distance between the source and the GEOMETRIC center of the lenses on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tEfloat

Einstein crossing time (days).

thetaE:

The size of the Einstein radius in (mas).

piSfloat

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_Efloat

The microlensing parallax in the East direction in units of thetaE

piE_Nfloat

The microlensing parallax in the North direction in units of thetaE

xS0_Efloat

R.A. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_Nfloat

Dec. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_Efloat

RA Source proper motion (mas/yr)

muS_Nfloat

Dec Source proper motion (mas/yr)

b_sffnumpy array or list

The ratio of the source flux to the total (source + neighbors + lenses). One for each filter.

\(b_sff = f_S / (f_S + f_L + f_N)\).

This must be passed in as a list or array, with one entry for each photometric filter.

mag_basenumpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing.
get_celerite_gp_object(mag_err_obs[, filt_idx])	Returns a celerite GP object that is used for all GP operations
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

centroidnumpy array, dtype=float, shape = [len(t), 2]

The flux-weighted centroid of all lensed images from the source and any luminous lenses.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_celerite_gp_object(mag_err_obs, filt_idx=0)

Returns a celerite GP object that is used for all GP operations

Parameters:

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. The mean of mag_err_obs is inputted into the jitter term of the kernel if ‘gp_log_jit_sigma’ is not a parameter.

filt_idxinteger

An integer indicating which photometric data set should be used for the GP.

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Returns:

gpa celerite GP object

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the astrometry for the foreground lens at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLarray_like, dtype=float, shape = [len(t), 2]

Position of the lens on the sky (arcsec).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_photometry_with_gp(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Parameters:

tarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t. This is the “predictive mean” of the GP.

mag_model_stdarray_like

Standard deviation of the magnitude of the unresolved microlensing event at t. This comes from the diagonal (the varainces) of the “predictive covariance” of the GP.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_idx] = True.

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_noPar_GP_Param1(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_PhotAstrom, PSPL_noParallax, PSPL_GP_PhotAstromParam1

PSPL model for astrometry and photometry - physical parameterization.

A Point Source Point Lens model for microlensing. This model uses a parameterization that depends on only physical quantities such as the lens mass and positions and proper motions of both the lens and source.

Note the attributes, RA (raL) and Dec (decL) are required if you are calculating a model with parallax.

Attributes:

mL: float

Mass of the lens (Msun)

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in Solar System barycentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

beta: float

Angular distance between the lens and source on the plane of the sky (mas). Can be

• positive (u0_amp > 0 when u0_hat[0] < 0) or

• negative (u0_amp < 0 when u0_hat[0] > 0).

dL: float

Distance from the observer to the lens (pc)

dL_dS: float

Ratio of Distance from the obersver to the lens to Distance from the observer to the source

xS0_E: float

RA Source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_N: float

Dec source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muL_E: float

RA Lens proper motion (mas/yr)

muL_N: float

Dec Lens proper motion (mas/yr)

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Dec Source proper motion (mas/yr)

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str or list[str], optional

The observers location for each photometric dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Not supported on this object.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing.
get_celerite_gp_object(mag_err_obs[, filt_idx])	Returns a celerite GP object that is used for all GP operations
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_lens_astrometry(t[, filt_idx])	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Not supported on this object.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

centroidnumpy array, dtype=float, shape = [len(t), 2]

The flux-weighted centroid of all lensed images from the source and any luminous lenses.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_celerite_gp_object(mag_err_obs, filt_idx=0)

Returns a celerite GP object that is used for all GP operations

Parameters:

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. The mean of mag_err_obs is inputted into the jitter term of the kernel if ‘gp_log_jit_sigma’ is not a parameter.

filt_idxinteger

An integer indicating which photometric data set should be used for the GP.

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Returns:

gpa celerite GP object

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_lens_astrometry(t, filt_idx=0)

Get the astrometry for the foreground lens at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLarray_like, dtype=float, shape = [len(t), 2]

Position of the lens on the sky (arcsec).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_photometry_with_gp(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Parameters:

tarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t. This is the “predictive mean” of the GP.

mag_model_stdarray_like

Standard deviation of the magnitude of the unresolved microlensing event at t. This comes from the diagonal (the varainces) of the “predictive covariance” of the GP.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_idx] = True.

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_noPar_GP_Param2(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_PhotAstrom, PSPL_noParallax, PSPL_GP_PhotAstromParam2

PSPL model for photometry and astrometry – photom-like parameterization

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky.

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in Solar System barycentric coordinates. This should be close, but not exactly aligned with the photometric peak, as seen from Earth or a Solar System satellite.

u0_amp: float

Angular distance between the lens and source on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tE: float

Einstein crossing time (days).

thetaE: float

The size of the Einstein radius in (mas).

piS: float

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_E: float

The microlensing parallax in the East direction in units of thetaE

piE_N: float

The microlensing parallax in the North direction in units of thetaE

xS0_E: float

RA Source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_N: float

Dec source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_E: float

RA Source proper motion (mas/yr)

muS_N: float

Source proper motion (mas/yr)

b_sff: numpy array or list

The ratio of the source flux to the total (source + neighbors + lens) \(b_sff = f_S / (f_S + f_L + f_N)\). This must be passed in as a list or array, with one entry for each photometric filter.

mag_src: numpy array or list

Photometric magnitude of the source. This must be passed in as a list or array, with one entry for each photometric filter.

raL: float, optional

Right ascension of the lens in decimal degrees.

decL: float, optional

Declination of the lens in decimal degrees.

obsLocation: str or list[str], optional

The observers location for each photometric dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Not supported on this object.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing.
get_celerite_gp_object(mag_err_obs[, filt_idx])	Returns a celerite GP object that is used for all GP operations
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_lens_astrometry(t[, filt_idx])	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Not supported on this object.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

centroidnumpy array, dtype=float, shape = [len(t), 2]

The flux-weighted centroid of all lensed images from the source and any luminous lenses.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_celerite_gp_object(mag_err_obs, filt_idx=0)

Returns a celerite GP object that is used for all GP operations

Parameters:

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. The mean of mag_err_obs is inputted into the jitter term of the kernel if ‘gp_log_jit_sigma’ is not a parameter.

filt_idxinteger

An integer indicating which photometric data set should be used for the GP.

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Returns:

gpa celerite GP object

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_lens_astrometry(t, filt_idx=0)

Get the astrometry for the foreground lens at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLarray_like, dtype=float, shape = [len(t), 2]

Position of the lens on the sky (arcsec).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_photometry_with_gp(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Parameters:

tarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t. This is the “predictive mean” of the GP.

mag_model_stdarray_like

Standard deviation of the magnitude of the unresolved microlensing event at t. This comes from the diagonal (the varainces) of the “predictive covariance” of the GP.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_idx] = True.

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_Par_GP_Param3_1(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_PhotAstrom, PSPL_Parallax, PSPL_GP_PhotAstromParam3_1

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky. It is the same as PSPL_PhotAstromParam4 except it fits for log10(thetaE) instead of thetaE.

Attributes:

t0float

Time of photometric peak, as seen from Earth (MJD.DDD)

u0_ampfloat

Angular distance between the source and the GEOMETRIC center of the lenses on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tEfloat

Einstein crossing time (days).

log10_thetaEfloat

The size of the Einstein radius in (mas).

piSfloat

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_Efloat

The microlensing parallax in the East direction in units of thetaE

piE_Nfloat

The microlensing parallax in the North direction in units of thetaE

xS0_Efloat

R.A. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_Nfloat

Dec. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_Efloat

RA Source proper motion (mas/yr)

muS_Nfloat

Dec Source proper motion (mas/yr)

b_sffnumpy array or list

The ratio of the source flux to the total (source + neighbors + lenses). One for each filter.

\(b_sff = f_S / (f_S + f_L + f_N)\).

This must be passed in as a list or array, with one entry for each photometric filter.

mag_basenumpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing.
get_celerite_gp_object(mag_err_obs[, filt_idx])	Returns a celerite GP object that is used for all GP operations
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

centroidnumpy array, dtype=float, shape = [len(t), 2]

The flux-weighted centroid of all lensed images from the source and any luminous lenses.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_celerite_gp_object(mag_err_obs, filt_idx=0)

Returns a celerite GP object that is used for all GP operations

Parameters:

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. The mean of mag_err_obs is inputted into the jitter term of the kernel if ‘gp_log_jit_sigma’ is not a parameter.

filt_idxinteger

An integer indicating which photometric data set should be used for the GP.

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Returns:

gpa celerite GP object

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the astrometry for the foreground lens at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLarray_like, dtype=float, shape = [len(t), 2]

Position of the lens on the sky (arcsec).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_photometry_with_gp(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Parameters:

tarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t. This is the “predictive mean” of the GP.

mag_model_stdarray_like

Standard deviation of the magnitude of the unresolved microlensing event at t. This comes from the diagonal (the varainces) of the “predictive covariance” of the GP.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_idx] = True.

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_Par_GP_Param3_2(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_PhotAstrom, PSPL_Parallax, PSPL_GP_PhotAstromParam3_2

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky. It is the same as PSPL_PhotAstromParam4 except it fits for log10(thetaE) instead of thetaE.

Attributes:

t0float

Time of photometric peak, as seen from Earth (MJD.DDD)

u0_ampfloat

Angular distance between the source and the GEOMETRIC center of the lenses on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tEfloat

Einstein crossing time (days).

log10_thetaEfloat

The size of the Einstein radius in (mas).

piSfloat

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_Efloat

The microlensing parallax in the East direction in units of thetaE

piE_Nfloat

The microlensing parallax in the North direction in units of thetaE

xS0_Efloat

R.A. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_Nfloat

Dec. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_Efloat

RA Source proper motion (mas/yr)

muS_Nfloat

Dec Source proper motion (mas/yr)

b_sffnumpy array or list

The ratio of the source flux to the total (source + neighbors + lenses). One for each filter.

\(b_sff = f_S / (f_S + f_L + f_N)\).

This must be passed in as a list or array, with one entry for each photometric filter.

mag_basenumpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing.
get_celerite_gp_object(mag_err_obs[, filt_idx])	Returns a celerite GP object that is used for all GP operations
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

centroidnumpy array, dtype=float, shape = [len(t), 2]

The flux-weighted centroid of all lensed images from the source and any luminous lenses.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_celerite_gp_object(mag_err_obs, filt_idx=0)

Returns a celerite GP object that is used for all GP operations

Parameters:

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. The mean of mag_err_obs is inputted into the jitter term of the kernel if ‘gp_log_jit_sigma’ is not a parameter.

filt_idxinteger

An integer indicating which photometric data set should be used for the GP.

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Returns:

gpa celerite GP object

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the astrometry for the foreground lens at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLarray_like, dtype=float, shape = [len(t), 2]

Position of the lens on the sky (arcsec).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_photometry_with_gp(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Parameters:

tarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t. This is the “predictive mean” of the GP.

mag_model_stdarray_like

Standard deviation of the magnitude of the unresolved microlensing event at t. This comes from the diagonal (the varainces) of the “predictive covariance” of the GP.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_idx] = True.

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_Par_GP_Param4_2(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_PhotAstrom, PSPL_Parallax, PSPL_GP_PhotAstromParam4_2

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky. It is the same as PSPL_PhotAstromParam2 except it fits for baseline instead of source magnitude.

Parameters:

t0float

Time of photometric peak, as seen from Earth (MJD.DDD)

u0_ampfloat

Angular distance between the source and the GEOMETRIC center of the lenses on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tEfloat

Einstein crossing time (days).

thetaE:

The size of the Einstein radius in (mas).

piSfloat

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_Efloat

The microlensing parallax in the East direction in units of thetaE

piE_Nfloat

The microlensing parallax in the North direction in units of thetaE

xS0_Efloat

R.A. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_Nfloat

Dec. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_Efloat

RA Source proper motion (mas/yr)

muS_Nfloat

Dec Source proper motion (mas/yr)

b_sffnumpy array or list

The ratio of the source flux to the total (source + neighbors + lenses). One for each filter.

\(b_sff = f_S / (f_S + f_L + f_N)\).

This must be passed in as a list or array, with one entry for each photometric filter.

mag_basenumpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing.
get_celerite_gp_object(mag_err_obs[, filt_idx])	Returns a celerite GP object that is used for all GP operations
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

centroidnumpy array, dtype=float, shape = [len(t), 2]

The flux-weighted centroid of all lensed images from the source and any luminous lenses.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_celerite_gp_object(mag_err_obs, filt_idx=0)

Returns a celerite GP object that is used for all GP operations

Parameters:

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. The mean of mag_err_obs is inputted into the jitter term of the kernel if ‘gp_log_jit_sigma’ is not a parameter.

filt_idxinteger

An integer indicating which photometric data set should be used for the GP.

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Returns:

gpa celerite GP object

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the astrometry for the foreground lens at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLarray_like, dtype=float, shape = [len(t), 2]

Position of the lens on the sky (arcsec).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_photometry_with_gp(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Parameters:

tarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t. This is the “predictive mean” of the GP.

mag_model_stdarray_like

Standard deviation of the magnitude of the unresolved microlensing event at t. This comes from the diagonal (the varainces) of the “predictive covariance” of the GP.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_idx] = True.

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_Par_GP_Param4_2(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSPL_PhotAstrom, PSPL_Parallax, PSPL_GP_PhotAstromParam4_2

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky. It is the same as PSPL_PhotAstromParam2 except it fits for baseline instead of source magnitude.

Parameters:

t0float

Time of photometric peak, as seen from Earth (MJD.DDD)

u0_ampfloat

Angular distance between the source and the GEOMETRIC center of the lenses on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tEfloat

Einstein crossing time (days).

thetaE:

The size of the Einstein radius in (mas).

piSfloat

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_Efloat

The microlensing parallax in the East direction in units of thetaE

piE_Nfloat

The microlensing parallax in the North direction in units of thetaE

xS0_Efloat

R.A. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_Nfloat

Dec. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_Efloat

RA Source proper motion (mas/yr)

muS_Nfloat

Dec Source proper motion (mas/yr)

b_sffnumpy array or list

The ratio of the source flux to the total (source + neighbors + lenses). One for each filter.

\(b_sff = f_S / (f_S + f_L + f_N)\).

This must be passed in as a list or array, with one entry for each photometric filter.

mag_basenumpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing.
get_celerite_gp_object(mag_err_obs[, filt_idx])	Returns a celerite GP object that is used for all GP operations
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

centroidnumpy array, dtype=float, shape = [len(t), 2]

The flux-weighted centroid of all lensed images from the source and any luminous lenses.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_celerite_gp_object(mag_err_obs, filt_idx=0)

Returns a celerite GP object that is used for all GP operations

Parameters:

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. The mean of mag_err_obs is inputted into the jitter term of the kernel if ‘gp_log_jit_sigma’ is not a parameter.

filt_idxinteger

An integer indicating which photometric data set should be used for the GP.

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Returns:

gpa celerite GP object

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the astrometry for the foreground lens at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLarray_like, dtype=float, shape = [len(t), 2]

Position of the lens on the sky (arcsec).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_photometry_with_gp(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Parameters:

tarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t. This is the “predictive mean” of the GP.

mag_model_stdarray_like

Standard deviation of the magnitude of the unresolved microlensing event at t. This comes from the diagonal (the varainces) of the “predictive covariance” of the GP.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

Note

The GP will only be used for filters where use_gp_phot[filt_idx] = True.

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

class model.PSPL_PhotAstrom_Par_GPnoJitter_Param3_1(*args, **kwargs)

Bases: ModelClassABC, PSPL_GPnoJitter, PSPL_PhotAstrom, PSPL_Parallax, PSPL_GP_PhotAstromParam3_1

Point Source Point Lens model for microlensing. This model includes proper motions of the source and the source position on the sky. It is the same as PSPL_PhotAstromParam4 except it fits for log10(thetaE) instead of thetaE.

Attributes:

t0float

Time of photometric peak, as seen from Earth (MJD.DDD)

u0_ampfloat

Angular distance between the source and the GEOMETRIC center of the lenses on the plane of the sky at closest approach in units of thetaE. Can be

• positive (u0_amp > 0 when u0_hat[0] > 0) or

• negative (u0_amp < 0 when u0_hat[0] < 0).

tEfloat

Einstein crossing time (days).

log10_thetaEfloat

The size of the Einstein radius in (mas).

piSfloat

Amplitude of the parallax (1AU/dS) of the source. (mas)

piE_Efloat

The microlensing parallax in the East direction in units of thetaE

piE_Nfloat

The microlensing parallax in the North direction in units of thetaE

xS0_Efloat

R.A. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

xS0_Nfloat

Dec. of source position on sky at t = t0 (arcsec) in an arbitrary ref. frame.

muS_Efloat

RA Source proper motion (mas/yr)

muS_Nfloat

Dec Source proper motion (mas/yr)

b_sffnumpy array or list

The ratio of the source flux to the total (source + neighbors + lenses). One for each filter.

\(b_sff = f_S / (f_S + f_L + f_N)\).

This must be passed in as a list or array, with one entry for each photometric filter.

mag_basenumpy array or list

Photometric magnitude of the base. This must be passed in as a list or array, with one entry for each photometric filter.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic([filt_idx])	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_amplification(t[, filt_idx])	Get an array of the total photometric amplifications at the input times.
get_astrometry(t[, filt_idx])	Get the astrometry of the unresolved (observed) position of the lensed source at the input times.
get_astrometry_unlensed(t[, filt_idx])	Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing.
get_celerite_gp_object([filt_idx])	Returns a celerite GP object that is used for all GP operations
get_centroid_shift(t[, filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
get_chi2_photometry(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
get_geoproj_ast_params(t0par[, plot])	Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_geoproj_params(t0par[, plot])	Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par.
get_lens_astrometry(t[, filt_idx])	Get the astrometry for the foreground lens at the input times.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_photometry(t[, filt_idx])	Get the predicted photomety at the specified times for the specified photometric filter or data set.
get_photometry_with_gp(t, mag_obs, mag_err_obs)	Returns photometry with GP noise added in.
get_resolved_amplification(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t[, filt_idx])	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
get_source_astrometry_unlensed(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
get_u(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
log_likely_astrometry(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t, mag_obs, mag_err_obs)	For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
log_likely_photometry_each(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.

start

Notes

Note

Required parameters if calculating with parallax

• raL: Right ascension of the lens in decimal degrees.

• decL: Declination of the lens in decimal degrees.

• obsLocation: The observers location for each photometric

  dataset (def=[‘earth’]) such as ‘jwst’ or ‘spitzer’. Can be a single string if all observer locations are identical. Otherwise, array of same length as mag_src or b_sff (e.g. other photometric parameters).

animate(tE, time_steps, frame_time, name, size, zoom, astrometry, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot

e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

number of time steps before/after peak, so total number of time steps will be 2 times this value

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

calc_piE_ecliptic(filt_idx=0)

Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.

Parameters:

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Get an array of the total photometric amplifications at the input times.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t)]

The total amplification (sum of +/- images)

get_astrometry(t, filt_idx=0)

Get the astrometry of the unresolved (observed) position of the lensed source at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

centroidnumpy array, dtype=float, shape = [len(t), 2]

The flux-weighted centroid of all lensed images from the source and any luminous lenses.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_celerite_gp_object(filt_idx=0)

Returns a celerite GP object that is used for all GP operations

Parameters:

filt_idxinteger

An integer indicating which photometric data set should be used for the GP.

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Returns:

gpa celerite GP object

get_centroid_shift(t, filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position (with lensed source + lens light) and the unlensed, unresolved position (with unlensed source + lens light). The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the photometric filter or data set.

get_chi2_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

The index of the astrometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and astrometric data.

get_chi2_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

chi2array_like

List of chi^2 values from the model and photometric data.

get_geoproj_ast_params(t0par, plot=False)

Get the astrometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

xS0E_gfloat

The East-component of source position vector on the sky, in the geocentric-projected frame.

xS0N_gfloat

The North-component of source position vector on the sky, in the geocentric-projected frame.

muSE_gfloat

The East-component of source proper motion vector, in the geocentric-projected frame.

muSN_gfloat

The North-component of source proper motion vector, in the geocentric-projected frame.

get_geoproj_params(t0par, plot=False)

Get the photometric microlensing model parameters in the geocentric-projected coordinate system, which just applies a rectalinear position and velocity offset into the geocentric frame at time t0par. Note, this is not a true geocentric frame. It is only geocentric at time t0par. However, this is a common convention for photometry-only microlens models in the literature. The benefits of the geocentric-projected frame is that the t0_{geoProj} can more closely match the observed peak in the light curve.

Parameters:

t0parfloat

Time in MJD at which to convert into the geocentric frame.

Returns:

t0_gfloat

The time (in MJD) of closest approach between the lens and source in the geocentric-projected frame.

u0_gfloat

The distance (in thetaE) at closest approach in the geocentric-projected frame.

tE_gfloat

The Einsten crossing time (in MJD) in the geocentric-projected frame.

piEE_gfloat

The East-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the East-component of the relative proper motion vector between the source and lens

piEN_gfloat

The North-component of the microlensing parallax vector, in the geocentric-projected frame. This also indicates the North-component of the relative proper motion vector between the source and lens

get_lens_astrometry(t, filt_idx=0)

Get the astrometry for the foreground lens at the input times. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xLarray_like, dtype=float, shape = [len(t), 2]

Position of the lens on the sky (arcsec).

get_lnL_constant(err_obs)

Get the natural log of the constant normalization terms of the likelihood.

\[-0.5 * \ln{2 \pi \sigma_{obs}^2}\]

Parameters:

err_obsarray_like

List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_log_det_covariance(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

get_photometry(t, filt_idx=0)

Get the predicted photomety at the specified times for the specified photometric filter or data set.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t.

get_photometry_with_gp(t, mag_obs, mag_err_obs, filt_idx=0, t_pred=None)

Returns photometry with GP noise added in.

Note

This will throw an error if this is a filter with use_gp_phot[filt_idx] = False.

Parameters:

tarray_like

List of times in MJD for the observations. These times are used as input to the GP. If t_pred is not specified, then t_pred = t.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. These values are used as input to the GP. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

t_predarray_like, optional

List of times in MJD on which to evalute the model. If t_pred is not specified, then t_pred = t.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t. This is the “predictive mean” of the GP.

mag_model_stdarray_like

Standard deviation of the magnitude of the unresolved microlensing event at t. This comes from the diagonal (the varainces) of the “predictive covariance” of the GP.

get_resolved_amplification(t, filt_idx=0)

Get the photometric amplification terms at a set of times, t for both the plus and minus images. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]

The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus. The returned tuple has two entries: (xS_plus, xS_minus), each with [len(t), 2] arrays where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

• xS_plus is the vector position of the plus image in arcsec with shape = [len(t), 2]

• xS_minus is the vector position of the plus image in arcsec with shape = [len(t), 2]

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. The returned array is in arcsec and has a shape of [len(t), 2] where the second dimension includes [RA, Dec] positions in arcsec.

Parameters:

tarray_like

Time (in MJD).

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]

The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.

Parameters:

tarray_like

List of times in MJD for the observations.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

u_unlensednumpy array, dtype=float, shape = len(t) x 2

The unlensed positions of the source in Einstein radii.

log_likely_astrometry(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_astrometry_each(t, x_obs, y_obs, x_err_obs, y_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets. Note, this function eturns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

x_obsarray_like

List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.

y_obsarray_like

List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.

x_err_obsarray_like

List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.

y_err_obsarray_like

List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.

filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each astrometric measurement.

log_likely_photometry(t, mag_obs, mag_err_obs, filt_idx=0)

For models that include a Gaussian Process, get the summed natural log of the likelihood for the input photometric data for the specified filter or data set. Note, this function returns the full ln(likelihood), including the normalization constant.

The GP will only be used for filters where use_gp_phot[filt_idx] = True.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Lfloat

ln(likelihood) summed over the photometric measurement

log_likely_photometry_each(t, mag_obs, mag_err_obs, filt_idx=0)

Get the natural log of the likelihood for the input photometric data in the specified filter or data sets. Note, this function returns a list and it is the full ln(likelihood), including the normalization constant.

Parameters:

tarray_like

List of times in MJD for the observations.

mag_obsarray_like

List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.

mag_err_obsarray_like

List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.