Data Class Family

class model.BSPL

Bases: PSPL

Methods

`animate`(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
`get_amplification`(t[, filt_idx])	Parallax: Get the photometric amplification term at a set of times, t.
`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])	Parallax: Get the photometric amplification term 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])
`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

get_amplification(t, filt_idx=0)

Parallax: Get the photometric amplification term at a set of times, t.

Note that this is a convenience function that combines amplifications from multiple sources. The returned amplification is

..math:

A = (f1 * A1 + f2 * A2) / (f1 + f2)

where the fluxes are the intrinsic source flux in the specified filter.

Parameters:

t: Array of times in MJD.DDD
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

Anumpy array: Array of combined amplifications in the specified filter.

Shape = [len(t)]

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)

Parallax: Get the photometric amplification term at a set of times, t for both the plus and minus images.

Parameters:

t: Array of times in MJD.DDD
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

A_resolvednumpy array: [shape = len(t), len(sources), 2]

Notes

For each time t and each source, we have:

A_plus is the amplification for the plus image.
A_minus is the amplification for the minus image.

In other words,

xS[0, 0, 0] returns the amplification of the first source’s “plus” image at the first time.

Similarly,

xS[0, 0, 1] returns the amplification of the first source’s “minus” image at the first time.

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)

Parameters:

tnumpy array: Times at which to evaluate the source-lens separation.
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

unumpy array: Shape = [len(t), 2 sources, 2 directions on sky]

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.BSPL_Phot

Bases: BSPL, PSPL_Phot

Contains methods for model a BSPL photometry only. This is a Data-type class in our hierarchy. It is abstract and should not be instantiated.

Attributes:

t0
tE
u0_amp
u0_E
u0_N
piE_E:: valid only if parallax model
piE_N:: valid only if parallax model
piE_amp
b_sff[#]
mag_src[#]:: add in
mag_base[#]:: add in
raL:: if parallax model
decL:: if parallax model

Methods

`animate`(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
`get_amplification`(t[, filt_idx])	Parallax: Get the photometric amplification term at a set of times, t.
`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])	Parallax: Get the photometric amplification term 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_resolved_source_astrometry_unlensed`(t[, ...])	Get the astrometry of the source if the lens didn't exist.
`get_source_astrometry_unlensed`(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
`get_u`(t[, filt_idx])
`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.

get_t0_sec

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

get_amplification(t, filt_idx=0)

Parallax: Get the photometric amplification term at a set of times, t.

Note that this is a convenience function that combines amplifications from multiple sources. The returned amplification is

..math:

A = (f1 * A1 + f2 * A2) / (f1 + f2)

where the fluxes are the intrinsic source flux in the specified filter.

Parameters:

t: Array of times in MJD.DDD
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

Anumpy array: Array of combined amplifications in the specified filter.

Shape = [len(t)]

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.

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)

Parallax: Get the photometric amplification term at a set of times, t for both the plus and minus images.

Parameters:

t: Array of times in MJD.DDD
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

A_resolvednumpy array: [shape = len(t), len(sources), 2]

Notes

For each time t and each source, we have:

A_plus is the amplification for the plus image.
A_minus is the amplification for the minus image.

In other words,

xS[0, 0, 0] returns the amplification of the first source’s “plus” image at the first time.

Similarly,

xS[0, 0, 1] returns the amplification of the first source’s “minus” image at the first time.

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_resolved_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. Note, this is a photometry only model, so units are in Einstein radii.

Returns:

xS_resolved_unlensednumpy array, [shape = len(t), N_sources, 2]: The unlensed positions of the sources in Einstein radii.
In other words,: xS[0, 0, :] returns the 2D sky position of the first source at the first time.
Similarly,: xS[0, 1, :] returns the 2D sky position of the second source at the first time.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist. This is the flux-weighted, centroid of the two sources. Note, this is a photometry only model, so units are in Einstein radii.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2: The unlensed positions of the source in Einstein radii.

get_u(t, filt_idx=0)

Parameters:

tnumpy array: Times at which to evaluate the source-lens separation.
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

unumpy array: Shape = [len(t), 2 sources, 2 directions on sky]

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.BSPL_PhotAstrom

Bases: BSPL, PSPL_PhotAstrom

Methods

`animate`(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
`get_amplification`(t[, filt_idx])	Parallax: Get the photometric amplification term at a set of times, t.
`get_astrometric_shift`(t[, filt_idx])	Parallax: Get unresolved centroid shift (due to lensing) for each of the binary source.
`get_astrometry`(t[, filt_idx])	Parallax: Get unresolved astrometry for binary source, point lens.
`get_astrometry_unlensed`(t[, filt_idx])	Get the flux-weighted centroid for the astrometry of the sources if the lens didn't exist.
`get_centroid_shift`(t[, filt_idx])	Parallax: Get the centroid shift (in mas) for a list of observation times (in MJD).
`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])	Parallax: Get the photometric amplification term at a set of times, t for both the plus and minus images.
`get_resolved_astrometry`(t[, filt_idx])	Parallax: For each source, get the x, y astrometry for the two lensed source images.
`get_resolved_source_astrometry_unlensed`(t[, ...])	Get the astrometry of the source if the lens didn't exist.
`get_source_astrometry_unlensed`(t[, filt_idx])	Get the flux-weighted centroid for the astrometry of the sources if the lens didn't exist.
`get_u`(t[, filt_idx])
`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.

get_t0_sec
get_u0_sec

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

Produces animation of microlensing event. This function takes the PSPL and makes an animation, the input variables are as follows

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

filt_idxint, optional

Index of the astrometric filter or data set.

get_amplification(t, filt_idx=0)

Parallax: Get the photometric amplification term at a set of times, t.

Note that this is a convenience function that combines amplifications from multiple sources. The returned amplification is

..math:

A = (f1 * A1 + f2 * A2) / (f1 + f2)

where the fluxes are the intrinsic source flux in the specified filter.

Parameters:

t: Array of times in MJD.DDD
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

Anumpy array: Array of combined amplifications in the specified filter.

Shape = [len(t)]

get_astrometric_shift(t, filt_idx=0)

Parallax: Get unresolved centroid shift (due to lensing) for each of the binary source. This is made for simulation purposes only.

Parameters:

t:: Array of times in MJD.DDD
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

xS_lensed: Returns flux-weighted average of lensed source positions.

get_astrometry(t, filt_idx=0)

Parallax: Get unresolved astrometry for binary source, point lens.

Parameters:

t:: Array of times in MJD.DDD
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

xS_lensed: Returns flux-weighted average of lensed source positions.

get_astrometry_unlensed(t, filt_idx=0)

Get the flux-weighted centroid for the astrometry of the sources if the lens didn’t exist.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2 directions: The unlensed positions of the combined sources in arcseconds.

Shape = [len(t), 2 directions]

get_centroid_shift(t, filt_idx=0)

Parallax: Get the centroid shift (in mas) for a list of observation times (in MJD). This is the difference between the unresolved, unlensed centroid and the unresolved, lensed centroid. Note that if the lens is luminous or both sources are luminous, both the unlensed and lensed trajectory will be belnded.

Parameters:

t:: Array of times in MJD.DDD
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

centroid_shiftnumpy array: [shape = len(t), 2] in milli-arcseoncds

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)

Parallax: Get the photometric amplification term at a set of times, t for both the plus and minus images.

Parameters:

t: Array of times in MJD.DDD
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

A_resolvednumpy array: [shape = len(t), len(sources), 2]

Notes

For each time t and each source, we have:

A_plus is the amplification for the plus image.
A_minus is the amplification for the minus image.

In other words,

xS[0, 0, 0] returns the amplification of the first source’s “plus” image at the first time.

Similarly,

xS[0, 0, 1] returns the amplification of the first source’s “minus” image at the first time.

get_resolved_astrometry(t, filt_idx=0)

Parallax: For each source, get the x, y astrometry for the two lensed source images. For each source, we label the two images as plus and minus.

Returns:

xS_resolvednumpy array: [shape = len(t), len(sources), 2, 2]

Notes

For each time t and each source, we have:

xS_plus is the vector position of the plus image.
xS_minus is the vector position of the minus image.

In other words,

xS[0, 0, 0, :] returns the 2D sky position of the first source’s “plus” image at the first time.

Similarly,

xS[0, 0, 1, :] returns the 2D sky position of the first source’s “minus” image at the first time.

get_resolved_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source if the lens didn’t exist.

Returns:

xS_resolved_unlensednumpy array, [shape = len(t), N_sources, 2]: The unlensed positions of the sources in arcseconds.
In other words,: xS[0, 0, :] returns the 2D sky position of the first source at the first time.
Similarly,: xS[0, 1, :] returns the 2D sky position of the second source at the first time.

get_source_astrometry_unlensed(t, filt_idx=0)

Get the flux-weighted centroid for the astrometry of the sources if the lens didn’t exist.

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t) x 2 directions: The unlensed positions of the combined sources in arcseconds.

Shape = [len(t), 2 directions]

get_u(t, filt_idx=0)

Parameters:

tnumpy array: Times at which to evaluate the source-lens separation.
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

unumpy array: Shape = [len(t), 2 sources, 2 directions on sky]

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.