PSBL User Classes

PSBL

class model.PSBL_PhotAstrom_noPar_Param1(*args, **kwargs)

Bases: ModelClassABC, PSBL_PhotAstrom, PSBL_noParallax, PSBL_PhotAstromParam1

Point source binary lens. It has 3 more parameters than PSPL (additional mass term, separation, and angle of approach). Note that this is a STATIC binary lens, i.e. there is no orbital motion.

Attributes:

mLp, mLsfloat

Masses of the lenses (Msun)

t0float

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

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.

betafloat

Angular distance between the source and the GEOMETRIC center of the lenses 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).

muL_Efloat

Lens system proper motion in the RA direction (mas/yr)

muL_Nfloat

Lens system proper motion in the Dec. direction (mas/yr)

muS_Efloat

Source proper motion in the RA direction (mas/yr)

muS_Nfloat

Source proper motion in the Dec. direction (mas/yr)

dLfloat

Distance from the observer to the lens system (pc)

dSfloat

Distance from the observer to the source (pc)

sepfloat

Angular separation of the two lenses (mas)

alphafloat

Angle made between the binary axis and North; measured in degrees East of North.

b_sffnumpy array or list

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

mag_srcnumpy array or list

Source magnitude, unlensed. One in each filter.

root_tolfloat

Tolerance in comparing the polynomial roots to the physical solutions. Default = 1e-8

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Not supported on this object.
get_all_arrays(t_obs[, check_sols, rescale])	Obtain the image and amplitude arrays for each t_obs.
get_amp_arr(z_arr, z1, z2)	Calculations amplification array
get_amplification(t_obs[, amp_arr])	noParallax: Get the photometric amplification term at a set of times, t.
get_astrometry(t_obs[, image_arr, amp_arr, ...])	Position of the observed (unresolved) source position in arcsec.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_centroid(t_obs[, ast_filt_idx, ...])	PSPL: Get the centroid shift (in mas) for a list of observation times (in MJD).
get_centroid_shift(t)	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, 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_obs, 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_complex_pos(t_obs)	Get the positions of the lenses and source as complex numbers.
get_image_pos_arr(w, z1, z2, m1, m2[, ...])	Gets image positions.
get_image_pos_arr_old(w, z1, z2[, check_sols])	Gets image positions.
get_lens_astrometry(t_obs)	Equation of motion for just the foreground lens system.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t_obs[, filt_idx, amp_arr, ...])	Get the photometry for each of the lensed source images.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs[, image_arr, ...])	Position of the observed source position in arcsec.
get_resolved_lens_astrometry(t_obs)	Equation of motion for just the foreground lenses, individually.
get_resolved_photometry(t_obs[, filt_idx, ...])	Get the photometry for each of the lensed source images.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_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_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
rescale_complex_pos(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

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

calc_piE_ecliptic()

Not supported on this object.

get_all_arrays(t_obs, check_sols=True, rescale=True)

Obtain the image and amplitude arrays for each t_obs.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

imagesarray_like

Array/tuple of complex positions of each images at each t_obs.

amp_arrarray_like

Array/tuple of amplification of each images at each t_obs.

get_amp_arr(z_arr, z1, z2)

Calculations amplification array

Calculates the amplification A from the Jacobian J, \(A = 1/|J|\)

Parameters:

z_arrarray_like

Complex position of images. Shape = [N_times, N_solutions, 1]

– note this could be jagged.

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

Returns:

amp_arrarray_like

BLEH

get_amplification(t_obs, amp_arr=None)

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

Parameters:

t:

Array of times in MJD.DDD

get_astrometry(t_obs, image_arr=None, amp_arr=None, ast_filt_idx=0)

Position of the observed (unresolved) source position in arcsec.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

ast_filt_idxint

The filter index for the astrometry.

get_astrometry_unlensed(t_obs)

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

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t_obs) x 2

The unlensed positions of the source in arcseconds.

get_centroid(t_obs, ast_filt_idx=0, image_arr=None, amp_arr=None)

PSPL: Get the centroid shift (in mas) for a list of observation times (in MJD).

Parameters:

t_obsarray or float

Returns:

Centroid offset on the plane of the sky in milli-arcseoncds.

Other Parameters:

ast_filt_idxint

Index into the photometry parameter lists for the photometry that corresponds to this astrometry data set.

image_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

amp_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

get_centroid_shift(t)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. No parallax is included. 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).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

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

Parameters:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_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_obs, mag_obs, mag_err_obs, filt_index=0)

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

Parameters:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_complex_pos(t_obs)

Get the positions of the lenses and source as complex numbers. This is needed for further calculations. Note that all units are still the same as before, this is just rewriting vectors \(z = (x,y)\) as \(z = x + iy\).

Parameters:

tarray_like

Array of times to model.

Returns:

wcomplex array

Source position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times, N_sources].

z1complex array

Lens primary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

z2complex array

Lens secondary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

get_image_pos_arr(w, z1, z2, m1, m2, check_sols=True)

Gets image positions.

Solve the fifth-order polynomial and get the image positions.

See PSBL writeup for full equations.

All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

m1float

m2float

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_image_pos_arr_old(w, z1, z2, check_sols=True)

Gets image positions. | Solve the fifth-order polynomial and get the image positions. | See PSBL writeup for full equations. | All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Position of the lensed source images. Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_lens_astrometry(t_obs)

Equation of motion for just the foreground lens system.

Parameters:

t_obsarray_like

Time (in MJD).

Return

——

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

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_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images.

Parameters:

t_obsarray_like

Array of times to model.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. No parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs, image_arr=None, amp_arr=None)

Position of the observed source position in arcsec.

Parameters:

t_obsarray_like, shape = [N_times]

Array of times to model.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

get_resolved_lens_astrometry(t_obs)

Equation of motion for just the foreground lenses, individually.

Parameters:

t_obsarray_like

Time (in MJD).

get_resolved_photometry(t_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images. Implement with no blending (since we don’t support different blendings for the different images).

Parameters:

t_obsarray_like

Array of times to model.

Returns:

mag_modelarray_like

Magnitude of each lensed image centroid at t_obs. Shape = [5, len(t_obs)]

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

filt_idxint

The filter index (def=0).

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

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

Parameters:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_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:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_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_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2)

Make sure everything is roughly centered on the origin in a 1 x 1 box.

class model.PSBL_PhotAstrom_noPar_Param2(*args, **kwargs)

Bases: ModelClassABC, PSBL_PhotAstrom, PSBL_noParallax, PSBL_PhotAstromParam2

Point source binary lens. It has 3 more parameters than PSPL (additional mass term, separation, and angle of approach). Note that this is a STATIC binary lens, i.e. there is no orbital motion.

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).

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)

qfloat

Mass ratio (M2 / M1)

sepfloat

Angular separation of the two lenses (mas)

alphafloat

Angle made between the binary axis and North; measured in degrees East of North.

b_sffnumpy array or list

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

mag_srcnumpy array or list

Source magnitude, unlensed. One in each filter.

root_tolfloat

Tolerance in comparing the polynomial roots to the physical solutions. Default = 1e-8

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Not supported on this object.
get_all_arrays(t_obs[, check_sols, rescale])	Obtain the image and amplitude arrays for each t_obs.
get_amp_arr(z_arr, z1, z2)	Calculations amplification array
get_amplification(t_obs[, amp_arr])	noParallax: Get the photometric amplification term at a set of times, t.
get_astrometry(t_obs[, image_arr, amp_arr, ...])	Position of the observed (unresolved) source position in arcsec.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_centroid(t_obs[, ast_filt_idx, ...])	PSPL: Get the centroid shift (in mas) for a list of observation times (in MJD).
get_centroid_shift(t)	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, 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_obs, 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_complex_pos(t_obs)	Get the positions of the lenses and source as complex numbers.
get_image_pos_arr(w, z1, z2, m1, m2[, ...])	Gets image positions.
get_image_pos_arr_old(w, z1, z2[, check_sols])	Gets image positions.
get_lens_astrometry(t_obs)	Equation of motion for just the foreground lens system.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t_obs[, filt_idx, amp_arr, ...])	Get the photometry for each of the lensed source images.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs[, image_arr, ...])	Position of the observed source position in arcsec.
get_resolved_lens_astrometry(t_obs)	Equation of motion for just the foreground lenses, individually.
get_resolved_photometry(t_obs[, filt_idx, ...])	Get the photometry for each of the lensed source images.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_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_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
rescale_complex_pos(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

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

calc_piE_ecliptic()

Not supported on this object.

get_all_arrays(t_obs, check_sols=True, rescale=True)

Obtain the image and amplitude arrays for each t_obs.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

imagesarray_like

Array/tuple of complex positions of each images at each t_obs.

amp_arrarray_like

Array/tuple of amplification of each images at each t_obs.

get_amp_arr(z_arr, z1, z2)

Calculations amplification array

Calculates the amplification A from the Jacobian J, \(A = 1/|J|\)

Parameters:

z_arrarray_like

Complex position of images. Shape = [N_times, N_solutions, 1]

– note this could be jagged.

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

Returns:

amp_arrarray_like

BLEH

get_amplification(t_obs, amp_arr=None)

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

Parameters:

t:

Array of times in MJD.DDD

get_astrometry(t_obs, image_arr=None, amp_arr=None, ast_filt_idx=0)

Position of the observed (unresolved) source position in arcsec.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

ast_filt_idxint

The filter index for the astrometry.

get_astrometry_unlensed(t_obs)

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

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t_obs) x 2

The unlensed positions of the source in arcseconds.

get_centroid(t_obs, ast_filt_idx=0, image_arr=None, amp_arr=None)

PSPL: Get the centroid shift (in mas) for a list of observation times (in MJD).

Parameters:

t_obsarray or float

Returns:

Centroid offset on the plane of the sky in milli-arcseoncds.

Other Parameters:

ast_filt_idxint

Index into the photometry parameter lists for the photometry that corresponds to this astrometry data set.

image_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

amp_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

get_centroid_shift(t)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. No parallax is included. 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).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

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

Parameters:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_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_obs, mag_obs, mag_err_obs, filt_index=0)

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

Parameters:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_complex_pos(t_obs)

Get the positions of the lenses and source as complex numbers. This is needed for further calculations. Note that all units are still the same as before, this is just rewriting vectors \(z = (x,y)\) as \(z = x + iy\).

Parameters:

tarray_like

Array of times to model.

Returns:

wcomplex array

Source position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times, N_sources].

z1complex array

Lens primary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

z2complex array

Lens secondary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

get_image_pos_arr(w, z1, z2, m1, m2, check_sols=True)

Gets image positions.

Solve the fifth-order polynomial and get the image positions.

See PSBL writeup for full equations.

All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

m1float

m2float

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_image_pos_arr_old(w, z1, z2, check_sols=True)

Gets image positions. | Solve the fifth-order polynomial and get the image positions. | See PSBL writeup for full equations. | All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Position of the lensed source images. Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_lens_astrometry(t_obs)

Equation of motion for just the foreground lens system.

Parameters:

t_obsarray_like

Time (in MJD).

Return

——

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

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_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images.

Parameters:

t_obsarray_like

Array of times to model.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. No parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs, image_arr=None, amp_arr=None)

Position of the observed source position in arcsec.

Parameters:

t_obsarray_like, shape = [N_times]

Array of times to model.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

get_resolved_lens_astrometry(t_obs)

Equation of motion for just the foreground lenses, individually.

Parameters:

t_obsarray_like

Time (in MJD).

get_resolved_photometry(t_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images. Implement with no blending (since we don’t support different blendings for the different images).

Parameters:

t_obsarray_like

Array of times to model.

Returns:

mag_modelarray_like

Magnitude of each lensed image centroid at t_obs. Shape = [5, len(t_obs)]

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

filt_idxint

The filter index (def=0).

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

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

Parameters:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_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:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_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_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2)

Make sure everything is roughly centered on the origin in a 1 x 1 box.

PSBL Parallax

class model.PSBL_PhotAstrom_Par_Param1(*args, **kwargs)

Bases: ModelClassABC, PSBL_PhotAstrom, PSBL_Parallax, PSBL_PhotAstromParam1

Point source binary lens. It has 3 more parameters than PSPL (additional mass term, separation, and angle of approach). Note that this is a STATIC binary lens, i.e. there is no orbital motion.

Attributes:

mLp, mLsfloat

Masses of the lenses (Msun)

t0float

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

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.

betafloat

Angular distance between the source and the GEOMETRIC center of the lenses 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).

muL_Efloat

Lens system proper motion in the RA direction (mas/yr)

muL_Nfloat

Lens system proper motion in the Dec. direction (mas/yr)

muS_Efloat

Source proper motion in the RA direction (mas/yr)

muS_Nfloat

Source proper motion in the Dec. direction (mas/yr)

dLfloat

Distance from the observer to the lens system (pc)

dSfloat

Distance from the observer to the source (pc)

sepfloat

Angular separation of the two lenses (mas)

alphafloat

Angle made between the binary axis and North; measured in degrees East of North.

b_sffnumpy array or list

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

mag_srcnumpy array or list

Source magnitude, unlensed. One in each filter.

root_tolfloat

Tolerance in comparing the polynomial roots to the physical solutions. Default = 1e-8

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_all_arrays(t_obs[, check_sols, rescale])	Obtain the image and amplitude arrays for each t_obs.
get_amp_arr(z_arr, z1, z2)	Calculations amplification array
get_amplification(t_obs[, amp_arr])	noParallax: Get the photometric amplification term at a set of times, t.
get_astrometry(t_obs[, image_arr, amp_arr, ...])	Position of the observed (unresolved) source position in arcsec.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_centroid(t_obs[, ast_filt_idx, ...])	PSPL: Get the centroid shift (in mas) for a list of observation times (in MJD).
get_centroid_shift(t[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, 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_obs, 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_complex_pos(t_obs)	Get the positions of the lenses and source as complex numbers.
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_image_pos_arr(w, z1, z2, m1, m2[, ...])	Gets image positions.
get_image_pos_arr_old(w, z1, z2[, check_sols])	Gets image positions.
get_lens_astrometry(t_obs)	Equation of motion for just the foreground lens system.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t_obs[, filt_idx, amp_arr, ...])	Get the photometry for each of the lensed source images.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs[, image_arr, ...])	Position of the observed source position in arcsec.
get_resolved_lens_astrometry(t_obs)	Equation of motion for just the foreground lenses, individually.
get_resolved_photometry(t_obs[, filt_idx, ...])	Get the photometry for each of the lensed source images.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_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_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
rescale_complex_pos(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

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

calc_piE_ecliptic()

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

get_all_arrays(t_obs, check_sols=True, rescale=True)

Obtain the image and amplitude arrays for each t_obs.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

imagesarray_like

Array/tuple of complex positions of each images at each t_obs.

amp_arrarray_like

Array/tuple of amplification of each images at each t_obs.

get_amp_arr(z_arr, z1, z2)

Calculations amplification array

Calculates the amplification A from the Jacobian J, \(A = 1/|J|\)

Parameters:

z_arrarray_like

Complex position of images. Shape = [N_times, N_solutions, 1]

– note this could be jagged.

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

Returns:

amp_arrarray_like

BLEH

get_amplification(t_obs, amp_arr=None)

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

Parameters:

t:

Array of times in MJD.DDD

get_astrometry(t_obs, image_arr=None, amp_arr=None, ast_filt_idx=0)

Position of the observed (unresolved) source position in arcsec.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

ast_filt_idxint

The filter index for the astrometry.

get_astrometry_unlensed(t_obs)

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

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t_obs) x 2

The unlensed positions of the source in arcseconds.

get_centroid(t_obs, ast_filt_idx=0, image_arr=None, amp_arr=None)

PSPL: Get the centroid shift (in mas) for a list of observation times (in MJD).

Parameters:

t_obsarray or float

Returns:

Centroid offset on the plane of the sky in milli-arcseoncds.

Other Parameters:

ast_filt_idxint

Index into the photometry parameter lists for the photometry that corresponds to this astrometry data set.

image_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

amp_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included. 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).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

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

Parameters:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_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_obs, mag_obs, mag_err_obs, filt_index=0)

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

Parameters:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_complex_pos(t_obs)

Get the positions of the lenses and source as complex numbers. This is needed for further calculations. Note that all units are still the same as before, this is just rewriting vectors \(z = (x,y)\) as \(z = x + iy\).

Parameters:

tarray_like

Array of times to model.

Returns:

wcomplex array

Source position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times, N_sources].

z1complex array

Lens primary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

z2complex array

Lens secondary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

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_image_pos_arr(w, z1, z2, m1, m2, check_sols=True)

Gets image positions.

Solve the fifth-order polynomial and get the image positions.

See PSBL writeup for full equations.

All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

m1float

m2float

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_image_pos_arr_old(w, z1, z2, check_sols=True)

Gets image positions. | Solve the fifth-order polynomial and get the image positions. | See PSBL writeup for full equations. | All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Position of the lensed source images. Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_lens_astrometry(t_obs)

Equation of motion for just the foreground lens system.

Parameters:

t_obsarray_like

Time (in MJD).

Return

——

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

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_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images.

Parameters:

t_obsarray_like

Array of times to model.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_resolved_amplification(t)

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

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs, image_arr=None, amp_arr=None)

Position of the observed source position in arcsec.

Parameters:

t_obsarray_like, shape = [N_times]

Array of times to model.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

get_resolved_lens_astrometry(t_obs)

Equation of motion for just the foreground lenses, individually.

Parameters:

t_obsarray_like

Time (in MJD).

get_resolved_photometry(t_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images. Implement with no blending (since we don’t support different blendings for the different images).

Parameters:

t_obsarray_like

Array of times to model.

Returns:

mag_modelarray_like

Magnitude of each lensed image centroid at t_obs. Shape = [5, len(t_obs)]

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

filt_idxint

The filter index (def=0).

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

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

Parameters:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_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:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_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_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2)

Make sure everything is roughly centered on the origin in a 1 x 1 box.

class model.PSBL_PhotAstrom_Par_Param2(*args, **kwargs)

Bases: ModelClassABC, PSBL_PhotAstrom, PSBL_Parallax, PSBL_PhotAstromParam2

Point source binary lens. It has 3 more parameters than PSPL (additional mass term, separation, and angle of approach). Note that this is a STATIC binary lens, i.e. there is no orbital motion.

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).

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)

qfloat

Mass ratio (M2 / M1)

sepfloat

Angular separation of the two lenses (mas)

alphafloat

Angle made between the binary axis and North; measured in degrees East of North.

b_sffnumpy array or list

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

mag_srcnumpy array or list

Source magnitude, unlensed. One in each filter.

root_tolfloat

Tolerance in comparing the polynomial roots to the physical solutions. Default = 1e-8

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_all_arrays(t_obs[, check_sols, rescale])	Obtain the image and amplitude arrays for each t_obs.
get_amp_arr(z_arr, z1, z2)	Calculations amplification array
get_amplification(t_obs[, amp_arr])	noParallax: Get the photometric amplification term at a set of times, t.
get_astrometry(t_obs[, image_arr, amp_arr, ...])	Position of the observed (unresolved) source position in arcsec.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_centroid(t_obs[, ast_filt_idx, ...])	PSPL: Get the centroid shift (in mas) for a list of observation times (in MJD).
get_centroid_shift(t[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, 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_obs, 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_complex_pos(t_obs)	Get the positions of the lenses and source as complex numbers.
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_image_pos_arr(w, z1, z2, m1, m2[, ...])	Gets image positions.
get_image_pos_arr_old(w, z1, z2[, check_sols])	Gets image positions.
get_lens_astrometry(t_obs)	Equation of motion for just the foreground lens system.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t_obs[, filt_idx, amp_arr, ...])	Get the photometry for each of the lensed source images.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs[, image_arr, ...])	Position of the observed source position in arcsec.
get_resolved_lens_astrometry(t_obs)	Equation of motion for just the foreground lenses, individually.
get_resolved_photometry(t_obs[, filt_idx, ...])	Get the photometry for each of the lensed source images.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_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_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
rescale_complex_pos(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

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

calc_piE_ecliptic()

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

get_all_arrays(t_obs, check_sols=True, rescale=True)

Obtain the image and amplitude arrays for each t_obs.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

imagesarray_like

Array/tuple of complex positions of each images at each t_obs.

amp_arrarray_like

Array/tuple of amplification of each images at each t_obs.

get_amp_arr(z_arr, z1, z2)

Calculations amplification array

Calculates the amplification A from the Jacobian J, \(A = 1/|J|\)

Parameters:

z_arrarray_like

Complex position of images. Shape = [N_times, N_solutions, 1]

– note this could be jagged.

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

Returns:

amp_arrarray_like

BLEH

get_amplification(t_obs, amp_arr=None)

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

Parameters:

t:

Array of times in MJD.DDD

get_astrometry(t_obs, image_arr=None, amp_arr=None, ast_filt_idx=0)

Position of the observed (unresolved) source position in arcsec.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

ast_filt_idxint

The filter index for the astrometry.

get_astrometry_unlensed(t_obs)

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

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t_obs) x 2

The unlensed positions of the source in arcseconds.

get_centroid(t_obs, ast_filt_idx=0, image_arr=None, amp_arr=None)

PSPL: Get the centroid shift (in mas) for a list of observation times (in MJD).

Parameters:

t_obsarray or float

Returns:

Centroid offset on the plane of the sky in milli-arcseoncds.

Other Parameters:

ast_filt_idxint

Index into the photometry parameter lists for the photometry that corresponds to this astrometry data set.

image_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

amp_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included. 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).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

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

Parameters:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_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_obs, mag_obs, mag_err_obs, filt_index=0)

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

Parameters:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_complex_pos(t_obs)

Get the positions of the lenses and source as complex numbers. This is needed for further calculations. Note that all units are still the same as before, this is just rewriting vectors \(z = (x,y)\) as \(z = x + iy\).

Parameters:

tarray_like

Array of times to model.

Returns:

wcomplex array

Source position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times, N_sources].

z1complex array

Lens primary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

z2complex array

Lens secondary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

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_image_pos_arr(w, z1, z2, m1, m2, check_sols=True)

Gets image positions.

Solve the fifth-order polynomial and get the image positions.

See PSBL writeup for full equations.

All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

m1float

m2float

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_image_pos_arr_old(w, z1, z2, check_sols=True)

Gets image positions. | Solve the fifth-order polynomial and get the image positions. | See PSBL writeup for full equations. | All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Position of the lensed source images. Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_lens_astrometry(t_obs)

Equation of motion for just the foreground lens system.

Parameters:

t_obsarray_like

Time (in MJD).

Return

——

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

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_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images.

Parameters:

t_obsarray_like

Array of times to model.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_resolved_amplification(t)

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

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs, image_arr=None, amp_arr=None)

Position of the observed source position in arcsec.

Parameters:

t_obsarray_like, shape = [N_times]

Array of times to model.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

get_resolved_lens_astrometry(t_obs)

Equation of motion for just the foreground lenses, individually.

Parameters:

t_obsarray_like

Time (in MJD).

get_resolved_photometry(t_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images. Implement with no blending (since we don’t support different blendings for the different images).

Parameters:

t_obsarray_like

Array of times to model.

Returns:

mag_modelarray_like

Magnitude of each lensed image centroid at t_obs. Shape = [5, len(t_obs)]

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

filt_idxint

The filter index (def=0).

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

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

Parameters:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_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:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_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_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2)

Make sure everything is roughly centered on the origin in a 1 x 1 box.

class model.PSBL_PhotAstrom_Par_Param3(*args, **kwargs)

Bases: ModelClassABC, PSBL_PhotAstrom, PSBL_Parallax, PSBL_PhotAstromParam3

Point source binary lens. It has 3 more parameters than PSPL (additional mass term, separation, and angle of approach). Note that this is a STATIC binary lens, i.e. there is no orbital motion.

Attributes:

t0float

Time of photometric peak, as seen from Earth (MJD.DDD) FIXME: THIS IS NOT RIGHT

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

• 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)

qfloat

Mass ratio (M2 / M1)

sepfloat

Angular separation of the two lenses (mas)

alphafloat

Angle made between the binary axis and North; measured in degrees East of North.

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.

root_tolfloat

Tolerance in comparing the polynomial roots to the physical solutions. Default = 1e-8

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_all_arrays(t_obs[, check_sols, rescale])	Obtain the image and amplitude arrays for each t_obs.
get_amp_arr(z_arr, z1, z2)	Calculations amplification array
get_amplification(t_obs[, amp_arr])	noParallax: Get the photometric amplification term at a set of times, t.
get_astrometry(t_obs[, image_arr, amp_arr, ...])	Position of the observed (unresolved) source position in arcsec.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_centroid(t_obs[, ast_filt_idx, ...])	PSPL: Get the centroid shift (in mas) for a list of observation times (in MJD).
get_centroid_shift(t[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, 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_obs, 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_complex_pos(t_obs)	Get the positions of the lenses and source as complex numbers.
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_image_pos_arr(w, z1, z2, m1, m2[, ...])	Gets image positions.
get_image_pos_arr_old(w, z1, z2[, check_sols])	Gets image positions.
get_lens_astrometry(t_obs)	Equation of motion for just the foreground lens system.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t_obs[, filt_idx, amp_arr, ...])	Get the photometry for each of the lensed source images.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs[, image_arr, ...])	Position of the observed source position in arcsec.
get_resolved_lens_astrometry(t_obs)	Equation of motion for just the foreground lenses, individually.
get_resolved_photometry(t_obs[, filt_idx, ...])	Get the photometry for each of the lensed source images.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_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_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
rescale_complex_pos(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

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

calc_piE_ecliptic()

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

get_all_arrays(t_obs, check_sols=True, rescale=True)

Obtain the image and amplitude arrays for each t_obs.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

imagesarray_like

Array/tuple of complex positions of each images at each t_obs.

amp_arrarray_like

Array/tuple of amplification of each images at each t_obs.

get_amp_arr(z_arr, z1, z2)

Calculations amplification array

Calculates the amplification A from the Jacobian J, \(A = 1/|J|\)

Parameters:

z_arrarray_like

Complex position of images. Shape = [N_times, N_solutions, 1]

– note this could be jagged.

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

Returns:

amp_arrarray_like

BLEH

get_amplification(t_obs, amp_arr=None)

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

Parameters:

t:

Array of times in MJD.DDD

get_astrometry(t_obs, image_arr=None, amp_arr=None, ast_filt_idx=0)

Position of the observed (unresolved) source position in arcsec.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

ast_filt_idxint

The filter index for the astrometry.

get_astrometry_unlensed(t_obs)

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

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t_obs) x 2

The unlensed positions of the source in arcseconds.

get_centroid(t_obs, ast_filt_idx=0, image_arr=None, amp_arr=None)

PSPL: Get the centroid shift (in mas) for a list of observation times (in MJD).

Parameters:

t_obsarray or float

Returns:

Centroid offset on the plane of the sky in milli-arcseoncds.

Other Parameters:

ast_filt_idxint

Index into the photometry parameter lists for the photometry that corresponds to this astrometry data set.

image_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

amp_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included. 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).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

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

Parameters:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_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_obs, mag_obs, mag_err_obs, filt_index=0)

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

Parameters:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_complex_pos(t_obs)

Get the positions of the lenses and source as complex numbers. This is needed for further calculations. Note that all units are still the same as before, this is just rewriting vectors \(z = (x,y)\) as \(z = x + iy\).

Parameters:

tarray_like

Array of times to model.

Returns:

wcomplex array

Source position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times, N_sources].

z1complex array

Lens primary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

z2complex array

Lens secondary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

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_image_pos_arr(w, z1, z2, m1, m2, check_sols=True)

Gets image positions.

Solve the fifth-order polynomial and get the image positions.

See PSBL writeup for full equations.

All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

m1float

m2float

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_image_pos_arr_old(w, z1, z2, check_sols=True)

Gets image positions. | Solve the fifth-order polynomial and get the image positions. | See PSBL writeup for full equations. | All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Position of the lensed source images. Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_lens_astrometry(t_obs)

Equation of motion for just the foreground lens system.

Parameters:

t_obsarray_like

Time (in MJD).

Return

——

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

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_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images.

Parameters:

t_obsarray_like

Array of times to model.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_resolved_amplification(t)

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

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs, image_arr=None, amp_arr=None)

Position of the observed source position in arcsec.

Parameters:

t_obsarray_like, shape = [N_times]

Array of times to model.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

get_resolved_lens_astrometry(t_obs)

Equation of motion for just the foreground lenses, individually.

Parameters:

t_obsarray_like

Time (in MJD).

get_resolved_photometry(t_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images. Implement with no blending (since we don’t support different blendings for the different images).

Parameters:

t_obsarray_like

Array of times to model.

Returns:

mag_modelarray_like

Magnitude of each lensed image centroid at t_obs. Shape = [5, len(t_obs)]

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

filt_idxint

The filter index (def=0).

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

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

Parameters:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_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:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_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_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2)

Make sure everything is roughly centered on the origin in a 1 x 1 box.

class model.PSBL_PhotAstrom_Par_Param4(*args, **kwargs)

Bases: ModelClassABC, PSBL_PhotAstrom, PSBL_Parallax, PSBL_PhotAstromParam4

Point source binary lens. It has 3 more parameters than PSPL (additional mass term, separation, and angle of approach). Note that this is a STATIC binary lens, i.e. there is no orbital motion.

Attributes:

t0_comfloat

Time of photometric peak, as seen from Earth (MJD.DDD) FIXME: THIS IS NOT RIGHT

u0_amp_comfloat

Angular distance between the source and the binary lens COM 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).

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)

betafloat

Angular distance between the source and the GEOMETRIC center of the lenses on the plane of the sky (mas).

qfloat

Mass ratio (M2 / M1)

sepfloat

Angular separation of the two lenses (mas)

alphafloat

Angle made between the binary axis and North; measured in degrees East of North.

b_sffnumpy array or list

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

mag_srcnumpy array or list

Source magnitude, unlensed. One in each filter.

root_tolfloat

Tolerance in comparing the polynomial roots to the physical solutions. Default = 1e-8

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_all_arrays(t_obs[, check_sols, rescale])	Obtain the image and amplitude arrays for each t_obs.
get_amp_arr(z_arr, z1, z2)	Calculations amplification array
get_amplification(t_obs[, amp_arr])	noParallax: Get the photometric amplification term at a set of times, t.
get_astrometry(t_obs[, image_arr, amp_arr, ...])	Position of the observed (unresolved) source position in arcsec.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_centroid(t_obs[, ast_filt_idx, ...])	PSPL: Get the centroid shift (in mas) for a list of observation times (in MJD).
get_centroid_shift(t[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, 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_obs, 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_complex_pos(t_obs)	Get the positions of the lenses and source as complex numbers.
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_image_pos_arr(w, z1, z2, m1, m2[, ...])	Gets image positions.
get_image_pos_arr_old(w, z1, z2[, check_sols])	Gets image positions.
get_lens_astrometry(t_obs)	Equation of motion for just the foreground lens system.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t_obs[, filt_idx, amp_arr, ...])	Get the photometry for each of the lensed source images.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs[, image_arr, ...])	Position of the observed source position in arcsec.
get_resolved_lens_astrometry(t_obs)	Equation of motion for just the foreground lenses, individually.
get_resolved_photometry(t_obs[, filt_idx, ...])	Get the photometry for each of the lensed source images.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_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_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
rescale_complex_pos(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

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

calc_piE_ecliptic()

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

get_all_arrays(t_obs, check_sols=True, rescale=True)

Obtain the image and amplitude arrays for each t_obs.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

imagesarray_like

Array/tuple of complex positions of each images at each t_obs.

amp_arrarray_like

Array/tuple of amplification of each images at each t_obs.

get_amp_arr(z_arr, z1, z2)

Calculations amplification array

Calculates the amplification A from the Jacobian J, \(A = 1/|J|\)

Parameters:

z_arrarray_like

Complex position of images. Shape = [N_times, N_solutions, 1]

– note this could be jagged.

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

Returns:

amp_arrarray_like

BLEH

get_amplification(t_obs, amp_arr=None)

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

Parameters:

t:

Array of times in MJD.DDD

get_astrometry(t_obs, image_arr=None, amp_arr=None, ast_filt_idx=0)

Position of the observed (unresolved) source position in arcsec.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

ast_filt_idxint

The filter index for the astrometry.

get_astrometry_unlensed(t_obs)

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

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t_obs) x 2

The unlensed positions of the source in arcseconds.

get_centroid(t_obs, ast_filt_idx=0, image_arr=None, amp_arr=None)

PSPL: Get the centroid shift (in mas) for a list of observation times (in MJD).

Parameters:

t_obsarray or float

Returns:

Centroid offset on the plane of the sky in milli-arcseoncds.

Other Parameters:

ast_filt_idxint

Index into the photometry parameter lists for the photometry that corresponds to this astrometry data set.

image_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

amp_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included. 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).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

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

Parameters:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_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_obs, mag_obs, mag_err_obs, filt_index=0)

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

Parameters:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_complex_pos(t_obs)

Get the positions of the lenses and source as complex numbers. This is needed for further calculations. Note that all units are still the same as before, this is just rewriting vectors \(z = (x,y)\) as \(z = x + iy\).

Parameters:

tarray_like

Array of times to model.

Returns:

wcomplex array

Source position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times, N_sources].

z1complex array

Lens primary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

z2complex array

Lens secondary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

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_image_pos_arr(w, z1, z2, m1, m2, check_sols=True)

Gets image positions.

Solve the fifth-order polynomial and get the image positions.

See PSBL writeup for full equations.

All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

m1float

m2float

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_image_pos_arr_old(w, z1, z2, check_sols=True)

Gets image positions. | Solve the fifth-order polynomial and get the image positions. | See PSBL writeup for full equations. | All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Position of the lensed source images. Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_lens_astrometry(t_obs)

Equation of motion for just the foreground lens system.

Parameters:

t_obsarray_like

Time (in MJD).

Return

——

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

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_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images.

Parameters:

t_obsarray_like

Array of times to model.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_resolved_amplification(t)

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

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs, image_arr=None, amp_arr=None)

Position of the observed source position in arcsec.

Parameters:

t_obsarray_like, shape = [N_times]

Array of times to model.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

get_resolved_lens_astrometry(t_obs)

Equation of motion for just the foreground lenses, individually.

Parameters:

t_obsarray_like

Time (in MJD).

get_resolved_photometry(t_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images. Implement with no blending (since we don’t support different blendings for the different images).

Parameters:

t_obsarray_like

Array of times to model.

Returns:

mag_modelarray_like

Magnitude of each lensed image centroid at t_obs. Shape = [5, len(t_obs)]

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

filt_idxint

The filter index (def=0).

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

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

Parameters:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_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:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_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_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2)

Make sure everything is roughly centered on the origin in a 1 x 1 box.

PSBL_Phot

class model.PSBL_Phot_noPar_Param1(*args, **kwargs)

Bases: ModelClassABC, PSBL_Phot, PSBL_noParallax, PSBL_PhotParam1

Point source binary lens, photometry only.

It has 3 more parameters than PSPL_PhotParam1:

• mass ratio

• separation – in units of thetaE

• angle of approach

Note that this is a STATIC binary lens, i.e. there is no orbital motion.

Other Parameters:

raL: float

Right ascension of the lens in decimal degrees. Required if calculating with parallax

decL: float

Declination of the lens in decimal degrees. Required if calculating with parallax

obsLocation: str, optional

The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

root_tol: float

Tolerance in comparing the polynomial roots to the physical solutions.

Default = 0.0

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric 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 based on the system mass. [MJD]

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

q: float

Mass ratio (low-mass / high-mass)

sep: float

Angular separation of the two lenses in units of thetaE where thetaE is defined with the total binary mass.

phi: float

Angle made between the binary axis and the relative proper motion vector, measured in degrees.

b_sff: 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: 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.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Not supported on this object.
get_all_arrays(t_obs[, check_sols, rescale])	Obtain the image and amplitude arrays for each t_obs.
get_amp_arr(z_arr, z1, z2)	Calculations amplification array
get_amplification(t_obs[, amp_arr])	noParallax: Get the photometric amplification term at a set of times, t.
get_astrometry(t_obs[, image_arr, amp_arr, ...])	Position of the observed (unresolved) source position in Einstein radii.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_chi2_photometry(t_obs, 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_complex_pos(t_obs)	Get the positions of the lenses and source as complex numbers.
get_image_pos_arr(w, z1, z2, m1, m2[, ...])	Gets image positions.
get_image_pos_arr_old(w, z1, z2[, check_sols])	Gets image positions.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t_obs[, filt_idx, amp_arr, ...])	Get the photometry for each of the lensed source images.
get_resolved_astrometry(t_obs[, image_arr, ...])	Position of the observed source position in Einstein radii.
get_resolved_lens_astrometry(t_obs)	Equation of motion for just the foreground lenses, individually.
get_resolved_photometry(t_obs[, filt_idx, ...])	Get the photometry for each of the lensed source images.
log_likely_photometry(t_obs, mag_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_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
rescale_complex_pos(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

get_centroid_shift
get_lens_astrometry
get_resolved_amplification
log_likely_astrometry

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

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

calc_piE_ecliptic()

Not supported on this object.

get_all_arrays(t_obs, check_sols=True, rescale=True)

Obtain the image and amplitude arrays for each t_obs.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

imagesarray_like

Array/tuple of complex positions of each images at each t_obs.

amp_arrarray_like

Array/tuple of amplification of each images at each t_obs.

get_amp_arr(z_arr, z1, z2)

Calculations amplification array

Calculates the amplification A from the Jacobian J, \(A = 1/|J|\)

Parameters:

z_arrarray_like

Complex position of images. Shape = [N_times, N_solutions, 1]

– note this could be jagged.

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

Returns:

amp_arrarray_like

BLEH

get_amplification(t_obs, amp_arr=None)

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

Parameters:

t:

Array of times in MJD.DDD

get_astrometry(t_obs, image_arr=None, amp_arr=None, ast_filt_idx=0)

Position of the observed (unresolved) source position in Einstein radii.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

get_astrometry_unlensed(t_obs)

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_unlensednumpy array, dtype=float, shape = len(t_obs) x 2

The unlensed positions of the source in Einstein radii.

Notes

Note

Note, this is a photometry only model, so units are in Einstein radii.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. No parallax is included. 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).

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

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

Parameters:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_complex_pos(t_obs)

Get the positions of the lenses and source as complex numbers.

This is needed for further calculations. Note that all units are still the same as before, this is just rewriting vectors \(z = (x,y)\) as \(z = x + iy\).

Returns:

wcomplex array

Source position as an array of complex numbers with real = east component, imaginary = north component

z1complex array

Lens primary component position as an array of complex numbers with real = east component, imaginary = north component

z2complex array

Lens secondary component position as an array of complex numbers with real = east component, imaginary = north component

get_image_pos_arr(w, z1, z2, m1, m2, check_sols=True)

Gets image positions.

Solve the fifth-order polynomial and get the image positions.

See PSBL writeup for full equations.

All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

m1float

m2float

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_image_pos_arr_old(w, z1, z2, check_sols=True)

Gets image positions. | Solve the fifth-order polynomial and get the image positions. | See PSBL writeup for full equations. | All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Position of the lensed source images. Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_lens_astrometry(t)

Get the astrometry for the foreground lens at the input times. No parallax is included. 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).

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_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images.

Parameters:

t_obsarray_like

Array of times to model.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. No parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs, image_arr=None, amp_arr=None)

Position of the observed source position in Einstein radii.

Parameters:

t_obsarray_like, shape = [N_times]

Array of times to model.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

get_resolved_lens_astrometry(t_obs)

Equation of motion for just the foreground lenses, individually.

Parameters:

t_obsarray_like

Time (in MJD).

Notes

Note

Note, this is a photometry only model, so units are in Einstein radii.

get_resolved_photometry(t_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images. Implement with no blending (since we don’t support different blendings for the different images).

Parameters:

t_obsarray_like

Array of times to model.

Returns:

mag_modelarray_like

Magnitude of each lensed image centroid at t_obs. Shape = [5, len(t_obs)]

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

filt_idxint

The filter index (def=0).

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2)

Make sure everything is roughly centered on the origin in a 1 x 1 box.

PSBL_phot_parallax

class model.PSBL_Phot_Par_Param1(*args, **kwargs)

Bases: ModelClassABC, PSBL_Phot, PSBL_Parallax, PSBL_PhotParam1

Point source binary lens, photometry only.

It has 3 more parameters than PSPL_PhotParam1:

• mass ratio

• separation – in units of thetaE

• angle of approach

Note that this is a STATIC binary lens, i.e. there is no orbital motion.

Other Parameters:

raL: float

Right ascension of the lens in decimal degrees. Required if calculating with parallax

decL: float

Declination of the lens in decimal degrees. Required if calculating with parallax

obsLocation: str, optional

The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

root_tol: float

Tolerance in comparing the polynomial roots to the physical solutions.

Default = 0.0

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric 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 based on the system mass. [MJD]

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

q: float

Mass ratio (low-mass / high-mass)

sep: float

Angular separation of the two lenses in units of thetaE where thetaE is defined with the total binary mass.

phi: float

Angle made between the binary axis and the relative proper motion vector, measured in degrees.

b_sff: 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: 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.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_all_arrays(t_obs[, check_sols, rescale])	Obtain the image and amplitude arrays for each t_obs.
get_amp_arr(z_arr, z1, z2)	Calculations amplification array
get_amplification(t_obs[, amp_arr])	noParallax: Get the photometric amplification term at a set of times, t.
get_astrometry(t_obs[, image_arr, amp_arr, ...])	Position of the observed (unresolved) source position in Einstein radii.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_chi2_photometry(t_obs, 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_complex_pos(t_obs)	Get the positions of the lenses and source as complex numbers.
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_image_pos_arr(w, z1, z2, m1, m2[, ...])	Gets image positions.
get_image_pos_arr_old(w, z1, z2[, check_sols])	Gets image positions.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_photometry(t_obs[, filt_idx, amp_arr, ...])	Get the photometry for each of the lensed source images.
get_resolved_astrometry(t_obs[, image_arr, ...])	Position of the observed source position in Einstein radii.
get_resolved_lens_astrometry(t_obs)	Equation of motion for just the foreground lenses, individually.
get_resolved_photometry(t_obs[, filt_idx, ...])	Get the photometry for each of the lensed source images.
log_likely_photometry(t_obs, mag_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_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
rescale_complex_pos(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

get_centroid_shift
get_lens_astrometry
get_resolved_amplification
log_likely_astrometry
set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

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

calc_piE_ecliptic()

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

get_all_arrays(t_obs, check_sols=True, rescale=True)

Obtain the image and amplitude arrays for each t_obs.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

imagesarray_like

Array/tuple of complex positions of each images at each t_obs.

amp_arrarray_like

Array/tuple of amplification of each images at each t_obs.

get_amp_arr(z_arr, z1, z2)

Calculations amplification array

Calculates the amplification A from the Jacobian J, \(A = 1/|J|\)

Parameters:

z_arrarray_like

Complex position of images. Shape = [N_times, N_solutions, 1]

– note this could be jagged.

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

Returns:

amp_arrarray_like

BLEH

get_amplification(t_obs, amp_arr=None)

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

Parameters:

t:

Array of times in MJD.DDD

get_astrometry(t_obs, image_arr=None, amp_arr=None, ast_filt_idx=0)

Position of the observed (unresolved) source position in Einstein radii.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

get_astrometry_unlensed(t_obs)

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_unlensednumpy array, dtype=float, shape = len(t_obs) x 2

The unlensed positions of the source in Einstein radii.

Notes

Note

Note, this is a photometry only model, so units are in Einstein radii.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included. 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).

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

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

Parameters:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_complex_pos(t_obs)

Get the positions of the lenses and source as complex numbers.

This is needed for further calculations. Note that all units are still the same as before, this is just rewriting vectors \(z = (x,y)\) as \(z = x + iy\).

Returns:

wcomplex array

Source position as an array of complex numbers with real = east component, imaginary = north component

z1complex array

Lens primary component position as an array of complex numbers with real = east component, imaginary = north component

z2complex array

Lens secondary component position as an array of complex numbers with real = east component, imaginary = north component

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_image_pos_arr(w, z1, z2, m1, m2, check_sols=True)

Gets image positions.

Solve the fifth-order polynomial and get the image positions.

See PSBL writeup for full equations.

All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

m1float

m2float

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_image_pos_arr_old(w, z1, z2, check_sols=True)

Gets image positions. | Solve the fifth-order polynomial and get the image positions. | See PSBL writeup for full equations. | All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Position of the lensed source images. Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_lens_astrometry(t)

Get the astrometry for the foreground lens at the input times. Parallax is included. 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).

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_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images.

Parameters:

t_obsarray_like

Array of times to model.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_resolved_amplification(t)

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

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs, image_arr=None, amp_arr=None)

Position of the observed source position in Einstein radii.

Parameters:

t_obsarray_like, shape = [N_times]

Array of times to model.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

get_resolved_lens_astrometry(t_obs)

Equation of motion for just the foreground lenses, individually.

Parameters:

t_obsarray_like

Time (in MJD).

Notes

Note

Note, this is a photometry only model, so units are in Einstein radii.

get_resolved_photometry(t_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images. Implement with no blending (since we don’t support different blendings for the different images).

Parameters:

t_obsarray_like

Array of times to model.

Returns:

mag_modelarray_like

Magnitude of each lensed image centroid at t_obs. Shape = [5, len(t_obs)]

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

filt_idxint

The filter index (def=0).

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2)

Make sure everything is roughly centered on the origin in a 1 x 1 box.

PSBL PhotAstrom, no parallax with GP

class model.PSBL_PhotAstrom_noPar_GP_Param1(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSBL_PhotAstrom, PSBL_noParallax, PSBL_PhotAstromParam1

Point source binary lens. It has 3 more parameters than PSPL (additional mass term, separation, and angle of approach). Note that this is a STATIC binary lens, i.e. there is no orbital motion.

Attributes:

mLp, mLsfloat

Masses of the lenses (Msun)

t0float

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

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.

betafloat

Angular distance between the source and the GEOMETRIC center of the lenses 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).

muL_Efloat

Lens system proper motion in the RA direction (mas/yr)

muL_Nfloat

Lens system proper motion in the Dec. direction (mas/yr)

muS_Efloat

Source proper motion in the RA direction (mas/yr)

muS_Nfloat

Source proper motion in the Dec. direction (mas/yr)

dLfloat

Distance from the observer to the lens system (pc)

dSfloat

Distance from the observer to the source (pc)

sepfloat

Angular separation of the two lenses (mas)

alphafloat

Angle made between the binary axis and North; measured in degrees East of North.

b_sffnumpy array or list

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

mag_srcnumpy array or list

Source magnitude, unlensed. One in each filter.

root_tolfloat

Tolerance in comparing the polynomial roots to the physical solutions. Default = 1e-8

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Not supported on this object.
get_all_arrays(t_obs[, check_sols, rescale])	Obtain the image and amplitude arrays for each t_obs.
get_amp_arr(z_arr, z1, z2)	Calculations amplification array
get_amplification(t_obs[, amp_arr])	noParallax: Get the photometric amplification term at a set of times, t.
get_astrometry(t_obs[, image_arr, amp_arr, ...])	Position of the observed (unresolved) source position in arcsec.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_centroid(t_obs[, ast_filt_idx, ...])	PSPL: Get the centroid shift (in mas) for a list of observation times (in MJD).
get_centroid_shift(t)	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, 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_obs, 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_complex_pos(t_obs)	Get the positions of the lenses and source as complex numbers.
get_image_pos_arr(w, z1, z2, m1, m2[, ...])	Gets image positions.
get_image_pos_arr_old(w, z1, z2[, check_sols])	Gets image positions.
get_lens_astrometry(t_obs)	Equation of motion for just the foreground lens system.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_photometry(t_obs[, filt_idx, amp_arr, ...])	Get the photometry for each of the lensed source images.
get_photometry_with_gp(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs[, image_arr, ...])	Position of the observed source position in arcsec.
get_resolved_lens_astrometry(t_obs)	Equation of motion for just the foreground lenses, individually.
get_resolved_photometry(t_obs[, filt_idx, ...])	Get the photometry for each of the lensed source images.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_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_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
rescale_complex_pos(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

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

calc_piE_ecliptic()

Not supported on this object.

get_all_arrays(t_obs, check_sols=True, rescale=True)

Obtain the image and amplitude arrays for each t_obs.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

imagesarray_like

Array/tuple of complex positions of each images at each t_obs.

amp_arrarray_like

Array/tuple of amplification of each images at each t_obs.

get_amp_arr(z_arr, z1, z2)

Calculations amplification array

Calculates the amplification A from the Jacobian J, \(A = 1/|J|\)

Parameters:

z_arrarray_like

Complex position of images. Shape = [N_times, N_solutions, 1]

– note this could be jagged.

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

Returns:

amp_arrarray_like

BLEH

get_amplification(t_obs, amp_arr=None)

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

Parameters:

t:

Array of times in MJD.DDD

get_astrometry(t_obs, image_arr=None, amp_arr=None, ast_filt_idx=0)

Position of the observed (unresolved) source position in arcsec.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

ast_filt_idxint

The filter index for the astrometry.

get_astrometry_unlensed(t_obs)

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

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t_obs) x 2

The unlensed positions of the source in arcseconds.

get_centroid(t_obs, ast_filt_idx=0, image_arr=None, amp_arr=None)

PSPL: Get the centroid shift (in mas) for a list of observation times (in MJD).

Parameters:

t_obsarray or float

Returns:

Centroid offset on the plane of the sky in milli-arcseoncds.

Other Parameters:

ast_filt_idxint

Index into the photometry parameter lists for the photometry that corresponds to this astrometry data set.

image_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

amp_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

get_centroid_shift(t)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. No parallax is included. 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).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

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

Parameters:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_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_obs, mag_obs, mag_err_obs, filt_index=0)

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

Parameters:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_complex_pos(t_obs)

Get the positions of the lenses and source as complex numbers. This is needed for further calculations. Note that all units are still the same as before, this is just rewriting vectors \(z = (x,y)\) as \(z = x + iy\).

Parameters:

tarray_like

Array of times to model.

Returns:

wcomplex array

Source position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times, N_sources].

z1complex array

Lens primary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

z2complex array

Lens secondary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

get_image_pos_arr(w, z1, z2, m1, m2, check_sols=True)

Gets image positions.

Solve the fifth-order polynomial and get the image positions.

See PSBL writeup for full equations.

All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

m1float

m2float

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_image_pos_arr_old(w, z1, z2, check_sols=True)

Gets image positions. | Solve the fifth-order polynomial and get the image positions. | See PSBL writeup for full equations. | All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Position of the lensed source images. Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_lens_astrometry(t_obs)

Equation of motion for just the foreground lens system.

Parameters:

t_obsarray_like

Time (in MJD).

Return

——

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

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_obs, mag_obs, mag_err_obs, filt_index=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_index] = False.

get_photometry(t_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images.

Parameters:

t_obsarray_like

Array of times to model.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_photometry_with_gp(t_obs, mag_obs, mag_err_obs, filt_index=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_index] = False.

Parameters:

t_obsarray_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_obs.

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_obs.

mag_obs_errarray_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_obs.

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_obs.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. No parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs, image_arr=None, amp_arr=None)

Position of the observed source position in arcsec.

Parameters:

t_obsarray_like, shape = [N_times]

Array of times to model.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

get_resolved_lens_astrometry(t_obs)

Equation of motion for just the foreground lenses, individually.

Parameters:

t_obsarray_like

Time (in MJD).

get_resolved_photometry(t_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images. Implement with no blending (since we don’t support different blendings for the different images).

Parameters:

t_obsarray_like

Array of times to model.

Returns:

mag_modelarray_like

Magnitude of each lensed image centroid at t_obs. Shape = [5, len(t_obs)]

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

filt_idxint

The filter index (def=0).

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

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

Parameters:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_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:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_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_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_index] = True.

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2)

Make sure everything is roughly centered on the origin in a 1 x 1 box.

class model.PSBL_PhotAstrom_noPar_GP_Param2(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSBL_PhotAstrom, PSBL_noParallax, PSBL_PhotAstromParam2

Point source binary lens. It has 3 more parameters than PSPL (additional mass term, separation, and angle of approach). Note that this is a STATIC binary lens, i.e. there is no orbital motion.

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).

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)

qfloat

Mass ratio (M2 / M1)

sepfloat

Angular separation of the two lenses (mas)

alphafloat

Angle made between the binary axis and North; measured in degrees East of North.

b_sffnumpy array or list

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

mag_srcnumpy array or list

Source magnitude, unlensed. One in each filter.

root_tolfloat

Tolerance in comparing the polynomial roots to the physical solutions. Default = 1e-8

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Not supported on this object.
get_all_arrays(t_obs[, check_sols, rescale])	Obtain the image and amplitude arrays for each t_obs.
get_amp_arr(z_arr, z1, z2)	Calculations amplification array
get_amplification(t_obs[, amp_arr])	noParallax: Get the photometric amplification term at a set of times, t.
get_astrometry(t_obs[, image_arr, amp_arr, ...])	Position of the observed (unresolved) source position in arcsec.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_centroid(t_obs[, ast_filt_idx, ...])	PSPL: Get the centroid shift (in mas) for a list of observation times (in MJD).
get_centroid_shift(t)	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, 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_obs, 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_complex_pos(t_obs)	Get the positions of the lenses and source as complex numbers.
get_image_pos_arr(w, z1, z2, m1, m2[, ...])	Gets image positions.
get_image_pos_arr_old(w, z1, z2[, check_sols])	Gets image positions.
get_lens_astrometry(t_obs)	Equation of motion for just the foreground lens system.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_photometry(t_obs[, filt_idx, amp_arr, ...])	Get the photometry for each of the lensed source images.
get_photometry_with_gp(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs[, image_arr, ...])	Position of the observed source position in arcsec.
get_resolved_lens_astrometry(t_obs)	Equation of motion for just the foreground lenses, individually.
get_resolved_photometry(t_obs[, filt_idx, ...])	Get the photometry for each of the lensed source images.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_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_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
rescale_complex_pos(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

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

calc_piE_ecliptic()

Not supported on this object.

get_all_arrays(t_obs, check_sols=True, rescale=True)

Obtain the image and amplitude arrays for each t_obs.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

imagesarray_like

Array/tuple of complex positions of each images at each t_obs.

amp_arrarray_like

Array/tuple of amplification of each images at each t_obs.

get_amp_arr(z_arr, z1, z2)

Calculations amplification array

Calculates the amplification A from the Jacobian J, \(A = 1/|J|\)

Parameters:

z_arrarray_like

Complex position of images. Shape = [N_times, N_solutions, 1]

– note this could be jagged.

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

Returns:

amp_arrarray_like

BLEH

get_amplification(t_obs, amp_arr=None)

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

Parameters:

t:

Array of times in MJD.DDD

get_astrometry(t_obs, image_arr=None, amp_arr=None, ast_filt_idx=0)

Position of the observed (unresolved) source position in arcsec.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

ast_filt_idxint

The filter index for the astrometry.

get_astrometry_unlensed(t_obs)

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

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t_obs) x 2

The unlensed positions of the source in arcseconds.

get_centroid(t_obs, ast_filt_idx=0, image_arr=None, amp_arr=None)

PSPL: Get the centroid shift (in mas) for a list of observation times (in MJD).

Parameters:

t_obsarray or float

Returns:

Centroid offset on the plane of the sky in milli-arcseoncds.

Other Parameters:

ast_filt_idxint

Index into the photometry parameter lists for the photometry that corresponds to this astrometry data set.

image_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

amp_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

get_centroid_shift(t)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. No parallax is included. 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).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

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

Parameters:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_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_obs, mag_obs, mag_err_obs, filt_index=0)

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

Parameters:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_complex_pos(t_obs)

Get the positions of the lenses and source as complex numbers. This is needed for further calculations. Note that all units are still the same as before, this is just rewriting vectors \(z = (x,y)\) as \(z = x + iy\).

Parameters:

tarray_like

Array of times to model.

Returns:

wcomplex array

Source position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times, N_sources].

z1complex array

Lens primary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

z2complex array

Lens secondary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

get_image_pos_arr(w, z1, z2, m1, m2, check_sols=True)

Gets image positions.

Solve the fifth-order polynomial and get the image positions.

See PSBL writeup for full equations.

All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

m1float

m2float

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_image_pos_arr_old(w, z1, z2, check_sols=True)

Gets image positions. | Solve the fifth-order polynomial and get the image positions. | See PSBL writeup for full equations. | All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Position of the lensed source images. Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_lens_astrometry(t_obs)

Equation of motion for just the foreground lens system.

Parameters:

t_obsarray_like

Time (in MJD).

Return

——

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

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_obs, mag_obs, mag_err_obs, filt_index=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_index] = False.

get_photometry(t_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images.

Parameters:

t_obsarray_like

Array of times to model.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_photometry_with_gp(t_obs, mag_obs, mag_err_obs, filt_index=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_index] = False.

Parameters:

t_obsarray_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_obs.

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_obs.

mag_obs_errarray_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_obs.

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_obs.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. No parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs, image_arr=None, amp_arr=None)

Position of the observed source position in arcsec.

Parameters:

t_obsarray_like, shape = [N_times]

Array of times to model.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

get_resolved_lens_astrometry(t_obs)

Equation of motion for just the foreground lenses, individually.

Parameters:

t_obsarray_like

Time (in MJD).

get_resolved_photometry(t_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images. Implement with no blending (since we don’t support different blendings for the different images).

Parameters:

t_obsarray_like

Array of times to model.

Returns:

mag_modelarray_like

Magnitude of each lensed image centroid at t_obs. Shape = [5, len(t_obs)]

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

filt_idxint

The filter index (def=0).

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

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

Parameters:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_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:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_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_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_index] = True.

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2)

Make sure everything is roughly centered on the origin in a 1 x 1 box.

PSBL PhotAstrom, parallax with GP

class model.PSBL_PhotAstrom_Par_GP_Param1(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSBL_PhotAstrom, PSBL_Parallax, PSBL_PhotAstromParam1

Point source binary lens. It has 3 more parameters than PSPL (additional mass term, separation, and angle of approach). Note that this is a STATIC binary lens, i.e. there is no orbital motion.

Attributes:

mLp, mLsfloat

Masses of the lenses (Msun)

t0float

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

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.

betafloat

Angular distance between the source and the GEOMETRIC center of the lenses 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).

muL_Efloat

Lens system proper motion in the RA direction (mas/yr)

muL_Nfloat

Lens system proper motion in the Dec. direction (mas/yr)

muS_Efloat

Source proper motion in the RA direction (mas/yr)

muS_Nfloat

Source proper motion in the Dec. direction (mas/yr)

dLfloat

Distance from the observer to the lens system (pc)

dSfloat

Distance from the observer to the source (pc)

sepfloat

Angular separation of the two lenses (mas)

alphafloat

Angle made between the binary axis and North; measured in degrees East of North.

b_sffnumpy array or list

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

mag_srcnumpy array or list

Source magnitude, unlensed. One in each filter.

root_tolfloat

Tolerance in comparing the polynomial roots to the physical solutions. Default = 1e-8

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_all_arrays(t_obs[, check_sols, rescale])	Obtain the image and amplitude arrays for each t_obs.
get_amp_arr(z_arr, z1, z2)	Calculations amplification array
get_amplification(t_obs[, amp_arr])	noParallax: Get the photometric amplification term at a set of times, t.
get_astrometry(t_obs[, image_arr, amp_arr, ...])	Position of the observed (unresolved) source position in arcsec.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_centroid(t_obs[, ast_filt_idx, ...])	PSPL: Get the centroid shift (in mas) for a list of observation times (in MJD).
get_centroid_shift(t[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, 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_obs, 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_complex_pos(t_obs)	Get the positions of the lenses and source as complex numbers.
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_image_pos_arr(w, z1, z2, m1, m2[, ...])	Gets image positions.
get_image_pos_arr_old(w, z1, z2[, check_sols])	Gets image positions.
get_lens_astrometry(t_obs)	Equation of motion for just the foreground lens system.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_photometry(t_obs[, filt_idx, amp_arr, ...])	Get the photometry for each of the lensed source images.
get_photometry_with_gp(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs[, image_arr, ...])	Position of the observed source position in arcsec.
get_resolved_lens_astrometry(t_obs)	Equation of motion for just the foreground lenses, individually.
get_resolved_photometry(t_obs[, filt_idx, ...])	Get the photometry for each of the lensed source images.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_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_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
rescale_complex_pos(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

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

calc_piE_ecliptic()

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

get_all_arrays(t_obs, check_sols=True, rescale=True)

Obtain the image and amplitude arrays for each t_obs.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

imagesarray_like

Array/tuple of complex positions of each images at each t_obs.

amp_arrarray_like

Array/tuple of amplification of each images at each t_obs.

get_amp_arr(z_arr, z1, z2)

Calculations amplification array

Calculates the amplification A from the Jacobian J, \(A = 1/|J|\)

Parameters:

z_arrarray_like

Complex position of images. Shape = [N_times, N_solutions, 1]

– note this could be jagged.

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

Returns:

amp_arrarray_like

BLEH

get_amplification(t_obs, amp_arr=None)

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

Parameters:

t:

Array of times in MJD.DDD

get_astrometry(t_obs, image_arr=None, amp_arr=None, ast_filt_idx=0)

Position of the observed (unresolved) source position in arcsec.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

ast_filt_idxint

The filter index for the astrometry.

get_astrometry_unlensed(t_obs)

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

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t_obs) x 2

The unlensed positions of the source in arcseconds.

get_centroid(t_obs, ast_filt_idx=0, image_arr=None, amp_arr=None)

PSPL: Get the centroid shift (in mas) for a list of observation times (in MJD).

Parameters:

t_obsarray or float

Returns:

Centroid offset on the plane of the sky in milli-arcseoncds.

Other Parameters:

ast_filt_idxint

Index into the photometry parameter lists for the photometry that corresponds to this astrometry data set.

image_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

amp_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included. 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).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

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

Parameters:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_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_obs, mag_obs, mag_err_obs, filt_index=0)

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

Parameters:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_complex_pos(t_obs)

Get the positions of the lenses and source as complex numbers. This is needed for further calculations. Note that all units are still the same as before, this is just rewriting vectors \(z = (x,y)\) as \(z = x + iy\).

Parameters:

tarray_like

Array of times to model.

Returns:

wcomplex array

Source position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times, N_sources].

z1complex array

Lens primary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

z2complex array

Lens secondary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

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_image_pos_arr(w, z1, z2, m1, m2, check_sols=True)

Gets image positions.

Solve the fifth-order polynomial and get the image positions.

See PSBL writeup for full equations.

All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

m1float

m2float

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_image_pos_arr_old(w, z1, z2, check_sols=True)

Gets image positions. | Solve the fifth-order polynomial and get the image positions. | See PSBL writeup for full equations. | All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Position of the lensed source images. Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_lens_astrometry(t_obs)

Equation of motion for just the foreground lens system.

Parameters:

t_obsarray_like

Time (in MJD).

Return

——

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

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_obs, mag_obs, mag_err_obs, filt_index=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_index] = False.

get_photometry(t_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images.

Parameters:

t_obsarray_like

Array of times to model.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_photometry_with_gp(t_obs, mag_obs, mag_err_obs, filt_index=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_index] = False.

Parameters:

t_obsarray_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_obs.

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_obs.

mag_obs_errarray_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_obs.

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_obs.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

get_resolved_amplification(t)

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

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs, image_arr=None, amp_arr=None)

Position of the observed source position in arcsec.

Parameters:

t_obsarray_like, shape = [N_times]

Array of times to model.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

get_resolved_lens_astrometry(t_obs)

Equation of motion for just the foreground lenses, individually.

Parameters:

t_obsarray_like

Time (in MJD).

get_resolved_photometry(t_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images. Implement with no blending (since we don’t support different blendings for the different images).

Parameters:

t_obsarray_like

Array of times to model.

Returns:

mag_modelarray_like

Magnitude of each lensed image centroid at t_obs. Shape = [5, len(t_obs)]

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

filt_idxint

The filter index (def=0).

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

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

Parameters:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_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:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_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_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_index] = True.

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2)

Make sure everything is roughly centered on the origin in a 1 x 1 box.

class model.PSBL_PhotAstrom_Par_GP_Param2(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSBL_PhotAstrom, PSBL_Parallax, PSBL_PhotAstromParam2

Point source binary lens. It has 3 more parameters than PSPL (additional mass term, separation, and angle of approach). Note that this is a STATIC binary lens, i.e. there is no orbital motion.

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).

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)

qfloat

Mass ratio (M2 / M1)

sepfloat

Angular separation of the two lenses (mas)

alphafloat

Angle made between the binary axis and North; measured in degrees East of North.

b_sffnumpy array or list

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

mag_srcnumpy array or list

Source magnitude, unlensed. One in each filter.

root_tolfloat

Tolerance in comparing the polynomial roots to the physical solutions. Default = 1e-8

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_all_arrays(t_obs[, check_sols, rescale])	Obtain the image and amplitude arrays for each t_obs.
get_amp_arr(z_arr, z1, z2)	Calculations amplification array
get_amplification(t_obs[, amp_arr])	noParallax: Get the photometric amplification term at a set of times, t.
get_astrometry(t_obs[, image_arr, amp_arr, ...])	Position of the observed (unresolved) source position in arcsec.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_centroid(t_obs[, ast_filt_idx, ...])	PSPL: Get the centroid shift (in mas) for a list of observation times (in MJD).
get_centroid_shift(t[, ast_filt_idx])	Get the centroid shift (in mas) at the input times.
get_chi2_astrometry(t_obs, 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_obs, 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_complex_pos(t_obs)	Get the positions of the lenses and source as complex numbers.
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_image_pos_arr(w, z1, z2, m1, m2[, ...])	Gets image positions.
get_image_pos_arr_old(w, z1, z2[, check_sols])	Gets image positions.
get_lens_astrometry(t_obs)	Equation of motion for just the foreground lens system.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_photometry(t_obs[, filt_idx, amp_arr, ...])	Get the photometry for each of the lensed source images.
get_photometry_with_gp(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_resolved_amplification(t)	Get the photometric amplification term at a set of times, t for both the plus and minus images.
get_resolved_astrometry(t_obs[, image_arr, ...])	Position of the observed source position in arcsec.
get_resolved_lens_astrometry(t_obs)	Equation of motion for just the foreground lenses, individually.
get_resolved_photometry(t_obs[, filt_idx, ...])	Get the photometry for each of the lensed source images.
log_likely_astrometry(t_obs, x_obs, y_obs, ...)	Get the summed natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_astrometry_each(t_obs, x_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
log_likely_photometry(t_obs, mag_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_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
rescale_complex_pos(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

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

calc_piE_ecliptic()

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

get_all_arrays(t_obs, check_sols=True, rescale=True)

Obtain the image and amplitude arrays for each t_obs.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

imagesarray_like

Array/tuple of complex positions of each images at each t_obs.

amp_arrarray_like

Array/tuple of amplification of each images at each t_obs.

get_amp_arr(z_arr, z1, z2)

Calculations amplification array

Calculates the amplification A from the Jacobian J, \(A = 1/|J|\)

Parameters:

z_arrarray_like

Complex position of images. Shape = [N_times, N_solutions, 1]

– note this could be jagged.

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

Returns:

amp_arrarray_like

BLEH

get_amplification(t_obs, amp_arr=None)

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

Parameters:

t:

Array of times in MJD.DDD

get_astrometry(t_obs, image_arr=None, amp_arr=None, ast_filt_idx=0)

Position of the observed (unresolved) source position in arcsec.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

ast_filt_idxint

The filter index for the astrometry.

get_astrometry_unlensed(t_obs)

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

Returns:

xS_unlensednumpy array, dtype=float, shape = len(t_obs) x 2

The unlensed positions of the source in arcseconds.

get_centroid(t_obs, ast_filt_idx=0, image_arr=None, amp_arr=None)

PSPL: Get the centroid shift (in mas) for a list of observation times (in MJD).

Parameters:

t_obsarray or float

Returns:

Centroid offset on the plane of the sky in milli-arcseoncds.

Other Parameters:

ast_filt_idxint

Index into the photometry parameter lists for the photometry that corresponds to this astrometry data set.

image_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

amp_arrlist

List returned from PSPL get_all_arrays() used to improve efficiency.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included. 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).

get_chi2_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

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

Parameters:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_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_obs, mag_obs, mag_err_obs, filt_index=0)

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

Parameters:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_complex_pos(t_obs)

Get the positions of the lenses and source as complex numbers. This is needed for further calculations. Note that all units are still the same as before, this is just rewriting vectors \(z = (x,y)\) as \(z = x + iy\).

Parameters:

tarray_like

Array of times to model.

Returns:

wcomplex array

Source position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times, N_sources].

z1complex array

Lens primary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

z2complex array

Lens secondary component position (arcsec) as an array of complex numbers with real = east component, imaginary = north component shape = [N_times]

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_image_pos_arr(w, z1, z2, m1, m2, check_sols=True)

Gets image positions.

Solve the fifth-order polynomial and get the image positions.

See PSBL writeup for full equations.

All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

m1float

m2float

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_image_pos_arr_old(w, z1, z2, check_sols=True)

Gets image positions. | Solve the fifth-order polynomial and get the image positions. | See PSBL writeup for full equations. | All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Position of the lensed source images. Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_lens_astrometry(t_obs)

Equation of motion for just the foreground lens system.

Parameters:

t_obsarray_like

Time (in MJD).

Return

——

xLarray_like, shape = [N_times, 2 directions]

Position of the lens system (geometric center) over time.

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_obs, mag_obs, mag_err_obs, filt_index=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_index] = False.

get_photometry(t_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images.

Parameters:

t_obsarray_like

Array of times to model.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_photometry_with_gp(t_obs, mag_obs, mag_err_obs, filt_index=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_index] = False.

Parameters:

t_obsarray_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_obs.

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_obs.

mag_obs_errarray_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_obs.

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_obs.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

get_resolved_amplification(t)

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

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs, image_arr=None, amp_arr=None)

Position of the observed source position in arcsec.

Parameters:

t_obsarray_like, shape = [N_times]

Array of times to model.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

get_resolved_lens_astrometry(t_obs)

Equation of motion for just the foreground lenses, individually.

Parameters:

t_obsarray_like

Time (in MJD).

get_resolved_photometry(t_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images. Implement with no blending (since we don’t support different blendings for the different images).

Parameters:

t_obsarray_like

Array of times to model.

Returns:

mag_modelarray_like

Magnitude of each lensed image centroid at t_obs. Shape = [5, len(t_obs)]

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

filt_idxint

The filter index (def=0).

log_likely_astrometry(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_filt_idx=0)

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

Parameters:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_filt_idxint, optional

Index of the astrometric filter or data set.

Returns:

ln_Lfloat

The ln(likelihood) summed over all astrometric measurements.

log_likely_astrometry_each(t_obs, x_obs, y_obs, x_err_obs, y_err_obs, ast_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:

t_obsarray_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_obs.

y_obsarray_like

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

x_err_obsarray_like

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

y_err_obsarray_like

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

ast_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_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_index] = True.

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2)

Make sure everything is roughly centered on the origin in a 1 x 1 box.

PSBL Phot, no parallax with GP

class model.PSBL_Phot_noPar_GP_Param1(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSBL_Phot, PSBL_noParallax, PSBL_PhotParam1

Point source binary lens, photometry only.

It has 3 more parameters than PSPL_PhotParam1:

• mass ratio

• separation – in units of thetaE

• angle of approach

Note that this is a STATIC binary lens, i.e. there is no orbital motion.

Other Parameters:

raL: float

Right ascension of the lens in decimal degrees. Required if calculating with parallax

decL: float

Declination of the lens in decimal degrees. Required if calculating with parallax

obsLocation: str, optional

The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

root_tol: float

Tolerance in comparing the polynomial roots to the physical solutions.

Default = 0.0

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric 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 based on the system mass. [MJD]

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

q: float

Mass ratio (low-mass / high-mass)

sep: float

Angular separation of the two lenses in units of thetaE where thetaE is defined with the total binary mass.

phi: float

Angle made between the binary axis and the relative proper motion vector, measured in degrees.

b_sff: 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: 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.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Not supported on this object.
get_all_arrays(t_obs[, check_sols, rescale])	Obtain the image and amplitude arrays for each t_obs.
get_amp_arr(z_arr, z1, z2)	Calculations amplification array
get_amplification(t_obs[, amp_arr])	noParallax: Get the photometric amplification term at a set of times, t.
get_astrometry(t_obs[, image_arr, amp_arr, ...])	Position of the observed (unresolved) source position in Einstein radii.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_chi2_photometry(t_obs, 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_complex_pos(t_obs)	Get the positions of the lenses and source as complex numbers.
get_image_pos_arr(w, z1, z2, m1, m2[, ...])	Gets image positions.
get_image_pos_arr_old(w, z1, z2[, check_sols])	Gets image positions.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_photometry(t_obs[, filt_idx, amp_arr, ...])	Get the photometry for each of the lensed source images.
get_photometry_with_gp(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_resolved_astrometry(t_obs[, image_arr, ...])	Position of the observed source position in Einstein radii.
get_resolved_lens_astrometry(t_obs)	Equation of motion for just the foreground lenses, individually.
get_resolved_photometry(t_obs[, filt_idx, ...])	Get the photometry for each of the lensed source images.
log_likely_photometry(t_obs, mag_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_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
rescale_complex_pos(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

get_centroid_shift
get_lens_astrometry
get_resolved_amplification
log_likely_astrometry

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

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

calc_piE_ecliptic()

Not supported on this object.

get_all_arrays(t_obs, check_sols=True, rescale=True)

Obtain the image and amplitude arrays for each t_obs.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

imagesarray_like

Array/tuple of complex positions of each images at each t_obs.

amp_arrarray_like

Array/tuple of amplification of each images at each t_obs.

get_amp_arr(z_arr, z1, z2)

Calculations amplification array

Calculates the amplification A from the Jacobian J, \(A = 1/|J|\)

Parameters:

z_arrarray_like

Complex position of images. Shape = [N_times, N_solutions, 1]

– note this could be jagged.

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

Returns:

amp_arrarray_like

BLEH

get_amplification(t_obs, amp_arr=None)

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

Parameters:

t:

Array of times in MJD.DDD

get_astrometry(t_obs, image_arr=None, amp_arr=None, ast_filt_idx=0)

Position of the observed (unresolved) source position in Einstein radii.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

get_astrometry_unlensed(t_obs)

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_unlensednumpy array, dtype=float, shape = len(t_obs) x 2

The unlensed positions of the source in Einstein radii.

Notes

Note

Note, this is a photometry only model, so units are in Einstein radii.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. No parallax is included. 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).

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

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

Parameters:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_complex_pos(t_obs)

Get the positions of the lenses and source as complex numbers.

This is needed for further calculations. Note that all units are still the same as before, this is just rewriting vectors \(z = (x,y)\) as \(z = x + iy\).

Returns:

wcomplex array

Source position as an array of complex numbers with real = east component, imaginary = north component

z1complex array

Lens primary component position as an array of complex numbers with real = east component, imaginary = north component

z2complex array

Lens secondary component position as an array of complex numbers with real = east component, imaginary = north component

get_image_pos_arr(w, z1, z2, m1, m2, check_sols=True)

Gets image positions.

Solve the fifth-order polynomial and get the image positions.

See PSBL writeup for full equations.

All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

m1float

m2float

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_image_pos_arr_old(w, z1, z2, check_sols=True)

Gets image positions. | Solve the fifth-order polynomial and get the image positions. | See PSBL writeup for full equations. | All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Position of the lensed source images. Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_lens_astrometry(t)

Get the astrometry for the foreground lens at the input times. No parallax is included. 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).

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_obs, mag_obs, mag_err_obs, filt_index=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_index] = False.

get_photometry(t_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images.

Parameters:

t_obsarray_like

Array of times to model.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_photometry_with_gp(t_obs, mag_obs, mag_err_obs, filt_index=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_index] = False.

Parameters:

t_obsarray_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_obs.

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_obs.

mag_obs_errarray_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_obs.

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_obs.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

get_resolved_amplification(t)

Get the photometric amplification term at a set of times, t for both the plus and minus images. No parallax is included. The returned tuple has two entries: (A_plus, A_minus), each with len(t) arrays.

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs, image_arr=None, amp_arr=None)

Position of the observed source position in Einstein radii.

Parameters:

t_obsarray_like, shape = [N_times]

Array of times to model.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

get_resolved_lens_astrometry(t_obs)

Equation of motion for just the foreground lenses, individually.

Parameters:

t_obsarray_like

Time (in MJD).

Notes

Note

Note, this is a photometry only model, so units are in Einstein radii.

get_resolved_photometry(t_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images. Implement with no blending (since we don’t support different blendings for the different images).

Parameters:

t_obsarray_like

Array of times to model.

Returns:

mag_modelarray_like

Magnitude of each lensed image centroid at t_obs. Shape = [5, len(t_obs)]

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

filt_idxint

The filter index (def=0).

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_index] = True.

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2)

Make sure everything is roughly centered on the origin in a 1 x 1 box.

PSBL Phot, parallax with GP

class model.PSBL_Phot_Par_GP_Param1(*args, **kwargs)

Bases: ModelClassABC, PSPL_GP, PSBL_Phot, PSBL_Parallax, PSBL_PhotParam1

Point source binary lens, photometry only.

It has 3 more parameters than PSPL_PhotParam1:

• mass ratio

• separation – in units of thetaE

• angle of approach

Note that this is a STATIC binary lens, i.e. there is no orbital motion.

Other Parameters:

raL: float

Right ascension of the lens in decimal degrees. Required if calculating with parallax

decL: float

Declination of the lens in decimal degrees. Required if calculating with parallax

obsLocation: str, optional

The observers location (def=’earth’) such as ‘jwst’ or ‘spitzer’.

root_tol: float

Tolerance in comparing the polynomial roots to the physical solutions.

Default = 0.0

Attributes:

t0: float

Time (MJD.DDD) of closest projected approach between source and lens as seen in heliocentric 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 based on the system mass. [MJD]

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

q: float

Mass ratio (low-mass / high-mass)

sep: float

Angular separation of the two lenses in units of thetaE where thetaE is defined with the total binary mass.

phi: float

Angle made between the binary axis and the relative proper motion vector, measured in degrees.

b_sff: 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: 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.

Methods

animate(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
calc_piE_ecliptic()	Get piE_ecliptic, the microlensing parallax vector in the ecliptic coorindate system.
get_all_arrays(t_obs[, check_sols, rescale])	Obtain the image and amplitude arrays for each t_obs.
get_amp_arr(z_arr, z1, z2)	Calculations amplification array
get_amplification(t_obs[, amp_arr])	noParallax: Get the photometric amplification term at a set of times, t.
get_astrometry(t_obs[, image_arr, amp_arr, ...])	Position of the observed (unresolved) source position in Einstein radii.
get_astrometry_unlensed(t_obs)	Get the astrometry of the source if the lens didn't exist.
get_chi2_photometry(t_obs, 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_complex_pos(t_obs)	Get the positions of the lenses and source as complex numbers.
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_image_pos_arr(w, z1, z2, m1, m2[, ...])	Gets image positions.
get_image_pos_arr_old(w, z1, z2[, check_sols])	Gets image positions.
get_lnL_constant(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
get_log_det_covariance(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_photometry(t_obs[, filt_idx, amp_arr, ...])	Get the photometry for each of the lensed source images.
get_photometry_with_gp(t_obs, mag_obs, ...)	Returns photometry with GP noise added in.
get_resolved_astrometry(t_obs[, image_arr, ...])	Position of the observed source position in Einstein radii.
get_resolved_lens_astrometry(t_obs)	Equation of motion for just the foreground lenses, individually.
get_resolved_photometry(t_obs[, filt_idx, ...])	Get the photometry for each of the lensed source images.
log_likely_photometry(t_obs, mag_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_obs, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
rescale_complex_pos(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

get_centroid_shift
get_lens_astrometry
get_resolved_amplification
log_likely_astrometry
set_observer_location
start

animate(tE, time_steps, frame_time, name, size, zoom, astrometry)

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

calc_piE_ecliptic()

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

get_all_arrays(t_obs, check_sols=True, rescale=True)

Obtain the image and amplitude arrays for each t_obs.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

imagesarray_like

Array/tuple of complex positions of each images at each t_obs.

amp_arrarray_like

Array/tuple of amplification of each images at each t_obs.

get_amp_arr(z_arr, z1, z2)

Calculations amplification array

Calculates the amplification A from the Jacobian J, \(A = 1/|J|\)

Parameters:

z_arrarray_like

Complex position of images. Shape = [N_times, N_solutions, 1]

– note this could be jagged.

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

Returns:

amp_arrarray_like

BLEH

get_amplification(t_obs, amp_arr=None)

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

Parameters:

t:

Array of times in MJD.DDD

get_astrometry(t_obs, image_arr=None, amp_arr=None, ast_filt_idx=0)

Position of the observed (unresolved) source position in Einstein radii.

Parameters:

t_obsarray_like

Array of times to model.

Returns:

model_posarray_like

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

get_astrometry_unlensed(t_obs)

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_unlensednumpy array, dtype=float, shape = len(t_obs) x 2

The unlensed positions of the source in Einstein radii.

Notes

Note

Note, this is a photometry only model, so units are in Einstein radii.

get_centroid_shift(t, ast_filt_idx=0)

Get the centroid shift (in mas) at the input times. The centroid shift is the difference between the lensed, unresolved position and the intrinsic position of the source. Parallax is included. 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).

get_chi2_photometry(t_obs, mag_obs, mag_err_obs, filt_index=0)

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

Parameters:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_complex_pos(t_obs)

Get the positions of the lenses and source as complex numbers.

This is needed for further calculations. Note that all units are still the same as before, this is just rewriting vectors \(z = (x,y)\) as \(z = x + iy\).

Returns:

wcomplex array

Source position as an array of complex numbers with real = east component, imaginary = north component

z1complex array

Lens primary component position as an array of complex numbers with real = east component, imaginary = north component

z2complex array

Lens secondary component position as an array of complex numbers with real = east component, imaginary = north component

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_image_pos_arr(w, z1, z2, m1, m2, check_sols=True)

Gets image positions.

Solve the fifth-order polynomial and get the image positions.

See PSBL writeup for full equations.

All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

m1float

m2float

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_image_pos_arr_old(w, z1, z2, check_sols=True)

Gets image positions. | Solve the fifth-order polynomial and get the image positions. | See PSBL writeup for full equations. | All angular distances are in arcsec.

Parameters:

warray_like

Complex position(s) of the source. Shape = [N_times, 1]

z1array_like

Complex position(s) of lens 1 (primary). Shape = [N_times, 1]

z2array_like

Complex position(s) of lens 2 (secondary). Shape = [N_times, 1]

check_solsbool, optional

If True, calculated roots are checked against the lens equation, and output will only contain those within self.root_tol. If False, all calculated roots are returned.

Returns:

z_arrarray_like

Position of the lensed source images. Rank-1 array of polynomial roots, possibly complex. If check_sols = True, only roots solving the lens equation are returned.

get_lens_astrometry(t)

Get the astrometry for the foreground lens at the input times. Parallax is included. 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).

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_obs, mag_obs, mag_err_obs, filt_index=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_index] = False.

get_photometry(t_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images.

Parameters:

t_obsarray_like

Array of times to model.

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

print_warningbool, optional

Print a warning in the rare case that the magnitude exceeds a zeropoint of 30 and conversions result in NaN returned.

get_photometry_with_gp(t_obs, mag_obs, mag_err_obs, filt_index=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_index] = False.

Parameters:

t_obsarray_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_obs.

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_obs.

mag_obs_errarray_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_obs.

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_obs.

Returns:

mag_modelarray_like

Magnitude of the unresolved microlensing event at t_obs.

get_resolved_amplification(t)

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

Parameters:

tarray_like

Array of times in MJD.DDD

get_resolved_astrometry(t_obs, image_arr=None, amp_arr=None)

Position of the observed source position in Einstein radii.

Parameters:

t_obsarray_like, shape = [N_times]

Array of times to model.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]

Array of vector positions of the centroid at each t_obs.

Other Parameters:

image_arrarray_like

Array of complex image positions at each t_obs, i.e. image_arr.shape = (len(t_obs), number of images at each t_obs). Each value in this array is complex (real = north component, imaginary = east component)

amp_arrarray_like

Array of magnifications of each images. Same shape as image_arr.

get_resolved_lens_astrometry(t_obs)

Equation of motion for just the foreground lenses, individually.

Parameters:

t_obsarray_like

Time (in MJD).

Notes

Note

Note, this is a photometry only model, so units are in Einstein radii.

get_resolved_photometry(t_obs, filt_idx=0, amp_arr=None, print_warning=True)

Get the photometry for each of the lensed source images. Implement with no blending (since we don’t support different blendings for the different images).

Parameters:

t_obsarray_like

Array of times to model.

Returns:

mag_modelarray_like

Magnitude of each lensed image centroid at t_obs. Shape = [5, len(t_obs)]

Other Parameters:

amp_arrarray_like

Amplifications of each individual image at each time, i.e. amp_arr.shape = (len(t_obs), number of images at each t_obs).

This will over-ride t_obs; but is more efficient when calculating both photometry and astrometry. If None, then just use t_obs.

filt_idxint

The filter index (def=0).

log_likely_photometry(t_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

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_index] = True.

log_likely_photometry_each(t_obs, mag_obs, mag_err_obs, filt_index=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:

t_obsarray_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_obs.

mag_obs_errarray_like

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

filt_idxint, optional

Index of the photometric filter or data set.

Returns:

ln_Larray_like

List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2)

Make sure everything is roughly centered on the origin in a 1 x 1 box.