Data Class Family

class model.PSBL

Bases: PSPL

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

Methods

`animate`(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
`get_all_arrays`(t[, filt_idx, check_sols, ...])	Obtain the lensed image and amplitude arrays for each t.
`get_amp_arr`(z_arr, z1, z2)	Calculations amplification array
`get_amplification`(t[, amp_arr, filt_idx])	Get the photometric amplification term at a set of times, t.
`get_astrometry`(t[, image_arr, amp_arr, filt_idx])	Position of the observed (unresolved) source + lens position in arcsec.
`get_astrometry_unlensed`(t[, filt_idx])	Get the unresolved astrometry of the combined source and lens if there was no gravitational lensing.
`get_caustics`(t[, N_pts, amp_inv])	Get the caustic in the source plane generated by the binary lens system.
`get_centroid_shift`(t[, amp_arr, image_arr, ...])	PSBL: Get the centroid shift (in mas) for a list of observation times (in MJD).
`get_chi2_astrometry`(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
`get_chi2_photometry`(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
`get_critical_curves`(t[, N_pts, amp_inv])	Get the critical curve in the lens plane generated by the binary lens system.
`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[, filt_idx])	Get the astrometry for the foreground lens at the input times.
`get_lens_photometry`([filt_idx])	Get the combined lens photometry.
`get_lnL_constant`(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
`get_photometry`(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
`get_resolved_amplification`(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
`get_resolved_astrometry`(t[, filt_idx])	Get the relative RA and Dec astrometry for each of the two source images, which we label plus and minus.
`get_resolved_lens_photometry`([filt_idx])	Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors).
`get_resolved_photometry`(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
`get_source_astrometry_unlensed`(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
`get_u`(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
`lens_map`(t, z)	Gets source plane position from lens plane position via the lens map.
`log_likely_astrometry`(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
`log_likely_astrometry_each`(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
`log_likely_photometry`(t, mag_obs, mag_err_obs)	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
`log_likely_photometry_each`(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
`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, filt_idx=0)

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot: e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

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

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

get_all_arrays(t, filt_idx=0, check_sols=True, rescale=True)

Obtain the lensed image and amplitude arrays for each t.

Parameters:

tarray_like: Array of times to model.
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

imagesarray_like: Array/tuple of complex positions of each lensed image at each t.
amp_arrarray_like: Array/tuple of amplification of each images at each t.

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, amp_arr=None, filt_idx=0)

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

Parameters:

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

get_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Position of the observed (unresolved) source + lens position in arcsec. This accounts for the source magnification and the contamination by any luminous lens. Note: we assume no other luminous neighbors.

Parameters:

tarray_like: Array of times to model.
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

model_posarray_like: Array of vector positions of the centroid at each t.

Other Parameters:

image_arrarray_like: Array of complex image positions at each t, i.e. image_arr.shape = (len(t), number of images at each t). 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.
filt_idxint: The filter index for the astrometry.

get_astrometry_unlensed(t, filt_idx=0)

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

Parameters:

tarray_like: Time (in MJD).
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]: The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_caustics(t, N_pts=2000, amp_inv=0)

Get the caustic in the source plane generated by the binary lens system. Casutics in units of thetaE. Plot using plot_models.plot_caustics().

Parameters:

tfloat: Time to model.
N_ptsint, optional: Number of points to sample along the critical curve.

Returns:

w_arrarray_like: Complex positions of caustic points in the source plane. Shape = [N_pts, 4]

get_centroid_shift(t, amp_arr=None, image_arr=None, filt_idx=0)

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

Parameters:

tarray_like: Time (in MJD).
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

Centroid offset on the plane of the sky in arcseoncds.

Other Parameters:

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

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

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

Parameters:

tarray_like: List of times in MJD for the observations.
x_obsarray_like: List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.
y_obsarray_like: List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.
x_err_obsarray_like: List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.
y_err_obsarray_like: List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.
filt_idxint, optional: The index of the astrometric filter or data set.

Returns:

chi2array_like: List of chi^2 values from the model and astrometric data.

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

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

Parameters:

tarray_like: List of times in MJD for the observations.
mag_obsarray_like: List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.
mag_err_obsarray_like: List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.
filt_idxint, optional: Index of the photometric filter or data set.

Returns:

chi2array_like: List of chi^2 values from the model and photometric data.

get_critical_curves(t, N_pts=2000, amp_inv=0.0)

Get the critical curve in the lens plane generated by the binary lens system. Critical curves in units of thetaE. Plot using plot_models.plot_critical_curves().

Parameters:

tfloat: Times to model.
N_ptsint, optional: Number of points to sample along the critical curve.
amp_invfloat, optional: Reciprocal amplification of points in the lens plane with parity; 0.0 corresponds to points along the critical curve (i.e. infinite amplification)

Returns:

z_arrarray_like: Complex positions of critical curve points in the lens plane which satisfy |m1/(z - z1)**2 + m2/(z - z2)**2| = sqrt(1 - amp_inv). Shape = [N_times, N_pts, 4]

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, filt_idx=0)

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

Parameters:

tarray_like: Time (in MJD).
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

xLarray_like, dtype=float, shape = [len(t), 2]: Position of the lens on the sky (arcsec).

get_lens_photometry(filt_idx=0)

Get the combined lens photometry.

Parameters:

filt_idxint, optional: Filter index.

Returns:

mag_Lfloat: Magnitude of the combined primary (L1) and secondary (L2) lens brightness.

get_lnL_constant(err_obs)

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

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

Parameters:

err_obsarray_like: List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0, amp_arr=None)

Get the photometry for each of the lensed source images.

Parameters:

tarray_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.

Other Parameters:

amp_arrarray_like

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

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

get_resolved_amplification(t, filt_idx=0)

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

Parameters:

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

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]: The amplification for the + and - lensed images.

get_resolved_astrometry(t, filt_idx=0)

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

Parameters:

tarray_like: Time (in MJD).
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

(xS_plus, xS_minus)tuple of numpy arrays

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

get_resolved_lens_photometry(filt_idx=0)

Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors). We split the light amongst the lenses based on the input lens flux ratio quantities.

Parameters:

filt_idxint, optional: Filter index.

Returns:

mag_L1, mag_L2float, float: Magnitude of the primary lens (L1) and the secondary lens (L2).

get_resolved_photometry(t, filt_idx=0, amp_arr=None)

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:

tarray_like: Array of times to model.
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

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

Other Parameters:

amp_arrarray_like

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

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

filt_idxint

The filter index (def=0).

get_source_astrometry_unlensed(t, filt_idx=0)

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

Parameters:

tarray_like: Time (in MJD).
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]: The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

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

Parameters:

tarray_like: List of times in MJD for the observations.
filt_idxint, optional: Index of the photometric filter or data set.

Returns:

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

lens_map(t, z)

Gets source plane position from lens plane position via the lens map.

Parameters:

tarray_like: Times to model. Shape = [N_times, 1]
zarray_like: Complex position(s) of objects in the lens plane. Shape = [N_times, N_positions]

Returns:

w_arrarray_like: Corresponding complex position(s) of objects in the source plane. Shape = [N_times, N_positions]

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

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

Parameters:

tarray_like: List of times in MJD for the observations.
x_obsarray_like: List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.
y_obsarray_like: List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.
x_err_obsarray_like: List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.
y_err_obsarray_like: List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

ln_Larray_like: List of ln(likelihood) for each astrometric measurement.

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

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

Parameters:

tarray_like: List of times in MJD for the observations.
x_obsarray_like: List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.
y_obsarray_like: List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.
x_err_obsarray_like: List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.
y_err_obsarray_like: List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

ln_Larray_like: List of ln(likelihood) for each astrometric measurement.

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

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

Parameters:

tarray_like: List of times in MJD for the observations.
mag_obsarray_like: List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.
mag_err_obsarray_like: List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.
filt_idxint, optional: Index of the photometric filter or data set.

Returns:

ln_Lfloat: ln(likelihood) summed over the photometric measurement

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

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

Parameters:

tarray_like: List of times in MJD for the observations.
mag_obsarray_like: List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.
mag_err_obsarray_like: List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.
filt_idxint, optional: Index of the photometric filter or data set.

Returns:

ln_Larray_like: List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2): Make sure everything is roughly centered on the origin in a 1 x 1 box.

class model.PSBL_Phot

Bases: PSBL, PSPL_Phot

Methods

`animate`(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
`get_all_arrays`(t[, filt_idx, check_sols, ...])	Obtain the lensed image and amplitude arrays for each t.
`get_amp_arr`(z_arr, z1, z2)	Calculations amplification array
`get_amplification`(t[, amp_arr, filt_idx])	Get the photometric amplification term at a set of times, t.
`get_astrometry`(t[, image_arr, amp_arr, filt_idx])	Position of the observed (unresolved) source + lens position in arcsec.
`get_astrometry_unlensed`(t[, filt_idx])	Get the unresolved astrometry of the source and lens if there was no gravitational lensing.
`get_caustics`(t[, N_pts, amp_inv])	Get the caustic in the source plane generated by the binary lens system.
`get_centroid_shift`(t[, amp_arr, image_arr, ...])	PSBL: Get the centroid shift (in mas) for a list of observation times (in MJD).
`get_chi2_astrometry`(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
`get_chi2_photometry`(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
`get_complex_pos`(t[, filt_idx])	Get the positions of the lenses and source as complex numbers.
`get_critical_curves`(t[, N_pts, amp_inv])	Get the critical curve in the lens plane generated by the binary lens system.
`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[, filt_idx])	Get the astrometry for the foreground lens at the input times.
`get_lens_photometry`([filt_idx])	Get the combined lens photometry.
`get_lnL_constant`(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
`get_photometry`(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
`get_resolved_amplification`(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
`get_resolved_astrometry`(t[, image_arr, ...])	Position of the observed source position in Einstein radii.
`get_resolved_lens_astrometry`(t[, filt_idx])	Equation of motion for just the foreground lenses, individually.
`get_resolved_lens_photometry`([filt_idx])	Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors).
`get_resolved_photometry`(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
`get_source_astrometry_unlensed`(t[, filt_idx])	Get the astrometry of the source alone if there was no gravitational lensing and no lens.
`get_u`(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
`lens_map`(t, z)	Gets source plane position from lens plane position via the lens map.
`log_likely_astrometry`(t, x, y, xerr, yerr[, ...])	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
`log_likely_astrometry_each`(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
`log_likely_photometry`(t, mag_obs, mag_err_obs)	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
`log_likely_photometry_each`(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
`rescale_complex_pos`(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

get_me_some_orbital_parameters

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

Produces animation of microlensing event.

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot: e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

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

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

get_all_arrays(t, filt_idx=0, check_sols=True, rescale=True)

Obtain the lensed image and amplitude arrays for each t.

Parameters:

tarray_like: Array of times to model.
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

imagesarray_like: Array/tuple of complex positions of each lensed image at each t.
amp_arrarray_like: Array/tuple of amplification of each images at each t.

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, amp_arr=None, filt_idx=0)

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

Parameters:

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

get_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Position of the observed (unresolved) source + lens position in arcsec. This accounts for the source magnification and the contamination by any luminous lens. Note: we assume no other luminous neighbors.

Parameters:

tarray_like: Array of times to model.
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

model_posarray_like: Array of vector positions of the centroid at each t.

Other Parameters:

image_arrarray_like: Array of complex image positions at each t, i.e. image_arr.shape = (len(t), number of images at each t). 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.
filt_idxint: The filter index for the astrometry.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the source and lens if there was no gravitational lensing. Note, this is a photometry only model, so units are in Einstein radii.

Returns:

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

Notes

Note

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

get_caustics(t, N_pts=2000, amp_inv=0)

Get the caustic in the source plane generated by the binary lens system. Casutics in units of thetaE. Plot using plot_models.plot_caustics().

Parameters:

tfloat: Time to model.
N_ptsint, optional: Number of points to sample along the critical curve.

Returns:

w_arrarray_like: Complex positions of caustic points in the source plane. Shape = [N_pts, 4]

get_centroid_shift(t, amp_arr=None, image_arr=None, filt_idx=0)

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

Parameters:

tarray_like: Time (in MJD).
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

Centroid offset on the plane of the sky in arcseoncds.

Other Parameters:

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

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

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

Parameters:

tarray_like: List of times in MJD for the observations.
x_obsarray_like: List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.
y_obsarray_like: List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.
x_err_obsarray_like: List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.
y_err_obsarray_like: List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.
filt_idxint, optional: The index of the astrometric filter or data set.

Returns:

chi2array_like: List of chi^2 values from the model and astrometric data.

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

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

Parameters:

tarray_like: List of times in MJD for the observations.
mag_obsarray_like: List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.
mag_err_obsarray_like: List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.
filt_idxint, optional: Index of the photometric filter or data set.

Returns:

chi2array_like: List of chi^2 values from the model and photometric data.

get_complex_pos(t, filt_idx=0)

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.
filt_idxint, optional: Index of the photometric filter or data set.

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
filt_idxint, optional: Filter index.

get_critical_curves(t, N_pts=2000, amp_inv=0.0)

Get the critical curve in the lens plane generated by the binary lens system. Critical curves in units of thetaE. Plot using plot_models.plot_critical_curves().

Parameters:

tfloat: Times to model.
N_ptsint, optional: Number of points to sample along the critical curve.
amp_invfloat, optional: Reciprocal amplification of points in the lens plane with parity; 0.0 corresponds to points along the critical curve (i.e. infinite amplification)

Returns:

z_arrarray_like: Complex positions of critical curve points in the lens plane which satisfy |m1/(z - z1)**2 + m2/(z - z2)**2| = sqrt(1 - amp_inv). Shape = [N_times, N_pts, 4]

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, filt_idx=0)

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

Parameters:

tarray_like: Time (in MJD).
filt_idxint, optional: Filter index.

Notes

Note

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

get_lens_photometry(filt_idx=0)

Get the combined lens photometry.

Parameters:

filt_idxint, optional: Filter index.

Returns:

mag_Lfloat: Magnitude of the combined primary (L1) and secondary (L2) lens brightness.

get_lnL_constant(err_obs)

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

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

Parameters:

err_obsarray_like: List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0, amp_arr=None)

Get the photometry for each of the lensed source images.

Parameters:

tarray_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.

Other Parameters:

amp_arrarray_like

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

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

get_resolved_amplification(t, filt_idx=0)

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

Parameters:

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

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]: The amplification for the + and - lensed images.

get_resolved_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Position of the observed source position in Einstein radii.

Parameters:

tarray_like, shape = [N_times]: Array of times to model.
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]: Array of vector positions of the centroid at each t.

Other Parameters:

image_arrarray_like: Array of complex image positions at each t, i.e. image_arr.shape = (len(t), number of images at each t). 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.
filt_idxint, optional: Index of the photometric filter or data set.

get_resolved_lens_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lenses, individually.

Parameters:

tarray_like: Time (in MJD).
filt_idxint, optional: Filter index.

Notes

Note

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

get_resolved_lens_photometry(filt_idx=0)

Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors). We split the light amongst the lenses based on the input lens flux ratio quantities.

Parameters:

filt_idxint, optional: Filter index.

Returns:

mag_L1, mag_L2float, float: Magnitude of the primary lens (L1) and the secondary lens (L2).

get_resolved_photometry(t, filt_idx=0, amp_arr=None)

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:

tarray_like: Array of times to model.
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

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

Other Parameters:

amp_arrarray_like

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

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

filt_idxint

The filter index (def=0).

get_source_astrometry_unlensed(t, filt_idx=0)

Get the astrometry of the source alone if there was no gravitational lensing and no lens. Note, this is a photometry only model, so units are in Einstein radii.

Parameters:

tarray_like: List of times in MJD for the observations.
filt_idxint, optional: Index of the photometric filter or data set.

Returns:

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

Notes

Note

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

get_u(t, filt_idx=0)

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

Parameters:

tarray_like: List of times in MJD for the observations.
filt_idxint, optional: Index of the photometric filter or data set.

Returns:

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

lens_map(t, z)

Gets source plane position from lens plane position via the lens map.

Parameters:

tarray_like: Times to model. Shape = [N_times, 1]
zarray_like: Complex position(s) of objects in the lens plane. Shape = [N_times, N_positions]

Returns:

w_arrarray_like: Corresponding complex position(s) of objects in the source plane. Shape = [N_times, N_positions]

log_likely_astrometry(t, x, y, xerr, yerr, filt_idx=0)

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

Parameters:

tarray_like: List of times in MJD for the observations.
x_obsarray_like: List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.
y_obsarray_like: List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.
x_err_obsarray_like: List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.
y_err_obsarray_like: List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

ln_Larray_like: List of ln(likelihood) for each astrometric measurement.

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

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

Parameters:

tarray_like: List of times in MJD for the observations.
x_obsarray_like: List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.
y_obsarray_like: List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.
x_err_obsarray_like: List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.
y_err_obsarray_like: List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

ln_Larray_like: List of ln(likelihood) for each astrometric measurement.

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

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

Parameters:

tarray_like: List of times in MJD for the observations.
mag_obsarray_like: List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.
mag_err_obsarray_like: List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.
filt_idxint, optional: Index of the photometric filter or data set.

Returns:

ln_Lfloat: ln(likelihood) summed over the photometric measurement

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

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

Parameters:

tarray_like: List of times in MJD for the observations.
mag_obsarray_like: List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.
mag_err_obsarray_like: List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.
filt_idxint, optional: Index of the photometric filter or data set.

Returns:

ln_Larray_like: List of ln(likelihood) for each photometric measurement.

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

Bases: PSBL, PSPL_PhotAstrom

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

Methods

`animate`(tE, time_steps, frame_time, name, ...)	Produces animation of microlensing event.
`get_all_arrays`(t[, filt_idx, check_sols, ...])	Obtain the lensed image and amplitude arrays for each t.
`get_amp_arr`(z_arr, z1, z2)	Calculations amplification array
`get_amplification`(t[, amp_arr, filt_idx])	Get the photometric amplification term at a set of times, t.
`get_astrometry`(t[, image_arr, amp_arr, filt_idx])	Position of the observed (unresolved) source + lens position in arcsec.
`get_astrometry_unlensed`(t[, filt_idx])	Get the unresolved astrometry of the source and lens if there was no gravitational lensing.
`get_caustics`(t[, N_pts, amp_inv])	Get the caustic in the source plane generated by the binary lens system.
`get_centroid_shift`(t[, amp_arr, image_arr, ...])	PSBL: Get the centroid shift (in mas) for a list of observation times (in MJD).
`get_chi2_astrometry`(t, x_obs, y_obs, ...[, ...])	Get the chi^2 value for this model given input astrometry data and uncertainties for the specified astrometric data set.
`get_chi2_photometry`(t, mag_obs, mag_err_obs)	Get chi^2 values for the model and input photometric data in the specified photometric filter or data set.
`get_complex_pos`(t[, filt_idx])	Get the positions of the lenses and source as complex numbers.
`get_critical_curves`(t[, N_pts, amp_inv])	Get the critical curve in the lens plane generated by the binary lens system.
`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[, filt_idx])	Equation of motion for just the foreground lens system.
`get_lens_origin_astrometry`(t[, filt_idx])	Equation of motion for just the foreground lens system.
`get_lens_photometry`([filt_idx])	Get the combined lens photometry.
`get_lnL_constant`(err_obs)	Get the natural log of the constant normalization terms of the likelihood.
`get_photometry`(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
`get_resolved_amplification`(t[, filt_idx])	Get the photometric amplification terms at a set of times, t for both the plus and minus images.
`get_resolved_astrometry`(t[, image_arr, ...])	Position of the observed source position in arcsec.
`get_resolved_lens_astrometry`(t[, filt_idx])	Equation of motion for just the foreground lenses, individually.
`get_resolved_lens_photometry`([filt_idx])	Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors).
`get_resolved_photometry`(t[, filt_idx, amp_arr])	Get the photometry for each of the lensed source images.
`get_source_astrometry_unlensed`(t[, filt_idx])	Get the astrometry of the source if the lens didn't exist.
`get_u`(t[, filt_idx])	Get the unlensed, relative astrometry of the source and lens in units of the Einstein radius.
`lens_map`(t, z)	Gets source plane position from lens plane position via the lens map.
`log_likely_astrometry`(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
`log_likely_astrometry_each`(t, x_obs, y_obs, ...)	Get the natural log of the likelihood for the input astrometric data in the specified filter or data sets.
`log_likely_photometry`(t, mag_obs, mag_err_obs)	Get the summed natural log of the likelihood for the input photometric data for the specified filter or data set.
`log_likely_photometry_each`(t, mag_obs, ...)	Get the natural log of the likelihood for the input photometric data in the specified filter or data sets.
`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, filt_idx=0)

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

Parameters:

tE:

number of einstein crossings times before/after the peak you want the animation to plot: e.g tE = 2 => graph will go from -2 tE to 2 tE

time_steps:

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

frame_time:

times in ms of each frame in the animation

name: string

the animation will be saved as name.html

size: list

[horizontal, vertical] cm’s

zoom:

# of einstein radii plotted in vertical direction

get_all_arrays(t, filt_idx=0, check_sols=True, rescale=True)

Obtain the lensed image and amplitude arrays for each t.

Parameters:

tarray_like: Array of times to model.
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

imagesarray_like: Array/tuple of complex positions of each lensed image at each t.
amp_arrarray_like: Array/tuple of amplification of each images at each t.

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, amp_arr=None, filt_idx=0)

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

Parameters:

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

get_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Position of the observed (unresolved) source + lens position in arcsec. This accounts for the source magnification and the contamination by any luminous lens. Note: we assume no other luminous neighbors.

Parameters:

tarray_like: Array of times to model.
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

model_posarray_like: Array of vector positions of the centroid at each t.

Other Parameters:

image_arrarray_like: Array of complex image positions at each t, i.e. image_arr.shape = (len(t), number of images at each t). 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.
filt_idxint: The filter index for the astrometry.

get_astrometry_unlensed(t, filt_idx=0)

Get the unresolved astrometry of the source and lens if there was no gravitational lensing. 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).
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]: The unlensed, flux-weighted centroid position of the source+lens in arcseconds.

get_caustics(t, N_pts=2000, amp_inv=0)

Get the caustic in the source plane generated by the binary lens system. Casutics in units of thetaE. Plot using plot_models.plot_caustics().

Parameters:

tfloat: Time to model.
N_ptsint, optional: Number of points to sample along the critical curve.

Returns:

w_arrarray_like: Complex positions of caustic points in the source plane. Shape = [N_pts, 4]

get_centroid_shift(t, amp_arr=None, image_arr=None, filt_idx=0)

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

Parameters:

tarray_like: Time (in MJD).
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

Centroid offset on the plane of the sky in arcseoncds.

Other Parameters:

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

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

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

Parameters:

tarray_like: List of times in MJD for the observations.
x_obsarray_like: List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.
y_obsarray_like: List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.
x_err_obsarray_like: List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.
y_err_obsarray_like: List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.
filt_idxint, optional: The index of the astrometric filter or data set.

Returns:

chi2array_like: List of chi^2 values from the model and astrometric data.

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

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

Parameters:

tarray_like: List of times in MJD for the observations.
mag_obsarray_like: List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.
mag_err_obsarray_like: List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.
filt_idxint, optional: Index of the photometric filter or data set.

Returns:

chi2array_like: List of chi^2 values from the model and photometric data.

get_complex_pos(t, filt_idx=0)

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.
filt_idxint, optional: Index of the photometric filter or data set.

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_critical_curves(t, N_pts=2000, amp_inv=0.0)

Get the critical curve in the lens plane generated by the binary lens system. Critical curves in units of thetaE. Plot using plot_models.plot_critical_curves().

Parameters:

tfloat: Times to model.
N_ptsint, optional: Number of points to sample along the critical curve.
amp_invfloat, optional: Reciprocal amplification of points in the lens plane with parity; 0.0 corresponds to points along the critical curve (i.e. infinite amplification)

Returns:

z_arrarray_like: Complex positions of critical curve points in the lens plane which satisfy |m1/(z - z1)**2 + m2/(z - z2)**2| = sqrt(1 - amp_inv). Shape = [N_times, N_pts, 4]

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, filt_idx=0)

Equation of motion for just the foreground lens system.

Parameters:

tarray_like: Time (in MJD).
filt_idxint, optional: Index of the photometric filter or data set.

Returns:

xLarray_like, shape = [N_times, 2 directions]: Position of the lens system (geometric center) over time.

get_lens_origin_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lens system. This returns the lens-system origin motion (not the observed flux-weighted centroid).

Parameters:

tarray_like: Time (in MJD).
filt_idxint, optional: Index of the photometric filter or data set.

Returns:

xLarray_like, shape = [N_times, 2 directions]: Position of the lens system (geometric center) over time.

get_lens_photometry(filt_idx=0)

Get the combined lens photometry.

Parameters:

filt_idxint, optional: Filter index.

Returns:

mag_Lfloat: Magnitude of the combined primary (L1) and secondary (L2) lens brightness.

get_lnL_constant(err_obs)

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

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

Parameters:

err_obsarray_like: List of the uncertainties.

Returns:

List of ln(likelihood constants).

get_photometry(t, filt_idx=0, amp_arr=None)

Get the photometry for each of the lensed source images.

Parameters:

tarray_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.

Other Parameters:

amp_arrarray_like

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

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

get_resolved_amplification(t, filt_idx=0)

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

Parameters:

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

Returns:

Anumpy array, dtype=float, shape = [len(t), [+/-]: The amplification for the + and - lensed images.

get_resolved_astrometry(t, image_arr=None, amp_arr=None, filt_idx=0)

Position of the observed source position in arcsec.

Parameters:

tarray_like, shape = [N_times]: Array of times to model.
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

model_posarray_like. shape = [N_times, N_images, 2]: Array of vector positions of the centroid at each t.

Other Parameters:

image_arrarray_like: Array of complex image positions at each t, i.e. image_arr.shape = (len(t), number of images at each t). 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.
filt_idxint, optional: Index of the photometric filter or data set.

get_resolved_lens_astrometry(t, filt_idx=0)

Equation of motion for just the foreground lenses, individually.

Parameters:

tarray_like: Time (in MJD).
filt_idxint, optional: Index of the photometric filter or data set.

Returns:

xL1array_like, shape = [N_times, 2 directions]: Position of the lens primary (arcsec)
xL2array_like, shape = [N_times, 2 directions]: Position of the lens secondary (arcsec)

get_resolved_lens_photometry(filt_idx=0)

Get the resolved lens photometry, assuming that all the non-source light comes from the lens (and not neighbors). We split the light amongst the lenses based on the input lens flux ratio quantities.

Parameters:

filt_idxint, optional: Filter index.

Returns:

mag_L1, mag_L2float, float: Magnitude of the primary lens (L1) and the secondary lens (L2).

get_resolved_photometry(t, filt_idx=0, amp_arr=None)

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:

tarray_like: Array of times to model.
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

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

Other Parameters:

amp_arrarray_like

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

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

filt_idxint

The filter index (def=0).

get_source_astrometry_unlensed(t, filt_idx=0)

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

Parameters:

tarray_like: Time (in MJD).
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

xS_unlensednumpy array, dtype=float, shape = [len(t), 2]: The unlensed positions of the source in arcseconds.

get_u(t, filt_idx=0)

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

Parameters:

tarray_like: List of times in MJD for the observations.
filt_idxint, optional: Index of the photometric filter or data set.

Returns:

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

lens_map(t, z)

Gets source plane position from lens plane position via the lens map.

Parameters:

tarray_like: Times to model. Shape = [N_times, 1]
zarray_like: Complex position(s) of objects in the lens plane. Shape = [N_times, N_positions]

Returns:

w_arrarray_like: Corresponding complex position(s) of objects in the source plane. Shape = [N_times, N_positions]

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

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

Parameters:

tarray_like: List of times in MJD for the observations.
x_obsarray_like: List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.
y_obsarray_like: List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.
x_err_obsarray_like: List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.
y_err_obsarray_like: List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

ln_Larray_like: List of ln(likelihood) for each astrometric measurement.

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

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

Parameters:

tarray_like: List of times in MJD for the observations.
x_obsarray_like: List of relative R.A. astrometric positions on the sky in arcsec. Length must match t.
y_obsarray_like: List of relative Dec. astrometric positions on the sky in arcsec. Length must match t.
x_err_obsarray_like: List of relative R.A. astrometric positional errors on the sky in arcsec. Length must match t.
y_err_obsarray_like: List of relative Dec. astrometric positional errors on the sky in arcsec. Length must match t.
filt_idxint, optional: Index of the astrometric filter or data set.

Returns:

ln_Larray_like: List of ln(likelihood) for each astrometric measurement.

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

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

Parameters:

tarray_like: List of times in MJD for the observations.
mag_obsarray_like: List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.
mag_err_obsarray_like: List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.
filt_idxint, optional: Index of the photometric filter or data set.

Returns:

ln_Lfloat: ln(likelihood) summed over the photometric measurement

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

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

Parameters:

tarray_like: List of times in MJD for the observations.
mag_obsarray_like: List of observed photometric measurements of the microlensing event in magnitudes. Length must be the same as t.
mag_err_obsarray_like: List of observed photometric uncertainties of the microlensing event in magnitudes. Length must be the same as t.
filt_idxint, optional: Index of the photometric filter or data set.

Returns:

ln_Larray_like: List of ln(likelihood) for each photometric measurement.

rescale_complex_pos(w, z1, z2): Make sure everything is roughly centered on the origin in a 1 x 1 box.