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_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_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_photometry`(t_obs[, filt_idx, amp_arr, ...])	Get the photometry for each of the lensed source images.
`get_resolved_photometry`(t_obs[, filt_idx, ...])	Get the photometry for each of the lensed source images.
`rescale_complex_pos`(w, z1, z2)	Make sure everything is roughly centered on the origin in a 1 x 1 box.

get_chi2_photometry
get_lnL_constant
log_likely_photometry
log_likely_photometry_each

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

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

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_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]
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_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_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)]

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.

Returns

mag_modelarray_like: Magnitude of the centroid at t_obs.

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

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_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_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_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_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.
`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_chi2_photometry
get_lens_astrometry
get_lnL_constant
get_resolved_amplification
log_likely_astrometry
log_likely_photometry
log_likely_photometry_each

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_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_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_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.

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.

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

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_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]
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_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.

Returns

mag_modelarray_like: Magnitude of the centroid at t_obs.

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)]

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

get_chi2_astrometry
get_chi2_photometry
get_lnL_constant
log_likely_astrometry
log_likely_astrometry_each
log_likely_photometry
log_likely_photometry_each

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_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.

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.

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_lens_astrometry(t_obs)

Equation of motion for just the foreground lens system.

Parameters

t_obsarray_like: Time (in MJD).

get_resolved_lens_astrometry(t_obs)

Equation of motion for just the foreground lenses, individually.

Parameters

t_obsarray_like: Time (in MJD).

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.

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

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_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]
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_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.

Returns

mag_modelarray_like: Magnitude of the centroid at t_obs.

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)]

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