lenstronomy.Util package

Submodules

lenstronomy.Util.analysis_util module

lenstronomy.Util.analysis_util.half_light_radius(lens_light, x_grid, y_grid, center_x=0, center_y=0)[source]
Parameters:
  • lens_light – array of surface brightness
  • x_grid – x-axis coordinates
  • y_gird – y-axis coordinates
  • center_x – center of light
  • center_y – center of light
Returns:

lenstronomy.Util.analysis_util.radial_profile(light_grid, x_grid, y_grid, center_x=0, center_y=0, n=None)[source]
Parameters:
  • light_grid – array of surface brightness
  • x_grid – x-axis coordinates
  • y_gird – y-axis coordinates
  • center_x – center of light
  • center_y – center of light
  • n – number of discrete steps
Returns:

lenstronomy.Util.analysis_util.azimuthalAverage(image, center=None)[source]

Calculate the azimuthally averaged radial profile.

image - The 2D image center - The [x,y] pixel coordinates used as the center. The default is None, which then uses the center of the image (including fractional pixels). :return: I(r) (averaged), r of bin edges

lenstronomy.Util.analysis_util.moments(I_xy_input, x, y)[source]

compute quadrupole moments from a light distribution

Parameters:
  • I_xy – light distribution
  • x – x-coordinates of I_xy
  • y – y-coordinates of I_xy
Returns:

Q_xx, Q_xy, Q_yy

lenstronomy.Util.analysis_util.ellipticities(I_xy, x, y)[source]

compute ellipticities of a light distribution

Parameters:
  • I_xy
  • x
  • y
Returns:

lenstronomy.Util.analysis_util.bic_model(logL, num_data, num_param)[source]

Bayesian information criteria

Parameters:
  • logL – log likelihood value
  • num_data – numbers of data
  • num_param – numbers of model parameters
Returns:

BIC value

lenstronomy.Util.analysis_util.profile_center(kwargs_list, center_x=None, center_y=None)[source]

utility routine that results in the centroid estimate for the profile estimates

Parameters:
  • kwargs_list – light parameter keyword argument list (can be light or mass)
  • center_x – None or center
  • center_y – None or center
Returns:

center_x, center_y

lenstronomy.Util.class_creator module

lenstronomy.Util.class_creator.create_class_instances(lens_model_list=[], z_lens=None, z_source=None, lens_redshift_list=None, kwargs_interp=None, multi_plane=False, observed_convention_index=None, source_light_model_list=[], lens_light_model_list=[], point_source_model_list=[], fixed_magnification_list=None, flux_from_point_source_list=None, additional_images_list=None, kwargs_lens_eqn_solver=None, source_deflection_scaling_list=None, source_redshift_list=None, cosmo=None, index_lens_model_list=None, index_source_light_model_list=None, index_lens_light_model_list=None, index_point_source_model_list=None, optical_depth_model_list=[], index_optical_depth_model_list=None, band_index=0, tau0_index_list=None, all_models=False, point_source_magnification_limit=None, surface_brightness_smoothing=0.001, sersic_major_axis=None)[source]
Parameters:
  • lens_model_list – list of strings indicating the type of lens models
  • z_lens – redshift of the deflector (for single lens plane mode, but only relevant when computing physical quantities)
  • z_source – redshift of source (for single source plane mode, or for multiple source planes the redshift of the point source). In regard to this redshift the reduced deflection angles are defined in the lens model.
  • lens_redshift_list
  • multi_plane
  • kwargs_interp – interpolation keyword arguments specifying the numerics. See description in the Interpolate() class. Only applicable for ‘INTERPOL’ and ‘INTERPOL_SCALED’ models.
  • observed_convention_index
  • source_light_model_list
  • lens_light_model_list
  • point_source_model_list
  • fixed_magnification_list
  • flux_from_point_source_list – list of bools (optional), if set, will only return image positions (for imaging modeling) for the subset of the point source lists that =True. This option enables to model
  • additional_images_list
  • kwargs_lens_eqn_solver – keyword arguments specifying the numerical settings for the lens equation solver see LensEquationSolver() class for details
  • source_deflection_scaling_list – List of floats for each source ligth model (optional, and only applicable for single-plane lensing. The factors re-scale the reduced deflection angles described from the lens model. =1 means identical source position as without this option. This option enables multiple source planes. The geometric difference between the different source planes needs to be pre-computed and is cosmology dependent.
  • source_redshift_list
  • cosmo – astropy.cosmology instance
  • index_lens_model_list
  • index_source_light_model_list
  • index_lens_light_model_list
  • index_point_source_model_list
  • optical_depth_model_list – list of strings indicating the optical depth model to compute (differential) extinctions from the source
  • index_optical_depth_model_list
  • band_index – int, index of band to consider. Has an effect if only partial models are considered for a specific band
  • tau0_index_list – list of integers of the specific extinction scaling parameter tau0 for each band
  • all_models – bool, if True, will make class instances of all models ignoring potential keywords that are excluding specific models as indicated.
  • point_source_magnification_limit – float >0 or None, if set and additional images are computed, then it will cut the point sources computed to the limiting (absolute) magnification
  • surface_brightness_smoothing – float, smoothing scale of light profile (minimal distance to the center of a profile) this can help to avoid inaccuracies in the very center of a cuspy light profile
  • sersic_major_axis – boolean or None, if True, uses the semi-major axis as the definition of the Sersic half-light radius, if False, uses the product average of semi-major and semi-minor axis. If None, uses the convention in the lenstronomy yaml setting (which by default is =False)
Returns:

lenstronomy.Util.class_creator.create_image_model(kwargs_data, kwargs_psf, kwargs_numerics, kwargs_model, likelihood_mask=None)[source]
Parameters:
  • kwargs_data – ImageData keyword arguments
  • kwargs_psf – PSF keyword arguments
  • kwargs_model – model keyword arguments
Returns:

ImageLinearFit() instance

lenstronomy.Util.class_creator.create_im_sim(multi_band_list, multi_band_type, kwargs_model, bands_compute=None, likelihood_mask_list=None, band_index=0, kwargs_pixelbased=None)[source]
Parameters:multi_band_type – string, option when having multiple imaging data sets modelled simultaneously. Options are:
  • ‘multi-linear’: linear amplitudes are inferred on single data set
  • ‘linear-joint’: linear amplitudes ae jointly inferred
  • ‘single-band’: single band
Parameters:kwargs_pixelbased – keyword arguments with various settings related to the pixel-based solver (see SLITronomy documentation)
Returns:MultiBand class instance

lenstronomy.Util.constants module

lenstronomy.Util.constants.delay_arcsec2days(delay_arcsec, D_dt)[source]

given a delay in arcsec^2 and a Delay distance, the delay is computed in days

Parameters:
  • delay_arcsec – gravitational delay in units of arcsec^2 (e.g. Fermat potential)
  • D_dt – Time delay distance (in units of Mpc)
Returns:

time-delay in units of days

lenstronomy.Util.correlation module

lenstronomy.Util.correlation.correlation_2D(image)[source]

#TODO document normalization output in units

Parameters:image – 2d image
Returns:2d fourier transform
lenstronomy.Util.correlation.power_spectrum_2d(image)[source]
Parameters:image – 2d numpy array
Returns:2d power spectrum in frequency units of the pixels
lenstronomy.Util.correlation.power_spectrum_1d(image)[source]
Parameters:image – 2d numpy array
Returns:1d radially averaged power spectrum of image in frequency units of pixels

lenstronomy.Util.data_util module

lenstronomy.Util.data_util.bkg_noise(readout_noise, exposure_time, sky_brightness, pixel_scale, num_exposures=1)[source]

computes the expected Gaussian background noise of a pixel in units of counts/second

Parameters:
  • readout_noise – noise added per readout
  • exposure_time – exposure time per exposure (in seconds)
  • sky_brightness – counts per second per unit arcseconds square
  • pixel_scale – size of pixel in units arcseonds
  • num_exposures – number of exposures (with same exposure time) to be co-added
Returns:

estimated Gaussian noise sqrt(variance)

lenstronomy.Util.data_util.flux_noise(cps_pixel, exposure_time)[source]

computes the variance of the shot noise Gaussian approximation of Poisson noise term

Parameters:
  • cps_pixel – counts per second of the intensity per pixel unit
  • exposure_time – total exposure time (in units seconds or equivalent unit as cps_pixel)
Returns:

sqrt(variance) of pixel value

lenstronomy.Util.data_util.magnitude2cps(magnitude, magnitude_zero_point)[source]

converts an apparent magnitude to counts per second

The zero point of an instrument, by definition, is the magnitude of an object that produces one count (or data number, DN) per second. The magnitude of an arbitrary object producing DN counts in an observation of length EXPTIME is therefore: m = -2.5 x log10(DN / EXPTIME) + ZEROPOINT

Parameters:
  • magnitude – astronomical magnitude
  • magnitude_zero_point – magnitude zero point (astronomical magnitude with 1 count per second)
Returns:

counts per second of astronomical object

lenstronomy.Util.data_util.cps2magnitude(cps, magnitude_zero_point)[source]
Parameters:
  • cps – float, count-per-second
  • magnitude_zero_point – magnitude zero point
Returns:

magnitude for given counts

lenstronomy.Util.data_util.absolute2apparent_magnitude(absolute_magnitude, d_parsec)[source]

converts absolute to apparent magnitudes

Parameters:
  • absolute_magnitude – absolute magnitude of object
  • d_parsec – distance to object in units parsec
Returns:

apparent magnitude

lenstronomy.Util.data_util.adu2electrons(adu, ccd_gain)[source]

converts analog-to-digital units into electron counts

Parameters:adu – counts in analog-to-digital unit
Returns:counts in electrons
lenstronomy.Util.data_util.electrons2adu(electrons, ccd_gain)[source]

converts electron counts into analog-to-digital unit

Parameters:electrons
Returns:adu value corresponding to electron count

lenstronomy.Util.derivative_util module

routines to compute derivatives of spherical functions

lenstronomy.Util.derivative_util.d_r_dx(x, y)[source]

derivative of r with respect to x :param x: :param y: :return:

lenstronomy.Util.derivative_util.d_r_dy(x, y)[source]

differential dr/dy

Parameters:
  • x
  • y
Returns:

lenstronomy.Util.derivative_util.d_r_dxx(x, y)[source]

second derivative dr/dxdx :param x: :param y: :return:

lenstronomy.Util.derivative_util.d_r_dyy(x, y)[source]

second derivative dr/dxdx :param x: :param y: :return:

lenstronomy.Util.derivative_util.d_r_dxy(x, y)[source]

second derivative dr/dxdx :param x: :param y: :return:

lenstronomy.Util.derivative_util.d_phi_dx(x, y)[source]

angular derivative in respect to x when phi = arctan2(y, x)

Parameters:
  • x
  • y
Returns:

lenstronomy.Util.derivative_util.d_phi_dy(x, y)[source]

angular derivative in respect to y when phi = arctan2(y, x)

Parameters:
  • x
  • y
Returns:

lenstronomy.Util.derivative_util.d_phi_dxx(x, y)[source]

second derivative of the orientation angle

Parameters:
  • x
  • y
Returns:

lenstronomy.Util.derivative_util.d_phi_dyy(x, y)[source]

second derivative of the orientation angle in dydy

Parameters:
  • x
  • y
Returns:

lenstronomy.Util.derivative_util.d_phi_dxy(x, y)[source]

second derivative of the orientation angle in dxdy

Parameters:
  • x
  • y
Returns:

lenstronomy.Util.derivative_util.d_x_diffr_dx(x, y)[source]

derivative of d(x/r)/dx equivalent to second order derivatives dr_dxx

Parameters:
  • x
  • y
Returns:

lenstronomy.Util.derivative_util.d_y_diffr_dy(x, y)[source]

derivative of d(y/r)/dy equivalent to second order derivatives dr_dyy

Parameters:
  • x
  • y
Returns:

lenstronomy.Util.derivative_util.d_y_diffr_dx(x, y)[source]

derivative of d(y/r)/dx equivalent to second order derivatives dr_dxy

Parameters:
  • x
  • y
Returns:

lenstronomy.Util.derivative_util.d_x_diffr_dy(x, y)[source]

derivative of d(x/r)/dy equivalent to second order derivatives dr_dyx

Parameters:
  • x
  • y
Returns:

lenstronomy.Util.image_util module

lenstronomy.Util.image_util.add_layer2image(grid2d, x_pos, y_pos, kernel, order=1)[source]

adds a kernel on the grid2d image at position x_pos, y_pos with an interpolated subgrid pixel shift of order=order :param grid2d: 2d pixel grid (i.e. image) :param x_pos: x-position center (pixel coordinate) of the layer to be added :param y_pos: y-position center (pixel coordinate) of the layer to be added :param kernel: the layer to be added to the image :param order: interpolation order for sub-pixel shift of the kernel to be added :return: image with added layer, cut to original size

lenstronomy.Util.image_util.add_layer2image_int(grid2d, x_pos, y_pos, kernel)[source]

adds a kernel on the grid2d image at position x_pos, y_pos at integer positions of pixel :param grid2d: 2d pixel grid (i.e. image) :param x_pos: x-position center (pixel coordinate) of the layer to be added :param y_pos: y-position center (pixel coordinate) of the layer to be added :param kernel: the layer to be added to the image :return: image with added layer

lenstronomy.Util.image_util.add_background(image, sigma_bkd)[source]

adds background noise to image :param image: pixel values of image :param sigma_bkd: background noise (sigma) :return: a realisation of Gaussian noise of the same size as image

lenstronomy.Util.image_util.add_poisson(image, exp_time)[source]

adds a poison (or Gaussian) distributed noise with mean given by surface brightness :param image: pixel values (photon counts per unit exposure time) :param exp_time: exposure time :return: Poisson noise realization of input image

lenstronomy.Util.image_util.rotateImage(img, angle)[source]

querries scipy.ndimage.rotate routine :param img: image to be rotated :param angle: angle to be rotated (radian) :return: rotated image

lenstronomy.Util.image_util.re_size_array(x_in, y_in, input_values, x_out, y_out)[source]

resizes 2d array (i.e. image) to new coordinates. So far only works with square output aligned with coordinate axis. :param x_in: :param y_in: :param input_values: :param x_out: :param y_out: :return:

lenstronomy.Util.image_util.symmetry_average(image, symmetry)[source]

symmetry averaged image :param image: :param symmetry: :return:

lenstronomy.Util.image_util.findOverlap(x_mins, y_mins, min_distance)[source]

finds overlapping solutions, deletes multiples and deletes non-solutions and if it is not a solution, deleted as well

lenstronomy.Util.image_util.coordInImage(x_coord, y_coord, numPix, deltapix)[source]

checks whether image positions are within the pixel image in units of arcsec if not: remove it

Parameters:imcoord ((n,4) numpy array) – image coordinate (in units of angels) [[x,y,delta,magnification][…]]
Returns:image positions within the pixel image
lenstronomy.Util.image_util.re_size(image, factor=1)[source]

re-sizes image with nx x ny to nx/factor x ny/factor :param image: 2d image with shape (nx,ny) :param factor: integer >=1 :return:

lenstronomy.Util.image_util.rebin_image(bin_size, image, wht_map, sigma_bkg, ra_coords, dec_coords, idex_mask)[source]

rebins pixels, updates cutout image, wht_map, sigma_bkg, coordinates, PSF :param bin_size: number of pixels (per axis) to merge :return:

lenstronomy.Util.image_util.rebin_coord_transform(factor, x_at_radec_0, y_at_radec_0, Mpix2coord, Mcoord2pix)[source]

adopt coordinate system and transformation between angular and pixel coordinates of a re-binned image :param bin_size: :param ra_0: :param dec_0: :param x_0: :param y_0: :param Matrix: :param Matrix_inv: :return:

lenstronomy.Util.image_util.stack_images(image_list, wht_list, sigma_list)[source]

stacks images and saves new image as a fits file :param image_name_list: list of image_names to be stacked :return:

lenstronomy.Util.image_util.cut_edges(image, numPix)[source]

cuts out the edges of a 2d image and returns re-sized image to numPix center is well defined for odd pixel sizes. :param image: 2d numpy array :param numPix: square size of cut out image :return: cutout image with size numPix

lenstronomy.Util.image_util.radial_profile(data, center=[0, 0])[source]

computes radial profile

Parameters:
  • data – 2d numpy array
  • center – center [x, y] from where to compute the radial profile
Returns:

radial profile (in units pixel)

lenstronomy.Util.image_util.gradient_map(image)[source]

computes gradients of images with the sobel transform

Parameters:image – 2d numpy array
Returns:array of same size as input, with gradients between neighboring pixels

lenstronomy.Util.kernel_util module

routines that manipulate convolution kernels

lenstronomy.Util.kernel_util.de_shift_kernel(kernel, shift_x, shift_y, iterations=20, fractional_step_size=1)[source]

de-shifts a shifted kernel to the center of a pixel. This is performed iteratively.

The input kernel is the solution of a linear interpolated shift of a sharper kernel centered in the middle of the
pixel. To find the de-shifted kernel, we perform an iterative correction of proposed de-shifted kernels and compare its shifted version with the input kernel.
Parameters:
  • kernel – (shifted) kernel, e.g. a star in an image that is not centered in the pixel grid
  • shift_x – x-offset relative to the center of the pixel (sub-pixel shift)
  • shift_y – y-offset relative to the center of the pixel (sub-pixel shift)
  • iterations – number of repeated iterations of shifting a new de-shifted kernel and apply corrections
  • fractional_step_size – float (0, 1] correction factor relative to previous proposal (can be used for stability
Returns:

de-shifted kernel such that the interpolated shift boy (shift_x, shift_y) results in the input kernel

lenstronomy.Util.kernel_util.center_kernel(kernel, iterations=20)[source]

given a kernel that might not be perfectly centered, this routine computes its light weighted center and then moves the center in an iterative process such that it is centered

Parameters:
  • kernel – 2d array (odd numbers)
  • iterations – int, number of iterations
Returns:

centered kernel

lenstronomy.Util.kernel_util.kernel_norm(kernel)[source]
Parameters:kernel
Returns:normalisation of the psf kernel
lenstronomy.Util.kernel_util.subgrid_kernel(kernel, subgrid_res, odd=False, num_iter=100)[source]

creates a higher resolution kernel with subgrid resolution as an interpolation of the original kernel in an iterative approach

Parameters:
  • kernel – initial kernel
  • subgrid_res – subgrid resolution required
Returns:

kernel with higher resolution (larger)

lenstronomy.Util.kernel_util.averaging_even_kernel(kernel_high_res, subgrid_res)[source]

makes a lower resolution kernel based on the kernel_high_res (odd numbers) and the subgrid_res (even number), both meant to be centered.

Parameters:
  • kernel_high_res – high resolution kernel with even subsampling resolution, centered
  • subgrid_res – subsampling resolution (even number)
Returns:

averaged undersampling kernel

lenstronomy.Util.kernel_util.kernel_pixelsize_change(kernel, deltaPix_in, deltaPix_out)[source]

change the pixel size of a given kernel :param kernel: :param deltaPix_in: :param deltaPix_out: :return:

lenstronomy.Util.kernel_util.cut_psf(psf_data, psf_size)[source]

cut the psf properly :param psf_data: image of PSF :param psf_size: size of psf :return: re-sized and re-normalized PSF

lenstronomy.Util.kernel_util.pixel_kernel(point_source_kernel, subgrid_res=7)[source]

converts a pixelised kernel of a point source to a kernel representing a uniform extended pixel

Parameters:
  • point_source_kernel
  • subgrid_res
Returns:

convolution kernel for an extended pixel

lenstronomy.Util.kernel_util.kernel_average_pixel(kernel_super, supersampling_factor)[source]

computes the effective convolution kernel assuming a uniform surface brightness on the scale of a pixel

Parameters:
  • kernel_super – supersampled PSF of a point source (odd number per axis
  • supersampling_factor – supersampling factor (int)
Returns:

lenstronomy.Util.kernel_util.kernel_gaussian(kernel_numPix, deltaPix, fwhm)[source]
lenstronomy.Util.kernel_util.split_kernel(kernel_super, supersampling_kernel_size, supersampling_factor, normalized=True)[source]

pixel kernel and subsampling kernel such that the convolution of both applied on an image can be performed, i.e. smaller subsampling PSF and hole in larger PSF

Parameters:
  • kernel – PSF kernel of the size of the pixel
  • kernel_super – super-sampled kernel
  • supersampling_kernel_size – size of super-sampled PSF in units of degraded pixels
  • normalized – boolean, if True returns a split kernel that is area normalized=1 representing a convolution kernel
Returns:

degraded kernel with hole and super-sampled kernel

lenstronomy.Util.kernel_util.degrade_kernel(kernel_super, degrading_factor)[source]
Parameters:
  • kernel_super – higher resolution kernel (odd number per axis)
  • degrading_factor – degrading factor (effectively the super-sampling resolution of the kernel given
Returns:

degraded kernel with odd axis number with the sum of the flux/values in the kernel being preserved

lenstronomy.Util.kernel_util.cutout_source(x_pos, y_pos, image, kernelsize, shift=True)[source]

cuts out point source (e.g. PSF estimate) out of image and shift it to the center of a pixel :param x_pos: :param y_pos: :param image: :param kernelsize: :return:

lenstronomy.Util.kernel_util.fwhm_kernel(kernel)[source]
Parameters:kernel
Returns:
lenstronomy.Util.kernel_util.estimate_amp(data, x_pos, y_pos, psf_kernel)[source]

estimates the amplitude of a point source located at x_pos, y_pos :param data: :param x_pos: :param y_pos: :param deltaPix: :return:

lenstronomy.Util.kernel_util.mge_kernel(kernel, order=5)[source]

azimutal Multi-Gaussian expansion of a pixelized kernel

Parameters:kernel – 2d numpy array
Returns:

lenstronomy.Util.mask_util module

lenstronomy.Util.mask_util.mask_center_2d(center_x, center_y, r, x_grid, y_grid)[source]
Parameters:
  • center_x – x-coordinate of center position of circular mask
  • center_y – y-coordinate of center position of circular mask
  • r – radius of mask in pixel values
  • x_grid – x-coordinate grid
  • y_grid – y-coordinate grid
Returns:

mask array of shape x_grid with =0 inside the radius and =1 outside

lenstronomy.Util.mask_util.mask_azimuthal(x, y, center_x, center_y, r)[source]
Parameters:
  • x – x-coordinates (1d or 2d array numpy array)
  • y – y-coordinates (1d or 2d array numpy array)
  • center_x – center of azimuthal mask in x
  • center_y – center of azimuthal mask in y
  • r – radius of azimuthal mask
Returns:

array with zeros outside r and ones inside azimuthal radius r

lenstronomy.Util.mask_util.mask_ellipse(x, y, center_x, center_y, a, b, angle)[source]
Parameters:
  • x – x-coordinates of pixels
  • y – y-coordinates of pixels
  • center_x – center of mask
  • center_y – center of mask
  • a – major axis
  • b – minor axis
  • angle – angle of major axis
Returns:

mask (list of zeros and ones)

lenstronomy.Util.mask_util.mask_half_moon(x, y, center_x, center_y, r_in, r_out, phi0=0, delta_phi=6.283185307179586)[source]
Parameters:
  • x
  • y
  • center_x
  • center_y
  • r_in
  • r_out
  • phi
  • delta_phi
Returns:

lenstronomy.Util.multi_gauss_expansion module

lenstronomy.Util.multi_gauss_expansion.gaussian(R, sigma, amp)[source]
Parameters:
  • R – radius
  • sigma – gaussian sigma
  • amp – normalization
Returns:

Gaussian function

lenstronomy.Util.multi_gauss_expansion.mge_1d(r_array, flux_r, N=20, linspace=False)[source]
Parameters:
  • r_array – list or radii (numpy array)
  • flux_r – list of flux values (numpy array)
  • N – number of Gaussians
Returns:

amplitudes and Gaussian sigmas for the best 1d flux profile

lenstronomy.Util.multi_gauss_expansion.de_projection_3d(amplitudes, sigmas)[source]

de-projects a gaussian (or list of multiple Gaussians from a 2d projected to a 3d profile) :param amplitudes: :param sigmas: :return:

lenstronomy.Util.numba_util module

lenstronomy.Util.numba_util.jit(nopython=True, cache=True, parallel=False, fastmath=False, error_model='numpy')[source]
lenstronomy.Util.numba_util.generated_jit(nopython=True, cache=True, parallel=False, fastmath=False, error_model='numpy')[source]

Wrapper around numba.generated_jit. Allows you to redirect a function to another based on its type - see the Numba docs for more info

lenstronomy.Util.param_util module

lenstronomy.Util.param_util.cart2polar(x, y, center_x=0, center_y=0)[source]

transforms cartesian coords [x,y] into polar coords [r,phi] in the frame of the lens center

Parameters:
  • x (array of size (n)) – set of x-coordinates
  • y (array of size (n)) – set of x-coordinates
  • center_x (float) – rotation point
  • center_y (float) – rotation point
Returns:

array of same size with coords [r,phi]

lenstronomy.Util.param_util.polar2cart(r, phi, center)[source]

transforms polar coords [r,phi] into cartesian coords [x,y] in the frame of the lense center

Parameters:
  • coord (array of size (n,2)) – set of coordinates
  • center (array of size (2)) – rotation point
Returns:

array of same size with coords [x,y]

Raises:

AttributeError, KeyError

lenstronomy.Util.param_util.shear_polar2cartesian(phi, gamma)[source]
Parameters:
  • phi – shear angle (radian)
  • gamma – shear strength
Returns:

shear components gamma1, gamma2

lenstronomy.Util.param_util.shear_cartesian2polar(gamma1, gamma2)[source]
Parameters:
  • gamma1 – cartesian shear component
  • gamma2 – cartesian shear component
Returns:

shear angle, shear strength

lenstronomy.Util.param_util.phi_q2_ellipticity[source]

transforms orientation angle and axis ratio into complex ellipticity moduli e1, e2

Parameters:
  • phi – angle of orientation (in radian)
  • q – axis ratio minor axis / major axis
Returns:

eccentricities e1 and e2 in complex ellipticity moduli

lenstronomy.Util.param_util.ellipticity2phi_q[source]

transforms complex ellipticity moduli in orientation angle and axis ratio

Parameters:
  • e1 – eccentricity in x-direction
  • e2 – eccentricity in xy-direction
Returns:

angle in radian, axis ratio (minor/major)

lenstronomy.Util.param_util.transform_e1e2_product_average(x, y, e1, e2, center_x, center_y)[source]

maps the coordinates x, y with eccentricities e1 e2 into a new elliptical coordinate system such that R = sqrt(R_major * R_minor)

Parameters:
  • x – x-coordinate
  • y – y-coordinate
  • e1 – eccentricity
  • e2 – eccentricity
  • center_x – center of distortion
  • center_y – center of distortion
Returns:

distorted coordinates x’, y’

lenstronomy.Util.param_util.transform_e1e2_square_average(x, y, e1, e2, center_x, center_y)[source]

maps the coordinates x, y with eccentricities e1 e2 into a new elliptical coordinate system such that R = sqrt(R_major**2 + R_minor**2)

Parameters:
  • x – x-coordinate
  • y – y-coordinate
  • e1 – eccentricity
  • e2 – eccentricity
  • center_x – center of distortion
  • center_y – center of distortion
Returns:

distorted coordinates x’, y’

lenstronomy.Util.prob_density module

class lenstronomy.Util.prob_density.SkewGaussian[source]

Bases: object

class for the Skew Gaussian distribution

map_mu_sigma_skw(mu, sigma, skw)[source]

map to parameters e, w, a :param mu: mean :param sigma: standard deviation :param skw: skewness :return: e, w, a

pdf(x, e=0.0, w=1.0, a=0.0)[source]

probability density function see: https://en.wikipedia.org/wiki/Skew_normal_distribution :param x: input value :param e: :param w: :param a: :return:

pdf_skew(x, mu, sigma, skw)[source]

function with different parameterisation :param x: :param mu: mean :param sigma: sigma :param skw: skewness :return:

class lenstronomy.Util.prob_density.KDE1D(values)[source]

Bases: object

class that allows to compute likelihoods based on a 1-d posterior sample

likelihood(x)[source]
Parameters:x – position where to evaluate the density
Returns:likelihood given the sample distribution
lenstronomy.Util.prob_density.compute_lower_upper_errors(sample, num_sigma=1)[source]

computes the upper and lower sigma from the median value. This functions gives good error estimates for skewed pdf’s :param sample: 1-D sample :param num_sigma: integer, number of sigmas to be returned :return: median, lower_sigma, upper_sigma

lenstronomy.Util.sampling_util module

lenstronomy.Util.sampling_util.unit2uniform(x, vmin, vmax)[source]

mapping from uniform distribution on parameter space to uniform distribution on unit hypercube

lenstronomy.Util.sampling_util.uniform2unit(theta, vmin, vmax)[source]

mapping from uniform distribution on unit hypercube to uniform distribution on parameter space

lenstronomy.Util.sampling_util.cube2args_uniform(cube, lowers, uppers, num_dims, copy=False)[source]

mapping from uniform distribution on unit hypercube ‘cube’ to uniform distribution on parameter space

Parameters:
  • cube – list or 1D-array of parameter values on unit hypercube
  • lowers – lower bounds for each parameter
  • uppers – upper bounds for each parameter
  • num_dims – parameter space dimension (= number of parameters)
  • copy – If False, this function modifies ‘cube’ in-place. Default to False.
Returns:

hypercube mapped to parameters space

lenstronomy.Util.sampling_util.cube2args_gaussian(cube, lowers, uppers, means, sigmas, num_dims, copy=False)[source]

mapping from uniform distribution on unit hypercube ‘cube’ to truncated gaussian distribution on parameter space, with mean ‘mu’ and std dev ‘sigma’

Parameters:
  • cube – list or 1D-array of parameter values on unit hypercube
  • lowers – lower bounds for each parameter
  • uppers – upper bounds for each parameter
  • means – gaussian mean for each parameter
  • sigmas – gaussian std deviation for each parameter
  • num_dims – parameter space dimension (= number of parameters)
  • copy – If False, this function modifies ‘cube’ in-place. Default to False.
Returns:

hypercube mapped to parameters space

lenstronomy.Util.sampling_util.scale_limits(lowers, uppers, scale)[source]
lenstronomy.Util.sampling_util.sample_ball(p0, std, size=1, dist='uniform')[source]

Produce a ball of walkers around an initial parameter value. this routine is from the emcee package as it became deprecated there

Parameters:
  • p0 – The initial parameter values (array).
  • std – The axis-aligned standard deviation (array).
  • size – The number of samples to produce.
  • dist – string, specifies the distribution being sampled, supports ‘uniform’ and ‘normal’

lenstronomy.Util.simulation_util module

lenstronomy.Util.simulation_util.data_configure_simple(numPix, deltaPix, exposure_time=None, background_rms=None, center_ra=0, center_dec=0, inverse=False)[source]

configures the data keyword arguments with a coordinate grid centered at zero.

Parameters:
  • numPix – number of pixel (numPix x numPix)
  • deltaPix – pixel size (in angular units)
  • exposure_time – exposure time
  • background_rms – background noise (Gaussian sigma)
  • center_ra – RA at the center of the image
  • center_dec – DEC at the center of the image
  • inverse – if True, coordinate system is ra to the left, if False, to the right
Returns:

keyword arguments that can be used to construct a Data() class instance of lenstronomy

lenstronomy.Util.simulation_util.simulate_simple(image_model_class, kwargs_lens=None, kwargs_source=None, kwargs_lens_light=None, kwargs_ps=None, no_noise=False, source_add=True, lens_light_add=True, point_source_add=True)[source]
Parameters:
  • image_model_class
  • kwargs_lens
  • kwargs_source
  • kwargs_lens_light
  • kwargs_ps
  • no_noise
  • source_add
  • lens_light_add
  • point_source_add
Returns:

lenstronomy.Util.util module

lenstronomy.Util.util.merge_dicts(*dict_args)[source]

Given any number of dicts, shallow copy and merge into a new dict, precedence goes to key value pairs in latter dicts.

lenstronomy.Util.util.approx_theta_E(ximg, yimg)[source]
lenstronomy.Util.util.sort_image_index(ximg, yimg, xref, yref)[source]
Parameters:
  • ximg – x coordinates to sort
  • yimg – y coordinates to sort
  • xref – reference x coordinate
  • yref – reference y coordinate
Returns:

indexes such that ximg[indexes],yimg[indexes] matches xref,yref

lenstronomy.Util.util.rotate[source]
Parameters:
  • xcoords – x points
  • ycoords – y points
  • angle – angle in radians
Returns:

x points and y points rotated ccw by angle theta

lenstronomy.Util.util.map_coord2pix(ra, dec, x_0, y_0, M)[source]

this routines performs a linear transformation between two coordinate systems. Mainly used to transform angular into pixel coordinates in an image :param ra: ra coordinates :param dec: dec coordinates :param x_0: pixel value in x-axis of ra,dec = 0,0 :param y_0: pixel value in y-axis of ra,dec = 0,0 :param M: 2x2 matrix to transform angular to pixel coordinates :return: transformed coordinate systems of input ra and dec

lenstronomy.Util.util.array2image(array, nx=0, ny=0)[source]

returns the information contained in a 1d array into an n*n 2d array (only works when length of array is n**2, or nx and ny are provided)

Parameters:array (array of size n**2) – image values
Returns:2d array
Raises:AttributeError, KeyError
lenstronomy.Util.util.image2array(image)[source]

returns the information contained in a 2d array into an n*n 1d array

Parameters:array (array of size (n,n)) – image values
Returns:1d array
Raises:AttributeError, KeyError
lenstronomy.Util.util.array2cube(array, n_1, n_23)[source]

returns the information contained in a 1d array of shape (n_1*n_23*n_23) into 3d array with shape (n_1, sqrt(n_23), sqrt(n_23))

Parameters:
  • array (1d array) – image values
  • n_1 – first dimension of returned array
  • n_23 – square of second and third dimensions of returned array
Returns:

3d array

Raises:

ValueError – when n_23 is not a perfect square

lenstronomy.Util.util.cube2array(cube)[source]

returns the information contained in a 3d array of shape (n_1, n_2, n_3) into 1d array with shape (n_1*n_2*n_3)

Parameters:array (3d array) – image values
Returns:1d array
lenstronomy.Util.util.make_grid(numPix, deltapix, subgrid_res=1, left_lower=False)[source]

creates pixel grid (in 1d arrays of x- and y- positions) default coordinate frame is such that (0,0) is in the center of the coordinate grid

Parameters:
  • numPix – number of pixels per axis Give an integers for a square grid, or a 2-length sequence (first, second axis length) for a non-square grid.
  • deltapix – pixel size
  • subgrid_res – sub-pixel resolution (default=1)
Returns:

x, y position information in two 1d arrays

lenstronomy.Util.util.make_grid_transformed(numPix, Mpix2Angle)[source]

returns grid with linear transformation (deltaPix and rotation) :param numPix: number of Pixels :param Mpix2Angle: 2-by-2 matrix to mat a pixel to a coordinate :return: coordinate grid

lenstronomy.Util.util.make_grid_with_coordtransform(numPix, deltapix, subgrid_res=1, center_ra=0, center_dec=0, left_lower=False, inverse=True)[source]

same as make_grid routine, but returns the transformation matrix and shift between coordinates and pixel

Parameters:
  • numPix – number of pixels per axis
  • deltapix – pixel scale per axis
  • subgrid_res – supersampling resolution relative to the stated pixel size
  • center_ra – center of the grid
  • center_dec – center of the grid
  • left_lower – sets the zero point at the lower left corner of the pixels
  • inverse – bool, if true sets East as left, otherwise East is righrt
Returns:

lenstronomy.Util.util.grid_from_coordinate_transform(nx, ny, Mpix2coord, ra_at_xy_0, dec_at_xy_0)[source]

return a grid in x and y coordinates that satisfy the coordinate system

Parameters:
  • nx – number of pixels in x-axis
  • ny – number of pixels in y-axis
  • Mpix2coord – transformation matrix (2x2) of pixels into coordinate displacements
  • ra_at_xy_0 – RA coordinate at (x,y) = (0,0)
  • dec_at_xy_0 – DEC coordinate at (x,y) = (0,0)
Returns:

RA coordinate grid, DEC coordinate grid

lenstronomy.Util.util.get_axes(x, y)[source]

computes the axis x and y of a given 2d grid :param x: :param y: :return:

lenstronomy.Util.util.averaging(grid, numGrid, numPix)[source]

resize 2d pixel grid with numGrid to numPix and averages over the pixels :param grid: higher resolution pixel grid :param numGrid: number of pixels per axis in the high resolution input image :param numPix: lower number of pixels per axis in the output image (numGrid/numPix is integer number) :return:

lenstronomy.Util.util.displaceAbs(x, y, sourcePos_x, sourcePos_y)[source]

calculates a grid of distances to the observer in angel

Parameters:
  • mapped_cartcoord (numpy array (n,2)) – mapped cartesian coordinates
  • sourcePos (numpy vector [x0,y0]) – source position
Returns:

array of displacement

Raises:

AttributeError, KeyError

lenstronomy.Util.util.get_distance(x_mins, y_mins, x_true, y_true)[source]
Parameters:
  • x_mins
  • y_mins
  • x_true
  • y_true
Returns:

lenstronomy.Util.util.compare_distance(x_mapped, y_mapped)[source]
Parameters:
  • x_mapped – array of x-positions of remapped catalogue image
  • y_mapped – array of y-positions of remapped catalogue image
Returns:

sum of distance square of positions

lenstronomy.Util.util.min_square_dist(x_1, y_1, x_2, y_2)[source]

return minimum of quadratic distance of pairs (x1, y1) to pairs (x2, y2) :param x_1: :param y_1: :param x_2: :param y_2: :return:

lenstronomy.Util.util.selectBest(array, criteria, numSelect, highest=True)[source]
Parameters:
  • array – numpy array to be selected from
  • criteria – criteria of selection
  • highest – bool, if false the lowest will be selected
  • numSelect – number of elements to be selected
Returns:

lenstronomy.Util.util.select_best(array, criteria, num_select, highest=True)[source]
Parameters:
  • array – numpy array to be selected from
  • criteria – criteria of selection
  • highest – bool, if false the lowest will be selected
  • num_select – number of elements to be selected
Returns:

lenstronomy.Util.util.points_on_circle(radius, num_points, connect_ends=True)[source]

returns a set of uniform points around a circle :param radius: radius of the circle :param num_points: number of points on the circle :param connect_ends: boolean, if True, start and end point are the same :return: x-coords, y-coords of points on the circle

lenstronomy.Util.util.neighborSelect[source]

#TODO replace by from scipy.signal import argrelextrema for speed up >>> from scipy.signal import argrelextrema >>> x = np.array([2, 1, 2, 3, 2, 0, 1, 0]) >>> argrelextrema(x, np.greater) (array([3, 6]),) >>> y = np.array([[1, 2, 1, 2], … [2, 2, 0, 0], … [5, 3, 4, 4]]) … >>> argrelextrema(y, np.less, axis=1) (array([0, 2]), array([2, 1]))

finds (local) minima in a 2d grid

Parameters:a (numpy array with length numPix**2 in float) – 1d array of displacements from the source positions
Returns:array of indices of local minima, values of those minima
Raises:AttributeError, KeyError
lenstronomy.Util.util.fwhm2sigma(fwhm)[source]
Parameters:fwhm – full-widt-half-max value
Returns:gaussian sigma (sqrt(var))
lenstronomy.Util.util.sigma2fwhm(sigma)[source]
Parameters:sigma
Returns:
lenstronomy.Util.util.hyper2F2_array(a, b, c, d, x)[source]
Parameters:
  • a
  • b
  • c
  • d
  • x
Returns:

lenstronomy.Util.util.make_subgrid(ra_coord, dec_coord, subgrid_res=2)[source]

return a grid with subgrid resolution :param ra_coord: :param dec_coord: :param subgrid_res: :return:

lenstronomy.Util.util.convert_bool_list(n, k=None)[source]

returns a bool list of the length of the lens models if k = None: returns bool list with True’s if k is int, returns bool list with False’s but k’th is True if k is a list of int, e.g. [0, 3, 5], returns a bool list with True’s in the integers listed and False elsewhere if k is a boolean list, checks for size to match the numbers of models and returns it

Parameters:
  • n – integer, total lenght of output boolean list
  • k – None, int, or list of ints
Returns:

bool list

Module contents