Source code for lenstronomy.LensModel.convergence_integrals

import numpy as np
import scipy.signal as scp
from lenstronomy.Util import util
from lenstronomy.Util import image_util
from lenstronomy.Util import kernel_util
"""
class to compute lensing potentials and deflection angles provided a convergence map
"""

from lenstronomy.Util.package_util import exporter
export, __all__ = exporter()


[docs]@export def potential_from_kappa_grid(kappa, grid_spacing): """ lensing potential on the convergence grid the computation is performed as a convolution of the Green's function with the convergence map using FFT :param kappa: 2d grid of convergence values :param grid_spacing: pixel size of grid :return: lensing potential in a 2d grid at positions x_grid, y_grid """ num_pix = len(kappa) * 2 if num_pix % 2 == 0: num_pix += 1 kernel = potential_kernel(num_pix, grid_spacing) f_ = scp.fftconvolve(kappa, kernel, mode='same') / np.pi * grid_spacing ** 2 return f_
[docs]@export def potential_from_kappa_grid_adaptive(kappa_high_res, grid_spacing, low_res_factor, high_res_kernel_size): """ lensing potential on the convergence grid the computation is performed as a convolution of the Green's function with the convergence map using FFT :param kappa_high_res: 2d grid of convergence values :param grid_spacing: pixel size of grid :param low_res_factor: lower resolution factor of larger scale kernel. :param high_res_kernel_size: int, size of high resolution kernel in units of degraded pixels :return: lensing potential in a 2d grid at positions x_grid, y_grid """ kappa_low_res = image_util.re_size(kappa_high_res, factor=low_res_factor) num_pix = len(kappa_high_res) * 2 if num_pix % 2 == 0: num_pix += 1 grid_spacing_low_res = grid_spacing * low_res_factor kernel = potential_kernel(num_pix, grid_spacing) kernel_low_res, kernel_high_res = kernel_util.split_kernel(kernel, high_res_kernel_size, low_res_factor, normalized=False) f_high_res = scp.fftconvolve(kappa_high_res, kernel_high_res, mode='same') / np.pi * grid_spacing ** 2 f_high_res = image_util.re_size(f_high_res, low_res_factor) f_low_res = scp.fftconvolve(kappa_low_res, kernel_low_res, mode='same') / np.pi * grid_spacing_low_res ** 2 return f_high_res + f_low_res
[docs]@export def deflection_from_kappa_grid(kappa, grid_spacing): """ deflection angles on the convergence grid the computation is performed as a convolution of the Green's function with the convergence map using FFT :param kappa: convergence values for each pixel (2-d array) :param grid_spacing: pixel size of grid :return: numerical deflection angles in x- and y- direction """ num_pix = len(kappa) * 2 if num_pix % 2 == 0: num_pix += 1 kernel_x, kernel_y = deflection_kernel(num_pix, grid_spacing) f_x = scp.fftconvolve(kappa, kernel_x, mode='same') / np.pi * grid_spacing ** 2 f_y = scp.fftconvolve(kappa, kernel_y, mode='same') / np.pi * grid_spacing ** 2 return f_x, f_y
[docs]@export def deflection_from_kappa_grid_adaptive(kappa_high_res, grid_spacing, low_res_factor, high_res_kernel_size): """ deflection angles on the convergence grid with adaptive FFT the computation is performed as a convolution of the Green's function with the convergence map using FFT The grid is returned in the lower resolution grid :param kappa_high_res: convergence values for each pixel (2-d array) :param grid_spacing: pixel size of high resolution grid :param low_res_factor: lower resolution factor of larger scale kernel. :param high_res_kernel_size: int, size of high resolution kernel in units of degraded pixels :return: numerical deflection angles in x- and y- direction """ kappa_low_res = image_util.re_size(kappa_high_res, factor=low_res_factor) num_pix = len(kappa_high_res) * 2 if num_pix % 2 == 0: num_pix += 1 #if high_res_kernel_size % low_res_factor != 0: # assert ValueError('fine grid kernel size needs to be a multiplicative factor of low_res_factor! Settings used: ' # 'fine_grid_kernel_size=%s, low_res_factor=%s' % (high_res_kernel_size, low_res_factor)) kernel_x, kernel_y = deflection_kernel(num_pix, grid_spacing) grid_spacing_low_res = grid_spacing * low_res_factor kernel_low_res_x, kernel_high_res_x = kernel_util.split_kernel(kernel_x, high_res_kernel_size, low_res_factor, normalized=False) f_x_high_res = scp.fftconvolve(kappa_high_res, kernel_high_res_x, mode='same') / np.pi * grid_spacing ** 2 f_x_high_res = image_util.re_size(f_x_high_res, low_res_factor) f_x_low_res = scp.fftconvolve(kappa_low_res, kernel_low_res_x, mode='same') / np.pi * grid_spacing_low_res ** 2 f_x = f_x_high_res + f_x_low_res kernel_low_res_y, kernel_high_res_y = kernel_util.split_kernel(kernel_y, high_res_kernel_size, low_res_factor, normalized=False) f_y_high_res = scp.fftconvolve(kappa_high_res, kernel_high_res_y, mode='same') / np.pi * grid_spacing ** 2 f_y_high_res = image_util.re_size(f_y_high_res, low_res_factor) f_y_low_res = scp.fftconvolve(kappa_low_res, kernel_low_res_y, mode='same') / np.pi * grid_spacing_low_res ** 2 f_y = f_y_high_res + f_y_low_res return f_x, f_y
[docs]@export def potential_kernel(num_pix, delta_pix): """ numerical gridded integration kernel for convergence to lensing kernel with given pixel size :param num_pix: integer; number of pixels of kernel per axis :param delta_pix: pixel size (per dimension in units of angle) :return: kernel for lensing potential """ x_shift, y_shift = util.make_grid(numPix=num_pix, deltapix=delta_pix) r2 = x_shift ** 2 + y_shift ** 2 r2_max = np.max(r2) r2[r2 < (delta_pix / 2) ** 2] = (delta_pix / 2) ** 2 lnr = np.log(r2/r2_max) / 2. kernel = util.array2image(lnr) return kernel
[docs]@export def deflection_kernel(num_pix, delta_pix): """ numerical gridded integration kernel for convergence to deflection angle with given pixel size :param num_pix: integer; number of pixels of kernel per axis, should be odd number to have a defined center :param delta_pix: pixel size (per dimension in units of angle) :return: kernel for x-direction and kernel of y-direction deflection angles """ x_shift, y_shift = util.make_grid(numPix=num_pix, deltapix=delta_pix) r2 = x_shift**2 + y_shift**2 r2[r2 < (delta_pix/2)**2] = (delta_pix/2) ** 2 kernel_x = util.array2image(x_shift / r2) kernel_y = util.array2image(y_shift / r2) return kernel_x, kernel_y