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