def assert_differentials(self, lens_model, kwargs):
lensModelNum = NumericLens(lens_model)
x, y = 1., 2.
lensModel = LensModel(lens_model)
f_x, f_y = lensModel.lens_model.alpha(x, y, [kwargs])
f_xx, f_xy, f_yy = lensModel.hessian(x, y, [kwargs])
f_x_num, f_y_num = lensModelNum.lens_model.alpha(x, y, [kwargs])
f_xx_num, f_xy_num, f_yx_num, f_yy_num = lensModelNum.hessian(
x, y, [kwargs])
print(f_xx_num, f_xx)
print(f_yy_num, f_yy)
print(f_xy_num, f_xy)
print((f_xx - f_yy)**2 / 4 + f_xy**2,
(f_xx_num - f_yy_num)**2 / 4 + f_xy_num**2)
npt.assert_almost_equal(f_x, f_x_num, decimal=5)
npt.assert_almost_equal(f_y, f_y_num, decimal=5)
npt.assert_almost_equal(f_xx, f_xx_num, decimal=3)
npt.assert_almost_equal(f_yy, f_yy_num, decimal=3)
npt.assert_almost_equal(f_xy, f_xy_num, decimal=3)
x, y = 1., 0.
f_x, f_y = lensModel.lens_model.alpha(x, y, [kwargs])
f_xx, f_xy, f_yy = lensModel.hessian(x, y, [kwargs])
f_x_num, f_y_num = lensModelNum.lens_model.alpha(x, y, [kwargs])
f_xx_num, f_xy_num, f_yx_num, f_yy_num = lensModelNum.hessian(
x, y, [kwargs])
print(f_xx_num, f_xx)
print(f_yy_num, f_yy)
print(f_xy_num, f_xy)
print((f_xx - f_yy)**2 / 4 + f_xy**2,
(f_xx_num - f_yy_num)**2 / 4 + f_xy_num**2)
npt.assert_almost_equal(f_x, f_x_num, decimal=5)
npt.assert_almost_equal(f_y, f_y_num, decimal=5)
npt.assert_almost_equal(f_xx, f_xx_num, decimal=3)
npt.assert_almost_equal(f_yy, f_yy_num, decimal=3)
npt.assert_almost_equal(f_xy, f_xy_num, decimal=3)
def assert_differentials(self, lens_model, kwargs):
lensModelNum = NumericLens(lens_model)
lensModelNum.diff = 0.000001
#x, y = 1., 2.
x = np.linspace(start=0.1, stop=8, num=10)
y = np.zeros_like(x)
lensModel = LensModel(lens_model)
f_x, f_y = lensModel.lens_model.alpha(x, y, [kwargs])
f_xx, f_xy, f_yx, f_yy = lensModel.hessian(x, y, [kwargs])
f_x_num, f_y_num = lensModelNum.lens_model.alpha(x, y, [kwargs])
f_xx_num, f_xy_num, f_yx_num, f_yy_num = lensModelNum.hessian(
x, y, [kwargs])
print(f_xx_num, f_xx)
print(f_yy_num, f_yy)
print(f_xy_num, f_xy)
npt.assert_almost_equal(f_x, f_x_num, decimal=5)
npt.assert_almost_equal(f_y, f_y_num, decimal=5)
npt.assert_almost_equal(f_xx, f_xx_num, decimal=3)
npt.assert_almost_equal(f_yy, f_yy_num, decimal=3)
npt.assert_almost_equal(f_xy, f_xy_num, decimal=3)
x, y = 1., 0.
f_x, f_y = lensModel.lens_model.alpha(x, y, [kwargs])
f_xx, f_xy, f_yx, f_yy = lensModel.hessian(x, y, [kwargs])
f_x_num, f_y_num = lensModelNum.lens_model.alpha(x, y, [kwargs])
f_xx_num, f_xy_num, f_yx_num, f_yy_num = lensModelNum.hessian(
x, y, [kwargs])
print(f_xx_num, f_xx)
print(f_yy_num, f_yy)
print(f_xy_num, f_xy)
print(f_xx_num + f_yy_num, f_xx + f_yy)
npt.assert_almost_equal(f_x, f_x_num, decimal=5)
npt.assert_almost_equal(f_y, f_y_num, decimal=5)
npt.assert_almost_equal(f_xx, f_xx_num, decimal=3)
npt.assert_almost_equal(f_yy, f_yy_num, decimal=3)
npt.assert_almost_equal(f_xy, f_xy_num, decimal=3)
class TestNumerics(object):
"""
tests the source model routines
"""
def setup(self):
self.lensModel = LensModel(['GAUSSIAN'])
self.lensModelNum = NumericLens(['GAUSSIAN'])
self.kwargs = [{
'amp': 1. / 4.,
'sigma_x': 2.,
'sigma_y': 2.,
'center_x': 0.,
'center_y': 0.
}]
def test_kappa(self):
x, y = 1., 1.
output = self.lensModel.kappa(x, y, self.kwargs)
output_num = self.lensModelNum.kappa(x, y, self.kwargs)
npt.assert_almost_equal(output_num, output, decimal=5)
def test_gamma(self):
x, y = 1., 2.
output1, output2 = self.lensModel.gamma(x, y, self.kwargs)
output1_num, output2_num = self.lensModelNum.gamma(x, y, self.kwargs)
npt.assert_almost_equal(output1_num, output1, decimal=5)
npt.assert_almost_equal(output2_num, output2, decimal=5)
def test_magnification(self):
x, y = 1., 1.
output = self.lensModel.magnification(x, y, self.kwargs)
output_num = self.lensModelNum.magnification(x, y, self.kwargs)
npt.assert_almost_equal(output_num, output, decimal=5)
def test_differentials(self):
x, y = 1., 1.
f_xx, f_xy, f_yx, f_yy = self.lensModel.hessian(x, y, self.kwargs)
f_xx_num, f_xy_num, f_yx_num, f_yy_num = self.lensModelNum.hessian(
x, y, self.kwargs)
assert f_xy_num == f_yx_num
npt.assert_almost_equal(f_xx_num, f_xx, decimal=5)
npt.assert_almost_equal(f_xy_num, f_xy, decimal=5)
npt.assert_almost_equal(f_yx_num, f_yx, decimal=5)
npt.assert_almost_equal(f_yy_num, f_yy, decimal=5)
def light2mass_interpol(lens_light_model_list,
kwargs_lens_light,
numPix=100,
deltaPix=0.05,
subgrid_res=5,
center_x=0,
center_y=0):
"""
takes a lens light model and turns it numerically in a lens model
(with all lensmodel quantities computed on a grid). Then provides an interpolated grid for the quantities.
:param kwargs_lens_light: lens light keyword argument list
:param numPix: number of pixels per axis for the return interpolation
:param deltaPix: interpolation/pixel size
:param center_x: center of the grid
:param center_y: center of the grid
:param subgrid: subgrid for the numerical integrals
:return:
"""
# make sugrid
x_grid_sub, y_grid_sub = util.make_grid(numPix=numPix * 5,
deltapix=deltaPix,
subgrid_res=subgrid_res)
import lenstronomy.Util.mask as mask_util
mask = mask_util.mask_sphere(x_grid_sub,
y_grid_sub,
center_x,
center_y,
r=1)
x_grid, y_grid = util.make_grid(numPix=numPix, deltapix=deltaPix)
# compute light on the subgrid
lightModel = LightModel(light_model_list=lens_light_model_list)
flux = lightModel.surface_brightness(x_grid_sub, y_grid_sub,
kwargs_lens_light)
flux_norm = np.sum(flux[mask == 1]) / np.sum(mask)
flux /= flux_norm
from lenstronomy.LensModel.numerical_profile_integrals import ConvergenceIntegrals
integral = ConvergenceIntegrals()
# compute lensing quantities with subgrid
convergence_sub = flux
f_x_sub, f_y_sub = integral.deflection_from_kappa(convergence_sub,
x_grid_sub,
y_grid_sub,
deltaPix=deltaPix /
float(subgrid_res))
f_sub = integral.potential_from_kappa(convergence_sub,
x_grid_sub,
y_grid_sub,
deltaPix=deltaPix /
float(subgrid_res))
# interpolation function on lensing quantities
x_axes_sub, y_axes_sub = util.get_axes(x_grid_sub, y_grid_sub)
from lenstronomy.LensModel.Profiles.interpol import Interpol_func
interp_func = Interpol_func()
interp_func.do_interp(x_axes_sub, y_axes_sub, f_sub, f_x_sub, f_y_sub)
# compute lensing quantities on sparser grid
x_axes, y_axes = util.get_axes(x_grid, y_grid)
f_ = interp_func.function(x_grid, y_grid)
f_x, f_y = interp_func.derivatives(x_grid, y_grid)
# numerical differentials for second order differentials
from lenstronomy.LensModel.numeric_lens_differentials import NumericLens
lens_differential = NumericLens(lens_model_list=['INTERPOL'])
kwargs = [{
'grid_interp_x': x_axes_sub,
'grid_interp_y': y_axes_sub,
'f_': f_sub,
'f_x': f_x_sub,
'f_y': f_y_sub
}]
f_xx, f_xy, f_yx, f_yy = lens_differential.hessian(
x_grid, y_grid, kwargs)
kwargs_interpol = {
'grid_interp_x': x_axes,
'grid_interp_y': y_axes,
'f_': util.array2image(f_),
'f_x': util.array2image(f_x),
'f_y': util.array2image(f_y),
'f_xx': util.array2image(f_xx),
'f_xy': util.array2image(f_xy),
'f_yy': util.array2image(f_yy)
}
return kwargs_interpol