def test__solution_and_regularization_matrix_range_of_values(self):
matrix_shape = (3,3)
inv = inversions.Inversion(image_1d=np.ones(9), noise_map_1d=np.ones(9), convolver=MockConvolver(matrix_shape),
mapper=MockMapper(matrix_shape), regularization=MockRegularization(matrix_shape))
# G_l term, Warren & Dye 2003 / Nightingale /2015 2018
# G_l = s_T * H * s
# Matrix multiplication:
# s_T * H = [2.0, 3.0, 5.0] * [2.0, -1.0, 0.0] = [(2.0* 2.0) + (3.0*-1.0) + (5.0 *0.0)] = [1.0, -1.0, 7.0]
# [-1.0, 2.0, -1.0] [(2.0*-1.0) + (3.0* 2.0) + (5.0*-1.0)]
# [ 0.0, -1.0, 2.0] [(2.0* 0.0) + (3.0*-1.0) + (5.0 *2.0)]
# (s_T * H) * s = [1.0, -1.0, 7.0] * [2.0] = 34.0
# [3.0]
# [5.0]
inv.solution_vector = np.array([2.0, 3.0, 5.0])
inv.regularization_matrix = np.array([[2.0, -1.0, 0.0],
[-1.0, 2.0, -1.0],
[0.0, -1.0, 2.0]])
assert inv.regularization_term == 34.0
def test__solution_all_1s__regularization_matrix_simple(self):
matrix_shape = (3,3)
inv = inversions.Inversion(image_1d=np.ones(9), noise_map_1d=np.ones(9), convolver=MockConvolver(matrix_shape),
mapper=MockMapper(matrix_shape), regularization=MockRegularization(matrix_shape))
inv.solution_vector = np.array([1.0, 1.0, 1.0])
inv.regularization_matrix = np.array([[1.0, 0.0, 0.0],
[0.0, 1.0, 0.0],
[0.0, 0.0, 1.0]])
# G_l term, Warren & Dye 2003 / Nightingale /2015 2018
# G_l = s_T * H * s
# Matrix multiplication:
# s_T * H = [1.0, 1.0, 1.0] * [1.0, 1.0, 1.0] = [(1.0*1.0) + (1.0*0.0) + (1.0*0.0)] = [1.0, 1.0, 1.0]
# [1.0, 1.0, 1.0] [(1.0*0.0) + (1.0*1.0) + (1.0*0.0)]
# [1.0, 1.0, 1.0] [(1.0*0.0) + (1.0*0.0) + (1.0*1.0)]
# (s_T * H) * s = [1.0, 1.0, 1.0] * [1.0] = 3.0
# [1.0]
# [1.0]
assert inv.regularization_term == 3.0
def test__solution_different_values__simple_blurred_mapping_matrix__correct_reconstructed_image(self):
matrix_shape = (3,3)
msk = mask.Mask(array=np.array([[True, True, True],
[False, False, False],
[True, True, True]]), pixel_scale=1.0)
grid_stack = grids.GridStack.grid_stack_from_mask_sub_grid_size_and_psf_shape(mask=msk, sub_grid_size=1,
psf_shape=(1,1))
inv = inversions.Inversion(image_1d=np.ones(9), noise_map_1d=np.ones(9), convolver=MockConvolver(matrix_shape),
mapper=MockMapper(matrix_shape, grid_stack), regularization=MockRegularization(matrix_shape))
inv.solution_vector = np.array([1.0, 2.0, 3.0, 4.0])
inv.blurred_mapping_matrix = np.array([[1.0, 1.0, 1.0, 1.0],
[1.0, 0.0, 1.0, 1.0],
[1.0, 0.0, 0.0, 0.0]])
# # CCD pixel 0 maps to 4 pixs pixxels -> value is 1.0 + 2.0 + 3.0 + 4.0 = 10.0
# # CCD pixel 1 maps to 3 pixs pixxels -> value is 1.0 + 3.0 + 4.0
# # CCD pixel 2 maps to 1 pixs pixxels -> value is 1.0
assert (inv.reconstructed_data_vector == np.array([10.0, 8.0, 1.0])).all()
assert (inv.reconstructed_data == np.array([[0.0, 0.0, 0.0],
[10.0, 8.0, 1.0],
[0.0, 0.0, 0.0]]))
def test__matrix_not_positive_definite__raises_reconstruction_exception(self):
matrix_shape = (3,3)
inv = inversions.Inversion(image_1d=np.ones(9), noise_map_1d=np.ones(9), convolver=MockConvolver(matrix_shape),
mapper=MockMapper(matrix_shape), regularization=MockRegularization(matrix_shape))
matrix = np.array([[2.0, 0.0, 0.0],
[-1.0, 2.0, -1.0],
[0.0, -1.0, 0.0]])
with pytest.raises(exc.InversionException):
assert pytest.approx(inv.log_determinant_of_matrix_cholesky(matrix), 1e-4)
def test__determinant_of_positive_definite_matrix_2_via_cholesky(self):
matrix_shape = (3,3)
inv = inversions.Inversion(image_1d=np.ones(9), noise_map_1d=np.ones(9), convolver=MockConvolver(matrix_shape),
mapper=MockMapper(matrix_shape), regularization=MockRegularization(matrix_shape))
matrix = np.array([[2.0, -1.0, 0.0],
[-1.0, 2.0, -1.0],
[0.0, -1.0, 2.0]])
log_determinant = np.log(np.linalg.det(matrix))
assert log_determinant == pytest.approx(inv.log_determinant_of_matrix_cholesky(matrix), 1e-4)
# We'll use another rectangular pixelization and mapper to perform the reconstruction
rectangular = pix.Rectangular(shape=(25, 25))
mapper = rectangular.mapper_from_grid_stack_and_border(
grid_stack=tracer.source_plane.grid_stack, border=None)
mapper_plotters.plot_image_and_mapper(ccd_data=ccd_data,
mask=mask,
mapper=mapper,
should_plot_grid=True)
# And now, finally, we're going to use our mapper to invert the image using the 'inversions' module, which is imported
# as 'inv'. I'll explain how this works in a second - but lets just go ahead and perform the inversion first.
# (Ignore the 'regularization' input below for now, we'll cover this in the next tutorial).
inversion = inv.Inversion(image_1d=lens_data.image_1d,
noise_map_1d=lens_data.noise_map_1d,
convolver=lens_data.convolver_mapping_matrix,
mapper=mapper,
regularization=reg.Constant(coefficients=(1.0, )))
# Our inversion has a reconstructed image and pixeilzation, whcih we can plot using an inversion plotter
inversion_plotters.plot_reconstructed_image(inversion=inversion, mask=mask)
inversion_plotters.plot_reconstructed_pixelization(inversion=inversion,
should_plot_grid=True)
# And there we have it, we've successfully reconstructed, or, *inverted*, our source using the mapper's rectangular
# grid. Whilst this source was simple (a blob of light in the centre of the source-plane), inversions come into their
# own when fitting sources with complex morphologies. Infact, given we're having so much fun inverting things, lets
# simulate a really complex source and invert it!
def simulate_complex_source():