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522 lines
20 KiB
Python
522 lines
20 KiB
Python
import numpy as np
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from scipy import linalg as la
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from scipy.sparse import linalg as spla
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import torch as t
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from itertools import combinations
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from cdtools.tools import analysis, initializers
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def test_product_svd():
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rank = 4
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shape_A = (12, rank)
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shape_B = (rank, 9)
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A = np.random.rand(*shape_A) + 1j * np.random.rand(*shape_A)
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B = np.random.rand(*shape_B) + 1j * np.random.rand(*shape_B)
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AB = np.matmul(A,B)
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U_1, S_1, Vh_1 = t.linalg.svd(t.as_tensor(AB), full_matrices=False)
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U_2, S_2, Vh_2 = analysis.product_svd(t.as_tensor(A),t.as_tensor(B))
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check_AB = U_2 @ t.diag_embed(S_2).to(dtype=Vh_2.dtype) @ Vh_2
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# So, at a minimum, U S Vh = AB
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assert np.allclose(AB, check_AB.numpy())
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# SVD is only defined up to an arbitrary complex valued phase per
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# singular vector, so all we can ask for in the comparison is that the
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# magnitudes here are
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assert np.allclose(S_1[:rank].numpy(), S_2.numpy())
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prod_U = U_1[:,:rank].transpose(0,1).conj() @ U_2
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prod_Vh = Vh_1[:rank,:] @ Vh_2.transpose(0,1).conj()
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assert np.allclose(t.abs(prod_U).numpy(), np.eye(rank))
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assert np.allclose(t.abs(prod_Vh).numpy(), np.eye(rank))
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# Confirms that the phases are consistent between the two, I think
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# it's redundant with the first check but I'm not sure
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assert np.allclose(prod_Vh.numpy(), prod_U.numpy())
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# test with numpy
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U_3, S_3, Vh_3 = analysis.product_svd(A,B)
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assert isinstance(U_3, np.ndarray)
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assert isinstance(S_3, np.ndarray)
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assert isinstance(Vh_3, np.ndarray)
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assert np.allclose(S_1[:rank].numpy(), S_3)
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prod_U = U_1[:,:rank].transpose(0,1).numpy().conj() @ U_3
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prod_Vh = Vh_1[:rank,:].numpy() @ Vh_3.transpose().conj()
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assert np.allclose(np.abs(prod_U), np.eye(rank))
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assert np.allclose(np.abs(prod_Vh), np.eye(rank))
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# Confirms that the phases are consistent between the two, I think
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# it's redundant with the first check but I'm not sure
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assert np.allclose(prod_Vh, prod_U)
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def test_orthogonalize_probes():
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op = analysis.orthogonalize_probes
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probe_xs = np.arange(64) - 32
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probe_ys = np.arange(76) - 38
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probe_Ys, probe_Xs = np.meshgrid(probe_ys, probe_xs)
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probe_Rs = np.sqrt(probe_Xs**2 + probe_Ys**2)
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probes = np.array([10*np.exp(-probe_Rs**2 / (2 * 10**2 + 1j)),
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3*np.exp(-probe_Rs**2 / (2 * 12**2 - 3j)),
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1*np.exp(-probe_Rs**2 / (2 * 15**2))])
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weight_matrix_none = None
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weight_matrix_single = np.random.randn(1,3) + 1j * np.random.randn(1,3)
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weight_matrix_small = np.random.randn(2,3) + 1j * np.random.randn(2,3)
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weight_matrix_medium = np.random.randn(3,3) + 1j * np.random.randn(3,3)
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weight_matrix_large = np.random.randn(7,3) + 1j * np.random.randn(7,3)
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weight_matrices = [
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weight_matrix_none,
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weight_matrix_single,
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weight_matrix_small,
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weight_matrix_medium,
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weight_matrix_large
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]
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for weight_matrix in weight_matrices:
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ortho_probes_np, rwm_np = op(probes, weight_matrix=weight_matrix,
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return_reexpressed_weights=True)
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assert isinstance(ortho_probes_np, np.ndarray)
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assert isinstance(rwm_np, np.ndarray)
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probes_t = t.as_tensor(probes)
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wm_t = (t.as_tensor(weight_matrix) if weight_matrix is not None
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else weight_matrix)
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ortho_probes_t, rwm_t = op(probes_t, weight_matrix=wm_t,
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return_reexpressed_weights=True)
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assert t.is_tensor(ortho_probes_t)
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assert t.is_tensor(rwm_t)
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assert np.allclose(ortho_probes_np, ortho_probes_t.numpy())
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assert np.allclose(rwm_np, rwm_t.numpy())
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# Now we test a if wm @ ortho_probes is actually the original
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# input
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if weight_matrix is not None:
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realized_probes = np.tensordot(weight_matrix, probes, axes=1)
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else:
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realized_probes = probes
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calculated_probes = np.tensordot(rwm_np, ortho_probes_np, axes=1)
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assert np.allclose(realized_probes, calculated_probes)
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# Now we test if the orthogonalized probes are orthogonalized
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reshaped_probes = ortho_probes_np.reshape(
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(ortho_probes_np.shape[0],
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ortho_probes_np.shape[1] * ortho_probes_np.shape[2]))
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products = np.matmul(reshaped_probes,
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reshaped_probes.conj().transpose())
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if weight_matrix is not None:
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output_nmodes = min(weight_matrix.shape[0], probes.shape[0])
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else:
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output_nmodes = probes.shape[0]
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for i in range(output_nmodes):
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for j in range(i+1, output_nmodes):
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assert np.isclose(products[i,j], 0)
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# And now we test if they multiply to the same density matrix as
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# the original probes + weight matrix
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reshaped_realized_probes = realized_probes.reshape(
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(realized_probes.shape[0],
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realized_probes.shape[1] * realized_probes.shape[2]))
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dm_original = np.matmul(
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reshaped_realized_probes.conj().transpose(),
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reshaped_realized_probes
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)
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dm_output = np.matmul(
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reshaped_probes.conj().transpose(),
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reshaped_probes
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)
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assert np.allclose(dm_original, dm_output)
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# And finally, we confirm that what we have are the eigenvectors/values
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# of that density matrix
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w, v = spla.eigsh(dm_original, k=output_nmodes)
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assert np.allclose(w, np.diag(products))
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cross_products = np.matmul(reshaped_probes, np.sqrt(w) * v)
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# The abs accounts for the fact that the phase of the eigenvectors
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# is undefined
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assert np.allclose(np.abs(cross_products), np.abs(products))
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def test_standardize():
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# Start by making a probe and object that should meet the standardization
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# conditions
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probe = initializers.gaussian((230,240),(20,20),curvature=(0.01,0.01)).numpy()
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probe = probe * np.sqrt(len(probe.ravel()) / np.sum(np.abs(probe)**2))
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probe = probe * np.exp(-1j * np.angle(np.sum(probe)))
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assert np.isclose(1, np.sum(np.abs(probe)**2)/ len(probe.ravel()))
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assert np.angle(np.sum(probe)) < 2e-7
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obj = 30 * np.random.rand(230,240) * np.exp(1j * (np.random.rand(230,240) - 0.5))
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obj_slice = np.s_[(obj.shape[0]//8)*3:(obj.shape[0]//8)*5,
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(obj.shape[1]//8)*3:(obj.shape[1]//8)*5]
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obj = obj * np.exp(-1j * np.angle(np.sum(obj[obj_slice])))
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assert np.isclose(0,np.angle(np.sum(obj[obj_slice])))
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# Then make a nonstandard version of them and standardize it
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# First, don't add a phase ramp and test
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test_probe = probe * 37.6 * np.exp(1j*0.35)
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test_obj = obj / 37.6 * np.exp(1j*1.43)
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s_probe, s_obj = analysis.standardize(test_probe, test_obj)
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assert np.allclose(probe, s_probe)
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assert np.allclose(obj, s_obj)
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# Test that it works on torch tensors
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s_probe, s_obj = analysis.standardize(t.as_tensor(test_probe,dtype=t.complex64), t.as_tensor(test_obj,dtype=t.complex64))
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s_probe = s_probe.numpy()
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s_obj = s_obj.numpy()
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assert np.allclose(probe, s_probe)
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assert np.allclose(obj, s_obj)
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# Then do one with a phase ramp
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phase_ramp_dir = (np.random.rand(2) - 0.5)
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probe_Xs, probe_Ys = np.mgrid[:probe.shape[0],:probe.shape[1]]
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phase_ramp = np.exp(1j*probe_Ys * phase_ramp_dir[1]+
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1j*probe_Xs * phase_ramp_dir[0])
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test_probe = test_probe * phase_ramp
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obj_Xs, obj_Ys = np.mgrid[:obj.shape[0],:obj.shape[1]]
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obj_phase_ramp = np.exp(-1j*obj_Ys * phase_ramp_dir[1]+
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-1j*obj_Xs * phase_ramp_dir[0])
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test_obj = test_obj * obj_phase_ramp
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s_probe, s_obj = analysis.standardize(test_probe, test_obj, correct_ramp=True)
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assert np.max(s_probe - probe) / np.max(np.abs(probe)) < 1e-4
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assert np.max(s_obj - obj) / np.max(np.abs(obj)) < 1e-4
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# Finally a test with the phase ramp and multiple probes
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subdominant_probe = 0.1*np.random.rand(230,240) * np.exp(1j * (np.random.rand(230,240) - 0.5))
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subdominant_probe = subdominant_probe * np.exp(-1j * np.angle(np.sum(subdominant_probe)))
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test_subdominant_probe = subdominant_probe * 37.6
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test_subdominant_probe = test_subdominant_probe * phase_ramp
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incoh_probe = np.array([test_probe,test_subdominant_probe])
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s_probe, s_obj = analysis.standardize(incoh_probe, test_obj, correct_ramp=True)
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assert np.max(s_probe[0] - probe) / np.max(np.abs(probe)) < 1e-4
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assert np.max(s_obj - obj) / np.max(np.abs(obj)) < 1e-4
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assert np.max(s_probe[1] - subdominant_probe) / np.max(np.abs(subdominant_probe)) < 1e-4
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def test_synthesize_reconstructions():
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# I can only really test for a lack of failures, so I think my plan
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# will be to create a dataset that just needs to be added and see that
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# it successfully doesn't mess it up.
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# Start by making a probe and object that should meet the standardization
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# conditions
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probe = initializers.gaussian((230,240),(20,20),curvature=(0.01,0.01)).numpy()
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probe = probe * np.sqrt(len(probe.ravel()) / np.sum(np.abs(probe)**2))
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probe = probe * np.exp(-1j * np.angle(np.sum(probe)))
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assert np.isclose(1, np.sum(np.abs(probe)**2)/ len(probe.ravel()))
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assert np.abs(np.angle(np.sum(probe))) < 2e-7
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obj = 30 * np.random.rand(230,240) * np.exp(1j * (np.random.rand(230,240) - 0.5))
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obj_slice = np.s_[(obj.shape[0]//8)*3:(obj.shape[0]//8)*5,
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(obj.shape[1]//8)*3:(obj.shape[1]//8)*5]
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obj = obj * np.exp(-1j * np.angle(np.sum(obj[obj_slice])))
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assert np.isclose(0,np.angle(np.sum(obj[obj_slice])))
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# Now I make stacks of identical probes and objects
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probes = [probe,probe,probe,probe]
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probe = np.copy(probe)
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objects = [obj,obj,obj,obj]
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obj = np.copy(obj)
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s_probe, s_obj, obj_stack = analysis.synthesize_reconstructions(probes,objects)
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assert np.max(s_probe - probe) < 2e-5
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assert np.max(s_obj - obj) < 2e-5
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for t_obj in obj_stack:
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assert np.max(t_obj - obj) < 5e-5
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def test_calc_consistency_prtf():
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# Create an object with a specific structure
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obj = 30 * np.random.rand(1030,1040) * np.exp(1j * (np.random.rand(1030,1040) - 0.5))
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#
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synth_obj = np.sqrt(0.7) * obj
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obj_stack = [obj,obj,obj,obj]
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basis = np.array([[0,2,0],
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[3,0,0]])
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freqs, prtf = analysis.calc_consistency_prtf(synth_obj, obj_stack, basis)
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assert np.allclose(prtf, 0.7)
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freqs, prtf = analysis.calc_consistency_prtf(synth_obj, obj_stack, basis, nbins=30)
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assert np.allclose(prtf, 0.7)
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# Check that it also works with torch input
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t_synth_obj = t.as_tensor(synth_obj)
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t_obj_stack = [t.as_tensor(obj) for obj in obj_stack]
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freqs, prtf = analysis.calc_consistency_prtf(t_synth_obj, t_obj_stack, basis, nbins=30)
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assert np.allclose(prtf.numpy(), 0.7)
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# And also when the basis is in torch
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t_synth_obj = t.as_tensor(synth_obj)
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t_obj_stack = [t.as_tensor(obj) for obj in obj_stack]
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freqs, prtf = analysis.calc_consistency_prtf(t_synth_obj, t_obj_stack, t.Tensor(basis), nbins=30)
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assert np.allclose(prtf.numpy(), 0.7)
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# Check that is uses the right number of bins
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assert len(prtf) == 30
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assert len(freqs) == 30
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# Check that the maximum frequency is correct for the basis
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assert np.isclose(freqs[-1]-freqs[-2] + freqs[-1], np.sqrt(1/4**2 + 1/6**2))
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def test_calc_deconvolved_cross_correlation():
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obj1 = np.random.rand(200,300) + 1j * np.random.rand(200,300)
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obj2 = np.random.rand(200,300) + 1j * np.random.rand(200,300)
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cor_fft = np.fft.fft2(obj1) * np.conj(np.fft.fft2(obj2))
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# Not sure if this is more or less stable than just the correlation
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# maximum - requires some testing
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np_cor = np.fft.ifft2(cor_fft / np.abs(cor_fft))
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# test with numpy inputs
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test_cor = analysis.calc_deconvolved_cross_correlation(obj1,obj2, im_slice=np.s_[:,:])
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assert np.allclose(test_cor, np_cor)
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# test with pytorch inputs
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obj1_t = t.as_tensor(obj1)
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obj2_t = t.as_tensor(obj2)
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test_cor_t = analysis.calc_deconvolved_cross_correlation(obj1_t,obj2_t, im_slice=np.s_[:,:])
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assert np.allclose(test_cor_t.numpy(), np_cor)
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def test_calc_frc():
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obj1 = np.random.rand(270,230) + 1j * np.random.rand(270,230)
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obj2 = np.random.rand(270,230) + 1j * np.random.rand(270,230)
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basis = np.array([[0,2,0],
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[3,0,0]])
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nbins = 100
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snr = 2
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cor_fft = np.fft.fftshift(np.fft.fft2(obj1[10:-10,20:-20])) * \
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np.fft.fftshift(np.conj(np.fft.fft2(obj2[10:-10,20:-20])))
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F1 = np.abs(np.fft.fftshift(np.fft.fft2(obj1[10:-10,20:-20])))**2
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F2 = np.abs(np.fft.fftshift(np.fft.fft2(obj2[10:-10,20:-20])))**2
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di = np.linalg.norm(basis[:,0])
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dj = np.linalg.norm(basis[:,1])
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i_freqs = np.fft.fftshift(np.fft.fftfreq(cor_fft.shape[0],d=di))
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j_freqs = np.fft.fftshift(np.fft.fftfreq(cor_fft.shape[1],d=dj))
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Js,Is = np.meshgrid(j_freqs,i_freqs)
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Rs = np.sqrt(Is**2+Js**2)
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numerator, bins = np.histogram(Rs,bins=nbins,weights=cor_fft)
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denominator_F1, bins = np.histogram(Rs,bins=nbins,weights=F1)
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denominator_F2, bins = np.histogram(Rs,bins=nbins,weights=F2)
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n_pix, bins = np.histogram(Rs,bins=nbins)
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bins = bins[:-1]
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frc = numerator / np.sqrt(denominator_F1*denominator_F2)
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# This moves from combined-image SNR to single-image SNR
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snr /= 2
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threshold = (snr + (2 * snr + 1) / np.sqrt(n_pix)) / \
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(1 + snr + (2 * np.sqrt(snr)) / np.sqrt(n_pix))
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test_bins, test_frc, test_threshold = analysis.calc_frc(
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obj1, obj2, basis, im_slice=np.s_[10:-10,20:-20],
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nbins=100, snr=2, limit='corner')
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assert np.allclose(bins, test_bins)
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assert np.allclose(frc, test_frc)
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assert np.allclose(threshold, test_threshold)
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# try again with complex
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obj1_torch = t.as_tensor(obj1)
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obj2_torch = t.as_tensor(obj2)
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basis_torch = t.tensor(basis)
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test_bins_t, test_frc_t, test_threshold_t = analysis.calc_frc(
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obj1_torch,
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obj2_torch,
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basis_torch,
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im_slice=np.s_[10:-10,20:-20], nbins=100, snr=2, limit='corner')
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assert np.allclose(bins, test_bins_t.numpy())
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assert np.allclose(frc, test_frc_t.numpy())
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assert np.allclose(threshold, test_threshold_t.numpy())
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def test_calc_rms_error():
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field_1 = t.rand(14,19, dtype=t.complex64)
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field_2 = t.rand(14,19, dtype=t.complex64)
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# Check that the calculation is insensitive to phase
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assert t.allclose(analysis.calc_rms_error(field_1, field_2),
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analysis.calc_rms_error(field_1, np.exp(0.7j) * field_2))
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# And that it is sensitive to phase if we turn off the
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assert not t.allclose(
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analysis.calc_rms_error(field_1, field_2, align_phases=False),
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analysis.calc_rms_error(field_1, np.exp(0.7j) * field_2,
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align_phases=False))
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# Check that the result is positive
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assert analysis.calc_rms_error(field_1, field_2) > 0
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|
|
# And that it is a smaller number with align_phases on
|
|
assert (analysis.calc_rms_error(field_1, field_2) <=
|
|
analysis.calc_rms_error(field_1, field_2, align_phases=False))
|
|
|
|
# Now we check against an explicit implementation:
|
|
gamma = field_1 * t.conj(field_2)
|
|
gamma /= t.abs(gamma)
|
|
|
|
# This is an alternate way of doing the calculation. Actually, would this
|
|
# be a better implementation anyway? Probably no difference tbh.
|
|
rms_error_nophase = t.sqrt((t.mean(t.abs(field_1)**2) +
|
|
t.mean(t.abs(field_2)**2) -
|
|
2 * t.abs(t.mean(field_1 * t.conj(field_2)))))
|
|
assert t.allclose(rms_error_nophase,
|
|
analysis.calc_rms_error(field_1, field_2))
|
|
|
|
rms_error_phase = t.sqrt((t.mean(t.abs(field_1)**2) +
|
|
t.mean(t.abs(field_2)**2) -
|
|
2 * t.real(t.mean(field_1 * t.conj(field_2)))))
|
|
|
|
assert t.allclose(rms_error_phase,
|
|
analysis.calc_rms_error(field_1, field_2,
|
|
align_phases=False))
|
|
|
|
# Now let's test that it works along a dimension:
|
|
|
|
field_1 = t.rand(3,14,19, dtype=t.complex64)
|
|
field_2 = t.rand(3,14,19, dtype=t.complex64)
|
|
result = analysis.calc_rms_error(field_1, field_2, normalize=True)
|
|
assert (result.shape == t.Size([3]))
|
|
|
|
for i in range(3):
|
|
assert t.allclose(analysis.calc_rms_error(field_1[i],
|
|
field_2[i],
|
|
normalize=True),
|
|
result[i])
|
|
|
|
|
|
def test_calc_fidelity():
|
|
|
|
fields_1 = t.rand(2,30,17, dtype=t.complex128)
|
|
fields_2 = t.rand(3,30,17, dtype=t.complex128)
|
|
|
|
dm_1 = t.reshape(fields_1, (2,-1))
|
|
dm_1 = t.tensordot(dm_1.transpose(0,1), dm_1.conj(), dims=1).numpy()
|
|
dm_2 = t.reshape(fields_2, (3,-1))
|
|
dm_2 = t.tensordot(dm_2.transpose(0,1), dm_2.conj(), dims=1).numpy()
|
|
|
|
sqrt_dm_1 = la.sqrtm(dm_1).astype(dm_1.dtype)
|
|
inner_mat = la.sqrtm(np.dot(np.dot(sqrt_dm_1,dm_2), sqrt_dm_1))
|
|
inner_mat = inner_mat.astype(dm_1.dtype) #la.sqrtm doubles the precision
|
|
fidelity = t.as_tensor(np.abs(np.trace(inner_mat))**2)
|
|
|
|
assert t.isclose(fidelity, analysis.calc_fidelity(fields_1, fields_2))
|
|
|
|
# Check that it reduces to the overlap for coherent fields
|
|
fields_1 = t.rand(1,30,17, dtype=t.complex128)
|
|
fields_2 = t.rand(1,30,17, dtype=t.complex128)
|
|
|
|
assert t.isclose(t.abs(t.sum(fields_1*fields_2.conj()))**2,
|
|
analysis.calc_fidelity(fields_1, fields_2))
|
|
# Checking that it works with extra dimensions
|
|
fields_1 = t.rand(3,3,30,17, dtype=t.complex128)
|
|
fields_2 = t.rand(3,1,30,17, dtype=t.complex128)
|
|
field_3 = t.rand(1,30,17, dtype=t.complex128)
|
|
|
|
fidelities = analysis.calc_fidelity(fields_1, fields_2)
|
|
fidelities_2 = analysis.calc_fidelity(fields_1, field_3)
|
|
for i in range(3):
|
|
assert t.isclose(analysis.calc_fidelity(fields_1[i], fields_2[i]),
|
|
fidelities[i])
|
|
assert t.isclose(analysis.calc_fidelity(fields_1[i], field_3),
|
|
fidelities_2[i])
|
|
|
|
# Check that the diensionality argument works
|
|
fields_1 = t.rand(3,2,12, dtype=t.complex128)
|
|
fields_2 = t.rand(3,2,12, dtype=t.complex128)
|
|
|
|
assert (analysis.calc_fidelity(fields_1, fields_2, dims=1).shape
|
|
== t.Size([3]))
|
|
|
|
fields_1 = t.rand(3,2,12,4,5, dtype=t.complex128)
|
|
fields_2 = t.rand(3,2,12,4,5, dtype=t.complex128)
|
|
|
|
assert (analysis.calc_fidelity(fields_1, fields_2, dims=3).shape
|
|
== t.Size([3]))
|
|
|
|
def test_calc_generalized_rms_error():
|
|
|
|
# Test that it matches the rms error for coherent fields
|
|
|
|
fields_1 = t.rand(1,30,17, dtype=t.complex128)
|
|
fields_2 = t.rand(1,30,17, dtype=t.complex128)
|
|
|
|
assert t.isclose(analysis.calc_generalized_rms_error(fields_1, fields_2),
|
|
analysis.calc_rms_error(fields_1[0], fields_2[0],
|
|
align_phases=True))
|
|
|
|
# Test that it is independent of field order
|
|
fields_1 = t.rand(5,30,17, dtype=t.complex128)
|
|
fields_2 = t.rand(3,30,17, dtype=t.complex128)
|
|
fields_3 = fields_2.flip(0)
|
|
|
|
assert t.isclose(analysis.calc_generalized_rms_error(fields_1, fields_2),
|
|
analysis.calc_generalized_rms_error(fields_1, fields_3))
|
|
|
|
# Test with leading dimensions
|
|
fields_1 = t.rand(3,4,2,10,17, dtype=t.complex128)
|
|
fields_2 = t.rand(3,4,3,10,17, dtype=t.complex128)
|
|
|
|
assert (analysis.calc_generalized_rms_error(fields_1, fields_2).shape
|
|
== t.Size([3,4]))
|
|
|
|
# And test with different number of dimensions dims
|
|
# Test that it is independent of field order
|
|
fields_1 = t.rand(3,6,17, dtype=t.complex128)
|
|
fields_2 = t.rand(3,1,17, dtype=t.complex128)
|
|
fields_3 = fields_2.flip(0)
|
|
|
|
assert (analysis.calc_generalized_rms_error(fields_1, fields_2, dims=1).shape == t.Size([3]))
|
|
|