242 lines
8.7 KiB
Python
242 lines
8.7 KiB
Python
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#******************************************************************************
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# Copyright (C) 2013 Kenneth L. Ho
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# Redistribution and use in source and binary forms, with or without
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# modification, are permitted provided that the following conditions are met:
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#
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# Redistributions of source code must retain the above copyright notice, this
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# list of conditions and the following disclaimer. Redistributions in binary
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# form must reproduce the above copyright notice, this list of conditions and
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# the following disclaimer in the documentation and/or other materials
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# provided with the distribution.
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#
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# None of the names of the copyright holders may be used to endorse or
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# promote products derived from this software without specific prior written
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# permission.
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#
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# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
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# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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# CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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# SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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# CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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# ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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# POSSIBILITY OF SUCH DAMAGE.
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#******************************************************************************
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import scipy.linalg.interpolative as pymatrixid
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import numpy as np
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from scipy.linalg import hilbert, svdvals, norm
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from scipy.sparse.linalg import aslinearoperator
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from scipy.linalg.interpolative import interp_decomp
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from numpy.testing import (assert_, assert_allclose, assert_equal,
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assert_array_equal)
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import pytest
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from pytest import raises as assert_raises
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import sys
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_IS_32BIT = (sys.maxsize < 2**32)
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@pytest.fixture()
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def eps():
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yield 1e-12
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@pytest.fixture(params=[np.float64, np.complex128])
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def A(request):
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# construct Hilbert matrix
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# set parameters
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n = 300
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yield hilbert(n).astype(request.param)
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@pytest.fixture()
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def L(A):
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yield aslinearoperator(A)
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@pytest.fixture()
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def rank(A, eps):
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S = np.linalg.svd(A, compute_uv=False)
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try:
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rank = np.nonzero(S < eps)[0][0]
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except IndexError:
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rank = A.shape[0]
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return rank
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class TestInterpolativeDecomposition:
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@pytest.mark.parametrize(
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"rand,lin_op",
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[(False, False), (True, False), (True, True)])
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def test_real_id_fixed_precision(self, A, L, eps, rand, lin_op):
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if _IS_32BIT and A.dtype == np.complex_ and rand:
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pytest.xfail("bug in external fortran code")
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# Test ID routines on a Hilbert matrix.
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A_or_L = A if not lin_op else L
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k, idx, proj = pymatrixid.interp_decomp(A_or_L, eps, rand=rand)
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B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
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assert_allclose(A, B, rtol=eps, atol=1e-08)
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@pytest.mark.parametrize(
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"rand,lin_op",
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[(False, False), (True, False), (True, True)])
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def test_real_id_fixed_rank(self, A, L, eps, rank, rand, lin_op):
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if _IS_32BIT and A.dtype == np.complex_ and rand:
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pytest.xfail("bug in external fortran code")
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k = rank
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A_or_L = A if not lin_op else L
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idx, proj = pymatrixid.interp_decomp(A_or_L, k, rand=rand)
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B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
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assert_allclose(A, B, rtol=eps, atol=1e-08)
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@pytest.mark.parametrize("rand,lin_op", [(False, False)])
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def test_real_id_skel_and_interp_matrices(
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self, A, L, eps, rank, rand, lin_op):
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k = rank
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A_or_L = A if not lin_op else L
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idx, proj = pymatrixid.interp_decomp(A_or_L, k, rand=rand)
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P = pymatrixid.reconstruct_interp_matrix(idx, proj)
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B = pymatrixid.reconstruct_skel_matrix(A, k, idx)
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assert_allclose(B, A[:, idx[:k]], rtol=eps, atol=1e-08)
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assert_allclose(B @ P, A, rtol=eps, atol=1e-08)
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@pytest.mark.parametrize(
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"rand,lin_op",
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[(False, False), (True, False), (True, True)])
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def test_svd_fixed_precison(self, A, L, eps, rand, lin_op):
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if _IS_32BIT and A.dtype == np.complex_ and rand:
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pytest.xfail("bug in external fortran code")
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A_or_L = A if not lin_op else L
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U, S, V = pymatrixid.svd(A_or_L, eps, rand=rand)
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B = U * S @ V.T.conj()
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assert_allclose(A, B, rtol=eps, atol=1e-08)
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@pytest.mark.parametrize(
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"rand,lin_op",
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[(False, False), (True, False), (True, True)])
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def test_svd_fixed_rank(self, A, L, eps, rank, rand, lin_op):
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if _IS_32BIT and A.dtype == np.complex_ and rand:
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pytest.xfail("bug in external fortran code")
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k = rank
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A_or_L = A if not lin_op else L
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U, S, V = pymatrixid.svd(A_or_L, k, rand=rand)
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B = U * S @ V.T.conj()
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assert_allclose(A, B, rtol=eps, atol=1e-08)
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def test_id_to_svd(self, A, eps, rank):
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k = rank
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idx, proj = pymatrixid.interp_decomp(A, k, rand=False)
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U, S, V = pymatrixid.id_to_svd(A[:, idx[:k]], idx, proj)
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B = U * S @ V.T.conj()
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assert_allclose(A, B, rtol=eps, atol=1e-08)
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def test_estimate_spectral_norm(self, A):
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s = svdvals(A)
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norm_2_est = pymatrixid.estimate_spectral_norm(A)
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assert_allclose(norm_2_est, s[0], rtol=1e-6, atol=1e-8)
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def test_estimate_spectral_norm_diff(self, A):
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B = A.copy()
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B[:, 0] *= 1.2
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s = svdvals(A - B)
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norm_2_est = pymatrixid.estimate_spectral_norm_diff(A, B)
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assert_allclose(norm_2_est, s[0], rtol=1e-6, atol=1e-8)
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def test_rank_estimates_array(self, A):
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B = np.array([[1, 1, 0], [0, 0, 1], [0, 0, 1]], dtype=A.dtype)
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for M in [A, B]:
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rank_tol = 1e-9
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rank_np = np.linalg.matrix_rank(M, norm(M, 2) * rank_tol)
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rank_est = pymatrixid.estimate_rank(M, rank_tol)
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assert_(rank_est >= rank_np)
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assert_(rank_est <= rank_np + 10)
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def test_rank_estimates_lin_op(self, A):
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B = np.array([[1, 1, 0], [0, 0, 1], [0, 0, 1]], dtype=A.dtype)
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for M in [A, B]:
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ML = aslinearoperator(M)
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rank_tol = 1e-9
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rank_np = np.linalg.matrix_rank(M, norm(M, 2) * rank_tol)
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rank_est = pymatrixid.estimate_rank(ML, rank_tol)
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assert_(rank_est >= rank_np - 4)
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assert_(rank_est <= rank_np + 4)
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def test_rand(self):
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pymatrixid.seed('default')
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assert_allclose(pymatrixid.rand(2), [0.8932059, 0.64500803],
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rtol=1e-4, atol=1e-8)
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pymatrixid.seed(1234)
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x1 = pymatrixid.rand(2)
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assert_allclose(x1, [0.7513823, 0.06861718], rtol=1e-4, atol=1e-8)
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np.random.seed(1234)
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pymatrixid.seed()
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x2 = pymatrixid.rand(2)
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np.random.seed(1234)
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pymatrixid.seed(np.random.rand(55))
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x3 = pymatrixid.rand(2)
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assert_allclose(x1, x2)
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assert_allclose(x1, x3)
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def test_badcall(self):
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A = hilbert(5).astype(np.float32)
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with assert_raises(ValueError):
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pymatrixid.interp_decomp(A, 1e-6, rand=False)
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def test_rank_too_large(self):
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# svd(array, k) should not segfault
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a = np.ones((4, 3))
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with assert_raises(ValueError):
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pymatrixid.svd(a, 4)
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def test_full_rank(self):
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eps = 1.0e-12
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# fixed precision
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A = np.random.rand(16, 8)
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k, idx, proj = pymatrixid.interp_decomp(A, eps)
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assert_equal(k, A.shape[1])
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P = pymatrixid.reconstruct_interp_matrix(idx, proj)
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B = pymatrixid.reconstruct_skel_matrix(A, k, idx)
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assert_allclose(A, B @ P)
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# fixed rank
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idx, proj = pymatrixid.interp_decomp(A, k)
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P = pymatrixid.reconstruct_interp_matrix(idx, proj)
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B = pymatrixid.reconstruct_skel_matrix(A, k, idx)
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assert_allclose(A, B @ P)
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@pytest.mark.parametrize("dtype", [np.float_, np.complex_])
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@pytest.mark.parametrize("rand", [True, False])
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@pytest.mark.parametrize("eps", [1, 0.1])
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def test_bug_9793(self, dtype, rand, eps):
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if _IS_32BIT and dtype == np.complex_ and rand:
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pytest.xfail("bug in external fortran code")
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A = np.array([[-1, -1, -1, 0, 0, 0],
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[0, 0, 0, 1, 1, 1],
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[1, 0, 0, 1, 0, 0],
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[0, 1, 0, 0, 1, 0],
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[0, 0, 1, 0, 0, 1]],
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dtype=dtype, order="C")
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B = A.copy()
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interp_decomp(A.T, eps, rand=rand)
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assert_array_equal(A, B)
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