File size: 7,994 Bytes
7885a28 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 |
# ******************************************************************************
# Copyright (C) 2013 Kenneth L. Ho
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are met:
#
# Redistributions of source code must retain the above copyright notice, this
# list of conditions and the following disclaimer. Redistributions in binary
# form must reproduce the above copyright notice, this list of conditions and
# the following disclaimer in the documentation and/or other materials
# provided with the distribution.
#
# None of the names of the copyright holders may be used to endorse or
# promote products derived from this software without specific prior written
# permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
# CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
# SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
# CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
# ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
# POSSIBILITY OF SUCH DAMAGE.
# ******************************************************************************
import scipy.linalg.interpolative as pymatrixid
import numpy as np
from scipy.linalg import hilbert, svdvals, norm
from scipy.sparse.linalg import aslinearoperator
from scipy.linalg.interpolative import interp_decomp
from numpy.testing import (assert_, assert_allclose, assert_equal,
assert_array_equal)
import pytest
from pytest import raises as assert_raises
@pytest.fixture()
def eps():
yield 1e-12
@pytest.fixture()
def rng():
rng = np.random.default_rng(1718313768084012)
yield rng
@pytest.fixture(params=[np.float64, np.complex128])
def A(request):
# construct Hilbert matrix
# set parameters
n = 300
yield hilbert(n).astype(request.param)
@pytest.fixture()
def L(A):
yield aslinearoperator(A)
@pytest.fixture()
def rank(A, eps):
S = np.linalg.svd(A, compute_uv=False)
try:
rank = np.nonzero(S < eps)[0][0]
except IndexError:
rank = A.shape[0]
return rank
class TestInterpolativeDecomposition:
@pytest.mark.parametrize(
"rand,lin_op",
[(False, False), (True, False), (True, True)])
def test_real_id_fixed_precision(self, A, L, eps, rand, lin_op, rng):
# Test ID routines on a Hilbert matrix.
A_or_L = A if not lin_op else L
k, idx, proj = pymatrixid.interp_decomp(A_or_L, eps, rand=rand, rng=rng)
B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
assert_allclose(A, B, rtol=eps, atol=1e-08)
@pytest.mark.parametrize(
"rand,lin_op",
[(False, False), (True, False), (True, True)])
def test_real_id_fixed_rank(self, A, L, eps, rank, rand, lin_op, rng):
k = rank
A_or_L = A if not lin_op else L
idx, proj = pymatrixid.interp_decomp(A_or_L, k, rand=rand, rng=rng)
B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
assert_allclose(A, B, rtol=eps, atol=1e-08)
@pytest.mark.parametrize("rand,lin_op", [(False, False)])
def test_real_id_skel_and_interp_matrices(
self, A, L, eps, rank, rand, lin_op, rng):
k = rank
A_or_L = A if not lin_op else L
idx, proj = pymatrixid.interp_decomp(A_or_L, k, rand=rand, rng=rng)
P = pymatrixid.reconstruct_interp_matrix(idx, proj)
B = pymatrixid.reconstruct_skel_matrix(A, k, idx)
assert_allclose(B, A[:, idx[:k]], rtol=eps, atol=1e-08)
assert_allclose(B @ P, A, rtol=eps, atol=1e-08)
@pytest.mark.parametrize(
"rand,lin_op",
[(False, False), (True, False), (True, True)])
def test_svd_fixed_precision(self, A, L, eps, rand, lin_op, rng):
A_or_L = A if not lin_op else L
U, S, V = pymatrixid.svd(A_or_L, eps, rand=rand, rng=rng)
B = U * S @ V.T.conj()
assert_allclose(A, B, rtol=eps, atol=1e-08)
@pytest.mark.parametrize(
"rand,lin_op",
[(False, False), (True, False), (True, True)])
def test_svd_fixed_rank(self, A, L, eps, rank, rand, lin_op, rng):
k = rank
A_or_L = A if not lin_op else L
U, S, V = pymatrixid.svd(A_or_L, k, rand=rand, rng=rng)
B = U * S @ V.T.conj()
assert_allclose(A, B, rtol=eps, atol=1e-08)
def test_id_to_svd(self, A, eps, rank):
k = rank
idx, proj = pymatrixid.interp_decomp(A, k, rand=False)
U, S, V = pymatrixid.id_to_svd(A[:, idx[:k]], idx, proj)
B = U * S @ V.T.conj()
assert_allclose(A, B, rtol=eps, atol=1e-08)
def test_estimate_spectral_norm(self, A, rng):
s = svdvals(A)
norm_2_est = pymatrixid.estimate_spectral_norm(A, rng=rng)
assert_allclose(norm_2_est, s[0], rtol=1e-6, atol=1e-8)
def test_estimate_spectral_norm_diff(self, A, rng):
B = A.copy()
B[:, 0] *= 1.2
s = svdvals(A - B)
norm_2_est = pymatrixid.estimate_spectral_norm_diff(A, B, rng=rng)
assert_allclose(norm_2_est, s[0], rtol=1e-6, atol=1e-8)
def test_rank_estimates_array(self, A, rng):
B = np.array([[1, 1, 0], [0, 0, 1], [0, 0, 1]], dtype=A.dtype)
for M in [A, B]:
rank_tol = 1e-9
rank_np = np.linalg.matrix_rank(M, norm(M, 2) * rank_tol)
rank_est = pymatrixid.estimate_rank(M, rank_tol, rng=rng)
assert_(rank_est >= rank_np)
assert_(rank_est <= rank_np + 10)
def test_rank_estimates_lin_op(self, A, rng):
B = np.array([[1, 1, 0], [0, 0, 1], [0, 0, 1]], dtype=A.dtype)
for M in [A, B]:
ML = aslinearoperator(M)
rank_tol = 1e-9
rank_np = np.linalg.matrix_rank(M, norm(M, 2) * rank_tol)
rank_est = pymatrixid.estimate_rank(ML, rank_tol, rng=rng)
assert_(rank_est >= rank_np - 4)
assert_(rank_est <= rank_np + 4)
def test_badcall(self):
A = hilbert(5).astype(np.float32)
with assert_raises(ValueError):
pymatrixid.interp_decomp(A, 1e-6, rand=False)
def test_rank_too_large(self):
# svd(array, k) should not segfault
a = np.ones((4, 3))
with assert_raises(ValueError):
pymatrixid.svd(a, 4)
def test_full_rank(self):
eps = 1.0e-12
# fixed precision
A = np.random.rand(16, 8)
k, idx, proj = pymatrixid.interp_decomp(A, eps)
assert_equal(k, A.shape[1])
P = pymatrixid.reconstruct_interp_matrix(idx, proj)
B = pymatrixid.reconstruct_skel_matrix(A, k, idx)
assert_allclose(A, B @ P)
# fixed rank
idx, proj = pymatrixid.interp_decomp(A, k)
P = pymatrixid.reconstruct_interp_matrix(idx, proj)
B = pymatrixid.reconstruct_skel_matrix(A, k, idx)
assert_allclose(A, B @ P)
@pytest.mark.parametrize("dtype", [np.float64, np.complex128])
@pytest.mark.parametrize("rand", [True, False])
@pytest.mark.parametrize("eps", [1, 0.1])
def test_bug_9793(self, dtype, rand, eps):
A = np.array([[-1, -1, -1, 0, 0, 0],
[0, 0, 0, 1, 1, 1],
[1, 0, 0, 1, 0, 0],
[0, 1, 0, 0, 1, 0],
[0, 0, 1, 0, 0, 1]],
dtype=dtype, order="C")
B = A.copy()
interp_decomp(A.T, eps, rand=rand)
assert_array_equal(A, B)
|