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#******************************************************************************
# 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
import time
from numpy.testing import assert_, assert_allclose, assert_raises
def _debug_print(s):
if 0:
print(s)
class TestInterpolativeDecomposition(object):
def test_id(self):
for dtype in [np.float64, np.complex128]:
yield self.check_id, dtype
def check_id(self, dtype):
# Test ID routines on a Hilbert matrix.
# set parameters
n = 300
eps = 1e-12
# construct Hilbert matrix
A = hilbert(n).astype(dtype)
if np.issubdtype(dtype, np.complexfloating):
A = A * (1 + 1j)
L = aslinearoperator(A)
# find rank
S = np.linalg.svd(A, compute_uv=False)
try:
rank = np.nonzero(S < eps)[0][0]
except:
rank = n
# print input summary
_debug_print("Hilbert matrix dimension: %8i" % n)
_debug_print("Working precision: %8.2e" % eps)
_debug_print("Rank to working precision: %8i" % rank)
# set print format
fmt = "%8.2e (s) / %5s"
# test real ID routines
_debug_print("-----------------------------------------")
_debug_print("Real ID routines")
_debug_print("-----------------------------------------")
# fixed precision
_debug_print("Calling iddp_id / idzp_id ...",)
t0 = time.clock()
k, idx, proj = pymatrixid.interp_decomp(A, eps, rand=False)
t = time.clock() - t0
B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
_debug_print("Calling iddp_aid / idzp_aid ...",)
t0 = time.clock()
k, idx, proj = pymatrixid.interp_decomp(A, eps)
t = time.clock() - t0
B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
_debug_print("Calling iddp_rid / idzp_rid ...",)
t0 = time.clock()
k, idx, proj = pymatrixid.interp_decomp(L, eps)
t = time.clock() - t0
B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
# fixed rank
k = rank
_debug_print("Calling iddr_id / idzr_id ...",)
t0 = time.clock()
idx, proj = pymatrixid.interp_decomp(A, k, rand=False)
t = time.clock() - t0
B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
_debug_print("Calling iddr_aid / idzr_aid ...",)
t0 = time.clock()
idx, proj = pymatrixid.interp_decomp(A, k)
t = time.clock() - t0
B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
_debug_print("Calling iddr_rid / idzr_rid ...",)
t0 = time.clock()
idx, proj = pymatrixid.interp_decomp(L, k)
t = time.clock() - t0
B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
# check skeleton and interpolation matrices
idx, proj = pymatrixid.interp_decomp(A, k, rand=False)
P = pymatrixid.reconstruct_interp_matrix(idx, proj)
B = pymatrixid.reconstruct_skel_matrix(A, k, idx)
assert_(np.allclose(B, A[:,idx[:k]], eps))
assert_(np.allclose(B.dot(P), A, eps))
# test SVD routines
_debug_print("-----------------------------------------")
_debug_print("SVD routines")
_debug_print("-----------------------------------------")
# fixed precision
_debug_print("Calling iddp_svd / idzp_svd ...",)
t0 = time.clock()
U, S, V = pymatrixid.svd(A, eps, rand=False)
t = time.clock() - t0
B = np.dot(U, np.dot(np.diag(S), V.T.conj()))
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
_debug_print("Calling iddp_asvd / idzp_asvd...",)
t0 = time.clock()
U, S, V = pymatrixid.svd(A, eps)
t = time.clock() - t0
B = np.dot(U, np.dot(np.diag(S), V.T.conj()))
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
_debug_print("Calling iddp_rsvd / idzp_rsvd...",)
t0 = time.clock()
U, S, V = pymatrixid.svd(L, eps)
t = time.clock() - t0
B = np.dot(U, np.dot(np.diag(S), V.T.conj()))
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
# fixed rank
k = rank
_debug_print("Calling iddr_svd / idzr_svd ...",)
t0 = time.clock()
U, S, V = pymatrixid.svd(A, k, rand=False)
t = time.clock() - t0
B = np.dot(U, np.dot(np.diag(S), V.T.conj()))
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
_debug_print("Calling iddr_asvd / idzr_asvd ...",)
t0 = time.clock()
U, S, V = pymatrixid.svd(A, k)
t = time.clock() - t0
B = np.dot(U, np.dot(np.diag(S), V.T.conj()))
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
_debug_print("Calling iddr_rsvd / idzr_rsvd ...",)
t0 = time.clock()
U, S, V = pymatrixid.svd(L, k)
t = time.clock() - t0
B = np.dot(U, np.dot(np.diag(S), V.T.conj()))
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
# ID to SVD
idx, proj = pymatrixid.interp_decomp(A, k, rand=False)
Up, Sp, Vp = pymatrixid.id_to_svd(A[:, idx[:k]], idx, proj)
B = U.dot(np.diag(S).dot(V.T.conj()))
assert_(np.allclose(A, B, eps))
# Norm estimates
s = svdvals(A)
norm_2_est = pymatrixid.estimate_spectral_norm(A)
assert_(np.allclose(norm_2_est, s[0], 1e-6))
B = A.copy()
B[:,0] *= 1.2
s = svdvals(A - B)
norm_2_est = pymatrixid.estimate_spectral_norm_diff(A, B)
assert_(np.allclose(norm_2_est, s[0], 1e-6))
# Rank estimates
B = np.array([[1, 1, 0], [0, 0, 1], [0, 0, 1]], dtype=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(M, rank_tol)
rank_est_2 = pymatrixid.estimate_rank(ML, rank_tol)
assert_(rank_est >= rank_np)
assert_(rank_est <= rank_np + 10)
assert_(rank_est_2 >= rank_np - 4)
assert_(rank_est_2 <= rank_np + 4)
def test_rand(self):
pymatrixid.seed('default')
assert_(np.allclose(pymatrixid.rand(2), [0.8932059, 0.64500803], 1e-4))
pymatrixid.seed(1234)
x1 = pymatrixid.rand(2)
assert_(np.allclose(x1, [0.7513823, 0.06861718], 1e-4))
np.random.seed(1234)
pymatrixid.seed()
x2 = pymatrixid.rand(2)
np.random.seed(1234)
pymatrixid.seed(np.random.rand(55))
x3 = pymatrixid.rand(2)
assert_allclose(x1, x2)
assert_allclose(x1, x3)
def test_badcall(self):
A = hilbert(5).astype(np.float32)
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)
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