295 lines
11 KiB
Python
295 lines
11 KiB
Python
#******************************************************************************
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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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import time
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import itertools
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from numpy.testing import assert_, assert_allclose
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from pytest import raises as assert_raises
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def _debug_print(s):
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if 0:
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print(s)
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class TestInterpolativeDecomposition(object):
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def test_id(self):
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for dtype in [np.float64, np.complex128]:
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self.check_id(dtype)
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def check_id(self, dtype):
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# Test ID routines on a Hilbert matrix.
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# set parameters
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n = 300
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eps = 1e-12
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# construct Hilbert matrix
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A = hilbert(n).astype(dtype)
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if np.issubdtype(dtype, np.complexfloating):
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A = A * (1 + 1j)
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L = aslinearoperator(A)
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# find rank
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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 = n
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# print input summary
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_debug_print("Hilbert matrix dimension: %8i" % n)
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_debug_print("Working precision: %8.2e" % eps)
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_debug_print("Rank to working precision: %8i" % rank)
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# set print format
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fmt = "%8.2e (s) / %5s"
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# test real ID routines
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_debug_print("-----------------------------------------")
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_debug_print("Real ID routines")
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_debug_print("-----------------------------------------")
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# fixed precision
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_debug_print("Calling iddp_id / idzp_id ...",)
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t0 = time.time()
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k, idx, proj = pymatrixid.interp_decomp(A, eps, rand=False)
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t = time.time() - t0
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B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
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_debug_print(fmt % (t, np.allclose(A, B, eps)))
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assert_(np.allclose(A, B, eps))
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_debug_print("Calling iddp_aid / idzp_aid ...",)
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t0 = time.time()
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k, idx, proj = pymatrixid.interp_decomp(A, eps)
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t = time.time() - t0
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B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
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_debug_print(fmt % (t, np.allclose(A, B, eps)))
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assert_(np.allclose(A, B, eps))
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_debug_print("Calling iddp_rid / idzp_rid ...",)
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t0 = time.time()
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k, idx, proj = pymatrixid.interp_decomp(L, eps)
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t = time.time() - t0
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B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
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_debug_print(fmt % (t, np.allclose(A, B, eps)))
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assert_(np.allclose(A, B, eps))
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# fixed rank
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k = rank
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_debug_print("Calling iddr_id / idzr_id ...",)
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t0 = time.time()
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idx, proj = pymatrixid.interp_decomp(A, k, rand=False)
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t = time.time() - t0
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B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
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_debug_print(fmt % (t, np.allclose(A, B, eps)))
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assert_(np.allclose(A, B, eps))
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_debug_print("Calling iddr_aid / idzr_aid ...",)
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t0 = time.time()
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idx, proj = pymatrixid.interp_decomp(A, k)
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t = time.time() - t0
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B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
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_debug_print(fmt % (t, np.allclose(A, B, eps)))
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assert_(np.allclose(A, B, eps))
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_debug_print("Calling iddr_rid / idzr_rid ...",)
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t0 = time.time()
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idx, proj = pymatrixid.interp_decomp(L, k)
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t = time.time() - t0
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B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
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_debug_print(fmt % (t, np.allclose(A, B, eps)))
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assert_(np.allclose(A, B, eps))
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# check skeleton and interpolation matrices
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idx, proj = pymatrixid.interp_decomp(A, k, rand=False)
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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_(np.allclose(B, A[:,idx[:k]], eps))
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assert_(np.allclose(B.dot(P), A, eps))
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# test SVD routines
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_debug_print("-----------------------------------------")
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_debug_print("SVD routines")
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_debug_print("-----------------------------------------")
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# fixed precision
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_debug_print("Calling iddp_svd / idzp_svd ...",)
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t0 = time.time()
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U, S, V = pymatrixid.svd(A, eps, rand=False)
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t = time.time() - t0
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B = np.dot(U, np.dot(np.diag(S), V.T.conj()))
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_debug_print(fmt % (t, np.allclose(A, B, eps)))
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assert_(np.allclose(A, B, eps))
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_debug_print("Calling iddp_asvd / idzp_asvd...",)
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t0 = time.time()
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U, S, V = pymatrixid.svd(A, eps)
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t = time.time() - t0
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B = np.dot(U, np.dot(np.diag(S), V.T.conj()))
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_debug_print(fmt % (t, np.allclose(A, B, eps)))
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assert_(np.allclose(A, B, eps))
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_debug_print("Calling iddp_rsvd / idzp_rsvd...",)
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t0 = time.time()
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U, S, V = pymatrixid.svd(L, eps)
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t = time.time() - t0
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B = np.dot(U, np.dot(np.diag(S), V.T.conj()))
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_debug_print(fmt % (t, np.allclose(A, B, eps)))
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assert_(np.allclose(A, B, eps))
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# fixed rank
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k = rank
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_debug_print("Calling iddr_svd / idzr_svd ...",)
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t0 = time.time()
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U, S, V = pymatrixid.svd(A, k, rand=False)
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t = time.time() - t0
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B = np.dot(U, np.dot(np.diag(S), V.T.conj()))
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_debug_print(fmt % (t, np.allclose(A, B, eps)))
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assert_(np.allclose(A, B, eps))
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_debug_print("Calling iddr_asvd / idzr_asvd ...",)
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t0 = time.time()
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U, S, V = pymatrixid.svd(A, k)
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t = time.time() - t0
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B = np.dot(U, np.dot(np.diag(S), V.T.conj()))
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_debug_print(fmt % (t, np.allclose(A, B, eps)))
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assert_(np.allclose(A, B, eps))
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_debug_print("Calling iddr_rsvd / idzr_rsvd ...",)
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t0 = time.time()
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U, S, V = pymatrixid.svd(L, k)
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t = time.time() - t0
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B = np.dot(U, np.dot(np.diag(S), V.T.conj()))
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_debug_print(fmt % (t, np.allclose(A, B, eps)))
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assert_(np.allclose(A, B, eps))
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# ID to SVD
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idx, proj = pymatrixid.interp_decomp(A, k, rand=False)
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Up, Sp, Vp = pymatrixid.id_to_svd(A[:, idx[:k]], idx, proj)
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B = U.dot(np.diag(S).dot(V.T.conj()))
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assert_(np.allclose(A, B, eps))
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# Norm estimates
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s = svdvals(A)
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norm_2_est = pymatrixid.estimate_spectral_norm(A)
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assert_(np.allclose(norm_2_est, s[0], 1e-6))
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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_(np.allclose(norm_2_est, s[0], 1e-6))
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# Rank estimates
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B = np.array([[1, 1, 0], [0, 0, 1], [0, 0, 1]], dtype=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(M, rank_tol)
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rank_est_2 = pymatrixid.estimate_rank(ML, 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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assert_(rank_est_2 >= rank_np - 4)
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assert_(rank_est_2 <= rank_np + 4)
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def test_rand(self):
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pymatrixid.seed('default')
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assert_(np.allclose(pymatrixid.rand(2), [0.8932059, 0.64500803], 1e-4))
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pymatrixid.seed(1234)
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x1 = pymatrixid.rand(2)
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assert_(np.allclose(x1, [0.7513823, 0.06861718], 1e-4))
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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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assert_raises(ValueError, 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_(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.dot(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.dot(P))
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def test_bug_9793(self):
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dtypes = [np.float_, np.complex_]
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rands = [True, False]
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epss = [1, 0.1]
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for dtype, eps, rand in itertools.product(dtypes, epss, rands):
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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_(np.array_equal(A, B))
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