def test_svd_v0():
# check that the v0 parameter works as expected
x = np.array([[1, 2, 3, 4], [5, 6, 7, 8]], float)
u, s, vh = svds(x, 1)
u2, s2, vh2 = svds(x, 1, v0=u[:,0])
assert_allclose(s, s2, atol=np.sqrt(1e-15))
def test_svd_which():
# check that the which parameter works as expected
x = hilbert(6)
for which in ['LM', 'SM']:
_, s, _ = sorted_svd(x, 2, which=which)
ss = svds(x, 2, which=which, return_singular_vectors=False)
ss.sort()
assert_allclose(s, ss, atol=np.sqrt(1e-15))
def test_svd_maxiter():
# check that maxiter works as expected
x = hilbert(6)
# ARPACK shouldn't converge on such an ill-conditioned matrix with just
# one iteration
assert_raises(ArpackNoConvergence, svds, x, 1, maxiter=1)
# but 100 iterations should be more than enough
u, s, vt = svds(x, 1, maxiter=100)
assert_allclose(s, [1.7], atol=0.5)
def test_svd_LM_zeros_matrix():
# Check that svds can deal with matrices containing only zeros.
k = 1
for n, m in (3, 4), (4, 4), (4, 3):
for t in float, complex:
A = np.zeros((n, m), dtype=t)
U, s, VH = svds(A, k)
# Check some generic properties of svd.
_check_svds(A, k, U, s, VH)
# Check that the singular values are zero.
assert_array_equal(s, 0)
def test_svd_LM_zeros_matrix_gh_3452():
# Regression test for a github issue.
# https://github.com/scipy/scipy/issues/3452
# Note that for complex dype the size of this matrix is too small for k=1.
n, m, k = 4, 2, 1
A = np.zeros((n, m))
U, s, VH = svds(A, k)
# Check some generic properties of svd.
_check_svds(A, k, U, s, VH)
# Check that the singular values are zero.
assert_array_equal(s, 0)
def test_svd_simple_complex():
x = np.array([[1, 2, 3], [3, 4, 3], [1 + 1j, 0, 2], [0, 0, 1]], np.complex)
y = np.array([[1, 2, 3, 8 + 5j], [3 - 2j, 4, 3, 5], [1, 0, 2, 3], [0, 0, 1, 0]], np.complex)
z = csc_matrix(x)
for m in [x, x.T.conjugate(), x.T, y, y.conjugate(), z, z.T]:
for k in range(1, min(m.shape) - 1):
u, s, vh = sorted_svd(m, k)
su, ss, svh = svds(m, k)
m_hat = svd_estimate(u, s, vh)
sm_hat = svd_estimate(su, ss, svh)
assert_array_almost_equal_nulp(m_hat, sm_hat, nulp=1000)
def test_svd_simple_real():
x = np.array([[1, 2, 3], [3, 4, 3], [1, 0, 2], [0, 0, 1]], np.float)
y = np.array([[1, 2, 3, 8], [3, 4, 3, 5], [1, 0, 2, 3], [0, 0, 1, 0]], np.float)
z = csc_matrix(x)
for m in [x.T, x, y, z, z.T]:
for k in range(1, min(m.shape)):
u, s, vh = sorted_svd(m, k)
su, ss, svh = svds(m, k)
m_hat = svd_estimate(u, s, vh)
sm_hat = svd_estimate(su, ss, svh)
assert_array_almost_equal_nulp(m_hat, sm_hat, nulp=1000)
def test_svd_simple_real():
x = np.array([[1, 2, 3], [3, 4, 3], [1, 0, 2], [0, 0, 1]], float)
y = np.array([[1, 2, 3, 8], [3, 4, 3, 5], [1, 0, 2, 3], [0, 0, 1, 0]],
float)
z = csc_matrix(x)
for m in [x.T, x, y, z, z.T]:
for k in range(1, min(m.shape)):
u, s, vh = sorted_svd(m, k)
su, ss, svh = svds(m, k)
m_hat = svd_estimate(u, s, vh)
sm_hat = svd_estimate(su, ss, svh)
assert_array_almost_equal_nulp(m_hat, sm_hat, nulp=1000)
def test_svd_LM_ones_matrix():
# Check that svds can deal with matrix_rank less than k in LM mode.
k = 3
for n, m in (6, 5), (5, 5), (5, 6):
for t in float, complex:
A = np.ones((n, m), dtype=t)
U, s, VH = svds(A, k)
# Check some generic properties of svd.
_check_svds(A, k, U, s, VH)
# Check that the largest singular value is near sqrt(n*m)
# and the other singular values have been forced to zero.
assert_allclose(np.max(s), np.sqrt(n*m))
assert_array_equal(sorted(s)[:-1], 0)
def test_svd_LM_ones_matrix():
# Check that svds can deal with matrix_rank less than k in LM mode.
k = 3
for n, m in (6, 5), (5, 5), (5, 6):
for t in float, complex:
A = np.ones((n, m), dtype=t)
U, s, VH = svds(A, k)
# Check some generic properties of svd.
_check_svds(A, k, U, s, VH)
# Check that the largest singular value is near sqrt(n*m)
# and the other singular values have been forced to zero.
assert_allclose(np.max(s), np.sqrt(n*m))
assert_array_equal(sorted(s)[:-1], 0)
def test_svd_simple_complex():
x = np.array([[1, 2, 3], [3, 4, 3], [1 + 1j, 0, 2], [0, 0, 1]], complex)
y = np.array(
[[1, 2, 3, 8 + 5j], [3 - 2j, 4, 3, 5], [1, 0, 2, 3], [0, 0, 1, 0]],
complex)
z = csc_matrix(x)
for m in [x, x.T.conjugate(), x.T, y, y.conjugate(), z, z.T]:
for k in range(1, min(m.shape) - 1):
u, s, vh = sorted_svd(m, k)
su, ss, svh = svds(m, k)
m_hat = svd_estimate(u, s, vh)
sm_hat = svd_estimate(su, ss, svh)
assert_array_almost_equal_nulp(m_hat, sm_hat, nulp=1000)
def test_svd_linop():
nmks = [(6, 7, 3),
(9, 5, 4),
(10, 8, 5)]
def reorder(args):
U, s, VH = args
j = np.argsort(s)
return U[:,j], s[j], VH[j,:]
for n, m, k in nmks:
# Test svds on a LinearOperator.
A = np.random.RandomState(52).randn(n, m)
L = CheckingLinearOperator(A)
v0 = np.ones(min(A.shape))
U1, s1, VH1 = reorder(svds(A, k, v0=v0))
U2, s2, VH2 = reorder(svds(L, k, v0=v0))
assert_allclose(np.abs(U1), np.abs(U2))
assert_allclose(s1, s2)
assert_allclose(np.abs(VH1), np.abs(VH2))
assert_allclose(np.dot(U1, np.dot(np.diag(s1), VH1)),
np.dot(U2, np.dot(np.diag(s2), VH2)))
# Try again with which="SM".
A = np.random.RandomState(1909).randn(n, m)
L = CheckingLinearOperator(A)
U1, s1, VH1 = reorder(svds(A, k, which="SM"))
U2, s2, VH2 = reorder(svds(L, k, which="SM"))
assert_allclose(np.abs(U1), np.abs(U2))
assert_allclose(s1, s2)
assert_allclose(np.abs(VH1), np.abs(VH2))
assert_allclose(np.dot(U1, np.dot(np.diag(s1), VH1)),
np.dot(U2, np.dot(np.diag(s2), VH2)))
if k < min(n, m) - 1:
# Complex input and explicit which="LM".
for (dt, eps) in [(complex, 1e-7), (np.complex64, 1e-3)]:
rng = np.random.RandomState(1648)
A = (rng.randn(n, m) + 1j * rng.randn(n, m)).astype(dt)
L = CheckingLinearOperator(A)
U1, s1, VH1 = reorder(svds(A, k, which="LM"))
U2, s2, VH2 = reorder(svds(L, k, which="LM"))
assert_allclose(np.abs(U1), np.abs(U2), rtol=eps)
assert_allclose(s1, s2, rtol=eps)
assert_allclose(np.abs(VH1), np.abs(VH2), rtol=eps)
assert_allclose(np.dot(U1, np.dot(np.diag(s1), VH1)),
np.dot(U2, np.dot(np.diag(s2), VH2)), rtol=eps)
def test_svd_linop():
nmks = [(6, 7, 3),
(9, 5, 4),
(10, 8, 5)]
def reorder(args):
U, s, VH = args
j = np.argsort(s)
return U[:,j], s[j], VH[j,:]
for n, m, k in nmks:
# Test svds on a LinearOperator.
A = np.random.RandomState(52).randn(n, m)
L = CheckingLinearOperator(A)
v0 = np.ones(min(A.shape))
U1, s1, VH1 = reorder(svds(A, k, v0=v0))
U2, s2, VH2 = reorder(svds(L, k, v0=v0))
assert_allclose(np.abs(U1), np.abs(U2))
assert_allclose(s1, s2)
assert_allclose(np.abs(VH1), np.abs(VH2))
assert_allclose(np.dot(U1, np.dot(np.diag(s1), VH1)),
np.dot(U2, np.dot(np.diag(s2), VH2)))
# Try again with which="SM".
A = np.random.RandomState(1909).randn(n, m)
L = CheckingLinearOperator(A)
U1, s1, VH1 = reorder(svds(A, k, which="SM"))
U2, s2, VH2 = reorder(svds(L, k, which="SM"))
assert_allclose(np.abs(U1), np.abs(U2))
assert_allclose(s1, s2)
assert_allclose(np.abs(VH1), np.abs(VH2))
assert_allclose(np.dot(U1, np.dot(np.diag(s1), VH1)),
np.dot(U2, np.dot(np.diag(s2), VH2)))
if k < min(n, m) - 1:
# Complex input and explicit which="LM".
for (dt, eps) in [(complex, 1e-7), (np.complex64, 1e-3)]:
rng = np.random.RandomState(1648)
A = (rng.randn(n, m) + 1j * rng.randn(n, m)).astype(dt)
L = CheckingLinearOperator(A)
U1, s1, VH1 = reorder(svds(A, k, which="LM"))
U2, s2, VH2 = reorder(svds(L, k, which="LM"))
assert_allclose(np.abs(U1), np.abs(U2), rtol=eps)
assert_allclose(s1, s2, rtol=eps)
assert_allclose(np.abs(VH1), np.abs(VH2), rtol=eps)
assert_allclose(np.dot(U1, np.dot(np.diag(s1), VH1)),
np.dot(U2, np.dot(np.diag(s2), VH2)), rtol=eps)
def test_svds_partial_return():
x = np.array([[1, 2, 3],
[3, 4, 3],
[1, 0, 2],
[0, 0, 1]], np.float)
# test vertical matrix
z = csr_matrix(x)
vh_full = svds(z, 2)[-1]
vh_partial = svds(z, 2, return_singular_vectors='vh')[-1]
dvh = np.linalg.norm(np.abs(vh_full) - np.abs(vh_partial))
if dvh > 1e-10:
raise AssertionError('right eigenvector matrices differ when using return_singular_vectors parameter')
if svds(z, 2, return_singular_vectors='vh')[0] is not None:
raise AssertionError('left eigenvector matrix was computed when it should not have been')
# test horizontal matrix
z = csr_matrix(x.T)
u_full = svds(z, 2)[0]
u_partial = svds(z, 2, return_singular_vectors='vh')[0]
du = np.linalg.norm(np.abs(u_full) - np.abs(u_partial))
if du > 1e-10:
raise AssertionError('left eigenvector matrices differ when using return_singular_vectors parameter')
if svds(z, 2, return_singular_vectors='u')[-1] is not None:
raise AssertionError('right eigenvector matrix was computed when it should not have been')
def test_svds_partial_return():
x = np.array([[1, 2, 3],
[3, 4, 3],
[1, 0, 2],
[0, 0, 1]], np.float)
# test vertical matrix
z = csr_matrix(x)
vh_full = svds(z, 2)[-1]
vh_partial = svds(z, 2, return_singular_vectors='vh')[-1]
dvh = np.linalg.norm(np.abs(vh_full) - np.abs(vh_partial))
if dvh > 1e-10:
raise AssertionError('right eigenvector matrices differ when using return_singular_vectors parameter')
if svds(z, 2, return_singular_vectors='vh')[0] is not None:
raise AssertionError('left eigenvector matrix was computed when it should not have been')
# test horizontal matrix
z = csr_matrix(x.T)
u_full = svds(z, 2)[0]
u_partial = svds(z, 2, return_singular_vectors='vh')[0]
du = np.linalg.norm(np.abs(u_full) - np.abs(u_partial))
if du > 1e-10:
raise AssertionError('left eigenvector matrices differ when using return_singular_vectors parameter')
if svds(z, 2, return_singular_vectors='u')[-1] is not None:
raise AssertionError('right eigenvector matrix was computed when it should not have been')
def test_svd_return():
# check that the return_singular_vectors parameter works as expected
x = hilbert(6)
_, s, _ = sorted_svd(x, 2)
ss = svds(x, 2, return_singular_vectors=False)
assert_allclose(s, ss)
def test_svd_return():
# check that the return_singular_vectors parameter works as expected
x = hilbert(6)
_, s, _ = sorted_svd(x, 2)
ss = svds(x, 2, return_singular_vectors=False)
assert_allclose(s, ss)
