def test_zcsr_isherm():
"spmath: zcsr_isherm"
N = 100
for kk in range(100):
A = rand_herm(N, 0.1)
B = rand_herm(N, 0.05) + 1j * rand_herm(N, 0.05)
assert_(zcsr_isherm(A.data))
assert_(zcsr_isherm(B.data) == 0)
def test_zcsr_isherm():
"spmath: zcsr_isherm"
N = 100
for kk in range(100):
A = rand_herm(N, 0.1)
B = rand_herm(N, 0.05) + 1j*rand_herm(N, 0.05)
assert_(zcsr_isherm(A.data))
assert_(zcsr_isherm(B.data)==0)
def test_zcsr_isherm_compare_implicit_zero():
"""
Regression test for gh-1350, comparing explicitly stored values in the
matrix (but below the tolerance for allowable Hermicity) to implicit zeros.
"""
tol = 1e-12
n = 10
base = sp.csr_matrix(np.array([[1, tol * 1e-3j], [0, 1]]))
base = fast_csr_matrix((base.data, base.indices, base.indptr), base.shape)
# If this first line fails, the zero has been stored explicitly and so the
# test is invalid.
assert base.data.size == 3
assert zcsr_isherm(base, tol=tol)
assert zcsr_isherm(base.T, tol=tol)
# A similar test if the structures are different, but it's not
# Hermitian.
base = sp.csr_matrix(np.array([[1, 1j], [0, 1]]))
base = fast_csr_matrix((base.data, base.indices, base.indptr), base.shape)
assert base.data.size == 3
assert not zcsr_isherm(base, tol=tol)
assert not zcsr_isherm(base.T, tol=tol)
# Catch possible edge case where it shouldn't be Hermitian, but faulty loop
# logic doesn't fully compare all rows.
base = sp.csr_matrix(
np.array([
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 0, 0],
],
dtype=np.complex128))
base = fast_csr_matrix((base.data, base.indices, base.indptr), base.shape)
assert base.data.size == 1
assert not zcsr_isherm(base, tol=tol)
assert not zcsr_isherm(base.T, tol=tol)
# Pure diagonal matrix.
base = fast_identity(n)
base.data *= np.random.rand(n)
assert zcsr_isherm(base, tol=tol)
assert not zcsr_isherm(base * 1j, tol=tol)
# Larger matrices where all off-diagonal elements are below the absolute
# tolerance, so everything should always appear Hermitian, but with random
# patterns of non-zero elements. It doesn't matter that it isn't Hermitian
# if scaled up; everything is below absolute tolerance, so it should appear
# so. We also set the diagonal to be larger to the tolerance to ensure
# isherm can't just compare everything to zero.
for density in np.linspace(0.2, 1, 21):
base = tol * 1e-2 * (np.random.rand(n, n) + 1j * np.random.rand(n, n))
# Mask some values out to zero.
base[np.random.rand(n, n) > density] = 0
np.fill_diagonal(base, tol * 1000)
nnz = np.count_nonzero(base)
base = sp.csr_matrix(base)
base = fast_csr_matrix((base.data, base.indices, base.indptr), (n, n))
assert base.data.size == nnz
assert zcsr_isherm(base, tol=tol)
assert zcsr_isherm(base.T, tol=tol)
# Similar test when it must be non-Hermitian. We set the diagonal to
# be real because we want to test off-diagonal implicit zeros, and
# having an imaginary first element would automatically fail.
nnz = 0
while nnz <= n:
# Ensure that we don't just have the real diagonal.
base = tol * 1000j * np.random.rand(n, n)
# Mask some values out to zero.
base[np.random.rand(n, n) > density] = 0
np.fill_diagonal(base, tol * 1000)
nnz = np.count_nonzero(base)
base = sp.csr_matrix(base)
base = fast_csr_matrix((base.data, base.indices, base.indptr), (n, n))
assert base.data.size == nnz
assert not zcsr_isherm(base, tol=tol)
assert not zcsr_isherm(base.T, tol=tol)