def test_matrix_log(self):
M = np.array([[-1, 0], [0, -1]],
'complex') # degenerate negative evals
mt.real_matrix_log(M, actionIfImaginary="raise", TOL=1e-6)
M = np.array(
[[-1, 1e-10], [1e-10, -1]], 'complex'
) # degenerate negative evals, but will generate complex evecs
mt.real_matrix_log(M, actionIfImaginary="raise", TOL=1e-6)
M = np.array(
[[1, 0], [0, -1]],
'd') # a negative *unparied* eigenvalue => log may be imaginary
mt.real_matrix_log(M, actionIfImaginary="ignore", TOL=1e-6)
self.assertWarns(mt.real_matrix_log,
M,
actionIfImaginary="warn",
TOL=1e-6)
with self.assertRaises(ValueError):
mt.real_matrix_log(M, actionIfImaginary="raise", TOL=1e-6)
with self.assertRaises(AssertionError):
mt.real_matrix_log(M, actionIfImaginary="foobar", TOL=1e-6)
def test_matrix_log(self):
M = np.array([[-1, 0], [0, -1]],
'complex') # degenerate negative evals
logM = mt.real_matrix_log(M, action_if_imaginary="raise", tol=1e-6)
self.assertArraysAlmostEqual(spl.expm(logM), M)
M = np.array(
[[-1, 1e-10], [1e-10, -1]], 'complex'
) # degenerate negative evals, but will generate complex evecs
logM = mt.real_matrix_log(M, action_if_imaginary="raise", tol=1e-6)
self.assertArraysAlmostEqual(spl.expm(logM), M)
with self.assertRaises(ValueError):
M = np.array([
[1, 0], [0, -1]
], 'd') # a negative *unparied* eigenvalue => log may be imaginary
mt.real_matrix_log(M, action_if_imaginary="raise", tol=1e-6)
M = np.array(
[[1, 0], [0, -1]],
'd') # a negative *unparied* eigenvalue => log may be imaginary
logM = mt.real_matrix_log(M, action_if_imaginary="ignore", tol=1e-6)
self.assertArraysAlmostEqual(spl.expm(logM), M)
def test_nullspace(self):
a = np.array([[1, 1], [1, 1]])
print("Nullspace = ", mt.nullspace(a))
expected = np.array([[0.70710678], [-0.70710678]])
diff1 = np.linalg.norm(mt.nullspace(a) - expected)
diff2 = np.linalg.norm(
mt.nullspace(a) +
expected) # -1*expected is OK too (just an eigenvector)
self.assertTrue(np.isclose(diff1, 0) or np.isclose(diff2, 0))
diff1 = np.linalg.norm(mt.nullspace_qr(a) - expected)
diff2 = np.linalg.norm(
mt.nullspace_qr(a) +
expected) # -1*expected is OK too (just an eigenvector)
self.assertTrue(np.isclose(diff1, 0) or np.isclose(diff2, 0))
mt.print_mx(a)
b = np.array([[1, 2], [3, 4]], dtype='complex')
with self.assertRaises(ValueError):
mt.real_matrix_log(b)
with self.assertRaises(AssertionError):
mt.real_matrix_log(a)
def test_matrix_log(self):
M = np.array([[-1, 0], [0, -1]],
'complex') # degenerate negative evals
mt.real_matrix_log(M, actionIfImaginary="raise", TOL=1e-6)
# TODO assert correctness
M = np.array(
[[-1, 1e-10], [1e-10, -1]], 'complex'
) # degenerate negative evals, but will generate complex evecs
mt.real_matrix_log(M, actionIfImaginary="raise", TOL=1e-6)
# TODO assert correctness
M = np.array(
[[1, 0], [0, -1]],
'd') # a negative *unparied* eigenvalue => log may be imaginary
mt.real_matrix_log(M, actionIfImaginary="ignore", TOL=1e-6)
def test_matrix_log_raise_on_no_real_log(self):
a = np.array([[1, 1], [1, 1]])
with self.assertRaises(AssertionError):
mt.real_matrix_log(a)
def test_matrix_log_raises_on_invalid_action(self):
M = np.array([[1, 0], [0, -1]], 'd')
with self.assertRaises(AssertionError):
mt.real_matrix_log(M, actionIfImaginary="foobar", TOL=1e-6)
def test_matrix_log_raises_on_imaginary(self):
M = np.array([[1, 0], [0, -1]], 'd')
with self.assertRaises(ValueError):
mt.real_matrix_log(M, actionIfImaginary="raise", TOL=1e-6)
