def test_real_spectrum_gives_self_adjoint_operator(self):
with self.cached_session():
# This is a real and hermitian spectrum.
spectrum = linear_operator_test_util.random_normal(
shape=(2, 2, 3, 5), dtype=dtypes.float32)
operator = linalg.LinearOperatorCirculant3D(spectrum)
self.assertAllEqual((2, 2 * 3 * 5, 2 * 3 * 5), operator.shape)
self.assertEqual(
operator.parameters, {
"input_output_dtype": dtypes.complex64,
"is_non_singular": None,
"is_positive_definite": None,
"is_self_adjoint": None,
"is_square": True,
"name": "LinearOperatorCirculant3D",
"spectrum": spectrum,
})
matrix_tensor = operator.to_dense()
self.assertEqual(matrix_tensor.dtype, dtypes.complex64)
matrix_h = linalg.adjoint(matrix_tensor)
matrix, matrix_h = self.evaluate([matrix_tensor, matrix_h])
self.assertAllEqual((2, 2 * 3 * 5, 2 * 3 * 5), matrix.shape)
self.assertAllClose(matrix, matrix_h)
def test_compare_to_numpy(self):
for dtype in np.float64, np.float64, np.complex64, np.complex128:
matrix_np = np.array([[1 + 1j, 2 + 2j, 3 + 3j], [4 + 4j, 5 + 5j,
6 + 6j]]).astype(dtype)
expected_transposed = np.conj(matrix_np.T)
with self.session():
matrix = ops.convert_to_tensor(matrix_np)
transposed = linalg.adjoint(matrix)
self.assertEqual((3, 2), transposed.get_shape())
self.assertAllEqual(expected_transposed, self.evaluate(transposed))
def test_simple_positive_real_spectrum_gives_self_adjoint_pos_def_oper(self):
with self.cached_session() as sess:
spectrum = math_ops.cast([6., 4, 2], dtypes.complex64)
operator = linalg.LinearOperatorCirculant(
spectrum, input_output_dtype=dtypes.complex64)
matrix, matrix_h = sess.run(
[operator.to_dense(),
linalg.adjoint(operator.to_dense())])
self.assertAllClose(matrix, matrix_h)
operator.assert_positive_definite().run() # Should not fail
operator.assert_self_adjoint().run() # Should not fail
def test_simple_positive_real_spectrum_gives_self_adjoint_pos_def_oper(self):
with self.cached_session() as sess:
spectrum = math_ops.cast([6., 4, 2], dtypes.complex64)
operator = linalg.LinearOperatorCirculant(
spectrum, input_output_dtype=dtypes.complex64)
matrix, matrix_h = sess.run(
[operator.to_dense(),
linalg.adjoint(operator.to_dense())])
self.assertAllClose(matrix, matrix_h)
operator.assert_positive_definite().run() # Should not fail
operator.assert_self_adjoint().run() # Should not fail
def test_real_spectrum_gives_self_adjoint_operator(self):
with self.cached_session():
# This is a real and hermitian spectrum.
spectrum = linear_operator_test_util.random_normal(
shape=(3, 3), dtype=dtypes.float32)
operator = linalg.LinearOperatorCirculant2D(spectrum)
matrix_tensor = operator.to_dense()
self.assertEqual(matrix_tensor.dtype, dtypes.complex64)
matrix_h = linalg.adjoint(matrix_tensor)
matrix, matrix_h = self.evaluate([matrix_tensor, matrix_h])
self.assertAllClose(matrix, matrix_h, atol=0)
def test_real_spectrum_gives_self_adjoint_operator(self):
with self.cached_session():
# This is a real and hermitian spectrum.
spectrum = linear_operator_test_util.random_normal(
shape=(3, 3), dtype=dtypes.float32)
operator = linalg.LinearOperatorCirculant2D(spectrum)
matrix_tensor = operator.to_dense()
self.assertEqual(matrix_tensor.dtype, dtypes.complex64)
matrix_h = linalg.adjoint(matrix_tensor)
matrix, matrix_h = self.evaluate([matrix_tensor, matrix_h])
self.assertAllClose(matrix, matrix_h, atol=0)
def test_real_spectrum_gives_self_adjoint_operator(self):
with self.test_session() as sess:
# This is a real and hermitian spectrum.
spectrum = linear_operator_test_util.random_normal(
shape=(3, 3), dtype=dtypes.float32)
operator = linalg.LinearOperatorCirculant2D(spectrum)
matrix_tensor = operator.to_dense()
self.assertEqual(matrix_tensor.dtype,
linear_operator_circulant._DTYPE_COMPLEX)
matrix_h = linalg.adjoint(matrix_tensor)
matrix, matrix_h = sess.run([matrix_tensor, matrix_h])
self.assertAllClose(matrix, matrix_h, atol=0)
def test_real_spectrum_gives_self_adjoint_operator(self):
with self.test_session() as sess:
# This is a real and hermitian spectrum.
spectrum = linear_operator_test_util.random_normal(
shape=(3, 3), dtype=dtypes.float32)
operator = linalg.LinearOperatorCirculant2D(spectrum)
matrix_tensor = operator.to_dense()
self.assertEqual(matrix_tensor.dtype,
linear_operator_circulant._DTYPE_COMPLEX)
matrix_h = linalg.adjoint(matrix_tensor)
matrix, matrix_h = sess.run([matrix_tensor, matrix_h])
self.assertAllClose(matrix, matrix_h, atol=0)
def test_real_spectrum_gives_self_adjoint_operator(self):
with self.cached_session() as sess:
# This is a real and hermitian spectrum.
spectrum = linear_operator_test_util.random_normal(
shape=(2, 2, 3, 5), dtype=dtypes.float32)
operator = linalg.LinearOperatorCirculant3D(spectrum)
self.assertAllEqual((2, 2 * 3 * 5, 2 * 3 * 5), operator.shape)
matrix_tensor = operator.to_dense()
self.assertEqual(matrix_tensor.dtype,
linear_operator_circulant._DTYPE_COMPLEX)
matrix_h = linalg.adjoint(matrix_tensor)
matrix, matrix_h = self.evaluate([matrix_tensor, matrix_h])
self.assertAllEqual((2, 2 * 3 * 5, 2 * 3 * 5), matrix.shape)
self.assertAllClose(matrix, matrix_h)
def test_real_spectrum_gives_self_adjoint_operator(self):
with self.cached_session() as sess:
# This is a real and hermitian spectrum.
spectrum = linear_operator_test_util.random_normal(
shape=(2, 2, 3, 5), dtype=dtypes.float32)
operator = linalg.LinearOperatorCirculant3D(spectrum)
self.assertAllEqual((2, 2 * 3 * 5, 2 * 3 * 5), operator.shape)
matrix_tensor = operator.to_dense()
self.assertEqual(matrix_tensor.dtype,
linear_operator_circulant._DTYPE_COMPLEX)
matrix_h = linalg.adjoint(matrix_tensor)
matrix, matrix_h = self.evaluate([matrix_tensor, matrix_h])
self.assertAllEqual((2, 2 * 3 * 5, 2 * 3 * 5), matrix.shape)
self.assertAllClose(matrix, matrix_h)
def TriAngSolveCompositeGrad(l, grad):
# Gradient is l^{-H} @ ((l^{H} @ grad) * (tril(ones)-1/2*eye)) @ l^{-1}
# Compute ((l^{H} @ grad) * (tril(ones)-1/2*eye)) = middle
middle = math_ops.matmul(l, grad, adjoint_a=True)
middle = array_ops.matrix_set_diag(middle,
0.5 * array_ops.matrix_diag_part(middle))
middle = array_ops.matrix_band_part(middle, -1, 0)
# Compute l^{-H} @ middle = z
l_inverse_middle = linalg_ops.matrix_triangular_solve(l, middle, adjoint=True)
# We need to compute z @ l^{-1}. With matrix_triangular_solve we
# actually compute l^{-H} @ z^{H} = grad. Since we later add grad^{H}
# we can ommit the conjugate transpose here.
z_h = math_ops.conj(array_ops.matrix_transpose(l_inverse_middle))
grad_a = linalg_ops.matrix_triangular_solve(l, z_h, adjoint=True)
grad_a += linalg.adjoint(grad_a)
return grad_a * 0.5
def test_real_spectrum_gives_self_adjoint_operator(self):
if test.is_built_with_rocm():
# ROCm does not yet support BLAS operations with complext types
self.skipTest("ROCm does not support BLAS operations for complex types")
with self.cached_session():
# This is a real and hermitian spectrum.
spectrum = linear_operator_test_util.random_normal(
shape=(2, 2, 3, 5), dtype=dtypes.float32)
operator = linalg.LinearOperatorCirculant3D(spectrum)
self.assertAllEqual((2, 2 * 3 * 5, 2 * 3 * 5), operator.shape)
matrix_tensor = operator.to_dense()
self.assertEqual(matrix_tensor.dtype, dtypes.complex64)
matrix_h = linalg.adjoint(matrix_tensor)
matrix, matrix_h = self.evaluate([matrix_tensor, matrix_h])
self.assertAllEqual((2, 2 * 3 * 5, 2 * 3 * 5), matrix.shape)
self.assertAllClose(matrix, matrix_h)
