def testPivoting(self):
with test_util.use_gpu():
# This matrix triggers partial pivoting because the first diagonal entry
# is small.
data = np.array([[1e-9, 1., 0.], [1., 0., 0], [0., 1., 5]])
self._verifyLu(data.astype(np.float32))
for dtype in (np.float32, np.float64):
self._verifyLu(data.astype(dtype))
_, p = linalg_ops.lu(data)
p_val = self.evaluate([p])
# Make sure p_val is not the identity permutation.
self.assertNotAllClose(np.arange(3), p_val)
# rocBLAS on ROCm stack doesn't support complex64 and complex128 types
if not test.is_built_with_rocm():
for dtype in (np.complex64, np.complex128):
complex_data = np.tril(1j * data, -1).astype(dtype)
complex_data += np.triu(-1j * data, 1).astype(dtype)
complex_data += data
self._verifyLu(complex_data)
_, p = linalg_ops.lu(data)
p_val = self.evaluate([p])
# Make sure p_val is not the identity permutation.
self.assertNotAllClose(np.arange(3), p_val)
def benchmarkLuOp(self):
for shape in self.shapes:
with ops.Graph().as_default(), \
session.Session(config=benchmark.benchmark_config()) as sess, \
ops.device("/cpu:0"):
matrix = variables.Variable(self._GenerateMatrix(shape))
lu, p = linalg_ops.lu(matrix)
variables.global_variables_initializer().run()
self.run_op_benchmark(
sess,
control_flow_ops.group(lu, p),
min_iters=25,
name="lu_cpu_{shape}".format(shape=shape))
if test.is_gpu_available(True):
with ops.Graph().as_default(), \
session.Session(config=benchmark.benchmark_config()) as sess, \
ops.device("/device:GPU:0"):
matrix = variables.Variable(self._GenerateMatrix(shape))
lu, p = linalg_ops.lu(matrix)
variables.global_variables_initializer().run()
self.run_op_benchmark(
sess,
control_flow_ops.group(lu, p),
min_iters=25,
name="lu_gpu_{shape}".format(shape=shape))
def benchmarkLuOp(self):
for shape in self.shapes:
with ops.Graph().as_default(), \
session.Session(config=benchmark.benchmark_config()) as sess, \
ops.device("/cpu:0"):
matrix = variables.Variable(self._GenerateMatrix(shape))
lu, p = linalg_ops.lu(matrix)
variables.global_variables_initializer().run()
self.run_op_benchmark(
sess,
control_flow_ops.group(lu, p),
min_iters=25,
name="lu_cpu_{shape}".format(shape=shape))
if test.is_gpu_available(True):
with ops.Graph().as_default(), \
session.Session(config=benchmark.benchmark_config()) as sess, \
ops.device("/device:GPU:0"):
matrix = variables.Variable(self._GenerateMatrix(shape))
lu, p = linalg_ops.lu(matrix)
variables.global_variables_initializer().run()
self.run_op_benchmark(
sess,
control_flow_ops.group(lu, p),
min_iters=25,
name="lu_gpu_{shape}".format(shape=shape))
def testConcurrentExecutesWithoutError(self):
matrix1 = random_ops.random_normal([5, 5], seed=42)
matrix2 = random_ops.random_normal([5, 5], seed=42)
lu1, p1 = linalg_ops.lu(matrix1)
lu2, p2 = linalg_ops.lu(matrix2)
lu1_val, p1_val, lu2_val, p2_val = self.evaluate([lu1, p1, lu2, p2])
self.assertAllEqual(lu1_val, lu2_val)
self.assertAllEqual(p1_val, p2_val)
def testConcurrentExecutesWithoutError(self): matrix1 = random_ops.random_normal([5, 5], seed=42) matrix2 = random_ops.random_normal([5, 5], seed=42) lu1, p1 = linalg_ops.lu(matrix1) lu2, p2 = linalg_ops.lu(matrix2) lu1_val, p1_val, lu2_val, p2_val = self.evaluate([lu1, p1, lu2, p2]) self.assertAllEqual(lu1_val, lu2_val) self.assertAllEqual(p1_val, p2_val)
def testConcurrentExecutesWithoutError(self):
with self.session(use_gpu=True) as sess:
matrix1 = random_ops.random_normal([5, 5], seed=42)
matrix2 = random_ops.random_normal([5, 5], seed=42)
lu1, p1 = linalg_ops.lu(matrix1)
lu2, p2 = linalg_ops.lu(matrix2)
lu1_val, p1_val, lu2_val, p2_val = sess.run([lu1, p1, lu2, p2])
self.assertAllEqual(lu1_val, lu2_val)
self.assertAllEqual(p1_val, p2_val)
def testConcurrentExecutesWithoutError(self):
matrix_shape = [5, 5]
seed = [42, 24]
matrix1 = stateless_random_ops.stateless_random_normal(
shape=matrix_shape, seed=seed)
matrix2 = stateless_random_ops.stateless_random_normal(
shape=matrix_shape, seed=seed)
self.assertAllEqual(matrix1, matrix2)
lu1, p1 = linalg_ops.lu(matrix1)
lu2, p2 = linalg_ops.lu(matrix2)
lu1_val, p1_val, lu2_val, p2_val = self.evaluate([lu1, p1, lu2, p2])
self.assertAllEqual(lu1_val, lu2_val)
self.assertAllEqual(p1_val, p2_val)
def testInvalidMatrix(self):
# LU factorization gives an error when the input is singular.
# Note: A singular matrix may return without error but it won't be a valid
# factorization.
for dtype in self.float_types:
with self.assertRaises(errors.InvalidArgumentError):
self.evaluate(
linalg_ops.lu(
np.array([[1., 2., 3.], [2., 4., 6.], [2., 3., 4.]],
dtype=dtype)))
with self.assertRaises(errors.InvalidArgumentError):
self.evaluate(
linalg_ops.lu(
np.array([[[1., 2., 3.], [2., 4., 6.], [1., 2., 3.]],
[[1., 2., 3.], [3., 4., 5.], [5., 6., 7.]]],
dtype=dtype)))
def testInvalidMatrix(self):
# LU factorization gives an error when the input is singular.
# Note: A singular matrix may return without error but it won't be a valid
# factorization.
for dtype in self.float_types:
with self.assertRaises(errors.InvalidArgumentError):
self.evaluate(
linalg_ops.lu(
np.array([[1., 2., 3.], [2., 4., 6.], [2., 3., 4.]],
dtype=dtype)))
with self.assertRaises(errors.InvalidArgumentError):
self.evaluate(
linalg_ops.lu(
np.array([[[1., 2., 3.], [2., 4., 6.], [1., 2., 3.]],
[[1., 2., 3.], [3., 4., 5.], [5., 6., 7.]]],
dtype=dtype)))
def _verifyLu(self, x, output_idx_type=dtypes.int64):
# Verify that Px = LU.
lu, perm = linalg_ops.lu(x, output_idx_type=output_idx_type)
# Prepare the lower factor of shape num_rows x num_rows
lu_shape = np.array(lu.shape.as_list())
batch_shape = lu_shape[:-2]
num_rows = lu_shape[-2]
num_cols = lu_shape[-1]
lower = array_ops.matrix_band_part(lu, -1, 0)
if num_rows > num_cols:
eye = linalg_ops.eye(num_rows,
batch_shape=batch_shape,
dtype=lower.dtype)
lower = array_ops.concat([lower, eye[..., num_cols:]], axis=-1)
elif num_rows < num_cols:
lower = lower[..., :num_rows]
# Fill the diagonal with ones.
ones_diag = array_ops.ones(np.append(batch_shape, num_rows),
dtype=lower.dtype)
lower = array_ops.matrix_set_diag(lower, ones_diag)
# Prepare the upper factor.
upper = array_ops.matrix_band_part(lu, 0, -1)
verification = test_util.matmul_without_tf32(lower, upper)
# Permute the rows of product of the Cholesky factors.
if num_rows > 0:
# Reshape the product of the triangular factors and permutation indices
# to a single batch dimension. This makes it easy to apply
# invert_permutation and gather_nd ops.
perm_reshaped = array_ops.reshape(perm, [-1, num_rows])
verification_reshaped = array_ops.reshape(verification,
[-1, num_rows, num_cols])
# Invert the permutation in each batch.
inv_perm_reshaped = map_fn.map_fn(array_ops.invert_permutation,
perm_reshaped)
batch_size = perm_reshaped.shape.as_list()[0]
# Prepare the batch indices with the same shape as the permutation.
# The corresponding batch index is paired with each of the `num_rows`
# permutation indices.
batch_indices = math_ops.cast(array_ops.broadcast_to(
math_ops.range(batch_size)[:, None], perm_reshaped.shape),
dtype=output_idx_type)
if inv_perm_reshaped.shape == [0]:
inv_perm_reshaped = array_ops.zeros_like(batch_indices)
permuted_verification_reshaped = array_ops.gather_nd(
verification_reshaped,
array_ops.stack([batch_indices, inv_perm_reshaped], axis=-1))
# Reshape the verification matrix back to the original shape.
verification = array_ops.reshape(permuted_verification_reshaped,
lu_shape)
self._verifyLuBase(x, lower, upper, perm, verification,
output_idx_type)
def _verifyLu(self, x, output_idx_type=dtypes.int64):
# Verify that Px = LU.
lu, perm = linalg_ops.lu(x, output_idx_type=output_idx_type)
# Prepare the lower factor of shape num_rows x num_rows
lu_shape = np.array(lu.shape.as_list())
batch_shape = lu_shape[:-2]
num_rows = lu_shape[-2]
num_cols = lu_shape[-1]
lower = array_ops.matrix_band_part(lu, -1, 0)
if num_rows > num_cols:
eye = linalg_ops.eye(
num_rows, batch_shape=batch_shape, dtype=lower.dtype)
lower = array_ops.concat([lower, eye[..., num_cols:]], axis=-1)
elif num_rows < num_cols:
lower = lower[..., :num_rows]
# Fill the diagonal with ones.
ones_diag = array_ops.ones(
np.append(batch_shape, num_rows), dtype=lower.dtype)
lower = array_ops.matrix_set_diag(lower, ones_diag)
# Prepare the upper factor.
upper = array_ops.matrix_band_part(lu, 0, -1)
verification = math_ops.matmul(lower, upper)
# Permute the rows of product of the Cholesky factors.
if num_rows > 0:
# Reshape the product of the triangular factors and permutation indices
# to a single batch dimension. This makes it easy to apply
# invert_permutation and gather_nd ops.
perm_reshaped = array_ops.reshape(perm, [-1, num_rows])
verification_reshaped = array_ops.reshape(verification,
[-1, num_rows, num_cols])
# Invert the permutation in each batch.
inv_perm_reshaped = map_fn.map_fn(array_ops.invert_permutation,
perm_reshaped)
batch_size = perm_reshaped.shape.as_list()[0]
# Prepare the batch indices with the same shape as the permutation.
# The corresponding batch index is paired with each of the `num_rows`
# permutation indices.
batch_indices = math_ops.cast(
array_ops.broadcast_to(
math_ops.range(batch_size)[:, None], perm_reshaped.shape),
dtype=output_idx_type)
permuted_verification_reshaped = array_ops.gather_nd(
verification_reshaped,
array_ops.stack([batch_indices, inv_perm_reshaped], axis=-1))
# Reshape the verification matrix back to the original shape.
verification = array_ops.reshape(permuted_verification_reshaped,
lu_shape)
self._verifyLuBase(x, lower, upper, perm, verification,
output_idx_type)
def testPivoting(self):
# This matrix triggers partial pivoting because the first diagonal entry
# is small.
data = np.array([[1e-9, 1., 0.], [1., 0., 0], [0., 1., 5]])
self._verifyLu(data.astype(np.float32))
for dtype in (np.float32, np.float64):
self._verifyLu(data.astype(dtype))
_, p = linalg_ops.lu(data)
p_val = self.evaluate([p])
# Make sure p_val is not the identity permutation.
self.assertNotAllClose(np.arange(3), p_val)
for dtype in (np.complex64, np.complex128):
complex_data = np.tril(1j * data, -1).astype(dtype)
complex_data += np.triu(-1j * data, 1).astype(dtype)
complex_data += data
self._verifyLu(complex_data)
_, p = linalg_ops.lu(data)
p_val = self.evaluate([p])
# Make sure p_val is not the identity permutation.
self.assertNotAllClose(np.arange(3), p_val)
def testPivoting(self):
# This matrix triggers partial pivoting because the first diagonal entry
# is small.
data = np.array([[1e-9, 1., 0.], [1., 0., 0], [0., 1., 5]])
self._verifyLu(data.astype(np.float32))
for dtype in (np.float32, np.float64):
self._verifyLu(data.astype(dtype))
_, p = linalg_ops.lu(data)
p_val = self.evaluate([p])
# Make sure p_val is not the identity permutation.
self.assertNotAllClose(np.arange(3), p_val)
for dtype in (np.complex64, np.complex128):
complex_data = np.tril(1j * data, -1).astype(dtype)
complex_data += np.triu(-1j * data, 1).astype(dtype)
complex_data += data
self._verifyLu(complex_data)
_, p = linalg_ops.lu(data)
p_val = self.evaluate([p])
# Make sure p_val is not the identity permutation.
self.assertNotAllClose(np.arange(3), p_val)
