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# Copyright 2015 The TensorFlow Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
"""Tests for tensorflow.ops.math_ops.matrix_triangular_solve."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import numpy as np
from tensorflow.python.framework import constant_op
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import linalg_ops
from tensorflow.python.platform import test
class MatrixTriangularSolveOpTest(test.TestCase):
def _verifySolveAllWays(self, x, y, dtypes, batch_dims=None):
for lower in True, False:
for adjoint in True, False:
for use_placeholder in True, False:
self._verifySolve(
x,
y,
lower=lower,
adjoint=adjoint,
batch_dims=batch_dims,
use_placeholder=use_placeholder,
dtypes=dtypes)
def _verifySolveAllWaysReal(self, x, y, batch_dims=None):
self._verifySolveAllWays(x, y, (np.float32, np.float64), batch_dims)
def _verifySolveAllWaysComplex(self, x, y, batch_dims=None):
self._verifySolveAllWays(x, y, (np.complex64, np.complex128), batch_dims)
def _verifySolve(self,
x,
y,
lower=True,
adjoint=False,
batch_dims=None,
use_placeholder=False,
dtypes=(np.float32, np.float64)):
for np_type in dtypes:
a = x.astype(np_type)
b = y.astype(np_type)
# For numpy.solve we have to explicitly zero out the strictly
# upper or lower triangle.
if lower and a.size > 0:
a_np = np.tril(a)
elif a.size > 0:
a_np = np.triu(a)
else:
a_np = a
if adjoint:
a_np = np.conj(np.transpose(a_np))
if batch_dims is not None:
a = np.tile(a, batch_dims + [1, 1])
a_np = np.tile(a_np, batch_dims + [1, 1])
b = np.tile(b, batch_dims + [1, 1])
with self.test_session(use_gpu=True) as sess:
if use_placeholder:
a_tf = array_ops.placeholder(a.dtype)
b_tf = array_ops.placeholder(b.dtype)
tf_ans = linalg_ops.matrix_triangular_solve(
a_tf, b_tf, lower=lower, adjoint=adjoint)
tf_val = sess.run(tf_ans, feed_dict={a_tf: a, b_tf: b})
np_ans = np.linalg.solve(a_np, b)
else:
a_tf = constant_op.constant(a)
b_tf = constant_op.constant(b)
tf_ans = linalg_ops.matrix_triangular_solve(
a_tf, b_tf, lower=lower, adjoint=adjoint)
tf_val = tf_ans.eval()
np_ans = np.linalg.solve(a_np, b)
self.assertEqual(np_ans.shape, tf_ans.get_shape())
self.assertEqual(np_ans.shape, tf_val.shape)
self.assertAllClose(np_ans, tf_val)
def testSolve(self):
# 1x1 matrix, single rhs.
matrix = np.array([[0.1]])
rhs0 = np.array([[1.]])
self._verifySolveAllWaysReal(matrix, rhs0)
# 2x2 matrices, single right-hand side.
matrix = np.array([[1., 2.], [3., 4.]])
rhs0 = np.array([[1.], [1.]])
self._verifySolveAllWaysReal(matrix, rhs0)
# 2x2 matrices, 3 right-hand sides.
rhs1 = np.array([[1., 0., 1.], [0., 1., 1.]])
self._verifySolveAllWaysReal(matrix, rhs1)
def testSolveComplex(self):
# 1x1 matrix, single rhs.
matrix = np.array([[0.1 + 1j * 0.1]])
rhs0 = np.array([[1. + 1j]])
self._verifySolveAllWaysComplex(matrix, rhs0)
# 2x2 matrices, single right-hand side.
matrix = np.array([[1., 2.], [3., 4.]]).astype(np.complex64)
matrix += 1j * matrix
rhs0 = np.array([[1.], [1.]]).astype(np.complex64)
rhs0 += 1j * rhs0
self._verifySolveAllWaysComplex(matrix, rhs0)
# 2x2 matrices, 3 right-hand sides.
rhs1 = np.array([[1., 0., 1.], [0., 1., 1.]]).astype(np.complex64)
rhs1 += 1j * rhs1
self._verifySolveAllWaysComplex(matrix, rhs1)
def testSolveBatch(self):
matrix = np.array([[1., 2.], [3., 4.]])
rhs = np.array([[1., 0., 1.], [0., 1., 1.]])
# Batch of 2x3x2x2 matrices, 2x3x2x3 right-hand sides.
self._verifySolveAllWaysReal(matrix, rhs, batch_dims=[2, 3])
# Batch of 3x2x2x2 matrices, 3x2x2x3 right-hand sides.
self._verifySolveAllWaysReal(matrix, rhs, batch_dims=[3, 2])
def testSolveBatchComplex(self):
matrix = np.array([[1., 2.], [3., 4.]]).astype(np.complex64)
matrix += 1j * matrix
rhs = np.array([[1., 0., 1.], [0., 1., 1.]]).astype(np.complex64)
rhs += 1j * rhs
# Batch of 2x3x2x2 matrices, 2x3x2x3 right-hand sides.
self._verifySolveAllWaysComplex(matrix, rhs, batch_dims=[2, 3])
# Batch of 3x2x2x2 matrices, 3x2x2x3 right-hand sides.
self._verifySolveAllWaysComplex(matrix, rhs, batch_dims=[3, 2])
def testNonSquareMatrix(self):
# A non-square matrix should cause an error.
matrix = np.array([[1., 2., 3.], [3., 4., 5.]])
with self.cached_session():
with self.assertRaises(ValueError):
self._verifySolve(matrix, matrix)
with self.assertRaises(ValueError):
self._verifySolve(matrix, matrix, batch_dims=[2, 3])
def testWrongDimensions(self):
# The matrix should have the same number of rows as the
# right-hand sides.
matrix = np.array([[1., 0.], [0., 1.]])
rhs = np.array([[1., 0.]])
with self.cached_session():
with self.assertRaises(ValueError):
self._verifySolve(matrix, rhs)
with self.assertRaises(ValueError):
self._verifySolve(matrix, rhs, batch_dims=[2, 3])
def testNotInvertible(self):
# The input should be invertible.
# The matrix is singular because it has a zero on the diagonal.
singular_matrix = np.array([[1., 0., -1.], [-1., 0., 1.], [0., -1., 1.]])
with self.cached_session():
with self.assertRaisesOpError("Input matrix is not invertible."):
self._verifySolve(singular_matrix, singular_matrix)
with self.assertRaisesOpError("Input matrix is not invertible."):
self._verifySolve(singular_matrix, singular_matrix, batch_dims=[2, 3])
def testEmpty(self):
self._verifySolve(np.empty([0, 2, 2]), np.empty([0, 2, 2]), lower=True)
self._verifySolve(np.empty([2, 0, 0]), np.empty([2, 0, 0]), lower=True)
self._verifySolve(np.empty([2, 0, 0]), np.empty([2, 0, 0]), lower=False)
self._verifySolve(
np.empty([2, 0, 0]), np.empty([2, 0, 0]), lower=True, batch_dims=[3, 2])
if __name__ == "__main__":
test.main()
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