def _verifyRegularized(self, x, y, l2_regularizer):
for np_type in [np.float32, np.float64]:
# Test with a single matrix.
a = x.astype(np_type)
b = y.astype(np_type)
np_ans = BatchRegularizedLeastSquares(a, b, l2_regularizer)
with self.test_session():
# Test with the batch version of matrix_solve_ls on regular matrices
tf_ans = tf.batch_matrix_solve_ls(
a, b, l2_regularizer=l2_regularizer, fast=True).eval()
self.assertAllClose(np_ans, tf_ans, atol=1e-5, rtol=1e-5)
# Test with the simple matrix_solve_ls on regular matrices
tf_ans = tf.matrix_solve_ls(
a, b, l2_regularizer=l2_regularizer, fast=True).eval()
self.assertAllClose(np_ans, tf_ans, atol=1e-5, rtol=1e-5)
# Test with a 2x3 batch of matrices.
a = np.tile(x.astype(np_type), [2, 3, 1, 1])
b = np.tile(y.astype(np_type), [2, 3, 1, 1])
np_ans = BatchRegularizedLeastSquares(a, b, l2_regularizer)
with self.test_session():
tf_ans = tf.batch_matrix_solve_ls(
a, b, l2_regularizer=l2_regularizer, fast=True).eval()
self.assertAllClose(np_ans, tf_ans, atol=1e-5, rtol=1e-5)
def _verifyRegularized(self, x, y, l2_regularizer):
for np_type in [np.float32, np.float64]:
# Test with a single matrix.
a = x.astype(np_type)
b = y.astype(np_type)
np_ans = BatchRegularizedLeastSquares(a, b, l2_regularizer)
with self.test_session():
# Test with the batch version of matrix_solve_ls on regular matrices
tf_ans = tf.batch_matrix_solve_ls(
a, b, l2_regularizer=l2_regularizer, fast=True).eval()
self.assertAllClose(np_ans, tf_ans, atol=1e-5, rtol=1e-5)
# Test with the simple matrix_solve_ls on regular matrices
tf_ans = tf.matrix_solve_ls(a,
b,
l2_regularizer=l2_regularizer,
fast=True).eval()
self.assertAllClose(np_ans, tf_ans, atol=1e-5, rtol=1e-5)
# Test with a 2x3 batch of matrices.
a = np.tile(x.astype(np_type), [2, 3, 1, 1])
b = np.tile(y.astype(np_type), [2, 3, 1, 1])
np_ans = BatchRegularizedLeastSquares(a, b, l2_regularizer)
with self.test_session():
tf_ans = tf.batch_matrix_solve_ls(
a, b, l2_regularizer=l2_regularizer, fast=True).eval()
self.assertAllClose(np_ans, tf_ans, atol=1e-5, rtol=1e-5)
def testWrongDimensions(self):
# The matrix and right-hand sides should have the same number of rows.
with self.test_session():
matrix = tf.constant([[1., 0.], [0., 1.]])
rhs = tf.constant([[1., 0.]])
with self.assertRaises(ValueError):
tf.matrix_solve_ls(matrix, rhs)
with self.assertRaises(ValueError):
tf.batch_matrix_solve_ls(matrix, rhs)
def testWrongDimensions(self):
# The matrix and right-hand sides should have the same number of rows.
with self.test_session():
matrix = tf.constant([[1., 0.], [0., 1.]])
rhs = tf.constant([[1., 0.]])
with self.assertRaises(ValueError):
tf.matrix_solve_ls(matrix, rhs)
with self.assertRaises(ValueError):
tf.batch_matrix_solve_ls(matrix, rhs)
def _verifySolveBatch(self, x, y):
# Since numpy.linalg.lsqr does not support batch solves, as opposed
# to numpy.linalg.solve, we just perform this test for a fixed batch size
# of 2x3.
for np_type in [np.float32, np.float64]:
a = np.tile(x.astype(np_type), [2, 3, 1, 1])
b = np.tile(y.astype(np_type), [2, 3, 1, 1])
np_ans = np.empty([2, 3, a.shape[-1], b.shape[-1]])
for dim1 in range(2):
for dim2 in range(3):
np_ans[dim1, dim2, :, :], _, _, _ = np.linalg.lstsq(
a[dim1, dim2, :, :], b[dim1, dim2, :, :])
for fast in [True, False]:
with self.test_session():
tf_ans = tf.batch_matrix_solve_ls(a, b, fast=fast).eval()
self.assertEqual(np_ans.shape, tf_ans.shape)
# Check residual norm.
tf_r = b - BatchMatMul(a, tf_ans)
tf_r_norm = np.sum(tf_r * tf_r)
np_r = b - BatchMatMul(a, np_ans)
np_r_norm = np.sum(np_r * np_r)
self.assertAllClose(np_r_norm, tf_r_norm)
# Check solution.
if fast or a.shape[-2] >= a.shape[-1]:
# We skip this test for the underdetermined case when using the
# slow path, because Eigen does not return a minimum norm solution.
# TODO(rmlarsen): Enable this check for all paths if/when we fix
# Eigen's solver.
self.assertAllClose(np_ans, tf_ans, atol=1e-5, rtol=1e-5)
def _verifySolveBatch(self, x, y):
# Since numpy.linalg.lsqr does not support batch solves, as opposed
# to numpy.linalg.solve, we just perform this test for a fixed batch size
# of 2x3.
for np_type in [np.float32, np.float64]:
a = np.tile(x.astype(np_type), [2, 3, 1, 1])
b = np.tile(y.astype(np_type), [2, 3, 1, 1])
np_ans = np.empty([2, 3, a.shape[-1], b.shape[-1]])
for dim1 in range(2):
for dim2 in range(3):
np_ans[dim1, dim2, :, :], _, _, _ = np.linalg.lstsq(
a[dim1, dim2, :, :], b[dim1, dim2, :, :])
for fast in [True, False]:
with self.test_session():
tf_ans = tf.batch_matrix_solve_ls(a, b, fast=fast).eval()
self.assertEqual(np_ans.shape, tf_ans.shape)
# Check residual norm.
tf_r = b - BatchMatMul(a, tf_ans)
tf_r_norm = np.sum(tf_r * tf_r)
np_r = b - BatchMatMul(a, np_ans)
np_r_norm = np.sum(np_r * np_r)
self.assertAllClose(np_r_norm, tf_r_norm)
# Check solution.
if fast or a.shape[-2] >= a.shape[-1]:
# We skip this test for the underdetermined case when using the
# slow path, because Eigen does not return a minimum norm solution.
# TODO(rmlarsen): Enable this check for all paths if/when we fix
# Eigen's solver.
self.assertAllClose(np_ans, tf_ans, atol=1e-5, rtol=1e-5)
def testBatchResultSize(self): # 3x3x3 matrices, 3x3x1 right-hand sides. matrix = np.array([1., 2., 3., 4., 5., 6., 7., 8., 9.] * 3).reshape(3, 3, 3) rhs = np.array([1., 2., 3.] * 3).reshape(3, 3, 1) answer = tf.batch_matrix_solve(matrix, rhs) ls_answer = tf.batch_matrix_solve_ls(matrix, rhs) self.assertEqual(ls_answer.get_shape(), [3, 3, 1]) self.assertEqual(answer.get_shape(), [3, 3, 1])
def testBatchResultSize(self): # 3x3x3 matrices, 3x3x1 right-hand sides. matrix = np.array([1., 2., 3., 4., 5., 6., 7., 8., 9.] * 3).reshape(3, 3, 3) rhs = np.array([1., 2., 3.] * 3).reshape(3, 3, 1) answer = tf.batch_matrix_solve(matrix, rhs) ls_answer = tf.batch_matrix_solve_ls(matrix, rhs) self.assertEqual(ls_answer.get_shape(), [3, 3, 1]) self.assertEqual(answer.get_shape(), [3, 3, 1])
