def test_eigvalsh(self):
with self.test_session(graph=ops.Graph()) as sess:
sess.graph.seed = random_seed.DEFAULT_GRAPH_SEED
operator, mat = self.operator_and_matrix(
shapes_info,
dtype,
use_placeholder=use_placeholder,
ensure_self_adjoint_and_pd=True)
# Eigenvalues are real, so we'll cast these to float64 and sort
# for comparison.
op_eigvals = sort_ops.sort(math_ops.cast(operator.eigvals(),
dtype=dtypes.float64),
axis=-1)
if dtype.is_complex:
mat = math_ops.cast(mat, dtype=dtypes.complex128)
else:
mat = math_ops.cast(mat, dtype=dtypes.float64)
mat_eigvals = sort_ops.sort(math_ops.cast(
linalg_ops.self_adjoint_eigvals(mat), dtype=dtypes.float64),
axis=-1)
op_eigvals_v, mat_eigvals_v = sess.run([op_eigvals, mat_eigvals])
atol = self._atol[dtype] # pylint: disable=protected-access
rtol = self._rtol[dtype] # pylint: disable=protected-access
if dtype == dtypes.float32 or dtype == dtypes.complex64:
atol = 2e-4
rtol = 2e-4
self.assertAllClose(op_eigvals_v,
mat_eigvals_v,
atol=atol,
rtol=rtol)
def Test(self):
np.random.seed(1)
n = shape_[-1]
batch_shape = shape_[:-2]
np_dtype = dtype_.as_numpy_dtype
a = np.random.uniform(
low=-1.0, high=1.0, size=n * n).reshape([n, n]).astype(np_dtype)
if dtype_.is_complex:
a += 1j * np.random.uniform(
low=-1.0, high=1.0, size=n * n).reshape([n, n]).astype(np_dtype)
a += np.conj(a.T)
a = np.tile(a, batch_shape + (1, 1))
if dtype_ in (dtypes_lib.float32, dtypes_lib.complex64):
atol = 1e-4
else:
atol = 1e-12
np_e, np_v = np.linalg.eigh(a)
with self.test_session():
if compute_v_:
tf_e, tf_v = linalg_ops.self_adjoint_eig(constant_op.constant(a))
# Check that V*diag(E)*V^T is close to A.
a_ev = math_ops.matmul(
math_ops.matmul(tf_v, array_ops.matrix_diag(tf_e)),
tf_v,
adjoint_b=True)
self.assertAllClose(a_ev.eval(), a, atol=atol)
# Compare to numpy.linalg.eigh.
CompareEigenDecompositions(self, np_e, np_v,
tf_e.eval(), tf_v.eval(), atol)
else:
tf_e = linalg_ops.self_adjoint_eigvals(constant_op.constant(a))
self.assertAllClose(
np.sort(np_e, -1), np.sort(tf_e.eval(), -1), atol=atol)
def Test(self):
np.random.seed(1)
n = shape_[-1]
batch_shape = shape_[:-2]
a = np.random.uniform(
low=-1.0, high=1.0, size=n * n).reshape([n, n]).astype(dtype_)
a += np.conj(a.T)
a = np.tile(a, batch_shape + (1, 1))
if dtype_ == np.float32 or dtype_ == np.complex64:
atol = 1e-4
else:
atol = 1e-12
for compute_v in False, True:
np_e, np_v = np.linalg.eig(a)
with self.test_session():
if compute_v:
tf_e, tf_v = linalg_ops.self_adjoint_eig(constant_op.constant(a))
# Check that V*diag(E)*V^T is close to A.
a_ev = math_ops.matmul(
math_ops.matmul(tf_v, array_ops.matrix_diag(tf_e)),
tf_v,
adjoint_b=True)
self.assertAllClose(a_ev.eval(), a, atol=atol)
# Compare to numpy.linalg.eig.
CompareEigenDecompositions(self, np_e, np_v,
tf_e.eval(), tf_v.eval(), atol)
else:
tf_e = linalg_ops.self_adjoint_eigvals(constant_op.constant(a))
self.assertAllClose(
np.sort(np_e, -1), np.sort(tf_e.eval(), -1), atol=atol)
def Test(self):
np.random.seed(1)
n = shape_[-1]
batch_shape = shape_[:-2]
np_dtype = dtype_.as_numpy_dtype
a = np.random.uniform(
low=-1.0, high=1.0, size=n * n).reshape([n, n]).astype(np_dtype)
if dtype_.is_complex:
a += 1j * np.random.uniform(
low=-1.0, high=1.0, size=n * n).reshape([n, n]).astype(np_dtype)
a += np.conj(a.T)
a = np.tile(a, batch_shape + (1, 1))
if dtype_ in (dtypes_lib.float32, dtypes_lib.complex64):
atol = 1e-4
else:
atol = 1e-12
np_e, np_v = np.linalg.eigh(a)
with self.session(use_gpu=True):
if compute_v_:
tf_e, tf_v = linalg_ops.self_adjoint_eig(constant_op.constant(a))
# Check that V*diag(E)*V^T is close to A.
a_ev = math_ops.matmul(
math_ops.matmul(tf_v, array_ops.matrix_diag(tf_e)),
tf_v,
adjoint_b=True)
self.assertAllClose(self.evaluate(a_ev), a, atol=atol)
# Compare to numpy.linalg.eigh.
CompareEigenDecompositions(self, np_e, np_v, self.evaluate(tf_e),
self.evaluate(tf_v), atol)
else:
tf_e = linalg_ops.self_adjoint_eigvals(constant_op.constant(a))
self.assertAllClose(
np.sort(np_e, -1), np.sort(self.evaluate(tf_e), -1), atol=atol)
def Test(self):
np.random.seed(1)
n = shape_[-1]
batch_shape = shape_[:-2]
np_dtype = dtype_.as_numpy_dtype
a = np.random.uniform(low=-1.0, high=1.0,
size=n * n).reshape([n, n]).astype(np_dtype)
if dtype_.is_complex:
a += 1j * np.random.uniform(low=-1.0, high=1.0, size=n *
n).reshape([n, n]).astype(np_dtype)
a += np.conj(a.T)
a = np.tile(a, batch_shape + (1, 1))
# Optimal stepsize for central difference is O(epsilon^{1/3}).
epsilon = np.finfo(np_dtype).eps
delta = 0.1 * epsilon**(1.0 / 3.0)
# tolerance obtained by looking at actual differences using
# np.linalg.norm(theoretical-numerical, np.inf) on -mavx build
if dtype_ in (dtypes_lib.float32, dtypes_lib.complex64):
tol = 1e-2
else:
tol = 1e-7
with self.session(use_gpu=True):
tf_a = constant_op.constant(a)
if compute_v_:
tf_e, tf_v = linalg_ops.self_adjoint_eig(tf_a)
# (complex) Eigenvectors are only unique up to an arbitrary phase
# We normalize the vectors such that the first component has phase 0.
top_rows = tf_v[..., 0:1, :]
if tf_a.dtype.is_complex:
angle = -math_ops.angle(top_rows)
phase = math_ops.complex(math_ops.cos(angle),
math_ops.sin(angle))
else:
phase = math_ops.sign(top_rows)
tf_v *= phase
outputs = [tf_e, tf_v]
else:
tf_e = linalg_ops.self_adjoint_eigvals(tf_a)
outputs = [tf_e]
for b in outputs:
x_init = np.random.uniform(low=-1.0, high=1.0, size=n *
n).reshape([n, n]).astype(np_dtype)
if dtype_.is_complex:
x_init += 1j * np.random.uniform(
low=-1.0, high=1.0, size=n * n).reshape(
[n, n]).astype(np_dtype)
x_init += np.conj(x_init.T)
x_init = np.tile(x_init, batch_shape + (1, 1))
theoretical, numerical = gradient_checker.compute_gradient(
tf_a,
tf_a.get_shape().as_list(),
b,
b.get_shape().as_list(),
x_init_value=x_init,
delta=delta)
self.assertAllClose(theoretical, numerical, atol=tol, rtol=tol)
def Test(self):
np.random.seed(1)
n = shape_[-1]
batch_shape = shape_[:-2]
np_dtype = dtype_.as_numpy_dtype
a = np.random.uniform(
low=-1.0, high=1.0, size=n * n).reshape([n, n]).astype(np_dtype)
if dtype_.is_complex:
a += 1j * np.random.uniform(
low=-1.0, high=1.0, size=n * n).reshape([n, n]).astype(np_dtype)
a += np.conj(a.T)
a = np.tile(a, batch_shape + (1, 1))
# Optimal stepsize for central difference is O(epsilon^{1/3}).
epsilon = np.finfo(np_dtype).eps
delta = 0.1 * epsilon**(1.0 / 3.0)
# tolerance obtained by looking at actual differences using
# np.linalg.norm(theoretical-numerical, np.inf) on -mavx build
if dtype_ in (dtypes_lib.float32, dtypes_lib.complex64):
tol = 1e-2
else:
tol = 1e-7
with self.session(use_gpu=True):
tf_a = constant_op.constant(a)
if compute_v_:
tf_e, tf_v = linalg_ops.self_adjoint_eig(tf_a)
# (complex) Eigenvectors are only unique up to an arbitrary phase
# We normalize the vectors such that the first component has phase 0.
top_rows = tf_v[..., 0:1, :]
if tf_a.dtype.is_complex:
angle = -math_ops.angle(top_rows)
phase = math_ops.complex(math_ops.cos(angle), math_ops.sin(angle))
else:
phase = math_ops.sign(top_rows)
tf_v *= phase
outputs = [tf_e, tf_v]
else:
tf_e = linalg_ops.self_adjoint_eigvals(tf_a)
outputs = [tf_e]
for b in outputs:
x_init = np.random.uniform(
low=-1.0, high=1.0, size=n * n).reshape([n, n]).astype(np_dtype)
if dtype_.is_complex:
x_init += 1j * np.random.uniform(
low=-1.0, high=1.0, size=n * n).reshape([n, n]).astype(np_dtype)
x_init += np.conj(x_init.T)
x_init = np.tile(x_init, batch_shape + (1, 1))
theoretical, numerical = gradient_checker.compute_gradient(
tf_a,
tf_a.get_shape().as_list(),
b,
b.get_shape().as_list(),
x_init_value=x_init,
delta=delta)
self.assertAllClose(theoretical, numerical, atol=tol, rtol=tol)
def testConcurrentExecutesWithoutError(self):
all_ops = []
with self.session(use_gpu=True) as sess:
for compute_v_ in True, False:
matrix1 = random_ops.random_normal([5, 5], seed=42)
matrix2 = random_ops.random_normal([5, 5], seed=42)
if compute_v_:
e1, v1 = linalg_ops.self_adjoint_eig(matrix1)
e2, v2 = linalg_ops.self_adjoint_eig(matrix2)
all_ops += [e1, v1, e2, v2]
else:
e1 = linalg_ops.self_adjoint_eigvals(matrix1)
e2 = linalg_ops.self_adjoint_eigvals(matrix2)
all_ops += [e1, e2]
val = self.evaluate(all_ops)
self.assertAllEqual(val[0], val[2])
# The algorithm is slightly different for compute_v being True and False,
# so require approximate equality only here.
self.assertAllClose(val[2], val[4])
self.assertAllEqual(val[4], val[5])
self.assertAllEqual(val[1], val[3])
def testConcurrentExecutesWithoutError(self):
all_ops = []
with self.session(use_gpu=True) as sess:
for compute_v_ in True, False:
matrix1 = random_ops.random_normal([5, 5], seed=42)
matrix2 = random_ops.random_normal([5, 5], seed=42)
if compute_v_:
e1, v1 = linalg_ops.self_adjoint_eig(matrix1)
e2, v2 = linalg_ops.self_adjoint_eig(matrix2)
all_ops += [e1, v1, e2, v2]
else:
e1 = linalg_ops.self_adjoint_eigvals(matrix1)
e2 = linalg_ops.self_adjoint_eigvals(matrix2)
all_ops += [e1, e2]
val = sess.run(all_ops)
self.assertAllEqual(val[0], val[2])
# The algorithm is slightly different for compute_v being True and False,
# so require approximate equality only here.
self.assertAllClose(val[2], val[4])
self.assertAllEqual(val[4], val[5])
self.assertAllEqual(val[1], val[3])
def loop_fn(i):
return (linalg_ops.self_adjoint_eig(array_ops.gather(x, i)),
linalg_ops.self_adjoint_eigvals(array_ops.gather(x, i)))
def _eigvals(self):
return linalg_ops.self_adjoint_eigvals(self.to_dense())
