def testWrongDimensions(self):
# The input to self_adjoint_eig should be a tensor of
# at least rank 2.
scalar = constant_op.constant(1.)
with self.assertRaises(ValueError):
linalg_ops.eig(scalar)
vector = constant_op.constant([1., 2.])
with self.assertRaises(ValueError):
linalg_ops.eig(vector)
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.eig(matrix1)
e2, v2 = linalg_ops.eig(matrix2)
all_ops += [e1, v1, e2, v2]
else:
e1 = linalg_ops.eigvals(matrix1)
e2 = linalg_ops.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 _EigGrad(op, grad_e, grad_v):
"""Gradient for Eig.
Based on eq. 4.77 from paper by
Christoph Boeddeker et al.
https://arxiv.org/abs/1701.00392
See also
"Computation of eigenvalue and eigenvector derivatives
for a general complex-valued eigensystem" by Nico van der Aa.
As for now only distinct eigenvalue case is considered.
"""
e = op.outputs[0]
compute_v = op.get_attr("compute_v")
# a = op.inputs[0], which satisfies
# a[...,:,:] * v[...,:,i] = e[...,i] * v[...,i]
with ops.control_dependencies([grad_e, grad_v]):
if compute_v:
v = op.outputs[1]
vt = _linalg.adjoint(v)
# Construct the matrix f(i,j) = (i != j ? 1 / (e_i - e_j) : 0).
# Notice that because of the term involving f, the gradient becomes
# infinite (or NaN in practice) when eigenvalues are not unique.
# Mathematically this should not be surprising, since for (k-fold)
# degenerate eigenvalues, the corresponding eigenvectors are only defined
# up to arbitrary rotation in a (k-dimensional) subspace.
f = array_ops.matrix_set_diag(
_SafeReciprocal(
array_ops.expand_dims(e, -2) -
array_ops.expand_dims(e, -1)), array_ops.zeros_like(e))
f = math_ops.conj(f)
vgv = math_ops.matmul(vt, grad_v)
mid = array_ops.matrix_diag(grad_e)
diag_grad_part = array_ops.matrix_diag(
array_ops.matrix_diag_part(
math_ops.cast(math_ops.real(vgv), vgv.dtype)))
mid += f * (
vgv - math_ops.matmul(math_ops.matmul(vt, v), diag_grad_part))
# vt is formally invertible as long as the original matrix is
# diagonalizable. However, in practice, vt may
# be ill-conditioned when matrix original matrix is close to
# non-diagonalizable one
grad_a = linalg_ops.matrix_solve(vt, math_ops.matmul(mid, vt))
else:
_, v = linalg_ops.eig(op.inputs[0])
vt = _linalg.adjoint(v)
# vt is formally invertible as long as the original matrix is
# diagonalizable. However, in practice, vt may
# be ill-conditioned when matrix original matrix is close to
# non-diagonalizable one
grad_a = linalg_ops.matrix_solve(
vt, math_ops.matmul(array_ops.matrix_diag(grad_e), vt))
return math_ops.cast(grad_a, op.inputs[0].dtype)
def Compute(x):
e, v = linalg_ops.eig(x)
# We sort eigenvalues by e.real+e.imag to have consistent
# order between runs
b_dims = len(e.shape) - 1
idx = sort_ops.argsort(math_ops.real(e) + math_ops.imag(e), axis=-1)
e = array_ops.gather(e, idx, batch_dims=b_dims)
v = array_ops.gather(v, idx, batch_dims=b_dims)
# (complex) Eigenvectors are only unique up to an arbitrary phase
# We normalize the vectors such that the first component has phase 0.
top_rows = v[..., 0:1, :]
angle = -math_ops.angle(top_rows)
phase = math_ops.complex(math_ops.cos(angle), math_ops.sin(angle))
v *= phase
return e, v
def Test(self):
np.random.seed(1)
n = shape_[-1]
batch_shape = shape_[:-2]
np_dtype = dtype_.as_numpy_dtype
def RandomInput():
# Most matrices are diagonalizable
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.tile(a, batch_shape + (1, 1))
return a
if dtype_ in (dtypes_lib.float32, dtypes_lib.complex64):
atol = 1e-4
else:
atol = 1e-12
a = RandomInput()
np_e, np_v = np.linalg.eig(a)
with self.session():
if compute_v_:
tf_e, tf_v = linalg_ops.eig(constant_op.constant(a))
# Check that V*diag(E)*V^(-1) is close to A.
a_ev = math_ops.matmul(
math_ops.matmul(tf_v, array_ops.matrix_diag(tf_e)),
linalg_ops.matrix_inverse(tf_v))
self.assertAllClose(self.evaluate(a_ev), a, atol=atol)
# Compare to numpy.linalg.eig.
CompareEigenDecompositions(self, np_e, np_v,
self.evaluate(tf_e),
self.evaluate(tf_v), atol)
else:
tf_e = linalg_ops.eigvals(constant_op.constant(a))
self.assertAllClose(SortEigenValues(np_e),
SortEigenValues(self.evaluate(tf_e)),
atol=atol)
