TensorFlow 1 version | View source on GitHub |
Computes the singular value decompositions of one or more matrices.
tf.linalg.svd(
tensor, full_matrices=False, compute_uv=True, name=None
)
Computes the SVD of each inner matrix in tensor
such that
tensor[..., :, :] = u[..., :, :] * diag(s[..., :, :]) *
transpose(conj(v[..., :, :]))
# a is a tensor.
# s is a tensor of singular values.
# u is a tensor of left singular vectors.
# v is a tensor of right singular vectors.
s, u, v = svd(a)
s = svd(a, compute_uv=False)
Args | |
---|---|
tensor
|
Tensor of shape [..., M, N] . Let P be the minimum of M and
N .
|
full_matrices
|
If true, compute full-sized u and v . If false
(the default), compute only the leading P singular vectors.
Ignored if compute_uv is False .
|
compute_uv
|
If True then left and right singular vectors will be
computed and returned in u and v , respectively. Otherwise, only the
singular values will be computed, which can be significantly faster.
|
name
|
string, optional name of the operation. |
Returns | |
---|---|
s
|
Singular values. Shape is [..., P] . The values are sorted in reverse
order of magnitude, so s[..., 0] is the largest value, s[..., 1] is the
second largest, etc.
|
u
|
Left singular vectors. If full_matrices is False (default) then
shape is [..., M, P] ; if full_matrices is True then shape is
[..., M, M] . Not returned if compute_uv is False .
|
v
|
Right singular vectors. If full_matrices is False (default) then
shape is [..., N, P] . If full_matrices is True then shape is
[..., N, N] . Not returned if compute_uv is False .
|
Numpy Compatibility
Mostly equivalent to numpy.linalg.svd, except that
- The order of output arguments here is
s
,u
,v
whencompute_uv
isTrue
, as opposed tou
,s
,v
for numpy.linalg.svd. - full_matrices is
False
by default as opposed toTrue
for numpy.linalg.svd. - tf.linalg.svd uses the standard definition of the SVD
\(A = U \Sigma V^H\), such that the left singular vectors of
a
are the columns ofu
, while the right singular vectors ofa
are the columns ofv
. On the other hand, numpy.linalg.svd returns the adjoint \(V^H\) as the third output argument.
import tensorflow as tf
import numpy as np
s, u, v = tf.linalg.svd(a)
tf_a_approx = tf.matmul(u, tf.matmul(tf.linalg.diag(s), v, adjoint_b=True))
u, s, v_adj = np.linalg.svd(a, full_matrices=False)
np_a_approx = np.dot(u, np.dot(np.diag(s), v_adj))
# tf_a_approx and np_a_approx should be numerically close.