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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 . |
Mostly equivalent to numpy.linalg.svd, except that
s
, u
, v
when compute_uv
is True
, as opposed to u
, s
, v
for numpy.linalg.svd.False
by default as opposed to True
for numpy.linalg.svd.a
are the columns of u
, while the right singular vectors of a
are the columns of v
. 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.
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Licensed under the Creative Commons Attribution License 3.0.
Code samples licensed under the Apache 2.0 License.
https://www.tensorflow.org/versions/r2.3/api_docs/python/tf/linalg/svd