tf.linalg.svd

Computes the singular value decompositions of one or more matrices.

View aliases

Compat aliases for migration

See Migration guide for more details.

tf.compat.v1.linalg.svd, tf.compat.v1.svd

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)

Numpy Compatibility

Mostly equivalent to numpy.linalg.svd, except that

• The order of output arguments here is s, u, v when compute_uv is True, as opposed to u, s, v for numpy.linalg.svd.
• full_matrices is False by default as opposed to True 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 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.