`scipy.linalg.interpolative:svd`

source: build-install/usr/lib/python3.14/site-packages/scipy/linalg/interpolative.py:776

Signature

def svd(A, eps_or_k, rand = True, rng = None)

Summary

Compute SVD of a matrix via an ID.

Extended Summary

An SVD of a matrix A is a factorization

A = U @ np.diag(S) @ V.conj().T

where U and V have orthonormal columns and S is nonnegative.

The SVD can be computed to any relative precision or rank (depending on the value of eps_or_k).

Parameters

A : :class:`numpy.ndarray` or :class:`scipy.sparse.linalg.LinearOperator`: Matrix to be factored, given as either a numpy.ndarray or a scipy.sparse.linalg.LinearOperator with the matvec and rmatvec methods (to apply the matrix and its adjoint).
eps_or_k : float or int: Relative error (if eps_or_k < 1) or rank (if eps_or_k >= 1) of approximation.
rand : bool, optional: Whether to use random sampling if A is of type numpy.ndarray (randomized algorithms are always used if A is of type scipy.sparse.linalg.LinearOperator).
rng : `numpy.random.Generator`, optional: Pseudorandom number generator state. When rng is None, a new numpy.random.Generator is created using entropy from the operating system. Types other than numpy.random.Generator are passed to numpy.random.default_rng to instantiate a Generator. If rand is False, the argument is ignored.

Returns

U : :class:`numpy.ndarray`: 2D array of left singular vectors.
S : :class:`numpy.ndarray`: 1D array of singular values.
V : :class:`numpy.ndarray`: 2D array right singular vectors.

Examples

import numpy as np
from scipy.linalg.interpolative import svd
rng = np.random.default_rng()
A = rng.standard_normal((20, 5)) @ rng.standard_normal((5, 10))
U, S, V = svd(A, 5)
U.shape
S.shape
V.shape
np.allclose(A, U @ np.diag(S) @ V.T)

✓

True

Aliases

scipy.linalg.interpolative.svd