scipy.linalg.interpolative.

svd

scipy.linalg.interpolative.svd(A, eps_or_k, rand=True, rng=None)

Compute SVD of a matrix via an ID.

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).

See also interp_decomp and id_to_svd.

Parameters:

Anumpy.ndarray or 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_kfloat or int

Relative error (if eps_or_k < 1) or rank (if eps_or_k >= 1) of approximation.

randbool, 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).

rngnumpy.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:

Unumpy.ndarray

2D array of left singular vectors.

Snumpy.ndarray

1D array of singular values.

Vnumpy.ndarray

2D array right singular vectors.