scipy.linalg.interpolative.svd¶

scipy.linalg.interpolative.svd(A, eps_or_k, rand=True)[source]¶

Compute SVD of a matrix via an ID.

An SVD of a matrix A is a factorization:

A = numpy.dot(U, numpy.dot(numpy.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:

Parameters:	A : `numpy.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_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`).
Returns:	U : `numpy.ndarray` Left singular vectors. S : `numpy.ndarray` Singular values. V : `numpy.ndarray` Right singular vectors.

A : numpy.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_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).

Returns: