svd#
- scipy.linalg.interpolative.svd(A, eps_or_k, rand=True, rng=None)[source]#
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
andid_to_svd
.- Parameters:
- A
numpy.ndarray
orscipy.sparse.linalg.LinearOperator
Matrix to be factored, given as either a
numpy.ndarray
or ascipy.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 (ifeps_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 typescipy.sparse.linalg.LinearOperator
).- rng
numpy.random.Generator
NumPy generator for the randomization steps in the algorithm. If
rand
isFalse
, the argument is ignored.
- A
- Returns:
- U
numpy.ndarray
2D array of left singular vectors.
- S
numpy.ndarray
1D array of singular values.
- V
numpy.ndarray
2D array right singular vectors.
- U