svd(A, eps_or_k, rand=True)
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 :None:None:`eps_or_k`).
See also interp_decomp
and id_to_svd
.
<Comment:
|value: '.. This function automatically detects the form of the input parameters and\n passes them to the appropriate backend. For details, see\n :func:`_backend.iddp_svd`, :func:`_backend.iddp_asvd`,\n :func:`_backend.iddp_rsvd`, :func:`_backend.iddr_svd`,\n :func:`_backend.iddr_asvd`, :func:`_backend.iddr_rsvd`,\n :func:`_backend.idzp_svd`, :func:`_backend.idzp_asvd`,\n :func:`_backend.idzp_rsvd`, :func:`_backend.idzr_svd`,\n :func:`_backend.idzr_asvd`, and :func:`_backend.idzr_rsvd`.'
|>
Matrix to be factored, given as either a numpy.ndarray
or a scipy.sparse.linalg.LinearOperator
with the :None:None:`matvec` and :None:None:`rmatvec` methods (to apply the matrix and its adjoint).
Relative error (if :None:None:`eps_or_k < 1`) or rank (if :None:None:`eps_or_k >= 1`) of approximation.
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
).
Left singular vectors.
Singular values.
Right singular vectors.
Compute SVD of a matrix via an ID.
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