Module « scipy.linalg.interpolative »

Fonction svd - module scipy.linalg.interpolative

Signature de la fonction svd

def svd(A, eps_or_k, rand=True) 

Description

svd.__doc__

    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`).

    See also :func:`interp_decomp` and :func:`id_to_svd`.

    ..  This function automatically detects the form of the input parameters and
        passes them to the appropriate backend. For details, see
        :func:`backend.iddp_svd`, :func:`backend.iddp_asvd`,
        :func:`backend.iddp_rsvd`, :func:`backend.iddr_svd`,
        :func:`backend.iddr_asvd`, :func:`backend.iddr_rsvd`,
        :func:`backend.idzp_svd`, :func:`backend.idzp_asvd`,
        :func:`backend.idzp_rsvd`, :func:`backend.idzr_svd`,
        :func:`backend.idzr_asvd`, and :func:`backend.idzr_rsvd`.

    Parameters
    ----------
    A : :class:`numpy.ndarray` or :class:`scipy.sparse.linalg.LinearOperator`
        Matrix to be factored, given as either a :class:`numpy.ndarray` or a
        :class:`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 :class:`numpy.ndarray`
        (randomized algorithms are always used if `A` is of type
        :class:`scipy.sparse.linalg.LinearOperator`).

    Returns
    -------
    U : :class:`numpy.ndarray`
        Left singular vectors.
    S : :class:`numpy.ndarray`
        Singular values.
    V : :class:`numpy.ndarray`
        Right singular vectors.