Module « scipy.sparse.linalg »

Fonction svds - module scipy.sparse.linalg

Signature de la fonction svds

def svds(A, k=6, ncv=None, tol=0, which='LM', v0=None, maxiter=None, return_singular_vectors=True, solver='arpack') 

Description

svds.__doc__

Compute the largest or smallest k singular values/vectors for a sparse matrix. The order of the singular values is not guaranteed.

    Parameters
    ----------
    A : {sparse matrix, LinearOperator}
        Array to compute the SVD on, of shape (M, N)
    k : int, optional
        Number of singular values and vectors to compute.
        Must be 1 <= k < min(A.shape).
    ncv : int, optional
        The number of Lanczos vectors generated
        ncv must be greater than k+1 and smaller than n;
        it is recommended that ncv > 2*k
        Default: ``min(n, max(2*k + 1, 20))``
    tol : float, optional
        Tolerance for singular values. Zero (default) means machine precision.
    which : str, ['LM' | 'SM'], optional
        Which `k` singular values to find:

            - 'LM' : largest singular values
            - 'SM' : smallest singular values

        .. versionadded:: 0.12.0
    v0 : ndarray, optional
        Starting vector for iteration, of length min(A.shape). Should be an
        (approximate) left singular vector if N > M and a right singular
        vector otherwise.
        Default: random

        .. versionadded:: 0.12.0
    maxiter : int, optional
        Maximum number of iterations.

        .. versionadded:: 0.12.0
    return_singular_vectors : bool or str, optional
        - True: return singular vectors (True) in addition to singular values.

        .. versionadded:: 0.12.0

        - "u": only return the u matrix, without computing vh (if N > M).
        - "vh": only return the vh matrix, without computing u (if N <= M).

        .. versionadded:: 0.16.0
    solver : str, optional
            Eigenvalue solver to use. Should be 'arpack' or 'lobpcg'.
            Default: 'arpack'

    Returns
    -------
    u : ndarray, shape=(M, k)
        Unitary matrix having left singular vectors as columns.
        If `return_singular_vectors` is "vh", this variable is not computed,
        and None is returned instead.
    s : ndarray, shape=(k,)
        The singular values.
    vt : ndarray, shape=(k, N)
        Unitary matrix having right singular vectors as rows.
        If `return_singular_vectors` is "u", this variable is not computed,
        and None is returned instead.


    Notes
    -----
    This is a naive implementation using ARPACK or LOBPCG as an eigensolver
    on A.H * A or A * A.H, depending on which one is more efficient.

    Examples
    --------
    >>> from scipy.sparse import csc_matrix
    >>> from scipy.sparse.linalg import svds, eigs
    >>> A = csc_matrix([[1, 0, 0], [5, 0, 2], [0, -1, 0], [0, 0, 3]], dtype=float)
    >>> u, s, vt = svds(A, k=2)
    >>> s
    array([ 2.75193379,  5.6059665 ])
    >>> np.sqrt(eigs(A.dot(A.T), k=2)[0]).real
    array([ 5.6059665 ,  2.75193379])