Function svd

numpy/linalg/linalg.py:1500–1695

Singular Value Decomposition. When `a` is a 2D array, and ``full_matrices=False``, then it is factorized as ``u @ np.diag(s) @ vh = (u * s) @ vh``, where `u` and the Hermitian transpose of `vh` are 2D arrays with orthonormal columns and `s` is a 1D array of `a`'s singular v

(a, full_matrices=True, compute_uv=True, hermitian=False)

@array_function_dispatch(_svd_dispatcher)
def svd(a, full_matrices=True, compute_uv=True, hermitian=False):
    """
    Singular Value Decomposition.

    When `a` is a 2D array, and ``full_matrices=False``, then it is
    factorized as ``u @ np.diag(s) @ vh = (u * s) @ vh``, where
    `u` and the Hermitian transpose of `vh` are 2D arrays with
    orthonormal columns and `s` is a 1D array of `a`'s singular
    values. When `a` is higher-dimensional, SVD is applied in
    stacked mode as explained below.

    Parameters
    ----------
    a : (..., M, N) array_like
        A real or complex array with ``a.ndim >= 2``.
    full_matrices : bool, optional
        If True (default), `u` and `vh` have the shapes ``(..., M, M)`` and
        ``(..., N, N)``, respectively.  Otherwise, the shapes are
        ``(..., M, K)`` and ``(..., K, N)``, respectively, where
        ``K = min(M, N)``.
    compute_uv : bool, optional
        Whether or not to compute `u` and `vh` in addition to `s`.  True
        by default.
    hermitian : bool, optional
        If True, `a` is assumed to be Hermitian (symmetric if real-valued),
        enabling a more efficient method for finding singular values.
        Defaults to False.

        .. versionadded:: 1.17.0

    Returns
    -------
    When `compute_uv` is True, the result is a namedtuple with the following
    attribute names:

    U : { (..., M, M), (..., M, K) } array
        Unitary array(s). The first ``a.ndim - 2`` dimensions have the same
        size as those of the input `a`. The size of the last two dimensions
        depends on the value of `full_matrices`. Only returned when
        `compute_uv` is True.
    S : (..., K) array
        Vector(s) with the singular values, within each vector sorted in
        descending order. The first ``a.ndim - 2`` dimensions have the same
        size as those of the input `a`.
    Vh : { (..., N, N), (..., K, N) } array
        Unitary array(s). The first ``a.ndim - 2`` dimensions have the same
        size as those of the input `a`. The size of the last two dimensions
        depends on the value of `full_matrices`. Only returned when
        `compute_uv` is True.

    Raises
    ------
    LinAlgError
        If SVD computation does not converge.

    See Also
    --------
    scipy.linalg.svd : Similar function in SciPy.