Module « scipy.linalg »

Fonction pinvh - module scipy.linalg

Signature de la fonction pinvh

def pinvh(a, atol=None, rtol=None, lower=True, return_rank=False, check_finite=True, cond=None, rcond=None) 

Description

pinvh.__doc__

    Compute the (Moore-Penrose) pseudo-inverse of a Hermitian matrix.

    Calculate a generalized inverse of a copmlex Hermitian/real symmetric
    matrix using its eigenvalue decomposition and including all eigenvalues
    with 'large' absolute value.

    Parameters
    ----------
    a : (N, N) array_like
        Real symmetric or complex hermetian matrix to be pseudo-inverted
    atol: float, optional
        Absolute threshold term, default value is 0.

        .. versionadded:: 1.7.0

    rtol: float, optional
        Relative threshold term, default value is ``N * eps`` where
        ``eps`` is the machine precision value of the datatype of ``a``.

        .. versionadded:: 1.7.0

    lower : bool, optional
        Whether the pertinent array data is taken from the lower or upper
        triangle of `a`. (Default: lower)
    return_rank : bool, optional
        If True, return the effective rank of the matrix.
    check_finite : bool, optional
        Whether to check that the input matrix contains only finite numbers.
        Disabling may give a performance gain, but may result in problems
        (crashes, non-termination) if the inputs do contain infinities or NaNs.
    cond, rcond : float, optional
        In older versions, these values were meant to be used as ``atol`` with
        ``rtol=0``. If both were given ``rcond`` overwrote ``cond`` and hence
        the code was not correct. Thus using these are strongly discouraged and
        the tolerances above are recommended instead.  In fact, if provided,
        atol, rtol takes precedence over these keywords.

        .. versionchanged:: 1.7.0
            Deprecated in favor of ``rtol`` and ``atol`` parameters above and
            will be removed in future versions of SciPy.

        .. versionchanged:: 1.3.0
            Previously the default cutoff value was just ``eps*f`` where ``f``
            was ``1e3`` for single precision and ``1e6`` for double precision.

    Returns
    -------
    B : (N, N) ndarray
        The pseudo-inverse of matrix `a`.
    rank : int
        The effective rank of the matrix.  Returned if `return_rank` is True.

    Raises
    ------
    LinAlgError
        If eigenvalue algorithm does not converge.

    Examples
    --------
    >>> from scipy.linalg import pinvh
    >>> rng = np.random.default_rng()
    >>> a = rng.standard_normal((9, 6))
    >>> a = np.dot(a, a.T)
    >>> B = pinvh(a)
    >>> np.allclose(a, a @ B @ a)
    True
    >>> np.allclose(B, B @ a @ B)
    True