Module « scipy.linalg »

Fonction pinv - module scipy.linalg

Signature de la fonction pinv

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

Description

pinv.__doc__

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

    Calculate a generalized inverse of a matrix using its
    singular-value decomposition ``U @ S @ V`` in the economy mode and picking
    up only the columns/rows that are associated with significant singular
    values.

    If ``s`` is the maximum singular value of ``a``, then the
    significance cut-off value is determined by ``atol + rtol * s``. Any
    singular value below this value is assumed insignificant.

    Parameters
    ----------
    a : (M, N) array_like
        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 ``max(M, N) * eps`` where
        ``eps`` is the machine precision value of the datatype of ``a``.

        .. versionadded:: 1.7.0

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

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

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