Function slogdet

numpy/linalg/_linalg.py:2272–2352

Compute the sign and (natural) logarithm of the determinant of an array. If an array has a very small or very large determinant, then a call to `det` may overflow or underflow. This routine is more robust against such issues, because it computes the logarithm of the determinant rat

(a)

@array_function_dispatch(_unary_dispatcher)
def slogdet(a):
    """
    Compute the sign and (natural) logarithm of the determinant of an array.

    If an array has a very small or very large determinant, then a call to
    `det` may overflow or underflow. This routine is more robust against such
    issues, because it computes the logarithm of the determinant rather than
    the determinant itself.

    Parameters
    ----------
    a : (..., M, M) array_like
        Input array, has to be a square 2-D array.

    Returns
    -------
    A namedtuple with the following attributes:

    sign : (...) array_like
        A number representing the sign of the determinant. For a real matrix,
        this is 1, 0, or -1. For a complex matrix, this is a complex number
        with absolute value 1 (i.e., it is on the unit circle), or else 0.
    logabsdet : (...) array_like
        The natural log of the absolute value of the determinant.

    If the determinant is zero, then `sign` will be 0 and `logabsdet`
    will be -inf. In all cases, the determinant is equal to
    ``sign * np.exp(logabsdet)``.

    See Also
    --------
    det

    Notes
    -----
    Broadcasting rules apply, see the `numpy.linalg` documentation for
    details.

    The determinant is computed via LU factorization using the LAPACK
    routine ``z/dgetrf``.

    Examples
    --------
    The determinant of a 2-D array ``[[a, b], [c, d]]`` is ``ad - bc``:

    >>> import numpy as np
    >>> a = np.array([[1, 2], [3, 4]])
    >>> (sign, logabsdet) = np.linalg.slogdet(a)
    >>> (sign, logabsdet)
    (-1, 0.69314718055994529) # may vary
    >>> sign * np.exp(logabsdet)
    -2.0

    Computing log-determinants for a stack of matrices:

    >>> a = np.array([ [[1, 2], [3, 4]], [[1, 2], [2, 1]], [[1, 3], [3, 1]] ])
    >>> a.shape
    (3, 2, 2)