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Module « numpy.linalg »

Fonction slogdet - module numpy.linalg

Signature de la fonction slogdet

def slogdet(a) 

Description

help(numpy.linalg.slogdet)

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)
>>> sign, logabsdet = np.linalg.slogdet(a)
>>> (sign, logabsdet)
(array([-1., -1., -1.]), array([ 0.69314718,  1.09861229,  2.07944154]))
>>> sign * np.exp(logabsdet)
array([-2., -3., -8.])

This routine succeeds where ordinary `det` does not:

>>> np.linalg.det(np.eye(500) * 0.1)
0.0
>>> np.linalg.slogdet(np.eye(500) * 0.1)
(1, -1151.2925464970228)

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