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Module « scipy.linalg »

Fonction det - module scipy.linalg

Signature de la fonction det

def det(a, overwrite_a=False, check_finite=True) 

Description

help(scipy.linalg.det)

Compute the determinant of a matrix

The determinant is a scalar that is a function of the associated square
matrix coefficients. The determinant value is zero for singular matrices.

Parameters
----------
a : (..., M, M) array_like
    Input array to compute determinants for.
overwrite_a : bool, optional
    Allow overwriting data in a (may enhance performance).
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.

Returns
-------
det : (...) float or complex
    Determinant of `a`. For stacked arrays, a scalar is returned for each
    (m, m) slice in the last two dimensions of the input. For example, an
    input of shape (p, q, m, m) will produce a result of shape (p, q). If
    all dimensions are 1 a scalar is returned regardless of ndim.

Notes
-----
The determinant is computed by performing an LU factorization of the
input with LAPACK routine 'getrf', and then calculating the product of
diagonal entries of the U factor.

Even if the input array is single precision (float32 or complex64), the
result will be returned in double precision (float64 or complex128) to
prevent overflows.

Examples
--------
>>> import numpy as np
>>> from scipy import linalg
>>> a = np.array([[1,2,3], [4,5,6], [7,8,9]])  # A singular matrix
>>> linalg.det(a)
0.0
>>> b = np.array([[0,2,3], [4,5,6], [7,8,9]])
>>> linalg.det(b)
3.0
>>> # An array with the shape (3, 2, 2, 2)
>>> c = np.array([[[[1., 2.], [3., 4.]],
...                [[5., 6.], [7., 8.]]],
...               [[[9., 10.], [11., 12.]],
...                [[13., 14.], [15., 16.]]],
...               [[[17., 18.], [19., 20.]],
...                [[21., 22.], [23., 24.]]]])
>>> linalg.det(c)  # The resulting shape is (3, 2)
array([[-2., -2.],
       [-2., -2.],
       [-2., -2.]])
>>> linalg.det(c[0, 0])  # Confirm the (0, 0) slice, [[1, 2], [3, 4]]
-2.0

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