`scipy.linalg._basic:inv`

source: /scipy/linalg/_basic.py :1353

Signature

   def     inv (    a    ,    overwrite_a    =  False   ,    check_finite    =  True   ,  * ,     assume_a    =  None   ,    lower    =  False     )

Summary

Compute the inverse of a matrix.

Extended Summary

If the data matrix is known to be a particular type then supplying the corresponding string to assume_a key chooses the dedicated solver. The available options are

=============================  ================================
 general                        'general' (or 'gen')
 diagonal                       'diagonal'
 upper triangular               'upper triangular'
 lower triangular               'lower triangular'
 symmetric positive definite    'pos'
 symmetric                      'sym'
 Hermitian                      'her'
=============================  ================================

For the 'pos' option, only the triangle of the input matrix specified in the lower argument is used, and the other triangle is not referenced. Likewise, an explicit assume_a='diagonal' means that off-diagonal elements are not referenced.

Array argument(s) of this function may have additional "batch" dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see linalg_batch for details.

Parameters

a : array_like, shape (..., M, M): Square matrix (or a batch of matrices) to be inverted.
overwrite_a : bool, optional: Discard data in a (may improve performance). Default is False.
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.
assume_a : str, optional: Valid entries are described above. If omitted or None, checks are performed to identify structure so the appropriate solver can be called.
lower : bool, optional: Ignored unless assume_a is one of 'sym', 'her', or 'pos'. If True, the calculation uses only the data in the lower triangle of a; entries above the diagonal are ignored. If False (default), the calculation uses only the data in the upper triangle of a; entries below the diagonal are ignored.

Returns

ainv : ndarray: Inverse of the matrix a.

Raises

: LinAlgError: If a is singular.
: ValueError: If a is not square, or not 2D.

Notes

The input array a may represent a single matrix or a collection (a.k.a. a "batch") of square matrices. For example, if a.shape == (4, 3, 2, 2), it is interpreted as a (4, 3)-shaped batch of $2 \times 2$ matrices.

This routine checks the condition number of the a matrix and emits a LinAlgWarning for ill-conditioned inputs.

Examples

import numpy as np
from scipy import linalg
a = np.array([[1., 2.], [3., 4.]])
linalg.inv(a)

✓

np.dot(a, linalg.inv(a))