scipy.linalg.

inv#

scipy.linalg.inv(a, overwrite_a=False, check_finite=True, assume_a=None, lower=False)[source]#

Compute the inverse of a matrix.

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’)
upper triangular	‘upper triangular’
lower triangular	‘lower triangular’
symmetric positive definite	‘pos’

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.

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 Batched Linear Operations for details.

Parameters:

aarray_like, shape (…, M, M): Square matrix (or a batch of matrices) to be inverted.
overwrite_abool, optional: Discard data in a (may improve performance). Default is False.
check_finitebool, 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_astr, optional: Valid entries are described above. If omitted or None, checks are performed to identify structure so the appropriate solver can be called.
lowerbool, 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:

ainvndarray: 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)
array([[-2. ,  1. ],
       [ 1.5, -0.5]])
>>> np.dot(a, linalg.inv(a))
array([[ 1.,  0.],
       [ 0.,  1.]])