`numpy.linalg:tensorinv`

source: /numpy/linalg/_linalg.py :461

Signature

def tensorinv ( a , ind = 2 )

Summary

Compute the 'inverse' of an N-dimensional array.

Extended Summary

The result is an inverse for a relative to the tensordot operation tensordot(a, b, ind), i. e., up to floating-point accuracy, tensordot(tensorinv(a), a, ind) is the "identity" tensor for the tensordot operation.

Parameters

a : array_like: Tensor to 'invert'. Its shape must be 'square', i. e., prod(a.shape[:ind]) == prod(a.shape[ind:]).
ind : int, optional: Number of first indices that are involved in the inverse sum. Must be a positive integer, default is 2.

Returns

b : ndarray: a's tensordot inverse, shape a.shape[ind:] + a.shape[:ind].

Raises

: LinAlgError: If a is singular or not 'square' (in the above sense).

Examples

import numpy as np
a = np.eye(4*6).reshape((4, 6, 8, 3))
ainv = np.linalg.tensorinv(a, ind=2)
ainv.shape
rng = np.random.default_rng()
b = rng.normal(size=(4, 6))
np.allclose(np.tensordot(ainv, b), np.linalg.tensorsolve(a, b))

✓

a = np.eye(4*6).reshape((24, 8, 3))
ainv = np.linalg.tensorinv(a, ind=1)
ainv.shape
rng = np.random.default_rng()
b = rng.normal(size=24)
np.allclose(np.tensordot(ainv, b, 1), np.linalg.tensorsolve(a, b))

✓

Aliases

numpy.linalg.tensorinv