linalg.tensorinv

Description

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.

Mandatory Input Parameters

Parameter	Type	Description
a	array_like	Tensor to "invert". Its shape must be "square", i. e., prod(a.shape[:ind]) == prod(a.shape[ind:]).

Optional Input Parameters

Parameter	Type	Default Value	Description
ind	int	2	Number of first indices that are involved in the inverse sum. It must be a positive integer.

Return Value

Type	Description
ndarray	a's tensordot inverse. Shape: a.shape[ind:] + a.shape[:ind]

Examples

>>> import numpy as np
>>> a = np.eye(4*6)
>>> a.shape = (4, 6, 8, 3)
>>> 
>>> ainv = np.linalg.tensorinv(a, ind=2)
>>> ainv.shape
(8, 3, 4, 6)
>>> 
>>> b = np.random.randn(4, 6)
>>> np.allclose(np.tensordot(ainv,b), np.linalg.tensorsolve(a,b))
True
>>> 
>>> a = np.eye(4*6)
>>> a.shape = (24, 8, 3)
>>> ainv = np.linalg.tensorinv(a, ind=1)
>>> ainv.shape
(8, 3, 24)
>>> 
>>> b = np.random.randn(24)
>>> np.allclose(np.tensordot(ainv,b,1), np.linalg.tensorsolve(a,b))
True
>>>

Parent topic: Linear Algebra Functions