linalg.tensorsolve

Description

Solve the tensor equation a x = b for x.

Assume that all indices of x are summed over together with the rightmost indices of a, as is done in, for example, tensordot(a, x, axes=x.ndim).

Mandatory Input Parameters

Parameter	Type	Description
a	array_like	Coefficient tensor, of shape b.shape + Q. Q, a tuple, equals the shape of that sub-tensor of a consisting of the appropriate number of its rightmost indices, and must be such that prod(Q) == prod(b.shape) (in which sense a is said to be 'square').
b	array_like	RHS tensor, which can be of any shape.

Parameter

Type

Description

array_like

Coefficient tensor, of shape b.shape + Q.

Q, a tuple, equals the shape of that sub-tensor of a consisting of the appropriate number of its rightmost indices, and must be such that prod(Q) == prod(b.shape) (in which sense a is said to be 'square').

array_like

RHS tensor, which can be of any shape.

Optional Input Parameters

Parameter	Type	Default Value	Description
axes	tuple of ints	None	Axes in a to reorder to the right before inversion. If None, no reordering is done.

Return Value

Type	Description
ndarray, shape Q	Solution of tensor equation ax = b

Examples

>>> import numpy as np
>>> a = np.eye(2*3*4)
>>> a.shape = (2*3, 4, 2, 3, 4)
>>> b = np.random.randn(2*3, 4)
>>> x = np.linalg.tensorsolve(a, b)
>>> x.shape
(2, 3, 4)
>>> 
>>> np.allclose(np.tensordot(a, x, axes=3), b)
True
>>>

Parent topic: Linear Algebra Functions