numpy.linalg.tensorsolve#

linalg.tensorsolve(a, b, axes=None)[source]#

Solve the tensor equation a x = b for x.

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

Parameters:

aarray_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’).
barray_like: Right-hand tensor, which can be of any shape.
axestuple of ints, optional: Axes in a to reorder to the right, before inversion. If None (default), no reordering is done.

Returns:

xndarray, shape Q

Raises:

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

See also

numpy.tensordot, tensorinv, numpy.einsum

Examples

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