# 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).

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
```