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

Try it in your browser!

>>> import numpy as np
>>> a = np.eye(2*3*4).reshape((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

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