flopscope.

flopscope.numpy.linalg.tensorsolve

fnp.linalg.tensorsolve(a, b, axes=None)[flopscope source][numpy source]

Solve the tensor equation ``a x = b`` for x.

Adapted from NumPy docs np.linalg.tensorsolve

Arealinalg
Typecustom
Cost
n3n^3
Flopscope Context

Tensor solve. Cost: $n^3$ after reshape (delegates to solve).

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

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

Right-hand tensor, which can be of any shape.

axes:tuple of ints, optional

Axes in a to reorder to the right, before inversion. If None (default), no reordering is done.

Returns

x:ndarray, shape Q

Raises

:LinAlgError

If a is singular or not 'square' (in the above sense).

See also

Examples

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