Function tensorsolve

numpy/linalg/_linalg.py:294–367

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 Coe

(a, b, axes=None)

@array_function_dispatch(_tensorsolve_dispatcher)
def tensorsolve(a, b, axes=None):
    """
    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
    --------
    numpy.tensordot, tensorinv, numpy.einsum

    Examples
    --------
    >>> 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

    """
    a, wrap = _makearray(a)
    b = asarray(b)
    an = a.ndim

    if axes is not None:
        allaxes = list(range(an))
        for k in axes:
            allaxes.remove(k)
            allaxes.insert(an, k)
        a = a.transpose(allaxes)