Module « numpy.linalg »

Fonction tensorinv - module numpy.linalg

Signature de la fonction tensorinv

def tensorinv(a, ind=2) 

Description

tensorinv.__doc__

    Compute the 'inverse' of an N-dimensional array.

    The result is an inverse for `a` relative to the tensordot operation
    ``tensordot(a, b, ind)``, i. e., up to floating-point accuracy,
    ``tensordot(tensorinv(a), a, ind)`` is the "identity" tensor for the
    tensordot operation.

    Parameters
    ----------
    a : array_like
        Tensor to 'invert'. Its shape must be 'square', i. e.,
        ``prod(a.shape[:ind]) == prod(a.shape[ind:])``.
    ind : int, optional
        Number of first indices that are involved in the inverse sum.
        Must be a positive integer, default is 2.

    Returns
    -------
    b : ndarray
        `a`'s tensordot inverse, shape ``a.shape[ind:] + a.shape[:ind]``.

    Raises
    ------
    LinAlgError
        If `a` is singular or not 'square' (in the above sense).

    See Also
    --------
    numpy.tensordot, tensorsolve

    Examples
    --------
    >>> a = np.eye(4*6)
    >>> a.shape = (4, 6, 8, 3)
    >>> ainv = np.linalg.tensorinv(a, ind=2)
    >>> ainv.shape
    (8, 3, 4, 6)
    >>> b = np.random.randn(4, 6)
    >>> np.allclose(np.tensordot(ainv, b), np.linalg.tensorsolve(a, b))
    True

    >>> a = np.eye(4*6)
    >>> a.shape = (24, 8, 3)
    >>> ainv = np.linalg.tensorinv(a, ind=1)
    >>> ainv.shape
    (8, 3, 24)
    >>> b = np.random.randn(24)
    >>> np.allclose(np.tensordot(ainv, b, 1), np.linalg.tensorsolve(a, b))
    True