Module « numpy.linalg »

Fonction multi_dot - module numpy.linalg

Signature de la fonction multi_dot

def multi_dot(arrays, *, out=None) 

Description

multi_dot.__doc__

    Compute the dot product of two or more arrays in a single function call,
    while automatically selecting the fastest evaluation order.

    `multi_dot` chains `numpy.dot` and uses optimal parenthesization
    of the matrices [1]_ [2]_. Depending on the shapes of the matrices,
    this can speed up the multiplication a lot.

    If the first argument is 1-D it is treated as a row vector.
    If the last argument is 1-D it is treated as a column vector.
    The other arguments must be 2-D.

    Think of `multi_dot` as::

        def multi_dot(arrays): return functools.reduce(np.dot, arrays)


    Parameters
    ----------
    arrays : sequence of array_like
        If the first argument is 1-D it is treated as row vector.
        If the last argument is 1-D it is treated as column vector.
        The other arguments must be 2-D.
    out : ndarray, optional
        Output argument. This must have the exact kind that would be returned
        if it was not used. In particular, it must have the right type, must be
        C-contiguous, and its dtype must be the dtype that would be returned
        for `dot(a, b)`. This is a performance feature. Therefore, if these
        conditions are not met, an exception is raised, instead of attempting
        to be flexible.

        .. versionadded:: 1.19.0

    Returns
    -------
    output : ndarray
        Returns the dot product of the supplied arrays.

    See Also
    --------
    numpy.dot : dot multiplication with two arguments.

    References
    ----------

    .. [1] Cormen, "Introduction to Algorithms", Chapter 15.2, p. 370-378
    .. [2] https://en.wikipedia.org/wiki/Matrix_chain_multiplication

    Examples
    --------
    `multi_dot` allows you to write::

    >>> from numpy.linalg import multi_dot
    >>> # Prepare some data
    >>> A = np.random.random((10000, 100))
    >>> B = np.random.random((100, 1000))
    >>> C = np.random.random((1000, 5))
    >>> D = np.random.random((5, 333))
    >>> # the actual dot multiplication
    >>> _ = multi_dot([A, B, C, D])

    instead of::

    >>> _ = np.dot(np.dot(np.dot(A, B), C), D)
    >>> # or
    >>> _ = A.dot(B).dot(C).dot(D)

    Notes
    -----
    The cost for a matrix multiplication can be calculated with the
    following function::

        def cost(A, B):
            return A.shape[0] * A.shape[1] * B.shape[1]

    Assume we have three matrices
    :math:`A_{10x100}, B_{100x5}, C_{5x50}`.

    The costs for the two different parenthesizations are as follows::

        cost((AB)C) = 10*100*5 + 10*5*50   = 5000 + 2500   = 7500
        cost(A(BC)) = 10*100*50 + 100*5*50 = 50000 + 25000 = 75000