Function multi_dot

numpy/linalg/_linalg.py:2865–2981

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 spe

(arrays, *, out=None)

@array_function_dispatch(_multidot_dispatcher)
def multi_dot(arrays, *, out=None):
    """
    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.

    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::

    >>> import numpy as np
    >>> 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))