numpy.linalg.multi_dot — NumPy v2.2 Manual (original) (raw)

linalg.multi_dot(arrays, *, out=None)[source]#

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:

arrayssequence 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.

outndarray, 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:

outputndarray

Returns the dot product of the supplied arrays.

See also

numpy.dot

dot multiplication with two arguments.

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\(A_{10x100}, B_{100x5}, C_{5x50}\).

The costs for the two different parenthesizations are as follows:

cost((AB)C) = 101005 + 10550 = 5000 + 2500 = 7500 cost(A(BC)) = 1010050 + 100550 = 50000 + 25000 = 75000

References

[1]

Cormen, “Introduction to Algorithms”, Chapter 15.2, p. 370-378

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))

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)