`numpy.linalg:multi_dot`

source: /numpy/linalg/_linalg.py :2864

Signature

def multi_dot ( arrays , * , out = None )

Summary

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

Extended Summary

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.

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 $A_{10 \times 100}, B_{100 \times 5}, C_{5 \times 50}$ .

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

Examples

`multi_dot` allows you to write::

import numpy as np
from numpy.linalg import multi_dot
A = np.random.random((10000, 100))
B = np.random.random((100, 1000))
C = np.random.random((1000, 5))
D = np.random.random((5, 333))
_ = multi_dot([A, B, C, D])

✓

instead of::

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

✓

Aliases

numpy.linalg.multi_dot