numpy.linalg.multi_dot — NumPy v1.15 Manual (original) (raw)

numpy.linalg. multi_dot(arrays)[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)

See also

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]

Let’s assume we have three matricesA_{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

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)