numpy.linalg.multi_dot¶

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
chainsnumpy.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 1D it is treated as a row vector. If the last argument is 1D it is treated as a column vector. The other arguments must be 2D.
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 1D it is treated as row vector. If the last argument is 1D it is treated as column vector. The other arguments must be 2D.
Returns:  output : ndarray
Returns the dot product of the supplied 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 matrices 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
References
[1] (1, 2) Cormen, “Introduction to Algorithms”, Chapter 15.2, p. 370378 [2] (1, 2) http://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)