Compute the dot product of two or more arrays in a single function call, while automatically selecting the fastest evaluation order.
numpy.dotand uses optimal parenthesization of the matrices  . 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.
def multi_dot(arrays): return functools.reduce(np.dot, arrays)
- 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.
- output : ndarray
Returns the dot product of the supplied arrays.
- dot multiplication with two arguments.
The cost for a matrix multiplication can be calculated with the following function:
def cost(A, B): return A.shape * A.shape * B.shape
Let’s assume we have three matrices .
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
 (1, 2) Cormen, “Introduction to Algorithms”, Chapter 15.2, p. 370-378  (1, 2) http://en.wikipedia.org/wiki/Matrix_chain_multiplication
multi_dotallows 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])
>>> np.dot(np.dot(np.dot(A, B), C), D) >>> # or >>> A.dot(B).dot(C).dot(D)