multi_dot(arrays, *, out=None)¶
Compute the dot product of two or more arrays in a single function call, while automatically selecting the fastest evaluation order.
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)
- 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.
New in version 1.19.0.
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
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
Cormen, “Introduction to Algorithms”, Chapter 15.2, p. 370-378
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)