linalg.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.
chains
and 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.
Think of
as:
defmulti_dot(arrays):returnfunctools.reduce(np.dot,arrays)Parameters:arrayssequence of array_likeIf 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, optionalOutput 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:outputndarrayReturns the dot product of the supplied arrays.
See also
dot multiplication with two arguments.
Notes
The cost for a matrix multiplication can be calculated with the following function:
defcost(A,B):returnA.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=7500cost(A(BC))=10*100*50+100*5*50=50000+25000=75000References
[
]
Cormen, “Introduction to Algorithms”, Chapter 15.2, p. 370-378
Examples
allows you to write:
>>> importnumpyasnp>>> fromnumpy.linalgimportmulti_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)