Mass Multiplication of an np.einsum Array Using Multiple Cores

Question

I built numpy 1.6.2 and scipy with MKL, hoping to get better performance. Currently, I have code that relies mainly on np.einsum (), and I was told that einsum is not very good with MKL, because there is almost no vectorization. equals sign. So I was thinking of writing some of my codes using np.dot () and slicing, just to get some multi-core speed. I really like the simplicity of np.einsum (), and the readability is good. In any case, for example, I have multidimensional matrix multiplication of the form:

np.einsum('mi,mnijqk->njqk',A,B)

So, how do I convert something like that or other 3.4 and 5 dimensional array multiplications to np.dot () effective MKL operations?

I will add additional information: I am calculating this equation:

For this, I use the code:

np.einsum('mn,mni,nij,nik,mi->njk',a,np.exp(b[:,:,np.newaxis]*U[np.newaxis,:,:]),P,P,X)

, , cython, 5 :

    #STACKOVERFLOW QUESTION:
from __future__ import division
import numpy as np
cimport numpy as np
cimport cython

cdef extern from "math.h":
    double exp(double x)


DTYPE = np.float

ctypedef np.float_t DTYPE_t
@cython.boundscheck(False) # turn of bounds-checking for entire function
def cython_DX_h(np.ndarray[DTYPE_t, ndim=3] P, np.ndarray[DTYPE_t, ndim=1] a, np.ndarray[DTYPE_t, ndim=1] b, np.ndarray[DTYPE_t, ndim=2] U,  np.ndarray[DTYPE_t, ndim=2] X, int I, int M):
    assert P.dtype == DTYPE and a.dtype == DTYPE and b.dtype == DTYPE and U.dtype == DTYPE and X.dtype == DTYPE

cdef np.ndarray[DTYPE_t,ndim=3] DX_h=np.zeros((N,I,I),dtype=DTYPE)
cdef unsigned int j,n,k,m,i
for n in range(N):
    for j in range(I):
        for k in range(I):
            aux=0
            for m in range(N):
                for i in range(I):
                    aux+=a[m,n]*exp(b[m,n]*U[n,i])*P[n,i,j]*P[n,i,k]*X[m,i]
            DX_h[n,j,k]=aux
return DX_h

cython? ( , ) prange cython, gil nogil.

Answer 1

numpy.tensordot():

np.tensordot(A, B, axes=[[0, 1], [0, 2]])

, numpy.dot().