optimizing matrix operations in python, numpy -


this optimization problem. given matrices e, h, q, f , logic in method my_func_basic (see code block), populate matrix v. potential ways, such through vectorization, speed computation? thanks.

import timeit import numpy np n = 20 m = 90 # e: m x n e = np.random.randn(m,n) # h, q: m x m h = np.random.randn(m,m) q = np.random.randn(m,m) # f: n x n f = np.random.randn(n,n) # v: m x m v = np.zeros(shape=(m,m))  def my_func_basic():     x in range(n):         y in range(n):             if x == y:                 v[x][y] = np.nan                 continue                h = h[x][y]             e = np.array([e[x,:]+h*e[y,:]])             v1 = np.dot(np.dot(e,f),np.transpose(e))[0][0]             v2 = q[x][x]+h**2*q[y][y]             v[x][y] = v1/np.sqrt(v2)  print(timeit.timeit(my_func_basic,number=1000),'(sec), slow...')

this 1 way solve vectorized methods -

import numpy np  def vectorized_approach(v,h,e,f,q,n):      # create copy of v store output values     v_vectorized = v.copy()      # calculate v1 in vectorized fashion     e1 = (e[none,:n,:]*h[:n,:n,none] + e[:n,none,:]).reshape(-1,n)     e2 = np.dot(e1,f)     v1_vectorized = np.einsum('ij,ji->i',e2,e1.t).reshape(n,n)     np.fill_diagonal(v1_vectorized, np.nan)      # calculate v2 in vectorized fashion     q_diag = np.diag(q[:n,:n])     v2_vectorized = q_diag[:,none] + h[:n,:n]**2*q_diag[none,:]      # finally, vectorized version of output v     v_vectorized[:n,:n] = v1_vectorized/np.sqrt(v2_vectorized)     return v_vectorized

tests:

1) setup inputs -

in [314]: n = 20      ...: m = 90      ...: # e: m x n      ...: e = np.random.randn(m,n)      ...: # h, q: m x m      ...: h = np.random.randn(m,m)      ...: q = np.random.randn(m,m)      ...: # f: n x n      ...: f = np.random.randn(n,n)      ...: # v: m x m      ...: v = np.zeros(shape=(m,m))      ...:

2) verify results -

in [327]: out_basic_approach = my_func_basic(v,h,e,f,q,n)      ...: out_vectorized_approach = vectorized_approach(v,h,e,f,q,n)      ...:       ...: mask1 = ~np.isnan(out_basic_approach)      ...: mask2 = ~np.isnan(out_vectorized_approach)      ...:   in [328]: np.allclose(mask1,mask2) out[328]: true  in [329]: np.allclose(out_basic_approach[mask1],out_vectorized_approach[mask1]) out[329]: true

3) runtime tests -

in [330]: %timeit my_func_basic(v,h,e,f,q,n) 100 loops, best of 3: 12.2 ms per loop  in [331]: %timeit vectorized_approach(v,h,e,f,q,n) 1000 loops, best of 3: 222 µs per loop

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