I have a 3-Dimensional numpy array A. I would like to multiply every element A[i,j,k] by w*( i / Lx + j / Ly + k / Lz ) where w, Lx, Ly and Lz are real numbers (floats). Performing this operation in a for loop is highly impractical, since I need to be able to scale this for large arrays and a for loop over the three indices ijk scales in O(N^3).
Is there an efficient way to perform an operation on each element of a numpy array that cares about index?
You can use broadcasting -
M,N,R = A.shape
p1 = np.arange(M)[:,None,None]/Lx
p2 = np.arange(N)[:,None]/Ly
p3 = np.arange(R)/Lz
out = A/(w*(p1 + p2 + p3))
You can also use np.ix_ for a more elegant solution -
M,N,R = A.shape
X,Y,Z = np.ix_(np.arange(M),np.arange(N),np.arange(R))
out = A/(w*((X/Lx) + (Y/Ly) + (Z/Lz)))
Runtime tests and output verification -
Function definitions:
def vectorized_app1(A, w, Lx, Ly, Lz ):
M,N,R = A.shape
p1 = np.arange(M)[:,None,None]/Lx
p2 = np.arange(N)[:,None]/Ly
p3 = np.arange(R)/Lz
return A/(w*(p1 + p2 + p3))
def vectorized_app2(A, w, Lx, Ly, Lz ):
M,N,R = A.shape
X,Y,Z = np.ix_(np.arange(M),np.arange(N),np.arange(R))
return A/(w*((X/Lx) + (Y/Ly) + (Z/Lz)))
def original_app(A, w, Lx, Ly, Lz ):
out = np.empty_like(A)
M,N,R = A.shape
for i in range(M):
for j in range(N):
for k in range(R):
out[i,j,k] = A[i,j,k]/(w*( (i / Lx) + (j / Ly) + (k / Lz) ))
return out
Timings:
In [197]: # Inputs
...: A = np.random.rand(100,100,100)
...: w, Lx, Ly, Lz = 2.3, 3.2, 4.2, 5.2
...:
In [198]: np.allclose(original_app(A,w,Lx,Ly,Lz),vectorized_app1(A,w,Lx,Ly,Lz))
Out[198]: True
In [199]: np.allclose(original_app(A,w,Lx,Ly,Lz),vectorized_app2(A,w,Lx,Ly,Lz))
Out[199]: True
In [200]: %timeit original_app(A, w, Lx, Ly, Lz )
1 loops, best of 3: 1.39 s per loop
In [201]: %timeit vectorized_app1(A, w, Lx, Ly, Lz )
10 loops, best of 3: 24.6 ms per loop
In [202]: %timeit vectorized_app2(A, w, Lx, Ly, Lz )
10 loops, best of 3: 24.2 ms per loop
