Efficiently read arrays in python

Question

I have a 4-dimensional array L. L.shape = [31, 13, 250, 501]

I need to perform operations which use different elements.

Method 1:

for i1 in range(31):
    for i2 in range(15):
        for i3 in range(250):
            for i4 in range(501):
                L[i1, i2, i3, i4] # some operations involving this element

Method 2:

for i2 in range(15):
    for i1 in range(31):
        for i4 in range(501):
            for i3 in range(250):
                L[i1, i2, i3, i4] # some operations involving this element

Does the speed of execution dependent on how for loops are nested?

Answer 1

Note that the pattern

for i in range(a):
    for j in range(b):
        #do stuff

involves calling the range() function a+1 times. If a > b , this will be less efficient than

for j in range(b):
    for i in range(a):
        #do stuff

You can work out that

for i in range(a):
    for j in range(b):
        for k in range(c):
            for l in range(d):
                #do stuff

calls the range function 1 + a + a*b + a*b*c many times, which is minimized when a <= b <= c <= d . In your case, you can work out that the difference between the most efficient and least efficient ways of looping (measured by number of range calls) is a factor of roughly 34, which is more than I had initially expected. This doesn't mean that one approach will be 34 times quicker than the other. In typical code, the body of the inmost loop dominates the execution time no matter how you manage the bookkeeping.

Having said all this, switching to NumPy (if you are not already using it) is probably the best approach for making the code run fast.