Comparing computational speed of these two short codes

Question

In the two versions of the code, both v1 and v2 are large vectors (length ranging from 1,000 1,000,000 with len(v1)=len(v2)). I expected code 2 to be much master than code 1 , but it turns out code 1 is much faster and I do not know why. Could you please explain why code 2 is slow? Thank you.

Code 1:

norm1=math.sqrt(np.dot(v1,v1))
norm2=math.sqrt(np.dot(v2,v2))
kern=np.dot(v1,v2)/(norm1*norm2)

Code 2:

kern=0
for i in range(0, len(v1)):
    kern+=min(v1[i], v2[i])

Answer 1

The np.dot() calls also require loops through the vectors, but these loops are implemented (typically) natively / in C++. Loops implemented explicitly in python (as in your code 2) are notoriously slow in comparison to such C++-based loops.

Answer 2

In the first code, you are using functions from standard libraries numpy . These are highly optimised libraries for faster computation because implemented in C. refer this

In the second code, along with overhead of for loop, overhead of function call to min(v1[i]+v2[i]) each time you iterate the loop is also added and don't forget the overhead of range(0, len(v1)) .