Performance: Matlab vs Python

You want to get rid of those for loops. Try this:

def exampleKernelA(M, x, N, y):
    """Example kernel function A"""
    i, j = np.indices((N, M))
    # Define the custom kernel function here
    kernel[i, j] = np.sqrt((x[i, 0] - y[j, 0]) ** 2 + (x[i, 1] - y[j, 1]) ** 2)
    return kernel

You can also do it with broadcasting, which may be even faster, but a little less intuitive coming from MATLAB.

Upon further investigation I have found that using indices as indicated in the answer is still slower.

Solution: Use meshgrid

def exampleKernelA(M, x, N, y):
    """Example kernel function A"""
    # Euclidean norm function implemented using meshgrid idea.
    # Fastest
    x0, y0 = meshgrid(y[:, 0], x[:, 0])
    x1, y1 = meshgrid(y[:, 1], x[:, 1])
    # Define custom kernel here
    kernel = sqrt((x0 - y0) ** 2 + (x1 - y1) ** 2)
    return kernel

Result: Very very fast, 10 times faster than indices approach. I am getting times which are closer to C.

However: Using meshgrid with Matlab beats C and Numpy by being 10 times faster than both.

Still wondering why!

Matlab uses commerical MKL library. If you use free python distribution, check whether you have MKL or other high performance blas library used in python or it is the default ones, which could be much slower.