Performance: Matlab vs Python

Question

I recently switched from Matlab to Python. While converting one of my lengthy codes, I was surprised to find Python being very slow. I

Answer 1

Comparing Jit-Compilers

It has been mentioned that Matlab uses an internal Jit-compiler to get good performance on such tasks. Let's compare Matlabs jit-compiler with a Python jit-compiler (Numba).

Code

import numba as nb
import numpy as np
import math
import time

#If the arrays are somewhat larger it makes also sense to parallelize this problem
#cache ==True may also make sense
@nb.njit(fastmath=True) 
def exampleKernelA(M, x, N, y):
  """Example kernel function A"""
  #explicitly declaring the size of the second dim also improves performance a bit
  assert x.shape[1]==2
  assert y.shape[1]==2

  #Works with all dtypes, zeroing isn't necessary
  kernel = np.empty((M,N),dtype=x.dtype)
  for i in range(M):
    for j in range(N):
      # 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


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

@nb.njit() 
def exampleKernelC(M, x, N, y):
  """Example kernel function A"""
  #explicitly declaring the size of the second dim also improves performance a bit
  assert x.shape[1]==2
  assert y.shape[1]==2

  #Works with all dtypes, zeroing isn't necessary
  kernel = np.empty((M,N),dtype=x.dtype)
  for i in range(M):
    for j in range(N):
      # 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


#Your test data
xVec = np.array([
    [49.7030,  78.9590],
    [42.6730,  11.1390],
    [23.2790,  89.6720],
    [75.6050,  25.5890],
    [81.5820,  53.2920],
    [44.9680,   2.7770],
    [38.7890,  78.9050],
    [39.1570,  33.6790],
    [33.2640,  54.7200],
    [4.8060 ,  44.3660],
    [49.7030,  78.9590],
    [42.6730,  11.1390],
    [23.2790,  89.6720],
    [75.6050,  25.5890],
    [81.5820,  53.2920],
    [44.9680,   2.7770],
    [38.7890,  78.9050],
    [39.1570,  33.6790],
    [33.2640,  54.7200],
    [4.8060 ,  44.3660]
    ])

#compilation on first callable
#can be avoided with cache=True
res=exampleKernelA(xVec.shape[0], xVec, xVec.shape[0], xVec)
res=exampleKernelC(xVec.shape[0], xVec, xVec.shape[0], xVec)

t1=time.time()
for i in range(10_000):
  res=exampleKernelA(xVec.shape[0], xVec, xVec.shape[0], xVec)

print(time.time()-t1)

t1=time.time()
for i in range(10_000):
  res=exampleKernelC(xVec.shape[0], xVec, xVec.shape[0], xVec)

print(time.time()-t1)

t1=time.time()
for i in range(10_000):
  res=exampleKernelB(xVec.shape[0], xVec, xVec.shape[0], xVec)

print(time.time()-t1)

Performance

exampleKernelA: 0.03s
exampleKernelC: 0.03s
exampleKernelB: 1.02s
Matlab_2016b (your code, but 10000 rep., after few runs): 0.165s