This is one of the 100 recipes of the IPython Cookbook, the definitive guide to high-performance scientific computing and data science in Python.

# 5.4. Accelerating Python code with Cython¶

We use Cython to accelerate the generation of the Mandelbrot fractal.

In [ ]:
import numpy as np


We initialize the simulation and generate the grid in the complex plane.

In [ ]:
size = 200
iterations = 100


## Pure Python¶

In [ ]:
def mandelbrot_python(m, size, iterations):
for i in range(size):
for j in range(size):
c = -2 + 3./size*j + 1j*(1.5-3./size*i)
z = 0
for n in range(iterations):
if np.abs(z) <= 10:
z = z*z + c
m[i, j] = n
else:
break

In [ ]:
%%timeit -n1 -r1 m = np.zeros((size, size))
mandelbrot_python(m, size, iterations)


## Cython versions¶

We first import Cython.

In [ ]:
#%load_ext cythonmagic


### Take 1¶

First, we just add the %%cython magic.

In [ ]:
%%cython -a
import numpy as np

def mandelbrot_cython(m, size, iterations):
for i in range(size):
for j in range(size):
c = -2 + 3./size*j + 1j*(1.5-3./size*i)
z = 0
for n in range(iterations):
if np.abs(z) <= 10:
z = z*z + c
m[i, j] = n
else:
break

In [ ]:
%%timeit -n1 -r1 m = np.zeros((size, size), dtype=np.int32)
mandelbrot_cython(m, size, iterations)


Virtually no speedup.

### Take 2¶

Now, we add type information, using memory views for NumPy arrays.

In [ ]:
%%cython -a
import numpy as np

def mandelbrot_cython(int[:,::1] m,
int size,
int iterations):
cdef int i, j, n
cdef complex z, c
for i in range(size):
for j in range(size):
c = -2 + 3./size*j + 1j*(1.5-3./size*i)
z = 0
for n in range(iterations):
if z.real**2 + z.imag**2 <= 100:
z = z*z + c
m[i, j] = n
else:
break

In [ ]:
%%timeit -n1 -r1 m = np.zeros((size, size), dtype=np.int32)
mandelbrot_cython(m, size, iterations)


Interesting speedup!

You'll find all the explanations, figures, references, and much more in the book (to be released later this summer).

IPython Cookbook, by Cyrille Rossant, Packt Publishing, 2014 (500 pages).