Cython¶

Cython is an “optimizing static compiler ” that combines Python with C to generate optimized code. Since Cython is a superset of Python, all valid Python programs are also valid Cython programs. However, by providing hints and static typing, we can get much faster programs. Note that while numba often provides similar speedups with less work,, an advantage of Cython is that it is easy to distribute optimized Cython modules since they can be built with the standard Python setup.py script.

We have already seen how to use Cython to wrap C and C++ functions from existing libraries. Here we will see how to use Cython to speed up Python functions.

%matplotlib inline
import matplotlib.pyplot as plt

Resources¶

Utility function for timing functions

import time

def timer(f, *args, **kwargs):
    start = time.clock()
    ans = f(*args, **kwargs)
    return ans, time.clock() - start

def report(fs, *args, **kwargs):
    ans, t = timer(fs[0], *args, **kwargs)
    for f in fs[1:]:
        ans_, t_ = timer(f, *args, **kwargs)
        print('%s: %.1f' % (f.__name__, t/t_))

Incremental improvements¶

Generally, we start with a pure Python function, run it through Cython with the annotate -a flag, and incrementally modify the code until the yellow parts are minimized.

How to build Cython modules¶

From official docs

Using Cython consists of these steps:

Write a .pyx source file
Run the Cython compiler to generate a C file
Run a C compiler to generate a compiled library
Run the Python interpreter and ask it to import the module

In the Jupyter notebook, we can use the %%cython cell magic to automate these steps.

%load_ext cython

Matrix multiplication example¶

def matrix_multiply(u, v, res):
    m, n = u.shape
    n, p = v.shape
    for i in range(m):
        for j in range(p):
            res[i,j] = 0
            for k in range(n):
                res[i,j] += u[i,k] * v[k,j]
    return res

import numpy as np
u = np.random.random((10,20))
v = np.random.random((20,5))

res = np.zeros((u.shape[0], v.shape[1]))
matrix_multiply(u, v, res)

array([[ 3.11449823,  5.35977303,  5.48778181,  5.14085938,  4.54520686],
       [ 3.68374999,  4.67333347,  4.37704824,  4.61282881,  3.85293391],
       [ 4.01582061,  5.53693287,  5.23375753,  4.67309499,  4.59460048],
       [ 4.07493259,  4.63093078,  5.00670814,  4.92908673,  4.23099528],
       [ 3.56821364,  4.64831502,  3.89552072,  4.74094422,  3.83194289],
       [ 3.59114576,  4.14569789,  4.77227321,  4.45942977,  3.77867553],
       [ 5.17616931,  5.73851388,  5.6071998 ,  5.99414005,  5.01139514],
       [ 2.89575575,  4.00384915,  4.71317099,  4.75876412,  4.30115292],
       [ 4.08424318,  5.54013852,  5.29577668,  5.74588951,  4.45967311],
       [ 3.95142186,  5.68656356,  5.02933096,  5.7503449 ,  5.06054258]])

res = np.zeros((u.shape[0], v.shape[1]))
%timeit -r3 -n3 matrix_multiply(u, v, res)

3 loops, best of 3: 653 µs per loop

Using Cython annnotations to identify bottlenecks¶

%%cython -a

import numpy as np

def matrix_multiply1(u, v, res):
    m, n = u.shape
    n, p = v.shape
    for i in range(m):
        for j in range(p):
            res[i,j] = 0
            for k in range(n):
                res[i,j] += u[i,k] * v[k,j]
    return res

Cython: _cython_magic_65555dffd12a135eb525e1912be8f576.pyx

Generated by Cython 0.23.5

Yellow lines hint at Python interaction.
Click on a line that starts with a "+" to see the C code that Cython generated for it.

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Using Cython cdefs and directives¶

%%cython -a

import cython

@cython.boundscheck(False)
@cython.wraparound(False)
def matrix_multiply1(double[:,:] u, double[:, :] v, double[:, :] res):
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    cdef int m, n, p

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    n = u.shape[1]
    p = v.shape[1]

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        for i in range(m):
            for j in range(p):
                res[i,j] = 0
                for k in range(n):
                    res[i,j] += u[i,k] * v[k,j]

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Generated by Cython 0.23.5

Yellow lines hint at Python interaction.
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res = np.zeros((u.shape[0], v.shape[1]))
%timeit -r3 -n3 matrix_multiply1(u, v, res)

3 loops, best of 3: 12.4 µs per loop

Parallel execution with Cython¶

Will not work unless OpenMP is installed.

%%cython --compile-args=-fopenmp --link-args=-fopenmp --force

import cython
from cython.parallel import parallel, prange

@cython.boundscheck(False)
@cython.wraparound(False)
def matrix_multiply2(double[:,:] u, double[:, :] v, double[:, :] res):
    cdef int i, j, k
    cdef int m, n, p

    m = u.shape[0]
    n = u.shape[1]
    p = v.shape[1]

    with cython.nogil, parallel():
        for i in prange(m):
            for j in prange(p):
                res[i,j] = 0
                for k in range(n):
                    res[i,j] += u[i,k] * v[k,j]

res = np.zeros((u.shape[0], v.shape[1]))
%timeit -r3 -n3 matrix_multiply2(u, v, res)

The slowest run took 112.92 times longer than the fastest. This could mean that an intermediate result is being cached.
3 loops, best of 3: 90.2 µs per loop

import time

# color function for point at (x, y)
def mandel(x, y, max_iters):
    c = complex(x, y)
    z = 0.0j
    for i in range(max_iters):
        z = z*z + c
        if z.real*z.real + z.imag*z.imag >= 4:
            return i
    return max_iters

def create_fractal(xmin, xmax, ymin, ymax, image, iters):
    height, width = image.shape

    pixel_size_x = (xmax - xmin)/width
    pixel_size_y = (ymax - ymin)/height

    for x in range(width):
        real = xmin + x*pixel_size_x
        for y in range(height):
            imag = ymin + y*pixel_size_y
            color = mandel(real, imag, iters)
            image[y, x]  = color

gimage = np.zeros((1024, 1536), dtype=np.uint8)
xmin, xmax, ymin, ymax = np.array([-2.0, 1.0, -1.0, 1.0]).astype('float32')
iters = 50

start = time.clock()
create_fractal(xmin, xmax, ymin, ymax, gimage, iters)
dt = time.clock() - start

print("Mandelbrot created on CPU in %f s" % dt)
plt.grid(False)
plt.imshow(gimage, cmap='jet')
pass

Mandelbrot created on CPU in 15.622738 s

%%cython -a

cimport cython

cdef extern from "complex.h":
    double cabs(double complex)

# color function for point at (x, y)
cdef unsigned char mandel_cython(double x, double y, int max_iters):
    cdef double complex c, z

    c = x + y*1j
    z = 0.0j
    for i in range(max_iters):
        z = z*z + c
        if cabs(z) >= 2:
            return i
    return max_iters

@cython.cdivision(True)
def create_fractal_cython(double xmin, double xmax, double ymin, double ymax, unsigned char[:, :] image, int iters):

    cdef int x, y
    cdef int height, width
    cdef double pixel_size_x, pixel_size_y
    cdef double real, imag
    cdef unsigned char color

    height = image.shape[0]
    width = image.shape[1]

    pixel_size_x = (xmax - xmin)/width
    pixel_size_y = (ymax - ymin)/height

    for x in range(width):
        real = xmin + x*pixel_size_x
        for y in range(height):
            imag = ymin + y*pixel_size_y
            color = mandel_cython(real, imag, iters)
            image[y, x]  = color

Cython: _cython_magic_176141650497de6acdeb56d4e03ce71b.pyx

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Yellow lines hint at Python interaction.
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03:

 04: cdef extern from "complex.h":

 05:     double cabs(double complex)

06:

 07: # color function for point at (x, y)

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18:

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  __Pyx_GIVEREF(__pyx_tuple__14);
/* … */
  __pyx_t_1 = PyCFunction_NewEx(&__pyx_mdef_46_cython_magic_176141650497de6acdeb56d4e03ce71b_1create_fractal_cython, NULL, __pyx_n_s_cython_magic_176141650497de6acd); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 20; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __Pyx_GOTREF(__pyx_t_1);
  if (PyDict_SetItem(__pyx_d, __pyx_n_s_create_fractal_cython, __pyx_t_1) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 20; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  __pyx_codeobj__15 = (PyObject*)__Pyx_PyCode_New(6, 0, 15, 0, 0, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__14, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_home_jovyan_cache_ipython_cytho, __pyx_n_s_create_fractal_cython, 20, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__15)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 20; __pyx_clineno = __LINE__; goto __pyx_L1_error;}

21:

 22:     cdef int x, y

 23:     cdef int height, width

 24:     cdef double pixel_size_x, pixel_size_y

 25:     cdef double real, imag

 26:     cdef unsigned char color

27:

+28:     height = image.shape[0]

  __pyx_v_height = (__pyx_v_image.shape[0]);

+29:     width = image.shape[1]

  __pyx_v_width = (__pyx_v_image.shape[1]);

30:

+31:     pixel_size_x = (xmax - xmin)/width

  __pyx_v_pixel_size_x = ((__pyx_v_xmax - __pyx_v_xmin) / __pyx_v_width);

+32:     pixel_size_y = (ymax - ymin)/height

  __pyx_v_pixel_size_y = ((__pyx_v_ymax - __pyx_v_ymin) / __pyx_v_height);

33:

+34:     for x in range(width):

  __pyx_t_1 = __pyx_v_width;
  for (__pyx_t_2 = 0; __pyx_t_2 < __pyx_t_1; __pyx_t_2+=1) {
    __pyx_v_x = __pyx_t_2;

+35:         real = xmin + x*pixel_size_x

    __pyx_v_real = (__pyx_v_xmin + (__pyx_v_x * __pyx_v_pixel_size_x));

+36:         for y in range(height):

    __pyx_t_3 = __pyx_v_height;
    for (__pyx_t_4 = 0; __pyx_t_4 < __pyx_t_3; __pyx_t_4+=1) {
      __pyx_v_y = __pyx_t_4;

+37:             imag = ymin + y*pixel_size_y

      __pyx_v_imag = (__pyx_v_ymin + (__pyx_v_y * __pyx_v_pixel_size_y));

+38:             color = mandel_cython(real, imag, iters)

      __pyx_v_color = __pyx_f_46_cython_magic_176141650497de6acdeb56d4e03ce71b_mandel_cython(__pyx_v_real, __pyx_v_imag, __pyx_v_iters);

+39:             image[y, x]  = color

      __pyx_t_5 = __pyx_v_y;
      __pyx_t_6 = __pyx_v_x;
      __pyx_t_7 = -1;
      if (__pyx_t_5 < 0) {
        __pyx_t_5 += __pyx_v_image.shape[0];
        if (unlikely(__pyx_t_5 < 0)) __pyx_t_7 = 0;
      } else if (unlikely(__pyx_t_5 >= __pyx_v_image.shape[0])) __pyx_t_7 = 0;
      if (__pyx_t_6 < 0) {
        __pyx_t_6 += __pyx_v_image.shape[1];
        if (unlikely(__pyx_t_6 < 0)) __pyx_t_7 = 1;
      } else if (unlikely(__pyx_t_6 >= __pyx_v_image.shape[1])) __pyx_t_7 = 1;
      if (unlikely(__pyx_t_7 != -1)) {
        __Pyx_RaiseBufferIndexError(__pyx_t_7);
        {__pyx_filename = __pyx_f[0]; __pyx_lineno = 39; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
      }
      *((unsigned char *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_image.data + __pyx_t_5 * __pyx_v_image.strides[0]) ) + __pyx_t_6 * __pyx_v_image.strides[1]) )) = __pyx_v_color;
    }
  }

gimage = np.zeros((1024, 1536), dtype=np.uint8)
xmin, xmax, ymin, ymax = np.array([-2.0, 1.0, -1.0, 1.0]).astype('float32')
iters = 50

start = time.clock()
create_fractal_cython(xmin, xmax, ymin, ymax, gimage, iters)
dt = time.clock() - start

print("Mandelbrot created on CPU in %f s" % dt)
plt.grid(False)
plt.imshow(gimage, cmap='jet')
pass

Mandelbrot created on CPU in 0.462727 s

Cython¶

Resources¶

Incremental improvements¶

How to build Cython modules¶

Matrix multiplication example¶

Using Cython annnotations to identify bottlenecks¶

Using Cython cdefs and directives¶

Parallel execution with Cython¶

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