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.
In [1]:
%matplotlib inline
import matplotlib.pyplot as plt
Utility function for timing functions
In [2]:
import time
In [3]:
def timer(f, *args, **kwargs):
start = time.clock()
ans = f(*args, **kwargs)
return ans, time.clock() - start
In [4]:
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_))
From official docs
Using Cython consists of these steps:
In the Jupyter notebook, we can use the %%cython cell magic to automate these steps.
In [5]:
%load_ext cython
In [6]:
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
In [7]:
import numpy as np
u = np.random.random((10,20))
v = np.random.random((20,5))
In [8]:
res = np.zeros((u.shape[0], v.shape[1]))
matrix_multiply(u, v, res)
Out[8]:
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]])
In [9]:
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
In [10]:
%%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
Out[10]:
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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%%cython -a
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__pyx_t_1 = PyCFunction_NewEx(&__pyx_mdef_46_cython_magic_1d20d9c3ed3cbd86dd4904fc3a8795cf_1matrix_multiply1, NULL, __pyx_n_s_cython_magic_1d20d9c3ed3cbd86dd); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 6; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
__Pyx_GOTREF(__pyx_t_1);
if (PyDict_SetItem(__pyx_d, __pyx_n_s_matrix_multiply1, __pyx_t_1) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 6; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
__Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
__pyx_codeobj__15 = (PyObject*)__Pyx_PyCode_New(3, 0, 9, 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_matrix_multiply1, 6, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__15)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 6; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
07: cdef int i, j, k
08: cdef int m, n, p
09:
+10: m = u.shape[0]
__pyx_v_m = (__pyx_v_u.shape[0]);
+11: n = u.shape[1]
__pyx_v_n = (__pyx_v_u.shape[1]);
+12: p = v.shape[1]
__pyx_v_p = (__pyx_v_v.shape[1]);
13:
+14: with cython.nogil:
{
#ifdef WITH_THREAD
PyThreadState *_save;
Py_UNBLOCK_THREADS
#endif
/*try:*/ {
/* … */
/*finally:*/ {
/*normal exit:*/{
#ifdef WITH_THREAD
Py_BLOCK_THREADS
#endif
goto __pyx_L5;
}
__pyx_L5:;
}
}
+15: for i in range(m):
__pyx_t_1 = __pyx_v_m;
for (__pyx_t_2 = 0; __pyx_t_2 < __pyx_t_1; __pyx_t_2+=1) {
__pyx_v_i = __pyx_t_2;
+16: for j in range(p):
__pyx_t_3 = __pyx_v_p;
for (__pyx_t_4 = 0; __pyx_t_4 < __pyx_t_3; __pyx_t_4+=1) {
__pyx_v_j = __pyx_t_4;
+17: res[i,j] = 0
__pyx_t_5 = __pyx_v_i;
__pyx_t_6 = __pyx_v_j;
*((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_res.data + __pyx_t_5 * __pyx_v_res.strides[0]) ) + __pyx_t_6 * __pyx_v_res.strides[1]) )) = 0.0;
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__pyx_t_7 = __pyx_v_n;
for (__pyx_t_8 = 0; __pyx_t_8 < __pyx_t_7; __pyx_t_8+=1) {
__pyx_v_k = __pyx_t_8;
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__pyx_t_9 = __pyx_v_i;
__pyx_t_10 = __pyx_v_k;
__pyx_t_11 = __pyx_v_k;
__pyx_t_12 = __pyx_v_j;
__pyx_t_13 = __pyx_v_i;
__pyx_t_14 = __pyx_v_j;
*((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_res.data + __pyx_t_13 * __pyx_v_res.strides[0]) ) + __pyx_t_14 * __pyx_v_res.strides[1]) )) += ((*((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_u.data + __pyx_t_9 * __pyx_v_u.strides[0]) ) + __pyx_t_10 * __pyx_v_u.strides[1]) ))) * (*((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_v.data + __pyx_t_11 * __pyx_v_v.strides[0]) ) + __pyx_t_12 * __pyx_v_v.strides[1]) ))));
}
}
}
}
In [12]:
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
In [13]:
%%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]
In [14]:
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
In [15]:
import time
In [16]:
# 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
In [17]:
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
In [18]:
%%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
Out[18]:
Cython: _cython_magic_176141650497de6acdeb56d4e03ce71b.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.
01:
+02: cimport cython
__pyx_t_1 = PyDict_New(); if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 2; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
__Pyx_GOTREF(__pyx_t_1);
if (PyDict_SetItem(__pyx_d, __pyx_n_s_test, __pyx_t_1) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 2; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
__Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
03:
04: cdef extern from "complex.h":
05: double cabs(double complex)
06:
07: # color function for point at (x, y)
+08: cdef unsigned char mandel_cython(double x, double y, int max_iters):
static unsigned char __pyx_f_46_cython_magic_176141650497de6acdeb56d4e03ce71b_mandel_cython(double __pyx_v_x, double __pyx_v_y, int __pyx_v_max_iters) {
__pyx_t_double_complex __pyx_v_c;
__pyx_t_double_complex __pyx_v_z;
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unsigned char __pyx_r;
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09: cdef double complex c, z
10:
+11: c = x + y*1j
__pyx_v_c = __Pyx_c_sum(__pyx_t_double_complex_from_parts(__pyx_v_x, 0), __Pyx_c_prod(__pyx_t_double_complex_from_parts(__pyx_v_y, 0), __pyx_t_double_complex_from_parts(0, 1.0)));
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__pyx_v_z = __pyx_t_double_complex_from_parts(0, 0.0);
+13: for i in range(max_iters):
__pyx_t_1 = __pyx_v_max_iters;
for (__pyx_t_2 = 0; __pyx_t_2 < __pyx_t_1; __pyx_t_2+=1) {
__pyx_v_i = __pyx_t_2;
+14: z = z*z + c
__pyx_v_z = __Pyx_c_sum(__Pyx_c_prod(__pyx_v_z, __pyx_v_z), __pyx_v_c);
+15: if cabs(z) >= 2:
__pyx_t_3 = ((cabs(__pyx_v_z) >= 2.0) != 0);
if (__pyx_t_3) {
/* … */
}
}
+16: return i
__pyx_r = __pyx_v_i;
goto __pyx_L0;
+17: return max_iters
__pyx_r = __pyx_v_max_iters;
goto __pyx_L0;
18:
19: @cython.cdivision(True)
+20: def create_fractal_cython(double xmin, double xmax, double ymin, double ymax, unsigned char[:, :] image, int iters):
/* Python wrapper */
static PyObject *__pyx_pw_46_cython_magic_176141650497de6acdeb56d4e03ce71b_1create_fractal_cython(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/
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double __pyx_v_xmin;
double __pyx_v_xmax;
double __pyx_v_ymin;
double __pyx_v_ymax;
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if (unlikely(__pyx_kwds)) {
Py_ssize_t kw_args;
const Py_ssize_t pos_args = PyTuple_GET_SIZE(__pyx_args);
switch (pos_args) {
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case 5: values[4] = PyTuple_GET_ITEM(__pyx_args, 4);
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case 3: values[2] = PyTuple_GET_ITEM(__pyx_args, 2);
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switch (pos_args) {
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if (likely((values[0] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_xmin)) != 0)) kw_args--;
else goto __pyx_L5_argtuple_error;
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if (likely((values[1] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_xmax)) != 0)) kw_args--;
else {
__Pyx_RaiseArgtupleInvalid("create_fractal_cython", 1, 6, 6, 1); {__pyx_filename = __pyx_f[0]; __pyx_lineno = 20; __pyx_clineno = __LINE__; goto __pyx_L3_error;}
}
case 2:
if (likely((values[2] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_ymin)) != 0)) kw_args--;
else {
__Pyx_RaiseArgtupleInvalid("create_fractal_cython", 1, 6, 6, 2); {__pyx_filename = __pyx_f[0]; __pyx_lineno = 20; __pyx_clineno = __LINE__; goto __pyx_L3_error;}
}
case 3:
if (likely((values[3] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_ymax)) != 0)) kw_args--;
else {
__Pyx_RaiseArgtupleInvalid("create_fractal_cython", 1, 6, 6, 3); {__pyx_filename = __pyx_f[0]; __pyx_lineno = 20; __pyx_clineno = __LINE__; goto __pyx_L3_error;}
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case 4:
if (likely((values[4] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_image)) != 0)) kw_args--;
else {
__Pyx_RaiseArgtupleInvalid("create_fractal_cython", 1, 6, 6, 4); {__pyx_filename = __pyx_f[0]; __pyx_lineno = 20; __pyx_clineno = __LINE__; goto __pyx_L3_error;}
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case 5:
if (likely((values[5] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_iters)) != 0)) kw_args--;
else {
__Pyx_RaiseArgtupleInvalid("create_fractal_cython", 1, 6, 6, 5); {__pyx_filename = __pyx_f[0]; __pyx_lineno = 20; __pyx_clineno = __LINE__; goto __pyx_L3_error;}
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if (unlikely(kw_args > 0)) {
if (unlikely(__Pyx_ParseOptionalKeywords(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, "create_fractal_cython") < 0)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 20; __pyx_clineno = __LINE__; goto __pyx_L3_error;}
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} else if (PyTuple_GET_SIZE(__pyx_args) != 6) {
goto __pyx_L5_argtuple_error;
} else {
values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
values[2] = PyTuple_GET_ITEM(__pyx_args, 2);
values[3] = PyTuple_GET_ITEM(__pyx_args, 3);
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values[5] = PyTuple_GET_ITEM(__pyx_args, 5);
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__pyx_v_xmin = __pyx_PyFloat_AsDouble(values[0]); if (unlikely((__pyx_v_xmin == (double)-1) && PyErr_Occurred())) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 20; __pyx_clineno = __LINE__; goto __pyx_L3_error;}
__pyx_v_xmax = __pyx_PyFloat_AsDouble(values[1]); if (unlikely((__pyx_v_xmax == (double)-1) && PyErr_Occurred())) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 20; __pyx_clineno = __LINE__; goto __pyx_L3_error;}
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__pyx_v_image = __Pyx_PyObject_to_MemoryviewSlice_dsds_unsigned_char(values[4]); if (unlikely(!__pyx_v_image.memview)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 20; __pyx_clineno = __LINE__; goto __pyx_L3_error;}
__pyx_v_iters = __Pyx_PyInt_As_int(values[5]); if (unlikely((__pyx_v_iters == (int)-1) && PyErr_Occurred())) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 20; __pyx_clineno = __LINE__; goto __pyx_L3_error;}
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goto __pyx_L4_argument_unpacking_done;
__pyx_L5_argtuple_error:;
__Pyx_RaiseArgtupleInvalid("create_fractal_cython", 1, 6, 6, PyTuple_GET_SIZE(__pyx_args)); {__pyx_filename = __pyx_f[0]; __pyx_lineno = 20; __pyx_clineno = __LINE__; goto __pyx_L3_error;}
__pyx_L3_error:;
__Pyx_AddTraceback("_cython_magic_176141650497de6acdeb56d4e03ce71b.create_fractal_cython", __pyx_clineno, __pyx_lineno, __pyx_filename);
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int __pyx_v_x;
int __pyx_v_y;
int __pyx_v_height;
int __pyx_v_width;
double __pyx_v_pixel_size_x;
double __pyx_v_pixel_size_y;
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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]);
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33:
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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;
}
}
In [19]:
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
Content source: cliburn/sta-663-2017
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