Robert Johansson
Source code listings for Numerical Python - Scientific Computing and Data Science Applications with Numpy, SciPy and Matplotlib (ISBN 978-1-484242-45-2).
import numba
import pyximport
import cython
import numpy as np
%matplotlib inline
import matplotlib.pyplot as plt
np.random.seed(0)
data = np.random.randn(50000)
def py_sum(data):
s = 0
for d in data:
s += d
return s
def py_cumsum(data):
out = np.zeros(len(data), dtype=np.float64)
s = 0
for n in range(len(data)):
s += data[n]
out[n] = s
return out
%timeit py_sum(data)
7.25 ms ± 112 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
assert abs(py_sum(data) - np.sum(data)) < 1e-10
%timeit np.sum(data)
27.4 µs ± 523 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
%timeit py_cumsum(data)
13.8 ms ± 512 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
assert np.allclose(np.cumsum(data), py_cumsum(data))
%timeit np.cumsum(data)
150 µs ± 455 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
@numba.jit
def jit_sum(data):
s = 0
for d in data:
s += d
return s
assert abs(jit_sum(data) - np.sum(data)) < 1e-10
%timeit jit_sum(data)
47 µs ± 394 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
jit_cumsum = numba.jit()(py_cumsum)
assert np.allclose(np.cumsum(data), jit_cumsum(data))
%timeit jit_cumsum(data)
64.6 µs ± 499 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
def py_julia_fractal(z_re, z_im, j):
for m in range(len(z_re)):
for n in range(len(z_im)):
z = z_re[m] + 1j * z_im[n]
for t in range(256):
z = z ** 2 - 0.05 + 0.68j
if np.abs(z) > 2.0:
#if (z.real * z.real + z.imag * z.imag) > 4.0: # a bit faster
j[m, n] = t
break
jit_julia_fractal = numba.jit(nopython=True)(py_julia_fractal)
N = 1024
j = np.zeros((N, N), np.int64)
z_real = np.linspace(-1.5, 1.5, N)
z_imag = np.linspace(-1.5, 1.5, N)
jit_julia_fractal(z_real, z_imag, j)
fig, ax = plt.subplots(figsize=(14, 14))
ax.imshow(j, cmap=plt.cm.RdBu_r,
extent=[-1.5, 1.5, -1.5, 1.5])
ax.set_xlabel("$\mathrm{Re}(z)$", fontsize=18)
ax.set_ylabel("$\mathrm{Im}(z)$", fontsize=18)
fig.tight_layout()
fig.savefig("ch19-numba-julia-fractal.pdf")
%timeit py_julia_fractal(z_real, z_imag, j)
1min 47s ± 20.8 s per loop (mean ± std. dev. of 7 runs, 1 loop each)
%timeit jit_julia_fractal(z_real, z_imag, j)
145 ms ± 6.49 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)
def py_Heaviside(x):
if x == 0.0:
return 0.5
if x < 0.0:
return 0.0
else:
return 1.0
x = np.linspace(-2, 2, 50001)
%timeit [py_Heaviside(xx) for xx in x]
18.6 ms ± 261 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
np_vec_Heaviside = np.vectorize(py_Heaviside)
np_vec_Heaviside(x)
array([0., 0., 0., ..., 1., 1., 1.])
%timeit np_vec_Heaviside(x)
9.45 ms ± 84.2 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
def np_Heaviside(x):
return (x > 0.0) + (x == 0.0)/2.0
%timeit np_Heaviside(x)
206 µs ± 3.51 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)
@numba.vectorize([numba.float32(numba.float32),
numba.float64(numba.float64)])
def jit_Heaviside(x):
if x == 0.0:
return 0.5
if x < 0:
return 0.0
else:
return 1.0
%timeit jit_Heaviside(x)
34.7 µs ± 662 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
jit_Heaviside([-1, -0.5, 0.0, 0.5, 1.0])
array([0. , 0. , 0.5, 1. , 1. ])
!rm cy_sum.*
%%writefile cy_sum.pyx
def cy_sum(data):
s = 0.0
for d in data:
s += d
return s
Writing cy_sum.pyx
!cython cy_sum.pyx
/Users/rob/miniconda3/lib/python3.7/site-packages/Cython/Compiler/Main.py:367: FutureWarning: Cython directive 'language_level' not set, using 2 for now (Py2). This will change in a later release! File: /Users/rob/Desktop/numerical-python-apress-revision/numerical-python-book-code/cy_sum.pyx tree = Parsing.p_module(s, pxd, full_module_name)
# 5 lines of python code -> 1470 lines of C code ...
!wc cy_sum.c
2647 9105 103591 cy_sum.c
%%writefile setup.py
from distutils.core import setup
from Cython.Build import cythonize
import numpy as np
setup(ext_modules=cythonize('cy_sum.pyx'),
include_dirs=[np.get_include()],
requires=['Cython', 'numpy'] )
Overwriting setup.py
!/Users/rob/miniconda3/envs/py3.6/bin/python setup.py build_ext --inplace > /dev/null
from cy_sum import cy_sum
cy_sum(data)
-189.70046227549025
%timeit cy_sum(data)
5.14 ms ± 43 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
%timeit py_sum(data)
7 ms ± 85.9 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
%%writefile cy_cumsum.pyx
cimport numpy
import numpy
def cy_cumsum(data):
out = numpy.zeros_like(data)
s = 0
for n in range(len(data)):
s += data[n]
out[n] = s
return out
Overwriting cy_cumsum.pyx
pyximport.install(setup_args={'include_dirs': np.get_include()});
pyximport.install(setup_args=dict(include_dirs=np.get_include()));
from cy_cumsum import cy_cumsum
%timeit cy_cumsum(data)
5.96 ms ± 27.7 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
%timeit py_cumsum(data)
13.3 ms ± 207 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
%load_ext cython
%%cython -a
def cy_sum(data):
s = 0.0
for d in data:
s += d
return s
Generated by Cython 0.29.7
Yellow lines hint at Python interaction.
Click on a line that starts with a "+
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%timeit cy_sum(data)
5.2 ms ± 63.4 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
%timeit py_sum(data)
7.25 ms ± 128 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
assert np.allclose(np.sum(data), cy_sum(data))
%%cython -a
cimport numpy
cimport cython
@cython.boundscheck(False)
@cython.wraparound(False)
def cy_sum(numpy.ndarray[numpy.float64_t, ndim=1] data):
cdef numpy.float64_t s = 0.0
#cdef int n, N = data.shape[0]
cdef int n, N = len(data)
for n in range(N):
s += data[n]
return s
Generated by Cython 0.29.7
Yellow lines hint at Python interaction.
Click on a line that starts with a "+
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%timeit cy_sum(data)
48.6 µs ± 1.04 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)
%timeit jit_sum(data)
47.6 µs ± 722 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
%timeit np.sum(data)
27.5 µs ± 888 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
%%cython -a
cimport numpy
import numpy
cimport cython
ctypedef numpy.float64_t FTYPE_t
@cython.boundscheck(False)
@cython.wraparound(False)
def cy_cumsum(numpy.ndarray[FTYPE_t, ndim=1] data):
cdef int n, N = data.size
cdef numpy.ndarray[FTYPE_t, ndim=1] out = numpy.zeros(N, dtype=data.dtype)
cdef numpy.float64_t s = 0.0
for n in range(N):
s += data[n]
out[n] = s
return out
Generated by Cython 0.29.7
Yellow lines hint at Python interaction.
Click on a line that starts with a "+
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+01: cimport numpy
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06:
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%timeit py_cumsum(data)
13.8 ms ± 163 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
%timeit cy_cumsum(data)
70.2 µs ± 897 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
%timeit jit_cumsum(data)
64.9 µs ± 404 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
%timeit np.cumsum(data)
151 µs ± 728 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
assert np.allclose(cy_cumsum(data), np.cumsum(data))
py_sum([1.0, 2.0, 3.0, 4.0, 5.0])
15.0
py_sum([1, 2, 3, 4, 5])
15
cy_sum(np.array([1.0, 2.0, 3.0, 4.0, 5.0]))
15.0
cy_sum(np.array([1, 2, 3, 4, 5]))
--------------------------------------------------------------------------- ValueError Traceback (most recent call last) <ipython-input-104-482d97a8aad4> in <module> ----> 1 cy_sum(np.array([1, 2, 3, 4, 5])) _cython_magic_ca1303e3f76e8cc692e7b9140687359d.pyx in _cython_magic_ca1303e3f76e8cc692e7b9140687359d.cy_sum() ValueError: Buffer dtype mismatch, expected 'float64_t' but got 'long'
%%cython -a
cimport numpy
cimport cython
ctypedef fused I_OR_F_t:
numpy.int64_t
numpy.float64_t
@cython.boundscheck(False)
@cython.wraparound(False)
def cy_fused_sum(numpy.ndarray[I_OR_F_t, ndim=1] data):
cdef I_OR_F_t s = 0
cdef int n, N = data.size
for n in range(N):
s += data[n]
return s
Generated by Cython 0.29.7
Yellow lines hint at Python interaction.
Click on a line that starts with a "+
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cy_fused_sum(np.array([1.0, 2.0, 3.0, 4.0, 5.0]))
15.0
cy_fused_sum(np.array([1, 2, 3, 4, 5]))
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%%cython -a
cimport numpy
cimport cython
ctypedef numpy.int64_t ITYPE_t
ctypedef numpy.float64_t FTYPE_t
cpdef inline double abs2(double complex z):
return z.real * z.real + z.imag * z.imag
@cython.boundscheck(False)
@cython.wraparound(False)
def cy_julia_fractal(numpy.ndarray[FTYPE_t, ndim=1] z_re,
numpy.ndarray[FTYPE_t, ndim=1] z_im,
numpy.ndarray[ITYPE_t, ndim=2] j):
cdef int m, n, t, M = z_re.size, N = z_im.size
cdef double complex z
for m in range(M):
for n in range(N):
z = z_re[m] + 1.0j * z_im[n]
for t in range(256):
z = z ** 2 - 0.05 + 0.68j
if abs2(z) > 4.0:
j[m, n] = t
break
Generated by Cython 0.29.7
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: cimport numpy
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02: cimport cython
03:
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typedef __pyx_t_5numpy_int64_t __pyx_t_46_cython_magic_2d6248e2a8b34a7fee22dd6092c7b4a6_ITYPE_t;
05: ctypedef numpy.float64_t FTYPE_t
06:
+07: cpdef inline double abs2(double complex z):
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+08: return z.real * z.real + z.imag * z.imag
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09:
10: @cython.boundscheck(False)
11: @cython.wraparound(False)
+12: def cy_julia_fractal(numpy.ndarray[FTYPE_t, ndim=1] z_re,
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/* function exit code */ goto __pyx_L0; __pyx_L1_error:; __pyx_r = NULL; __pyx_L0:; __Pyx_RefNannyFinishContext(); return __pyx_r; } static PyObject *__pyx_pf_46_cython_magic_2d6248e2a8b34a7fee22dd6092c7b4a6_2cy_julia_fractal(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_z_re, PyArrayObject *__pyx_v_z_im, PyArrayObject *__pyx_v_j) { int __pyx_v_m; int __pyx_v_n; int __pyx_v_t; int __pyx_v_M; int __pyx_v_N; __pyx_t_double_complex __pyx_v_z; __Pyx_LocalBuf_ND __pyx_pybuffernd_j; __Pyx_Buffer __pyx_pybuffer_j; __Pyx_LocalBuf_ND __pyx_pybuffernd_z_im; __Pyx_Buffer __pyx_pybuffer_z_im; __Pyx_LocalBuf_ND __pyx_pybuffernd_z_re; __Pyx_Buffer __pyx_pybuffer_z_re; PyObject *__pyx_r = NULL; __Pyx_RefNannyDeclarations __Pyx_RefNannySetupContext("cy_julia_fractal", 0); __pyx_pybuffer_z_re.pybuffer.buf = NULL; __pyx_pybuffer_z_re.refcount = 0; __pyx_pybuffernd_z_re.data = NULL; __pyx_pybuffernd_z_re.rcbuffer = &__pyx_pybuffer_z_re; __pyx_pybuffer_z_im.pybuffer.buf = NULL; __pyx_pybuffer_z_im.refcount = 0; 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/* … */ __pyx_t_1 = PyCFunction_NewEx(&__pyx_mdef_46_cython_magic_2d6248e2a8b34a7fee22dd6092c7b4a6_3cy_julia_fractal, NULL, __pyx_n_s_cython_magic_2d6248e2a8b34a7fee); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 12, __pyx_L1_error) __Pyx_GOTREF(__pyx_t_1); if (PyDict_SetItem(__pyx_d, __pyx_n_s_cy_julia_fractal, __pyx_t_1) < 0) __PYX_ERR(0, 12, __pyx_L1_error) __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
13: numpy.ndarray[FTYPE_t, ndim=1] z_im,
14: numpy.ndarray[ITYPE_t, ndim=2] j):
+15: cdef int m, n, t, M = z_re.size, N = z_im.size
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16: cdef double complex z
+17: for m in range(M):
__pyx_t_2 = __pyx_v_M; __pyx_t_3 = __pyx_t_2; for (__pyx_t_4 = 0; __pyx_t_4 < __pyx_t_3; __pyx_t_4+=1) { __pyx_v_m = __pyx_t_4;
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__pyx_t_5 = __pyx_v_N; __pyx_t_6 = __pyx_t_5; for (__pyx_t_7 = 0; __pyx_t_7 < __pyx_t_6; __pyx_t_7+=1) { __pyx_v_n = __pyx_t_7;
+19: z = z_re[m] + 1.0j * z_im[n]
__pyx_t_8 = __pyx_v_m; __pyx_t_9 = __pyx_t_double_complex_from_parts(0, 1.0); __pyx_t_10 = __pyx_v_n; __pyx_t_11 = __Pyx_c_sum_npy_float64(__pyx_t_npy_float64_complex_from_parts((*__Pyx_BufPtrStrided1d(__pyx_t_46_cython_magic_2d6248e2a8b34a7fee22dd6092c7b4a6_FTYPE_t *, __pyx_pybuffernd_z_re.rcbuffer->pybuffer.buf, __pyx_t_8, __pyx_pybuffernd_z_re.diminfo[0].strides)), 0), __Pyx_c_prod_npy_float64(__pyx_t_npy_float64_complex_from_parts(__Pyx_CREAL(__pyx_t_9), __Pyx_CIMAG(__pyx_t_9)), __pyx_t_npy_float64_complex_from_parts((*__Pyx_BufPtrStrided1d(__pyx_t_46_cython_magic_2d6248e2a8b34a7fee22dd6092c7b4a6_FTYPE_t *, __pyx_pybuffernd_z_im.rcbuffer->pybuffer.buf, __pyx_t_10, __pyx_pybuffernd_z_im.diminfo[0].strides)), 0))); __pyx_v_z = __pyx_t_double_complex_from_parts(__Pyx_CREAL(__pyx_t_11), __Pyx_CIMAG(__pyx_t_11));
+20: for t in range(256):
for (__pyx_t_12 = 0; __pyx_t_12 < 0x100; __pyx_t_12+=1) { __pyx_v_t = __pyx_t_12;
+21: z = z ** 2 - 0.05 + 0.68j
__pyx_v_z = __Pyx_c_sum_double(__Pyx_c_diff_double(__Pyx_c_pow_double(__pyx_v_z, __pyx_t_double_complex_from_parts(2, 0)), __pyx_t_double_complex_from_parts(0.05, 0)), __pyx_t_double_complex_from_parts(0, 0.68));
+22: if abs2(z) > 4.0:
__pyx_t_13 = ((__pyx_f_46_cython_magic_2d6248e2a8b34a7fee22dd6092c7b4a6_abs2(__pyx_v_z, 0) > 4.0) != 0); if (__pyx_t_13) { /* … */ } } __pyx_L8_break:; } }
+23: j[m, n] = t
__pyx_t_14 = __pyx_v_m; __pyx_t_15 = __pyx_v_n; *__Pyx_BufPtrStrided2d(__pyx_t_46_cython_magic_2d6248e2a8b34a7fee22dd6092c7b4a6_ITYPE_t *, __pyx_pybuffernd_j.rcbuffer->pybuffer.buf, __pyx_t_14, __pyx_pybuffernd_j.diminfo[0].strides, __pyx_t_15, __pyx_pybuffernd_j.diminfo[1].strides) = __pyx_v_t;
+24: break
goto __pyx_L8_break;
N = 1024
j = np.zeros((N, N), dtype=np.int64)
z_real = np.linspace(-1.5, 1.5, N)
z_imag = np.linspace(-1.5, 1.5, N)
%timeit cy_julia_fractal(z_real, z_imag, j)
120 ms ± 1.53 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)
%timeit jit_julia_fractal(z_real, z_imag, j)
136 ms ± 5.66 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)
j1 = np.zeros((N, N), dtype=np.int64)
cy_julia_fractal(z_real, z_imag, j1)
j2 = np.zeros((N, N), dtype=np.int64)
jit_julia_fractal(z_real, z_imag, j2)
assert np.allclose(j1, j2)
%%cython
cdef extern from "math.h":
double acos(double)
def cy_acos1(double x):
return acos(x)
%timeit cy_acos1(0.5)
77.9 ns ± 0.495 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)
%%cython
from libc.math cimport acos
def cy_acos2(double x):
return acos(x)
%timeit cy_acos2(0.5)
92.4 ns ± 5.29 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)
from numpy import arccos
%timeit arccos(0.5)
1.12 µs ± 39.2 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)
from math import acos
%timeit acos(0.5)
95.6 ns ± 0.591 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)
assert cy_acos1(0.5) == acos(0.5)
assert cy_acos2(0.5) == acos(0.5)
%reload_ext version_information
%version_information numpy, cython, numba, matplotlib
Software | Version |
---|---|
Python | 3.6.8 64bit [GCC 4.2.1 Compatible Clang 4.0.1 (tags/RELEASE_401/final)] |
IPython | 7.5.0 |
OS | Darwin 18.5.0 x86_64 i386 64bit |
numpy | 1.14.3 |
cython | 0.29.7 |
numba | 0.43.1 |
matplotlib | 3.0.3 |
Mon May 06 22:35:03 2019 JST |