ch19-code-listing

Chapter 19: Code optimization

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).

In [1]:
import numba
In [2]:
import pyximport
In [3]:
import cython
In [4]:
import numpy as np
In [5]:
%matplotlib inline
import matplotlib.pyplot as plt

Numba

In [6]:
np.random.seed(0)
In [7]:
data = np.random.randn(50000)
In [8]:
def py_sum(data):
    s = 0
    for d in data:
        s += d
    return s
In [9]:
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
In [10]:
%timeit py_sum(data)
7.25 ms ± 112 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
In [11]:
assert abs(py_sum(data) - np.sum(data)) < 1e-10
In [12]:
%timeit np.sum(data)
27.4 µs ± 523 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
In [13]:
%timeit py_cumsum(data)
13.8 ms ± 512 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
In [14]:
assert np.allclose(np.cumsum(data), py_cumsum(data))
In [15]:
%timeit np.cumsum(data)
150 µs ± 455 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
In [16]:
@numba.jit
def jit_sum(data):
    s = 0 
    for d in data:
        s += d

    return s
In [17]:
assert abs(jit_sum(data) - np.sum(data)) < 1e-10
In [18]:
%timeit jit_sum(data)
47 µs ± 394 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
In [19]:
jit_cumsum = numba.jit()(py_cumsum)
In [20]:
assert np.allclose(np.cumsum(data), jit_cumsum(data))
In [21]:
%timeit jit_cumsum(data)
64.6 µs ± 499 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)

Julia fractal

In [22]:
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
In [23]:
jit_julia_fractal = numba.jit(nopython=True)(py_julia_fractal)
In [24]:
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)
In [25]:
jit_julia_fractal(z_real, z_imag, j)
In [26]:
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")
In [27]:
%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)
In [28]:
%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)

Vectorize

In [29]:
def py_Heaviside(x):
    if x == 0.0:
        return 0.5
    
    if x < 0.0:
        return 0.0
    else:
        return 1.0
In [30]:
x = np.linspace(-2, 2, 50001)
In [31]:
%timeit [py_Heaviside(xx) for xx in x]
18.6 ms ± 261 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
In [32]:
np_vec_Heaviside = np.vectorize(py_Heaviside)
In [33]:
np_vec_Heaviside(x)
Out[33]:
array([0., 0., 0., ..., 1., 1., 1.])
In [34]:
%timeit np_vec_Heaviside(x)
9.45 ms ± 84.2 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
In [35]:
def np_Heaviside(x):
    return (x > 0.0) + (x == 0.0)/2.0
In [36]:
%timeit np_Heaviside(x)
206 µs ± 3.51 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)
In [37]:
@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
In [38]:
%timeit jit_Heaviside(x)
34.7 µs ± 662 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
In [39]:
jit_Heaviside([-1, -0.5, 0.0, 0.5, 1.0])
Out[39]:
array([0. , 0. , 0.5, 1. , 1. ])

Cython

In [40]:
!rm cy_sum.*
In [41]:
%%writefile cy_sum.pyx

def cy_sum(data):
    s = 0.0
    for d in data:
        s += d
    return s
Writing cy_sum.pyx
In [42]:
!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)
In [43]:
# 5 lines of python code -> 1470 lines of C code ...
!wc cy_sum.c
    2647    9105  103591 cy_sum.c
In [59]:
%%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
In [73]:
!/Users/rob/miniconda3/envs/py3.6/bin/python setup.py build_ext --inplace > /dev/null
In [74]:
from cy_sum import cy_sum
In [75]:
cy_sum(data)
Out[75]:
-189.70046227549025
In [76]:
%timeit cy_sum(data)
5.14 ms ± 43 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
In [77]:
%timeit py_sum(data)
7 ms ± 85.9 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
In [78]:
%%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
In [79]:
pyximport.install(setup_args={'include_dirs': np.get_include()});
In [80]:
pyximport.install(setup_args=dict(include_dirs=np.get_include()));
In [81]:
from cy_cumsum import cy_cumsum
In [82]:
%timeit cy_cumsum(data)
5.96 ms ± 27.7 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
In [83]:
%timeit py_cumsum(data)
13.3 ms ± 207 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

Using IPython cython command

In [84]:
%load_ext cython
In [85]:
%%cython -a
def cy_sum(data):
    s = 0.0
    for d in data:
        s += d
    return s
Out[85]:
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In [86]:
%timeit cy_sum(data)
5.2 ms ± 63.4 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
In [87]:
%timeit py_sum(data)
7.25 ms ± 128 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
In [88]:
assert np.allclose(np.sum(data), cy_sum(data))
In [89]:
%%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
Out[89]:
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In [90]:
%timeit cy_sum(data)
48.6 µs ± 1.04 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)
In [91]:
%timeit jit_sum(data)
47.6 µs ± 722 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
In [92]:
%timeit np.sum(data)
27.5 µs ± 888 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)

Cummulative sum

In [93]:
%%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):
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    cdef numpy.float64_t s = 0.0
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        s += data[n]
        out[n] = s
    return out
Out[93]:
Cython: _cython_magic_11b25028d61ca29697d68d22b6117b41.pyx

Generated by Cython 0.29.7

Yellow lines hint at Python interaction.
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In [94]:
%timeit py_cumsum(data)
13.8 ms ± 163 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
In [95]:
%timeit cy_cumsum(data)
70.2 µs ± 897 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
In [96]:
%timeit jit_cumsum(data)
64.9 µs ± 404 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
In [97]:
%timeit np.cumsum(data)
151 µs ± 728 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
In [98]:
assert np.allclose(cy_cumsum(data), np.cumsum(data))

Fused types

In [99]:
py_sum([1.0, 2.0, 3.0, 4.0, 5.0])
Out[99]:
15.0
In [100]:
py_sum([1, 2, 3, 4, 5])
Out[100]:
15
In [101]:
cy_sum(np.array([1.0, 2.0, 3.0, 4.0, 5.0]))
Out[101]:
15.0
In [104]:
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'
In [105]:
%%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):
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    return s
Out[105]:
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Generated by Cython 0.29.7

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 06:     numpy.float64_t
 07: 
 08: @cython.boundscheck(False)
 09: @cython.wraparound(False)
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In [106]:
cy_fused_sum(np.array([1.0, 2.0, 3.0, 4.0, 5.0]))
Out[106]:
15.0
In [107]:
cy_fused_sum(np.array([1, 2, 3, 4, 5]))
Out[107]:
15

Julia fractal

In [108]:
%%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, 
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            for t in range(256):
                z = z ** 2 - 0.05 + 0.68j
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Out[108]:
Cython: _cython_magic_2d6248e2a8b34a7fee22dd6092c7b4a6.pyx

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.

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 09: 
 10: @cython.boundscheck(False)
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In [109]:
N = 1024
In [110]:
j = np.zeros((N, N), dtype=np.int64)
In [111]:
z_real = np.linspace(-1.5, 1.5, N)
In [112]:
z_imag = np.linspace(-1.5, 1.5, N)
In [113]:
%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)
In [114]:
%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)
In [115]:
j1 = np.zeros((N, N), dtype=np.int64)
In [116]:
cy_julia_fractal(z_real, z_imag, j1)
In [117]:
j2 = np.zeros((N, N), dtype=np.int64)
In [118]:
jit_julia_fractal(z_real, z_imag, j2)
In [119]:
assert np.allclose(j1, j2)

Calling C function

In [120]:
%%cython

cdef extern from "math.h":
     double acos(double)

def cy_acos1(double x):
    return acos(x)
In [121]:
%timeit cy_acos1(0.5)
77.9 ns ± 0.495 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)
In [122]:
%%cython

from libc.math cimport acos

def cy_acos2(double x):
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In [123]:
%timeit cy_acos2(0.5)
92.4 ns ± 5.29 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)
In [124]:
from numpy import arccos
In [125]:
%timeit arccos(0.5)
1.12 µs ± 39.2 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)
In [126]:
from math import acos
In [127]:
%timeit acos(0.5)
95.6 ns ± 0.591 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)
In [128]:
assert cy_acos1(0.5) == acos(0.5)
In [129]:
assert cy_acos2(0.5) == acos(0.5)

Versions

In [130]:
%reload_ext version_information
In [131]:
%version_information numpy, cython, numba, matplotlib
Out[131]:
SoftwareVersion
Python3.6.8 64bit [GCC 4.2.1 Compatible Clang 4.0.1 (tags/RELEASE_401/final)]
IPython7.5.0
OSDarwin 18.5.0 x86_64 i386 64bit
numpy1.14.3
cython0.29.7
numba0.43.1
matplotlib3.0.3
Mon May 06 22:35:03 2019 JST