Jupyter Snippet NP 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).

import numba

import pyximport

import cython

import numpy as np

%matplotlib inline
import matplotlib.pyplot as plt

Numba

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)

Julia fractal

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")

png

%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)

Vectorize

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. ])

Cython

!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)

Using IPython cython command

%load_ext cython

%%cython -a
def cy_sum(data):
    s = 0.0
    for d in data:
        s += d
    return s

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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):
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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)

Cummulative sum

%%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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%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))

Fused types

py_sum([1.0, 2.0, 3.0, 4.0, 5.0])

15.0

py_sum([1, 2, 3, 4, 5])

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):
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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]))

Julia fractal

%%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

body.cython { font-family: courier; font-size: 12; }

.cython.tag { } .cython.line { margin: 0em } .cython.code { font-size: 9; color: #444444; display: none; margin: 0px 0px 0px 8px; border-left: 8px none; }

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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)

Calling C function

%%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)

Versions

%reload_ext version_information

%version_information numpy, cython, numba, matplotlib