Notebook

Chapter 19: Code optimization¶

Robert Johansson

Source code listings for Numerical Python - Scientific Computing and Data Science Applications with Numpy, SciPy and Matplotlib (ISBN 979-8-8688-0412-0).

In [1]:

import numba

In [2]:

import pyximport

In [3]:

import cython

In [6]:

import numpy as np

In [7]:

%matplotlib inline
import matplotlib.pyplot as plt

Numba¶

In [8]:

np.random.seed(0)

In [9]:

data = np.random.randn(50000)

In [10]:

def py_sum(data):
    s = 0
    for d in data:
        s += d
    return s

In [11]:

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 [12]:

%timeit py_sum(data)

2.99 ms ± 39.3 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)

In [13]:

assert abs(py_sum(data) - np.sum(data)) < 1e-10

In [14]:

%timeit np.sum(data)

12.7 μs ± 164 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)

In [15]:

%timeit py_cumsum(data)

6.44 ms ± 14.1 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)

In [16]:

assert np.allclose(np.cumsum(data), py_cumsum(data))

In [17]:

%timeit np.cumsum(data)

106 μs ± 245 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)

In [18]:

@numba.jit
def jit_sum(data):
    s = 0 
    for d in data:
        s += d

    return s

In [19]:

assert abs(jit_sum(data) - np.sum(data)) < 1e-10

In [20]:

%timeit jit_sum(data)

46 μs ± 22.2 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)

In [21]:

jit_cumsum = numba.jit()(py_cumsum)

In [22]:

assert np.allclose(np.cumsum(data), jit_cumsum(data))

In [23]:

%timeit jit_cumsum(data)

52.9 μs ± 25.4 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)

Julia fractal¶

In [24]:

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 [25]:

jit_julia_fractal = numba.jit(nopython=True)(py_julia_fractal)

In [26]:

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 [27]:

jit_julia_fractal(z_real, z_imag, j)

In [28]:

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 [29]:

%timeit py_julia_fractal(z_real, z_imag, j)

15.6 s ± 82.5 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

In [30]:

%timeit jit_julia_fractal(z_real, z_imag, j)

175 ms ± 567 μs per loop (mean ± std. dev. of 7 runs, 10 loops each)

Vectorize¶

In [31]:

def py_Heaviside(x):
    if x == 0.0:
        return 0.5
    
    if x < 0.0:
        return 0.0
    else:
        return 1.0

In [32]:

x = np.linspace(-2, 2, 50001)

In [33]:

%timeit [py_Heaviside(xx) for xx in x]

6.44 ms ± 63.1 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)

In [34]:

np_vec_Heaviside = np.vectorize(py_Heaviside)

In [35]:

np_vec_Heaviside(x)

Out[35]:

array([0., 0., 0., ..., 1., 1., 1.])

In [36]:

%timeit np_vec_Heaviside(x)

4.93 ms ± 187 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)

In [37]:

def np_Heaviside(x):
    return (x > 0.0) + (x == 0.0)/2.0

In [38]:

%timeit np_Heaviside(x)

81.3 μs ± 456 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)

In [39]:

@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 [40]:

%timeit jit_Heaviside(x)

15.7 μs ± 368 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)

In [41]:

jit_Heaviside([-1, -0.5, 0.0, 0.5, 1.0])

Out[41]:

array([0. , 0. , 0.5, 1. , 1. ])

Cython¶

In [42]:

!rm cy_sum.*

rm: cannot remove 'cy_sum.*': No such file or directory

In [43]:

%%writefile cy_sum.pyx

def cy_sum(data):
    s = 0.0
    for d in data:
        s += d
    return s

Writing cy_sum.pyx

In [44]:

!cython cy_sum.pyx

/opt/conda/lib/python3.11/site-packages/Cython/Compiler/Main.py:381: FutureWarning: Cython directive 'language_level' not set, using '3str' for now (Py3). This has changed from earlier releases! File: /home/rob/notebooks/cy_sum.pyx
  tree = Parsing.p_module(s, pxd, full_module_name)

In [45]:

# 5 lines of python code -> 1470 lines of C code ...
!wc cy_sum.c

  6126  19777 233611 cy_sum.c

In [46]:

%%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'] )

Writing setup.py

In [52]:

!/opt/conda/envs/npbook_py310/bin/python setup.py build_ext --inplace > /dev/null

/opt/conda/envs/npbook_py310/lib/python3.10/site-packages/Cython/Compiler/Main.py:381: FutureWarning: Cython directive 'language_level' not set, using '3str' for now (Py3). This has changed from earlier releases! File: /home/rob/notebooks/cy_sum.pyx
  tree = Parsing.p_module(s, pxd, full_module_name)

In [53]:

from cy_sum import cy_sum

In [54]:

cy_sum(data)

Out[54]:

-189.70046227549025

In [55]:

%timeit cy_sum(data)

2.44 ms ± 115 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)

In [56]:

%timeit py_sum(data)

2.87 ms ± 71.3 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)

In [57]:

%%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

Writing cy_cumsum.pyx

In [58]:

pyximport.install(setup_args={'include_dirs': np.get_include()});

In [59]:

pyximport.install(setup_args=dict(include_dirs=np.get_include()));

In [ ]:

from cy_cumsum import cy_cumsum

In [61]:

%timeit cy_cumsum(data)

5.94 ms ± 165 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)

In [62]:

%timeit py_cumsum(data)

6.47 ms ± 41.1 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)

Using IPython cython command¶

In [63]:

%load_ext cython

In [64]:

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

Out[64]:

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In [65]:

%timeit cy_sum(data)

2.57 ms ± 56.3 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)

In [66]:

%timeit py_sum(data)

2.96 ms ± 107 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)

In [67]:

assert np.allclose(np.sum(data), cy_sum(data))

In [68]:

%%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

Content of stderr:
In file included from /opt/conda/envs/npbook_py310/lib/python3.10/site-packages/numpy/core/include/numpy/ndarraytypes.h:1929,
                 from /opt/conda/envs/npbook_py310/lib/python3.10/site-packages/numpy/core/include/numpy/ndarrayobject.h:12,
                 from /opt/conda/envs/npbook_py310/lib/python3.10/site-packages/numpy/core/include/numpy/arrayobject.h:5,
                 from /home/rob/.cache/ipython/cython/_cython_magic_16d506d9dddc3a141b0f412e0228a611fa6c09f1.c:1250:
/opt/conda/envs/npbook_py310/lib/python3.10/site-packages/numpy/core/include/numpy/npy_1_7_deprecated_api.h:17:2: warning: #warning "Using deprecated NumPy API, disable it with " "#define NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION" [-Wcpp]
   17 | #warning "Using deprecated NumPy API, disable it with " \
      |  ^~~~~~~

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In [69]:

%timeit cy_sum(data)

46 μs ± 9.16 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)

In [70]:

%timeit jit_sum(data)

46 μs ± 10.4 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)

In [71]:

%timeit np.sum(data)

12.7 μs ± 14.4 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)

Cummulative sum¶

In [72]:

%%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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Content of stderr:
In file included from /opt/conda/envs/npbook_py310/lib/python3.10/site-packages/numpy/core/include/numpy/ndarraytypes.h:1929,
                 from /opt/conda/envs/npbook_py310/lib/python3.10/site-packages/numpy/core/include/numpy/ndarrayobject.h:12,
                 from /opt/conda/envs/npbook_py310/lib/python3.10/site-packages/numpy/core/include/numpy/arrayobject.h:5,
                 from /home/rob/.cache/ipython/cython/_cython_magic_a7031120ac776f6c06c9d1ee05b4d71edd090747.c:1251:
/opt/conda/envs/npbook_py310/lib/python3.10/site-packages/numpy/core/include/numpy/npy_1_7_deprecated_api.h:17:2: warning: #warning "Using deprecated NumPy API, disable it with " "#define NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION" [-Wcpp]
   17 | #warning "Using deprecated NumPy API, disable it with " \
      |  ^~~~~~~

Out[72]:

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In [73]:

%timeit py_cumsum(data)

6.39 ms ± 28.2 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)

In [74]:

%timeit cy_cumsum(data)

53.4 μs ± 113 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)

In [75]:

%timeit jit_cumsum(data)

52.8 μs ± 11.8 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)

In [76]:

%timeit np.cumsum(data)

107 μs ± 404 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)

In [77]:

assert np.allclose(cy_cumsum(data), np.cumsum(data))

Fused types¶

In [78]:

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

Out[78]:

15.0

In [79]:

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

Out[79]:

In [80]:

cy_sum(np.array([1.0, 2.0, 3.0, 4.0, 5.0]))

Out[80]:

15.0

In [81]:

cy_sum(np.array([1, 2, 3, 4, 5]))

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In[81], line 1
----> 1 cy_sum(np.array([1, 2, 3, 4, 5]))

File _cython_magic_16d506d9dddc3a141b0f412e0228a611fa6c09f1.pyx:4, in _cython_magic_16d506d9dddc3a141b0f412e0228a611fa6c09f1.cy_sum()

ValueError: Buffer dtype mismatch, expected 'float64_t' but got 'long'

In [82]:

%%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

Content of stderr:
In file included from /opt/conda/envs/npbook_py310/lib/python3.10/site-packages/numpy/core/include/numpy/ndarraytypes.h:1929,
                 from /opt/conda/envs/npbook_py310/lib/python3.10/site-packages/numpy/core/include/numpy/ndarrayobject.h:12,
                 from /opt/conda/envs/npbook_py310/lib/python3.10/site-packages/numpy/core/include/numpy/arrayobject.h:5,
                 from /home/rob/.cache/ipython/cython/_cython_magic_c9ea336cdf929fb6c33bee737b5729b0932d7e9d.c:1252:
/opt/conda/envs/npbook_py310/lib/python3.10/site-packages/numpy/core/include/numpy/npy_1_7_deprecated_api.h:17:2: warning: #warning "Using deprecated NumPy API, disable it with " "#define NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION" [-Wcpp]
   17 | #warning "Using deprecated NumPy API, disable it with " \
      |  ^~~~~~~

Out[82]:

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In [83]:

cy_fused_sum(np.array([1.0, 2.0, 3.0, 4.0, 5.0]))

Out[83]:

15.0

In [84]:

cy_fused_sum(np.array([1, 2, 3, 4, 5]))

Out[84]:

Julia fractal¶

In [85]:

%%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

Content of stderr:
In file included from /opt/conda/envs/npbook_py310/lib/python3.10/site-packages/numpy/core/include/numpy/ndarraytypes.h:1929,
                 from /opt/conda/envs/npbook_py310/lib/python3.10/site-packages/numpy/core/include/numpy/ndarrayobject.h:12,
                 from /opt/conda/envs/npbook_py310/lib/python3.10/site-packages/numpy/core/include/numpy/arrayobject.h:5,
                 from /home/rob/.cache/ipython/cython/_cython_magic_6898fa0f5546b1e4516bdba3309b213764481d6c.c:1253:
/opt/conda/envs/npbook_py310/lib/python3.10/site-packages/numpy/core/include/numpy/npy_1_7_deprecated_api.h:17:2: warning: #warning "Using deprecated NumPy API, disable it with " "#define NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION" [-Wcpp]
   17 | #warning "Using deprecated NumPy API, disable it with " \
      |  ^~~~~~~

Out[85]:

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 11: @cython.wraparound(False)

 12: def cy_julia_fractal(numpy.ndarray[FTYPE_t, ndim=1] z_re,

 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):

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+21:                 z = z ** 2 - 0.05 + 0.68j

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+22:                 if abs2(z) > 4.0:

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+23:                     j[m, n] = t

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+24:                     break

          goto __pyx_L8_break;

In [86]:

N = 1024

In [87]:

j = np.zeros((N, N), dtype=np.int64)

In [88]:

z_real = np.linspace(-1.5, 1.5, N)

In [89]:

z_imag = np.linspace(-1.5, 1.5, N)

In [90]:

%timeit cy_julia_fractal(z_real, z_imag, j)

2.3 s ± 23.7 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

In [91]:

%timeit jit_julia_fractal(z_real, z_imag, j)

169 ms ± 5.53 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)

In [92]:

j1 = np.zeros((N, N), dtype=np.int64)

In [93]:

cy_julia_fractal(z_real, z_imag, j1)

In [94]:

j2 = np.zeros((N, N), dtype=np.int64)

In [95]:

jit_julia_fractal(z_real, z_imag, j2)

In [122]:

# assert np.allclose(j1, j2)

In [123]:

fig, axes = plt.subplots(1, 2, figsize=(14, 14))
axes[0].imshow(j1, cmap=plt.cm.RdBu_r,
          extent=[-1.5, 1.5, -1.5, 1.5])
axes[0].set_xlabel("$\mathrm{Re}(z)$", fontsize=18)
axes[0].set_ylabel("$\mathrm{Im}(z)$", fontsize=18)
axes[1].imshow(j2, cmap=plt.cm.RdBu_r,
          extent=[-1.5, 1.5, -1.5, 1.5])
axes[1].set_xlabel("$\mathrm{Re}(z)$", fontsize=18)
axes[1].set_ylabel("$\mathrm{Im}(z)$", fontsize=18)
fig.tight_layout()

Calling C function¶

In [124]:

%%cython

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

def cy_acos1(double x):
    return acos(x)

In [125]:

%timeit cy_acos1(0.5)

32.2 ns ± 0.0402 ns per loop (mean ± std. dev. of 7 runs, 10,000,000 loops each)

In [126]:

%%cython

from libc.math cimport acos

def cy_acos2(double x):
    return acos(x)

In [127]:

%timeit cy_acos2(0.5)

31.5 ns ± 0.0371 ns per loop (mean ± std. dev. of 7 runs, 10,000,000 loops each)

In [128]:

from numpy import arccos

In [129]:

%timeit arccos(0.5)

444 ns ± 8.64 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops each)

In [130]:

from math import acos

In [131]:

%timeit acos(0.5)

40 ns ± 1.26 ns per loop (mean ± std. dev. of 7 runs, 10,000,000 loops each)

In [132]:

assert cy_acos1(0.5) == acos(0.5)

In [133]:

assert cy_acos2(0.5) == acos(0.5)

Versions¶

In [1]:

%reload_ext version_information

In [2]:

%version_information numpy, cython, numba, matplotlib

Out[2]:

Software	Version
Python	3.10.12 64bit [Clang 14.0.6 ]
IPython	8.12.0
OS	macOS 10.15.7 x86\_64 i386 64bit
numpy	1.22.3
cython	3.0.0
numba	0.58.0
matplotlib	3.7.1
Sun Nov 03 19:47:42 2024 JST

In [ ]: