1.11. Examples

1.11.1. Mandelbrot

#! /usr/bin/env python
# -*- coding: utf-8 -*-
from __future__ import print_function, division, absolute_import

from timeit import default_timer as timer
from matplotlib.pylab import imshow, jet, show, ion
import numpy as np

from numba import jit


@jit
def mandel(x, y, max_iters):
    """
    Given the real and imaginary parts of a complex number,
    determine if it is a candidate for membership in the Mandelbrot
    set given a fixed number of iterations.
    """
    i = 0
    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 255

@jit
def create_fractal(min_x, max_x, min_y, max_y, image, iters):
    height = image.shape[0]
    width = image.shape[1]

    pixel_size_x = (max_x - min_x) / width
    pixel_size_y = (max_y - min_y) / height
    for x in range(width):
        real = min_x + x * pixel_size_x
        for y in range(height):
            imag = min_y + y * pixel_size_y
            color = mandel(real, imag, iters)
            image[y, x] = color

    return image

image = np.zeros((500 * 2, 750 * 2), dtype=np.uint8)
s = timer()
create_fractal(-2.0, 1.0, -1.0, 1.0, image, 20)
e = timer()
print(e - s)
imshow(image)
#jet()
#ion()
show()

1.11.2. Moving average

#!/usr/bin/env python
"""
A moving average function using @guvectorize.
"""

import numpy as np

from numba import guvectorize

@guvectorize(['void(float64[:], intp[:], float64[:])'], '(n),()->(n)')
def move_mean(a, window_arr, out):
    window_width = window_arr[0]
    asum = 0.0
    count = 0
    for i in range(window_width):
        asum += a[i]
        count += 1
        out[i] = asum / count
    for i in range(window_width, len(a)):
        asum += a[i] - a[i - window_width]
        out[i] = asum / count

arr = np.arange(20, dtype=np.float64).reshape(2, 10)
print(arr)
print(move_mean(arr, 3))

1.11.3. Multi-threading

The code below showcases the potential performance improvement when using the nogil feature. For example, on a 4-core machine, I get the following results printed out:

numpy (1 thread)       145 ms
numba (1 thread)       128 ms
numba (4 threads)       35 ms

Note

Under Python 3, you can use the standard concurrent.futures module rather than spawn threads and dispatch tasks by hand.

#!/usr/bin/env python
from __future__ import print_function, division, absolute_import

import math
import threading
from timeit import repeat

import numpy as np
from numba import jit

nthreads = 4
size = 1e6

def func_np(a, b):
    """
    Control function using Numpy.
    """
    return np.exp(2.1 * a + 3.2 * b)

@jit('void(double[:], double[:], double[:])', nopython=True, nogil=True)
def inner_func_nb(result, a, b):
    """
    Function under test.
    """
    for i in range(len(result)):
        result[i] = math.exp(2.1 * a[i] + 3.2 * b[i])

def timefunc(correct, s, func, *args, **kwargs):
    """
    Benchmark *func* and print out its runtime.
    """
    print(s.ljust(20), end=" ")
    # Make sure the function is compiled before we start the benchmark
    res = func(*args, **kwargs)
    if correct is not None:
        assert np.allclose(res, correct), (res, correct)
    # time it
    print('{:>5.0f} ms'.format(min(repeat(lambda: func(*args, **kwargs),
                                          number=5, repeat=2)) * 1000))
    return res

def make_singlethread(inner_func):
    """
    Run the given function inside a single thread.
    """
    def func(*args):
        length = len(args[0])
        result = np.empty(length, dtype=np.float64)
        inner_func(result, *args)
        return result
    return func

def make_multithread(inner_func, numthreads):
    """
    Run the given function inside *numthreads* threads, splitting its
    arguments into equal-sized chunks.
    """
    def func_mt(*args):
        length = len(args[0])
        result = np.empty(length, dtype=np.float64)
        args = (result,) + args
        chunklen = (length + numthreads - 1) // numthreads
        # Create argument tuples for each input chunk
        chunks = [[arg[i * chunklen:(i + 1) * chunklen] for arg in args]
                  for i in range(numthreads)]
        # Spawn one thread per chunk
        threads = [threading.Thread(target=inner_func, args=chunk)
                   for chunk in chunks]
        for thread in threads:
            thread.start()
        for thread in threads:
            thread.join()
        return result
    return func_mt


func_nb = make_singlethread(inner_func_nb)
func_nb_mt = make_multithread(inner_func_nb, nthreads)

a = np.random.rand(size)
b = np.random.rand(size)

correct = timefunc(None, "numpy (1 thread)", func_np, a, b)
timefunc(correct, "numba (1 thread)", func_nb, a, b)
timefunc(correct, "numba (%d threads)" % nthreads, func_nb_mt, a, b)