# Examples¶

## A Simple Function¶

Suppose we want to write an image-processing function in Python. Here’s how it might look.

import numpy

def filter2d(image, filt):
M, N = image.shape
Mf, Nf = filt.shape
Mf2 = Mf // 2
Nf2 = Nf // 2
result = numpy.zeros_like(image)
for i in range(Mf2, M - Mf2):
for j in range(Nf2, N - Nf2):
num = 0.0
for ii in range(Mf):
for jj in range(Nf):
num += (filt[Mf-1-ii, Nf-1-jj] * image[i-Mf2+ii, j-Nf2+jj])
result[i, j] = num
return result

# This kind of quadruply-nested for-loop is going to be quite slow.
# Using Numba we can compile this code to LLVM which then gets
# compiled to machine code:

from numba import double, jit

fastfilter_2d = jit(double[:,:](double[:,:], double[:,:]))(filter2d)

# Now fastfilter_2d runs at speeds as if you had first translated
# it to C, compiled the code and wrapped it with Python
image = numpy.random.random((100, 100))
filt = numpy.random.random((10, 10))
res = fastfilter_2d(image, filt)


Numba actually produces two functions. The first function is the low-level compiled version of filter2d. The second function is the Python wrapper to that low-level function so that the function can be called from Python. The first function can be called from other numba functions to eliminate all python overhead in function calling.

## Classes¶

"""
Example for extension classes.

Things that work:

- overriding Numba methods in Numba (all methods are virtual)
- inheritance
- instance attributes
- subclassing in python and calling overridden methods in Python
- arbitrary new attributes on extension classes and objects
- weakrefs to extension objects

Things that do NOT (yet) work:

- overriding methods in Python and calling the method from Numba
- multiple inheritance of Numba classes
(multiple inheritance with Python classes should work)
- subclassing variable sized objects like 'str' or 'tuple'
"""

from numba import jit, void, int_, double

# All methods must be given signatures

@jit
class Shrubbery(object):
@void(int_, int_)
def __init__(self, w, h):
# All instance attributes must be defined in the initializer
self.width = w
self.height = h

# Types can be explicitly specified through casts
self.some_attr = double(1.0)

@int_()
def area(self):
return self.width * self.height

@void()
def describe(self):
print("This shrubbery is ", self.width,
"by", self.height, "cubits.")

shrub = Shrubbery(10, 20)
print(shrub.area())
shrub.describe()
print(shrub.width, shrub.height)
shrub.width = 30
print(shrub.area())
print(shrub._numba_attrs._fields_) # This is an internal attribute subject to change!

class MyClass(Shrubbery):
def newmethod(self):
print("This is a new method.")

shrub2 = MyClass(30,40)
shrub2.describe()
shrub2.newmethod()
print(shrub._numba_attrs._fields_)


## Closures¶

"""
Example for closures. Closures may be of arbitrary dept, and they keep
the scope alive as long as the closure is alive. Only variables that are
closed over (cell variables in the defining function, free variables in the
"""

from numba import autojit, jit, float_
from numpy import linspace

@autojit
def generate_power_func(n):
@jit(float_(float_))
def nth_power(x):
return x ** n

# This is a native call
print nth_power(10)

# Return closure and keep all cell variables alive
return nth_power

for n in range(2, 5):
func = generate_power_func(n)
print [func(x) for x in linspace(1.,2.,10.)]


## Structs¶

from numba import struct, jit, double
import numpy as np

record_type = struct([('x', double), ('y', double)])
record_dtype = record_type.get_dtype()
a = np.array([(1.0, 2.0), (3.0, 4.0)], dtype=record_dtype)

@jit(argtypes=[record_type[:]])
def hypot(data):
# return types of numpy functions are inferred
result = np.empty_like(data, dtype=np.float64)
# notice access to structure elements 'x' and 'y' via attribute access
# You can also index by field name or field index:
#       data[i].x == data[i]['x'] == data[i]
for i in range(data.shape):
result[i] = np.sqrt(data[i].x * data[i].x + data[i].y * data[i].y)

return result

print hypot(a)

# Notice inferred return type
print hypot.signature
#print hypot.lfunc


## Pointers¶

import numba
from numba import *
from numba.tests.test_support import autojit_py3doc
import numpy as np

int32p = int32.pointer()
voidp = void.pointer()

@autojit_py3doc
def test_pointer_arithmetic():
"""
>>> test_pointer_arithmetic()
48L
"""
p = int32p(Py_uintptr_t(0))
p = p + 10
p += 2
return Py_uintptr_t(p) # 0 + 4 * 12

@autojit_py3doc(locals={"pointer_value": Py_uintptr_t})
def test_pointer_indexing(pointer_value, type_p):
"""
>>> a = np.array([1, 2, 3, 4], dtype=np.float32)
>>> test_pointer_indexing(a.ctypes.data, float32.pointer())
(1.0, 2.0, 3.0, 4.0)

>>> a = np.array([1, 2, 3, 4], dtype=np.int64)
>>> test_pointer_indexing(a.ctypes.data, int64.pointer())
(1L, 2L, 3L, 4L)
"""
p = type_p(pointer_value)
return p, p, p, p

@autojit
def test_compare_null():
"""
>>> test_compare_null()
True
"""
return voidp(Py_uintptr_t(0)) == numba.NULL

numba.testmod()


## Objects¶

from numba import double, autojit

class MyClass(object):
def mymethod(self, arg):
return arg * 2

@autojit(locals=dict(mydouble=double)) # specify types for local variables
def call_method(obj):
print obj.mymethod("hello")   # object result
mydouble = obj.mymethod(10.2) # native double
print mydouble * 2            # native multiplication

call_method(MyClass())


## Mandelbrot¶

from numba import autojit
import numpy as np
from pylab import imshow, jet, show, ion

@autojit
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

@autojit
def create_fractal(min_x, max_x, min_y, max_y, image, iters):
height = image.shape
width = image.shape

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, 750), dtype=np.uint8)
imshow(create_fractal(-2.0, 1.0, -1.0, 1.0, image, 20))
jet()
ion()
show()


## Filterbank Correlation¶

"""
This file demonstrates a filterbank correlation loop.
"""
import numpy as np
import numba
from numba.decorators import jit
nd4type = numba.double[:,:,:,:]

@jit(argtypes=(nd4type, nd4type, nd4type))
def fbcorr(imgs, filters, output):
n_imgs, n_rows, n_cols, n_channels = imgs.shape
n_filters, height, width, n_ch2 = filters.shape

for ii in range(n_imgs):
for rr in range(n_rows - height + 1):
for cc in range(n_cols - width + 1):
for hh in xrange(height):
for ww in xrange(width):
for jj in range(n_channels):
for ff in range(n_filters):
imgval = imgs[ii, rr + hh, cc + ww, jj]
filterval = filters[ff, hh, ww, jj]
output[ii, ff, rr, cc] += imgval * filterval

def main ():
imgs = np.random.randn(10, 64, 64, 3)
filt = np.random.randn(6, 5, 5, 3)
output = np.zeros((10, 60, 60, 6))

import time
t0 = time.time()
fbcorr(imgs, filt, output)
print time.time() - t0

if __name__ == "__main__":
main()