Python 3.6.9 : My colab tutorials - parts 006 - 007.

This tutorial is called: My colab tutorials - parts 006 - 007.
The only reason for synchronization with the source code from my GitHub account on the Colab project.
I like collab more and more because I can quickly test the source code.
The example is taken from here and adapted to work on Colab and the new version of numba
Here is a simple example with the python numba package to creat that Mandelbrot fractal set.

import numba
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.
  """
  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 max_iters

@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

image = np.zeros((1024, 1536), dtype = np.uint8)
start = timer()
create_fractal(-2.0, 1.0, -1.0, 1.0, image, 20) 
dt = timer() - start

print ("Mandelbrot created in %f s" % dt)
imshow(image)
show() 

Python 3.8.2 : The numba python package - part 001 .

The development of this python package comes with this short intro:
Numba is a just-in-time compiler for Python that works best on code that uses NumPy arrays and functions and loops. The most common way to use Numba is through its collection of decorators that can be applied to your functions to instruct Numba to compile them. When a call is made to a Numba decorated function it is compiled to machine code “just-in-time” for execution and all or part of your code can subsequently run at native machine code speed!
I installed this python package on my folder Python38:

D:\Python38>pip3 install numba
Collecting numba
...
Successfully installed numba-0.50.1
D:\Python38>python.exe
Python 3.8.2 (tags/v3.8.2:7b3ab59, Feb 25 2020, 22:45:29) [MSC v.1916 32 bit (Intel)] on win32
Type "help", "copyright", "credits" or "license" for more information.
>>> import numba
>>> numba.__version__
'0.50.1'

This package did not work with python install on the folder Python38_64:

D:\Python38_64>pip3 install numba
Collecting numba
...
Installing collected packages: numpy, llvmlite, numba
Successfully installed llvmlite-0.33.0 numba-0.50.1 numpy-1.19.1
WARNING: You are using pip version 20.1; however, version 20.1.1 is available.
...
D:\Python38_64>python.exe
Python 3.8.4 (tags/v3.8.4:dfa645a, Jul 13 2020, 16:46:45) [MSC v.1924 64 bit (AMD64)] on win32
Type "help", "copyright", "credits" or "license" for more information.
>>> import numba
Traceback (most recent call last):
...
ModuleNotFoundError: No module named 'numba'

You can write standard Python functions and run them on a CUDA-capable GPU.
First, I need to enable this feature:

D:\Python38>SET NUMBA_ENABLE_CUDASIM=1

D:\Python38>python
Python 3.8.2 (tags/v3.8.2:7b3ab59, Feb 25 2020, 22:45:29) [MSC v.1916 32 bit (Intel)] on win32
Type "help", "copyright", "credits" or "license" for more information.
>>> from numba import cuda
>>> print(cuda.gpus)
...Managed Device 0...

Let's test with a simple example to create a data and use it:

D:\Python38>python
Python 3.8.2 (tags/v3.8.2:7b3ab59, Feb 25 2020, 22:45:29) [MSC v.1916 32 bit (Intel)] on win32
Type "help", "copyright", "credits" or "license" for more information.
>>> import time
>>> import numpy as np
>>> from numba import cuda
>>>
>>> @cuda.jit
... def create(data):
...     data[cuda.blockIdx.x, cuda.threadIdx.x] = cuda.blockIdx.x
...
>>> numBlocks = 4
>>> threadsPerBlock = 6
>>>
>>> data = np.ones((numBlocks, threadsPerBlock), dtype=np.uint8)
>>> create[numBlocks, threadsPerBlock](data)
>>> print(data)
[[0 0 0 0 0 0]
 [1 1 1 1 1 1]
 [2 2 2 2 2 2]
 [3 3 3 3 3 3]]

The numba python module - part 002 .

Today I tested how fast is jit from numba python and fibonacci math function.
You will see strange output I got for some values.
First example:

import numba
from numba import jit
from timeit import default_timer as timer

def fibonacci(n):
    a, b = 1, 1
    for i in range(n):
        a, b = a+b, a
    return a
fibonacci_jit = jit(fibonacci)

start = timer()
fibonacci(100)
duration = timer() - start

startnext = timer()
fibonacci_jit(100)
durationnext = timer() - startnext

print(duration, durationnext)

The result of this run is:

C:\Python27>python numba_test_003.py
(0.00018731270733896962, 0.167499256682878)

C:\Python27>python numba_test_003.py
(1.6357787798437412e-05, 0.1683614083221368)

C:\Python27>python numba_test_003.py
(2.245186560569841e-05, 0.1758382003097716)

C:\Python27>python numba_test_003.py
(2.3093347480146938e-05, 0.16714964906130353)

C:\Python27>python numba_test_003.py
(1.5395564986764625e-05, 0.17471143739730277)

C:\Python27>python numba_test_003.py
(1.5074824049540363e-05, 0.1847134227837042)

As you can see the fibonacci function is not very fast.
The jit - just-in-time compile is very fast.
Let's see if the python source code may slow down.
Let's see the new source code with jit will not work well:

import numba
from numba import jit
from timeit import default_timer as timer

def fibonacci(n):
    a, b = 1, 1
    for i in range(n):
        a, b = a+b, a
    return a
fibonacci_jit = jit(fibonacci)

start = timer()
print fibonacci(100)
duration = timer() - start

startnext = timer()
print fibonacci_jit(100)
durationnext = timer() - startnext

print(duration, durationnext)

The result is this:

C:\Python27>python numba_test_003.py
927372692193078999176
1445263496
(0.0002334994022992635, 0.17628787910376)

C:\Python27>python numba_test_003.py
927372692193078999176
1445263496
(0.0006886307922204926, 0.17579169287387408)

C:\Python27>python numba_test_003.py
927372692193078999176
1445263496
(0.0008105123483657127, 0.18209553525407973)

C:\Python27>python numba_test_003.py
927372692193078999176
1445263496
(0.00025466830415606486, 0.17186550306131188)

C:\Python27>python numba_test_003.py
927372692193078999176
1445263496
(0.0007348174871807866, 0.17523103771560608)

The result for value 100 is not the same: 927372692193078999176 and 1445263496.
The first problem is:
The problem is that numba can't intuit the type of lookup. If you put a print nb.typeof(lookup) in your method, you'll see that numba is treating it as an object, which is slow.
The second problem is the output but can be from the same reason.
I test with value 5 and the result is :

C:\Python27>python numba_test_003.py
13
13
13
13
(0.0007258367409385072, 0.17057997338491704)

C:\Python27>python numba_test_003.py
13
13
(0.00033709872502270044, 0.17213235952108247)

C:\Python27>python numba_test_003.py
13
13
(0.0004836773333341886, 0.17184433415945508)

C:\Python27>python numba_test_003.py
13
13
(0.0006854233828482501, 0.17381272129120037)

The numba python module - part 001 .

Today I tested the numba python module.
This python module allows us to speed up applications with high-performance functions written directly in Python.
The numba python module works by generating optimized machine code using the LLVM compiler infrastructure at import time, runtime, or statically.
The code can be just-in-time compiled to native machine instructions, similar in performance to C, C++ and Fortran.
For the installation I used the pip tool:

C:\Python27>cd Scripts

C:\Python27\Scripts>pip install numba
Collecting numba
  Downloading numba-0.35.0-cp27-cp27m-win32.whl (1.4MB)
    100% |################################| 1.4MB 497kB/s
...
Installing collected packages: singledispatch, funcsigs, llvmlite, numba
Successfully installed funcsigs-1.0.2 llvmlite-0.20.0 numba-0.35.0 singledispatch-3.4.0.3

C:\Python27\Scripts>pip install numpy
Requirement already satisfied: numpy in c:\python27\lib\site-packages

The example test from official website working well:
The example source code is:

from numba import jit
from numpy import arange

# jit decorator tells Numba to compile this function.
# The argument types will be inferred by Numba when function is called.
@jit
def sum2d(arr):
    M, N = arr.shape
    result = 0.0
    for i in range(M):
        for j in range(N):
            result += arr[i,j]
    return result

a = arange(9).reshape(3,3)
print(sum2d(a))

The result of this run python script is:

C:\Python27>python.exe numba_test_001.py
36.0

Another example using just-in-time compile is used with Numba’s jit function:

import numba
from numba import jit

def fibonacci(n):
    a, b = 1, 1
    for i in range(n):
        a, b = a+b, a
    return a

print fibonacci(10)

fibonacci_jit = jit(fibonacci)
print fibonacci_jit(14)

Also, you can use jit is as a decorator:

@jit
def fibonacci_jit(n):
    a, b = 1, 1
    for i in range(n):
        a, b = a+b, a

    return a

Numba is a complex python module because use compiling.
First, compiling takes time, but will work especially for small functions.
The Numba python module tries to do its best by caching compilation as much as possible though.
Another note: not all code is compiled equally.