### The Magic of Numba and Python

Python is a great programming language. It's primary merits are readability and the numerous packages that are available online. However, being an interpreted language the speed of execution is always an issue. Here is a simple example of a piece of code written in Python that tries to add two numbers from a grid.

#!/usr/bin/python

def overlap_pp(x,y):
count = 0
for i in range(x):
for j in range(y):
count += i + j
return count

for _ in range(1000):
q = overlap_pp(500,500)


If you run the above script (saved as n.py) on the command line terminal with the time command you should see some numbers like the below

time ./n.py

real 0m22.379s
user 0m22.363s
sys 0m0.407s


The process running on one processor took about 22 seconds to complete the run. Now lets do something seemingly magical. Lets add a decorator. Decorators are python speak for a mechanism to do wrapper functions. The decorator we are going to add is '@jit'. The code looks like as it is shown below

#!/usr/bin/python

from numba import jit

@jit
def overlap_pp(x,y):
count = 0
for i in range(x):
for j in range(y):
count += i + j
return count

for _ in range(1000):
q = overlap_pp(500,500)


Now let's time this as before.

time ./n.py

real 0m0.420s
user 0m0.370s
sys 0m0.443s



Magic! The exact same code now runs 55x faster! This happens because the Just-In-Time (jit) feature of the numba package compiles the function to machine code on the fly. The timing you see is almost in line with what you would expect from a similar code done in C or Fortran. In fact you will be surprised that in this particular example, the numba version runs faster than the C version! The C code is shown below.
#include < stdio.h >

int overlap_pp(int x,int y){
int i,j,q;
for(i=0;i<= x;i++){
for(j=0;j<= y;j++){
q += i + j;
}
}
return(q);
}

int main(int argc,char** argv){
int i,q;
for(i = 0;i<=1000;i++){
q = overlap_pp(500,500);
}
return 0;
}


The timing results after compiling the above code 'gcc t.c -o t'

time ./t

real 0m0.774s
user 0m0.774s
sys 0m0.000s


Unfortunately there isn't a clear description online on how to get Numba installed on Ubuntu 14.04. After some hacking and poking around stackoverflow the following worked for me.

Step 1:
Numba uses llvm. You need to remove all llvm, llvm-config and llvmlite installations that you already have on your system. Numba needs llvm-3.8 upwards to work properly.

Step 2:
Follow instructions in this stackoverflow thread. But when you get installing do the following
sudo apt-get install zlib1g zlib1g-dev libedit2 libedit-dev llvm-3.8 llvm-3.8-dev
Notice change in version number to 3.8.

Step 3:
Next, install llvmlite. You also want to create a symbolic link on '/usr/bin/' to point to the latest 3.8 version of llvm-config.
"sudo ln -s /usr/bin/llvm-config-3.8 /usr/bin/llvm-config"
This step is important because the installation of numba appears to use llvm-config. After this you can install Numba directly using pip.

If you are interested in learning more about python programming, data science and probability here are a list of books that are worthwhile to buy.

### The Best Books to Learn Probability

If you are looking to buy some books in probability here are some of the best books to learn the art of Probability

The Probability Tutoring Book: An Intuitive Course for Engineers and Scientists (and Everyone Else!)
A good book for graduate level classes: has some practice problems in them which is a good thing. But that doesn't make this book any less of buy for the beginner.

An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd Edition
This is a two volume book and the first volume is what will likely interest a beginner because it covers discrete probability. The book tends to treat probability as a theory on its own

Discovering Statistics Using R
This is a good book if you are new to statistics & probability while simultaneously getting started with a programming language. The book supports R and is written in a casual humorous way making it an easy read. Great for beginners. Some of the data on the companion website could be missing.

Fifty Challenging Probl…

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Linear Algebra (2nd Edition)
This is the gold standard for linear algebra at an undergraduate level. This book has been around for quite sometime a great book to own.

Linear Algebra: A Modern Introduction
Good book if you want to learn more on the subject of linear algebra however typos in the text could be a problem.

Linear Algebra (Dover Books on Mathematics)
An excellent book to own if you are looking to get into, or want to understand linear algebra. Please keep in mind that you need to have some basic mathematical background before you can use this book.

Linear Algebra Done Right (Undergraduate Texts in Mathematics)
A great book that exposes the method of proof as it used in Linear Algebra. This book is not for the beginner though. You do need some prior knowledge of the basics at least. It would be a good add-on to an existing course you are doing in Linear Algebra.

Linear Algebra, 4th Edition
This is good book …

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If you are looking to learn time series analysis, the following are some of the best books in time series analysis.

Introductory Time Series with R (Use R!)
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Econometrics
A great book if you are in an economics stream or want to get into it. The nice thing in the book is it tries to bring out a oneness in all the methods used. Econ majors need to be up-to speed on the grounding mathematics for time series analysis to use this book. Outside of those prerequisites, this is one of the best books on econometrics and time series analysis.

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