Python on CyberSpy

Recursion Revisited

Tue, 28 Nov 2017 15:23:02 -0500

Recursion, from more than one point-of-view.

A common programming idiom in computer science is solving a problem by self-reference, also known as recursion. In this post, we look at two different implementations of the same problem.

Solve a recursive problem in two different programming language paradigms

Let’s look at the solution to a simple problem, compute $f(x)=e^{x}$.

We will illustrate two separate solutions - one in a procedural language (python), and the other in a functional language (elixir).

Let’s start off with the functional language. Were does recursion come into play?

We define the function $f(x)=e^x$ as the infinite sum, $\text{ }f(x) = \sum_{n=0}^\infty{\frac{x^n}{n!}}$

In our solution below, we define two separate recursive functions, exp/2 and fac/1. What’s interesting to note here is how each of these functions has two separate definitions. This is an aspect of programming in elixir that elegantly uses pattern-matching to return different results depending upon the input. Our two functions nicely dovetail into the base-case and recursive case of a recursive algorithm.

For example, looking at exp/2, the first function definition returns 1 for any value of x (as indicated by the _ preceding the variable) and returns 1. This is the mathematical equivalent of $x^0=1\text{ for any }x$.

The second definition of exp/2 is the recursive case. for any value of $n\gt0$. Moreover, we define exp(x, n) as $\frac{e^x}{n!}$ + exp(x, n-1).

Similarly for the definition of fac/1 we see two definitions; one for $n=0$ and another for all values of $n\gt0$.

Visualizing the News: Grab your PILlow

Sun, 12 Nov 2017 21:32:23 -0500

A Picture’s Worth a Gazillion Bits

newsapi

This weekend, I tripped over a neat news REST-ful api called newsapi. Grab an API key and you’re off to the races.

There are tons of live headlines - News API can provide headlines from 70 worldwide sources.

There are basically two api endpoints:

Accessing the API with Python

newsapi can easily be accessed using a browser since the REST-ful method used is a GET method. But, accessing the api from the browser is limiting.

Making Heads or Tails out of Recursion and Combinatorial Math

Thu, 09 Nov 2017 21:27:05 -0500

GNU — GNU’s Not Unix

I thought I’d take a look at two topics at once and make some fun by mashing them together. Today’s topic is recursion. In computer science (and in math, although we call the equation a recurrence relation) recursion is an often misunderstood concept causing lots of panic and anxiety. In reality - it’s pretty easy once you wrap you head around the idiom.

What is recursion?

When we define a function in such a way that it calls itself, we’ve defined a recusive function. The most basic example is the Factorial function, $f(n)=n!$. We define the function recursively by defining it in reference to itself. So, recursively, we define $f(n)$ as:

Getting Visual With It

Wed, 08 Nov 2017 10:26:20 -0500

Time to Get Vizzy With It!

Like Will says:

Gettin vizzy wit it Na na na na na na na nana Na na na na nana Gettin vizzy wit it…

Plot thickens

Time to turn on the lights and see what our data objects look like when we turn them into visualized plots. Sure, we can use the print function to see the numbers within our numpy objects. Better yet, let’s turn our objects into pretty graphical images. To do so, we turn to the matplotlib library. An extensive library of plotting routines that easily allows us to render image plots into many different formats (png, jpg, pdf, etc…) - both onto the screen for quick visual inspection, or written to a file for general use.

Do the Numpy

Tue, 07 Nov 2017 15:36:43 -0500

Do the Numpy Dance, Is your Chance to do the Nump!

Sir Numpy says:

The Numpy Dance is your chance to do the nump Do the Numpy Nump, come on and do the Numpty Nump Do the Numpy Nump, just watch me do the Numpty Nump Do ya know what I’m doin’, doin’ the Numpty Nump Do the Numpy Nump, do the Numpty Nump

Start at the beginning: `NumPy`

The first library that we will investigate is numpy. Simply put, numpy allows us to represent mathematical objects like arrays and matricies of different datatypes and performs operations on those objects thereby easing the burden of writing the tedious code within your applications to do the mundane representations and operations.