Previous posts have included an SVG library, memoization of factorials and Taylor Polynomials. In this post I will bring these all together to plot various sine waves created using Taylor Polynomials.
Very briefly, Taylor Polynomials are used to approximate functions, in this case sine and cosine, to any level of accuracy. We can plot these levels to show how they become increasingly accurate, which is the subject of this post.
This is a relatively short and simple project which will calculate a few simple statistics from an array of numbers. It covers the most basic areas of classical statistics which might seem a bit old-fashioned in an era of big data and machine learning algorithms, but even the most complex of data science investigations are likely to start out with a few simple statistics.
If you just need a few values then this approach is overkill, but some applications require very heavy use of trigonometry and so need all the optimization they can get. In particular 3D graphics consist of large numbers of triangles, the positioning and rendering of which requires some serious use of trigonometry.
In this post I will write a C library to calculate sines and cosines using Taylor polynomials. It is impossible to calculate these directly but they can be approximated to any accuracy using this method, and I will show how a Taylor series converges to ever-increasing accuracy.
I recently wrote an article on Bubble Sort, more as an academic exercise than a piece of practical and usable code. At the bottom of the post I suggested that the C library’s built-in qsort (Quicksort) function was the best option for sorting arrays in most situations.
However, there is more to using qsort than just throwing an array at a function: you need to provide your own comparator function, the implementation of which can be slightly fiddly if you are sorting anything other than primitive data types. In this article I’ll start off with a simple int-sorting example, and then go on to sort an array of structs, firstly by an int and then by a string.
In a previous post I implemented the Pearson Correlation Coefficient, a measure of how much one variable depends on another. The three sets of bivariate data I used for testing and demonstration are shown again below, along with their corresponding scatterplots. As you can see these scatterplots now have lines of best fit added, their gradients and heights being calculated using least-squares regression which is the subject of this article.
Prime numbers have been understood at least since the Ancient Greeks, and possibly since the Ancient Egyptians. In modern times their study has intensified greatly due to their usefulness, notably in encryption, and because computers enable them to be calculated to a massively higher level than could be done by hand.
The best know (and according to Wikipedia still the most widely used) method for identifying them is the Sieve of Eratosthenes, which I will implement here in C.
Correlation is the process of quantifying the relationship between two sets of values, and in this post I will be writing code in C to calculate possibly the best-known type of correlation - the Pearson Correlation Coefficient.