This portfolio is split up into 4 separate tasks which will test your knowledge of mathematics, C programming and concurrency. Each task should be zipped up into a single zip folder containing all C and resource files for the submission on Canvas.

Linear Regression (20% - 100 marks)

This task will test your knowledge of file input and mathematical formulas. Basic linear regression (LR) is used to find a relationship between two types of data. For example, you could use LR to find the relationship between glucose intake and heart rate. These initially would be plotted on a graph where the x axis represents glucose and the y axis represents heart rate. Using the LR formula, you can find y=bx+a (equation of a straight line (more commonly known as y=mx+c) between "n" number of points on a graph. Below are the formulas to find "a" and "b".
A = (Σy)(Σx^2) - (Σx)(Σxy) / n(Σx^2) - (Σx)^2
B = n(Σxy) - (Σx)(Σy) / n(Σx^2) - (Σx)^2
You will be given multiple text files containing "n" number of coordinates. Your program will read in the coordinates (x,y) and use the LR formula to produce the gradient (a) and the constant (b), and being able to print out y=bx+a. For example, if a = 0.5 and b=-2, your program will print out y=-2x+0.5. This equation now represents the trend in the data you will be given. Finally, your program will ask the user to type in a value of x which will then calculate y.
Read data from file appropriately (30 marks)
Use LR formula to process the data and print out the correct equation of a straight line (50 marks)
Find new value of "y" using user input (20 marks)

Calculating Pi using Leibniz formula and multithreading (20% - 100 marks)

The Leibniz formula is an infinite series method of calculating Pi. The formula is a very simple way of calculating Pi, however, it takes a large amount of iterations to produce a low precision value of Pi. This task requires a large amount of computation and therefore it is vital that you use multithreading to speed up the program. Below is the Leibniz formula:
Σ ((-1)^n) / (2n + 1) = π/4
(The summation runs from n=0 to infinity)
As the series can be iterated infinite amount of times, your program should allow the user to take in 2 command line arguments; the first is the number of iterations (argv[1]) and the second is the amount of threads (argv[2]) the user would like to use. This means that the slicing of workload needs to be dynamic. NOTE – this program should work with any amount of threads.
Calculating Pi using Leibniz formula (20 marks)
Using multithreading with appropriate slicing (60 marks)
Correct value of Pi printed out depending on iteration count (20 marks)

Finding prime numbers in a text file using multithreading (30% - 100 marks)

You will be given a file containing a list of numbers. The amount and numbers themselves will be random. You will create a C program which counts the number of prime numbers there are within the file and output to a file the amount of prime numbers found, along with the prime numbers themselves. The aim of this task is to use POSIX threads to parallelise the task to take advantage of the multicore processor within your machine to speed up the task. The threads you spawn within the program must compute an equal or close to an equal amount of computations to make the program more efficient in relation to speed. For this section, as you will only be reading one file and splitting it across many threads (determined by argv[1]), you should load in the file and split the file into equal parts, then process each slice within your threads. This task also tests your knowledge of dynamic memory allocation. NOTE – this program should work with any amount of threads.
Reading in an image file into a single or 2D array (10 marks)
Applying Box filter on image (20 marks)
Using multithreading appropriately to apply Box filter (40 marks)
Using dynamic memory – malloc (10 marks)
Outputting the correct image with Box Blur applied (20 marks)