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### linear regression (LR) is used to find a relationship between two types of data you could use LR to find the relationship between glucose intake and heart rate.

INSTRUCTIONS TO CANDIDATES

Assessment overview

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

The following tasks will be discussed during lecture 1

1. Linear Regression (25% - 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.”

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)

1. Calculating Pi using Leibniz formula and multithreading (25% - 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:

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 and the second is the amount of threads the user would like to use. This means that the slicing of workload needs to be dynamic.

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)

1. Finding prime numbers from multiple text files using multithreading (25% - 100 marks)

Creating an algorithm to detect prime numbers (10 marks)

Using dynamic memory – “malloc” (20 marks)

Using multithreading with equal computations (50 marks)

Outputting correct output to a file (20 marks)

1. Gaussian Blur with multithreading (25% - 100 marks)

Your program will decode a PNG file into an array and apply the gaussian blur filter. Blurring an image reduces noise by taking the average RGB values around a specific pixel and setting it’s RGB to the mean values you’ve just calculated. This smoothens the colour across a matrix of pixels. For this assessment, you will use a 3x3 matrix. For example, if you have a 5x5 image such as the following (be aware that the coordinate values will depend on how you format your 2D array):

 0,4 1,4 2,4 3,4 4,4 0,3 1,3 2,3 3,3 4,3 0,2 1,2 2,2 3,2 4,2 0,1 1,1 2,1 3,1 4,1 0,0 1,0 2,0 3,0 4,0

The shaded region above represents the pixel we want to blur, in this case, we are focusing on pixel 1,2 (x,y) (Centre of the matrix). to apply the blur for this pixel, you would sum all the Red values from the surrounding coordinates including 1,2 (total of 9 R values) and find the average (divide by 9). This is now the new Red value for coordinate 1,2. You must then repeat this for Green and Blue values. This must be repeated throughout the image. If you are working on a pixel which is not fully surrounded by pixels (8 pixels), you must take the average of however many neighbouring pixels there are.

Reading in an image file into a single or 2D array (10 marks)

Applying Gaussian filter on image (20 marks)

Using multithreading appropriately to apply Gaussian filter (40 marks)

Using dynamic memory – malloc (10 marks)

Outputting the correct image with Gaussian Blur applied (20 marks)

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