UNIVERSITY OF WEST ATTICA
SCHOOL OF ENGINEERING
DEPARTMENT OF COMPUTER ENGINEERING AND INFORMATICS

University of West Attica · Department of Computer Engineering and Informatics

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Parallel Systems

Covariance Register

Vasileios Evangelos Athanasiou
Student ID: 19390005

GitHub · LinkedIn

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Supervision

Supervisor: Vasileios Mamalis, Professor

UNIWA Profile

Co-supervisor: Michalis Iordanakis, Academic Scholar

UNIWA Profile · Scholar

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Athens, February 2025

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README

Covariance Register

This repository implements a CUDA-based program for calculating basic statistics and generating the covariance matrix of a 2D N×N integer array. The project was developed for the Parallel Systems course at the University of West Attica.

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Table of Contents

Section	Folder/File	Description
1	assign/	Assignment material for the Covariance Register CUDA workshop
1.1	assign/_Par_Sys_Ask_2-2_2024-25.pdf	Assignment description in English
1.2	assign/_Παρ_Συσ_Ασκ_2-2_2024-25.pdf	Assignment description in Greek
2	docs/	Documentation for covariance register computations
2.1	docs/Covariance-Register.pdf	English documentation
2.2	docs/Μητρώο-Συνδιακύμανσης.pdf	Greek documentation
3	src/	Source code and input/output files
3.1	src/cuda2.cu	Main CUDA program for covariance register
3.2	src/A/	Input data files for exercise A
3.2.1	src/A/A8.txt	Input matrix A for 8 elements
3.2.2	src/A/A_cov8.txt	Covariance matrix input for 8 elements
3.3	src/A_cov/	Intermediate covariance results
3.3.1	src/A_cov/g.txt	Covariance computation result
3.4	src/A_means/	Mean values for A
3.4.1	src/A_means/A_means8.txt	Mean values for 8 elements
3.4.2	src/A_means/j.txt	Additional mean data
3.5	src/A_submeans/	Subtracted mean matrices for A
3.5.1	src/A_submeans/A_submeans8.txt	Subtracted mean for 8 elements
3.5.2	src/A_submeans/l.txt	Additional submean data
3.6	src/AT_submeans/	Transposed subtracted mean matrices
3.6.1	src/AT_submeans/AT_submeans8.txt	Transposed subtracted mean for 8 elements
3.6.2	src/AT_submeans/l.txt	Additional transposed submean data
3.7	src/Output/	Output result files from CUDA execution
3.7.1	src/Output/Output_no_args.txt	Output without arguments
3.7.2	src/Output/Output8.txt	Output for 8 elements
3.7.3	src/Output/Output512.txt	Output for 512 elements
3.7.4	src/Output/Output1024.txt	Output for 1024 elements
3.7.5	src/Output/Output10000.txt	Output for 10000 elements
4	README.md	Project documentation
5	INSTALL.md	Usage instructions

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1. Overview

The program performs sequential operations on an input matrix to compute its covariance:

• Column Means: Computes the mean of each column.
• Mean Subtraction & Transpose: Subtracts the column mean from each element and creates a transposed difference matrix.
• Covariance Calculation: Generates the final covariance matrix using parallel computations.

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2. Design & Implementation

CUDA Kernels:

• calcColMeans: Each thread processes a column to calculate its mean.
• subMeansT: Organized threads remove column means and transpose the matrix simultaneously.
• calcCov: Calculates the upper triangular covariance matrix while exploiting symmetry for performance.

Technical Specifications:

• Synchronization: Uses __syncthreads() to coordinate threads within a block.
• Memory Management: Employs shared memory for intermediate storage and faster access.
• Optimization: Grid and block configurations (dimGrid, dimBlock) maximize GPU resource usage.