Overview

• Contains: An implementation of the Modified (and also Classical) Gram-Schmidt-based QR decomposition strategy for Singular Value Decomposition(SVD) for Principal Component Analysis(PCA) in the C language using OpenMP specification.
• Primary source file: lab2_omp.c
• Algorithm: Described in included problem statement docs, or refer to the Wikipedia article on the Method
• I/O: I/O format can be understood from the included header files and sample testcase files.
• Literature reference used included in repository.
• Wikipedia article on QR-decomposition: https://en.wikipedia.org/wiki/QR_decomposition
• Assignment attempted as a part of coursework requirements in COL380: Introduction to Parallel Programming and Distributed Computing (Sem-II, 2018-19) (Instructor: Prof. Subodh V. Sharma) at Indian Institute of Technology (IIT), Delhi.
• The problem statement is included. The following sections describe the assignment submission requirements and how to use the starter codes.
• Performance comments: Perhaps a strategy based on Givens-rotation-based QR-decomposition would enable a greater degree of parallelisation than the parallelised Modified-Gram-Schmidt-based implementation. It is therefore recommended that Givens rotation be employed for a parallelized QR decomposition requirement.

col380_lab2_suite

Problem Statement: Implement Principal Component Analysis with Singular Vector Decomposition

Forked from: https://github.com/dvynjli/col380_lab2_suite

Directories and files

testcase/: contains python script gen_testcase.py for sample testcase generation
lab2_io.h and lab2_io.c: functions to read matrix from file and check the correctness of the result
main_omp.c: function main()
lab2_omp.h: header file for the functions to be implemented
lab2_omp.c: implement the functions in this file
Refer to respective files for furthur details.
Do not change the directory structure and prototype of functions.

Building and Executing

g++ -fopenmp -lm lab2_io.c lab2_omp.c main_omp.c -o pca

Command Line Arguments

The program takes two command line arguments:

• arg1: input filename (consist M, N and D)
• arg2: retention (percentage of information to be retained by PCA)

Note that the retention percentage is integer. Please refer to main_omp.c for more details.
To run the program:

./pca <input filename> <retention>

Example:

./pca testcase/testcase_1000_1000 90

Generating testcases

Script gen_testcase.py generates testcases as per the parameters and output the generated testcase in file testcase_<M>_<N> in the desired format. You might need to change the values of variables M and N in the script. Read the comments in the script for more information.

python3 gen_testcase.py

Input-Output Specifications

Input dataset specifications

• M : number of rows (samples) in input matrix D
• N : number of columns (features) in input matrix D
• D : input matrix, #elements in D is (M * N)

The first line of the input file contains M followed by N. The second line contains elements of matrix D. All the values in one line are space separated.

Output Specification

Your program should perform SVD and PCA on the given input and store the results in the variables given in the program. We will check the correctness by calling the functions from the program. You should compute following matrices and values:

• U : N x N real matrix (to be computed by SVD)
• SIGMA : N x M diagonal matrix of positive real numbers ( to be computed by SVD)
• V_T : M x M real matrix (to be computed by SVD)
• K : number of columns (features) in reduced matrix D_HAT
• D_HAT : reduced matrix (to be computed by PCA)

Refer to lab2_omp.h for more details. Your program should not output anything on stdout.

Submission Instructions

• You are supposed to submit only one file named lab2_omp.c/cpp. Please make sure all the functions you have used are in this file.
• Do not submit other files
• Your code should build and execute as per the instructions given above. Please make sure that your code doesn't need any Makefile.
• Your program should not output anything in stdout.

We will not consider the submissions that don't comply with these guidelines.