Linear Solvers for Dense and Sparse Matrix Systems

This software library can be used to solve a linear system AX = B, a descretized version of many PDEs. Where A is a posititive definite matrix of a defined size, and X and B are vectors of different sizes. The library accounts for dense and sparse matrices as inputs to the linear system. Contained witthin it are different solvers that can be used based on type of input matrices and considerations for memory and time optimizations. Read our report linked here for further details.

Solvers in this Library

Dense Direct

• Gaussian Elimination
• LU Decomposition
• Cholesky Decomposition

Dense Iterative

• Gauss Siedel
• Jacobi
• Conjugate gradient

Sparse

• Jacobi
• Conjugate Gradient

Setup Instructions

Windows Recommendations

C++ : Version 11/17
IDE : Visual Studio Community/ Visual Studio Code
Compiler : g++ (v 13.0)

Installation Instructions

Download/clone the github repository into your local IDE of choice.
Open the project/folder and follow the example below- replace the solver given with the solver of your choice

Using the Library through the Terminal Interface

Step 1 : Select 1 to read Matrix Data from our Demo Text Files or input your own Matrix in a .txt format delimited by commas

-- Assuming you have chosen to read in from our Demo files ---
Step 2: Select the type of Solver you want to test - Dense or Sparse

Step 3 : Select a Matrix Size to test on

Step 4 : Verify whether matrix has been read-in from the text file. For the purposes of this demo we have chosen a 4x4 matrix to diplay the read-ins to terminal

Step 5 : Choose a Solver and generate the output

Compiling The Files

(To run the terminal tests )In the runInterface folder please execute :\

g++ " Matrix.h Matrix.cpp CSRMatrix.h CSRMAtrix.cpp Solver.h Test.h main.cpp "

Examples of Use as a Library

For examples of implementation of individual solvers, check the examples folder in the github repository) \

#include "../include/Solver.h"
#include "../src/Solver.cpp"
#include "../include/ReadFile.h"
#include "../src/ReadFile.cpp"

using namespace std;


int main()
{
	int size = 4;

	// Initialize martices with pointers

	auto* A = new Matrix<double>(size, size, true);
	auto* X = new Matrix<double>(size, 1, true);
	auto* B = new Matrix<double>(size, 1, true);

	// Read Matrix from text file
	readMatrix("../tests/mat4_A.txt", *A );
	readMatrix("../tests/mat4_B.txt", *B );

	// Print the read matrix to terminal (if needed)
	A->printMatrix();
	B->printMatrix();


    // set values of output matrix to zero
	for (int i = 0; i < size; i++){
		X->values[i] = 0;
	}

    // Use solver of choice by creating a solver object
	Solver<double> gauss;
	gauss.gaussElimination(*A, *B, *X);
   
   
	writeMatrix("gauss_output_4x4.txt", *X);

    delete[] A;
    delete[] X;
    delete[] B;

}

Results of Some Testing on a Solvers and their performances

For detailed review on analyis and code design and structure, please refer to the linked report

Version History

Version Files

License

This project is licensed under the MIT License - see the LICENSE.md file for details