ACSE 5: Matrix Library

This C++ library is meant for carrying out Matrix computations. Includes a total 4 types of matrices to use:

1. Dense Matrix: saves strictly all values within an ordinary matrix.

2. CSR (sparse) Matrix: consists of three arrays which save the (1) all non-zero values inside a matrix, (2) the row positioning and (3) the column indices of the non zero values.

3. Band Matrix: saves only the values inside user-specified diagonals.

4. Symmetric Matrix: saves only the upper triangle of of a matrix.

All matrix types save their values in ROW MAJOR order.

Getting Started

These instructions will get you a copy of the project up and running on your local machine for development and testing purposes. See deployment for notes on how to deploy the project on a live system.

Prerequisites

For the development of this library, only the standart c++11 libraries have been used.

#include <iostream>
#include <ctime>
#include <memory>
#include <cmath>
#include <vector>
#include <iomanip>
#include <vector>
#include <algorithm>

Installation

• Clone this repo to your local machine using:

git clone https://github.com/vagifaliyev/Matrix-Solver

Running the test

Test file runs all the avaliable linears solvers for the 4 matrix types.

Includes result comparison and time taken.

• Dense:
  • Inverse
  • Gauss
  • Lower–Upper (LU) decomposition
  • Conjugate Gradient(CG)
  • Successive over-relaxation (SOR)
  • Chebyshev
• Sparse(CSR):
  • Conjugate Gradient(CG)
  • Successive over-relaxation (SOR)
  • Chebyshev
• Band:
  • Conjugate Gradient(CG)
  • Successive over-relaxation (SOR)
  • Chebyshev
• Symmetric:
  • Conjugate Gradient(CG)
  • Successive over-relaxation (SOR)
  • Chebyshev
• Multi-Solver(Dense only):
  • Conjugate Gradient(CG)
  • Successive over-relaxation (SOR)

g++ Matrix.cpp CSRMatrix.cpp BandMatrix.cpp Symmetric.cpp verification.cpp -std=c++11

Note: The test call for inverse has been disabled for quicker testing as it is the most expensive function.

Example Code

Header file contain in-depth explation on how to call the functions

Creating a matrix

auto* dense_mat1 = new Matrix<double>(cols, rows, true);

// fill in matrices and print them     
dense_mat1->fillRandom();
dense_mat1->printMatrix();


// this Matrix object has been implemented without
// preallocated memory. The int pointer matrix_data
// will pass on the memory in which the matrix values
// will be stored in.
auto* matrix_data = new double[rows * cols];
auto* dense_mat1 = new Matrix<double>(cols, rows, matrix_data);
  

Call a function

double* vec_right = new double[cols];

// set values of RHS vector in memory space
for (int i = 0; i < cols; i++)
{
    vec_right[i] = 2;
}

// initiate new poiter and allocate memory
// for result vector
double* vec_out = new double[rows];

// do matrix vector product
dense_mat->matVecMult(vec_right, vec_out);

Documentation

Please read report.pdf for details on our code of conduct, and algorthims.

Penetration analysis results can be viewed in folder outputData

On the next Patch:

• Finish implementing MatMatMult for band & symmetric matrix
• Parallize with openMP
• Write a function to analyze the input matrix and direct it to the most aprropiate class.

Acknowledgments

Thanks to the teaching staff for their enthusiastic classes and all the Teaching Assistants for their assistance.

License

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