• Linear Algebra Module
• Required Packages
• Building the Project
• Supported Linear System Solutions
• Example

Linear Algebra Module

The intent of this module is to provide a drop-in module to handle creation and modification of Matrices.

Required Packages

A few packages are needed to be able to compile the tracking program. These packages are readily available using vcpkg provided by Microsoft. The installation of vcpkg should reside in the root directory. The following commands will install the needed packages.

$ vcpkg install --triplet=x64  gtest

Building the Project

This project is configured to build as a library and will produce no executable. The provided CMakeLists.txt build file is built to adhere to the following file structure.

./
+-- libs/
|   +-- LinearAlgebra/
|   |   +-- .gitignore
|   |   +-- .gitattributes
|   |   +-- include/
|   |   |   +-- LinearAlgebra/
|   |   |   |   +-- Cholesky.h
|   |   |   |   +-- GaussSeidel.h
|   |   |   |   +-- Jacobi.h
|   |   |   |   +-- LU.h
|   |   |   |   +-- Matrix.h
|   |   |   |   +-- Solver.h
|   |   |   |   +-- SolverFactory.h
|   |   |   |   +-- SOR.h
|   |   +-- src/
|   |   |   +--- Cholesky.cpp
|   |   |   +--- GaussSeidel.cpp
|   |   |   +--- Jacobi.cpp
|   |   |   +--- LU.cpp
|   |   |   +--- Matrix.cpp
|   |   |   +--- Solver.cpp
|   |   |   +--- SolverFactory.cpp
|   |   |   +--- SOR.cpp
|   |   +-- test/
|   |   |   +-- CMakeLists.txt
|   |   |   +-- matrix-test.cpp
|   |   +-- CHANGELOG.md
|   |   +-- CMakeLists.txt
|   |   +-- LICENSE.md
|   |   +-- README.md
+-- src/
|   +-- main.cpp
|   +-- CMakeLists.txt
+-- CMakeLists.txt

To follow this structure, add these lines to ./CMakeLists.txt

...
set(CMAKE_INCLUDE_CURRENT_DIR ON)

add_subdirectory(libs/LinearAlgebra)
add_subdirectory(src)
...

And add these lines to src/CMakeLists.txt

...
project(${CMAKE_PROJECT_NAME} CXX)
file(GLOB_RECURSE HEADER_FILES *.h)
file(GLOB_RECURSE SRC_FILES *.cpp)
...

...
target_link_libraries(${CMAKE_PROJECT_NAME}
    echo::linearalgebra
)
...

Supported Linear System Solutions

Currently, only solutions via LU Decomposition are supported. However, development is currently in progress to support the following.

• Cholesky Decomposition
• Gauss Seidel
• Jacobi Iteration
• Successive Overrelaxation

Example

The following example shows how the module can be used to solve a 3x3 linear system using the LU Decomposition method.

#include <iostream>
#include "LinearAlgebra/Matrix.h"
#include "LinearAlgebra/SolverFactory.h"

int main(int argc, char *argv[])
{
    Solver *solver = SolverFactory::create(SOLVER::LUDECOMP);
    Matrix A = Matrix({ {2,  -1, -2},
                        {-4,  6,  3},
                        {-4, -2,  8}});

    Matrix b = Matrix({-1, 5, 2});
    Matrix x = solver->solve(A, b);
    x.print();
    /*
        [ 1 ]
        [ 1 ]
        [ 1 ]
    */

    return 0;
}