moddyz / LinearAlgebra

A general-purpose header-only linear algebra library.

LinearAlgebra

LinearAlgebra is general-purpose header-only linear algebra library.

This is developed in tandem while working through MIT OpenCourseWare's 18.06 - thanks MIT and Professor Strang!

Table of Contents

• Dependencies
• Building
• Example Usage
• Documentation

Dependencies

The following dependencies are mandatory:

• C++ compiler (C++17)
• CMake (3.12 or greater)

The following dependencies are optional:

• Doxygen and graphiviz for documentation.

Building

Example snippet for building this project:

mkdir build && cd build
cmake -DBUILD_TESTING=ON -DCMAKE_INSTALL_PREFIX="/apps/LinearAlgebra/" ..
cmake --build  . -- VERBOSE=1 -j8 all test install

CMake options for configuring this project:

CMake Variable name	Description	Default
BUILD_TESTING	Enable automated testing.	OFF
BUILD_DOCUMENTATION	Build documentation.	OFF

Example Usage

Multiplication:

using MatrixT = linear::Matrix< 3, 3 >;
constexpr MatrixT A(
    1.0f, 0.0f, 0.0f,
    0.0f, 5.0f, 0.0f,
    2.0f, 3.0f, 1.0f
);
constexpr MatrixT B(
    1.0f, 1.0f, 0.0f,
    1.0f, 1.0f, 1.0f,
    0.0f, 1.0f, 1.0f
);
constexpr MatrixT AB = linear::Multiply( A, B );

Inversion:

using MatrixT = linear::Matrix< 3, 3 >;
MatrixT invertable(
    1.0f, 0.0f, 0.0f,
    0.0f, 5.0f, 0.0f,
    2.0f, 3.0f, 1.0f
);
MatrixT inverse;
assert( linear::Inverse( invertable, inverse ) );

Transpose:

constexpr MatrixT matrix = linear::Matrix< 3, 2 >(
    1.0f, 2.0f,
    1.0f, 1.0f,
    2.0f, 2.0f
);
static_assert( linear::Transpose( matrix ) == linear::Matrix< 2, 3 >(
    1.0f, 1.0f, 2.0f,
    2.0f, 1.0f, 2.0f
) );

Reduced row echelon form:

using MatrixT = linear::Matrix< 3, 4 >;
MatrixT matrix(
    1.0f, 2.0f, 2.0f, 2.0f,
    2.0f, 4.0f, 6.0f, 8.0f,
    3.0f, 6.0f, 8.0f, 10.0f
);

assert( linear::ReducedRowEchelonForm( matrix ) == MatrixT(
    1.0f, 2.0f, 0.0f, -2.0f,
    0.0f, 0.0f, 1.0f, 2.0f,
    0.0f, 0.0f, 0.0f, 0.0f
) );

Projection:

linear::Matrix< 3, 1 > vector(
    2.0f,
    3.0f,
    4.0f
);
linear::Matrix< 3, 2 > subspace(
    1.0f, 1.0f,
    0.0f, 1.0f,
    0.0f, 0.0f
);
assert( linear::Projection( vector, subspace ) == linear::Matrix< 3, 1 >(
        2.0f,
        3.0f,
        0.0f
    )
);

Orthonormalization:

using MatrixT = linear::Matrix< 3, 3 >;
MatrixT matrix(
    1.0f, 2.0f, 4.0f,
    0.0f, 0.0f, 5.0f,
    0.0f, 3.0f, 6.0f
);
MatrixT orthonormal = linear::Orthonormalize( matrix );
assert( orthonormal == MatrixT(
        1.0f, 0.0f, 0.0f,
        0.0f, 0.0f, 1.0f,
        0.0f, 1.0f, 0.0f
    )
);

Determinant:

linear::Matrix< 3, 3 > matrix(
    1.0f, 2.0f, 3.0f,
    2.0f, 2.0f, 3.0f,
    3.0f, 3.0f, 3.0f
);
assert( linear::Determinant( matrix ) == 3 );

Documentation

Doxygen documentation based on the latest state of the main branch is hosted by GitHub Pages.