linear_algebra_containers

Some basic, c++ template linear algebra classes (vector, matrix, quaternion) useful for non high performance calculations (the classes don't use template expressions, unrolling or other optimizations).

All files of this project are licensed under the MIT license. Have a look at the LICENSE file for more information.

Overview

Classes already implemented:

• Matrix: m x n matrix with entries of type T
• ColumnVector: column vector with n entries of type T
• Vector3: column vector with 3 entries of type T
• Quaternion: class for rotations etc., with 4 entries of type T

All classes are using templates. For example the Matrix template parameters are:

template<typename T, size_t row_count, size_t column_count>
class Matrix;

The ColumnVector is a partial specialization of the corresponding matrix type while the Vector3 class is a subclass of the ColumnVector.

Examples

Matrix operations are very easy to use and thanks to the template design only mathematically correct operations are possible. Example for a matrix product:

lin_algebra::Matrix<double,2,3> mat1; mat1.toIdentity();
lin_algebra::Matrix<double,3,1> mat2; mat2.toIdentity();
lin_algebra::Matrix<double,2,1> result = mat1*mat2;

The multiplication in reverse order will not work because the matrix dimensions do not match.

auto result = mat2*mat1;    // Won't compile

Suppose you want to calculate the 2-norm of a column vector. There are three ways to get the same result:

typedef lin_algebra::ColumnVector<double,4> vec4;
typedef lin_algebra::Matrix<double,4,1> mat4x1;

vec4 x{1.,2.,3.,4.};
mat4x1 y{1.,2.,3.,4.};

double res1 = std::sqrt(x.transposed()*x);          // 1
double res2 = std::sqrt(vec4::dotProduct(x,x));     // 2
double res3 = y.norm();                             // 3
assert(res1 == res2);
assert(res2 == res3);

ColumnVector<T,n> is just an alias for Matrix<T,n,1> so it's not surprising that everything above works. Additionally the partial specialization allows the following to work:

typedef lin_algebra::Matrix<double,4,4> mat4x4;

mat4x4 eye;
eye.toIdentity();
vec4 empty{0;0;0;0};

double res4 = (M*x + empty).norm();
assert(res4 == res1);

Todo

There is still much work to do on the classes even though most basic operations are working. If you want to help or if you find any bugs feel free to contact me.

Main areas of work:

• More quaternion methods
• More tests
• Matrix4x4 and Matrix3x3 classes with convenience methods
• More graphics related features like rotations etc.
• Point classes & coordinate system transformations