linear_algebra

A linear algebra library for C++.

Usage

#include <linear_algebra>

using namespace lina;

// vector construction
vector_4d v0; // zero vector
vector_4d v1{ 1, 2 }; // with components (1.0, 2.0, 0.0, 0.0)
vector_4d v2{ 1, 2, 3, 4 }; // with components (1.0, 2.0, 3.0, 4.0)
vector_4d v3(1, 2); // same as v1
if (v1 == v3)
std::cout << "v1 == v3\n";
if (+v1 != -v3)
std::cout << "+v1 != -v3\n";
v0[x_coord] = 0;

// vector normalize
vector_4d v4;
auto v5 = v4.normalize(); // v4 itself is not affected
v4.normalize_to_assign(); // normalize v4 itself, so that v4 == v5 then

// vector dot product
auto dotv = std::inner_product(v1, v2);

// vector cross product, only defined for 3d vectors
vector_3d v6 = cross_product(v1.reduce(), v2.reduce());

// make axis basis
auto xaxis = vector_3d::basis<x_coord>();
auto yaxis = vector_3d::basis<y_coord>();
auto zaxis = cross_product(xaxis, yaxis);

// matrix construction
square_matrix_4d m0; // zero matrix

// get an identity matrix
square_matrix_4d m1 = make_identity_matrix<double, 4>();

// matrix transpose
square_matrix_4d m2;
square_matrix_4d m3 = m2.transpose(); // m2 itself is not affected
m2.transpose_to_assign(); // transpose m2 itself

// matrix inverse
square_matrix_4d m4 = make_identity_matrix<double, 4>();
square_matrix_4d m5 = m4.inverse(); // m4 itself is not affected
m4.inverse_to_assign(); // inverse m4 itself

// no inverse or inverse_to_assign or transpose_to_assign is
// defined for non-sqare matrix
basic_matrix<double, 3, 4> nonsqrm;
// the following code will static_assert with false
//nonsqrm.inverse();
//nonsqrm.inverse_to_assign();
//nonsqrm.transpose_to_assign();
// but tranpose is allowed, it return a new matrix
auto nonsqrmT = nonsqrm.transpose();

// affine transform, treat vector as column vector
square_matrix_4d translMatrix, rotMatrix, scaleMatrix;
vector_3d localPosition;
vector_3d worldPosition = (translMatrix * rotMatrix * scaleMatrix * localPosition.homogeneous()).reduce();

// affine transform, treat vector as row vector
square_matrix_4d translMatrixT, rotMatrixT, scaleMatrixT;
vector_3d localPositionT;
vector_3d worldPositionT = (localPositionT.homogeneous() * scaleMatrixT * rotMatrixT * translMatrixT).reduce();