The Performant Embedded Algebra Kit (PEAK) is a lightweight, easy-to-use library for performing various algebraic operations. This library is built on Lukas Freiheit's matrix structures and linear algebra code, originally developed for Aquila Maris' caput firmware.

Features

Matrix operations: Perform matrix addition, subtraction, multiplication, and inversion.
Kalman Filter implementations
- basic Kalman Filter
- Dynamic Kalman Filter, with variable delta t (WIP)

Usage

Basics

The following example demonstrates the creation of matrices and basic operations on them.

#include <sta/math/linalg/matrix.hpp>
#include <sta/math/linalg/linalg.hpp>

// Create a 3x2 matrix with every entry initialized to 0:
sta::math::matrix m_0 = sta::math::matrix::zeros(3,2);

// Set specific entries in the matrix:
m_0.set(0, 1, 4); // set the entry in the first column and second column to 0
m_0.set(1, 0, 5);
//m_0.set(2, 2, 99); -> Column index out of range

// Display the matrix:
m_0.show_serial();

// Output:
// Matrix shape: (3 x 2)
// | 0.000000 | 4.000000 |
// | 5.000000 | 0.000000 |
// | 0.000000 | 0.000000 |

// Create a 3x2 matrix with every entry initialized to 10:
sta::math::matrix m_10 = sta::math::matrix::full(3,2,10); 

// Matrices of the same shape can be added together using the + operator:
sta::math::matrix m_a = m_0 + m_10;

// m_a:
// | 10.000000 | 14.000000 |
// | 15.000000 | 10.000000 |
// | 10.000000 | 10.000000 |

// Create an identity matrix of size 3 and multiply it by 5:
sta::math::matrix m_i = sta::math::matrix::eye(3) * 5;

// Set a specific entry in the identity matrix:
m_i.set(0, 2, 0.5);

// m_i:
// | 5.000000 | 0.000000 | 0.500000 |
// | 0.000000 | 5.000000 | 0.000000 |
// | 0.000000 | 0.000000 | 5.000000 |

// Matrices of the appropriate shape can be multiplied together using the * operator:
sta::math::matrix m_res = m_i * m_a;

// m_res:
// | 55.000000 | 75.000000 |
// | 75.000000 | 50.000000 |
// | 50.000000 | 50.000000 |

Kalman Filters

Every Kalman filter object requires a measurement matrix H and a measurement covariance matrix R. These matrices will be used when the correct method is called with only the current state and a measurement value. If you are using multiple sensors, you can also pass new H and R matrices directly, which will then be used instead. This also allows you to handle changes in measurement uncertainty over time.

Limitations

As of now, only matrices with no more than 256 elements are supported.