matrix.hpp File Reference

Minimal fixed-size matrix arithmetic (framework independent) More...

#include <array>
#include <cmath>
#include <cstddef>

Go to the source code of this file.

Classes
class	m5::math::Matrix< R, C >
	Fixed-size (R rows x C columns) float matrix, std::array backed (no heap allocation) More...

Namespaces
namespace	m5
	Top level namespace of M5Stack.

Functions
bool	m5::math::invert3x3 (const Matrix< 3, 3 > &m, Matrix< 3, 3 > &out)
	Closed-form inverse of a 3x3 matrix.
template<std::size_t N>
bool	m5::math::cholesky_solve (const Matrix< N, N > &a, const Matrix< N, 1 > &b, Matrix< N, 1 > &x)
	Solve A*x = b for a symmetric positive-definite A via Cholesky decomposition.

Variables
constexpr float	m5::math::MATRIX_ZERO_EPSILON {1e-9f}
	Magnitudes below this are treated as singular/non-positive-definite (matrix safety)

Detailed Description

Minimal fixed-size matrix arithmetic (framework independent)

Header-only, heap-free (std::array backed) fixed-size matrix type, providing only what src/imu/filter/ekf.hpp needs: element access, addition, subtraction, scalar and matrix multiplication, transpose, and identity for square matrices. General NxN inversion is intentionally not provided; instead two narrow numerical primitives are exposed as free functions:

• invert3x3(): closed-form 3x3 inverse, for a single 3-axis observation update (e.g. accel, then mag as a separate sequential step)
• cholesky_solve(): solves A*x = b for a symmetric positive-definite A of any fixed size via Cholesky decomposition, for callers that prefer a single combined observation update (e.g. a 6x6 accel+mag innovation covariance) instead of two sequential 3x3 updates

Function Documentation

cholesky_solve()

template<std::size_t N>

bool m5::math::cholesky_solve ( const Matrix< N, N > & a, const Matrix< N, 1 > & b, Matrix< N, 1 > & x )

inline

Solve A*x = b for a symmetric positive-definite A via Cholesky decomposition.

Parameters

	a	Symmetric positive-definite matrix (only the lower triangle, row >= col, is read)
	b	Right-hand side column vector
[out]	x	Solution; only written on success

Returns

False if a is not (numerically) positive-definite, leaving x unwritten

invert3x3()

bool m5::math::invert3x3 ( const Matrix< 3, 3 > & m, Matrix< 3, 3 > & out )

inline

Closed-form inverse of a 3x3 matrix.

Parameters

	m	Matrix to invert
[out]	out	Inverse of m; only written on success

Returns

False if m is (near) singular (determinant magnitude below MATRIX_ZERO_EPSILON), leaving out unwritten

Note

The singularity threshold MATRIX_ZERO_EPSILON is 1e-9 (absolute determinant magnitude). Matrices with very small scale (e.g., condition number > 1e9) will be treated as singular; the caller should handle failure gracefully by skipping the update (as in EKFFilter::apply_axis3_update()), which is safe because the Kalman gain computation is optional for each observation.