README.md

Math

Core mathematical primitives for numerical computation.

Algorithms

Algorithm	Description
CORDIC	Iterative shift-add engine for sin/cos, atan2, magnitude, and vector rotation — no multiplier
Quaternion	Unit-quaternion rotation type: Hamilton product, SLERP, rotation-matrix and Euler conversions
MatrixNorms	Frobenius, 1-norm, infinity-norm on matrices; vector L2 norm/normalize
Householder Transform	Householder reflector for a sub-column — orthogonal, backward-stable factorization primitive
Givens Rotation	Plane rotation zeroing one entry — streaming/sparse factorization primitive
Triangular Solve	Lower/upper-triangular forward and back-substitution shared by Gaussian elimination, Cholesky, and QR
Cholesky Decomposition	SPD factorization $A=LL^T$ with Factor (L) and Solve (SPD system) — twice as fast as LU
Matrix Operations	Structural matrix utilities — Symmetrize (closest symmetric matrix)
Step Response Metrics	Rise time, settling time, percent overshoot, peak time, and steady-state error from a bounded step-response vector
Matrix Exponential	Scaling-and-squaring with diagonal (6,6) Padé approximant — exact ODE solution operator and discretisation engine
Consistency Metrics	NEES/NIS estimator consistency with χ² gates — normalised estimation error squared and normalised innovation squared
Angle Utilities	Wrap to $(-\pi, \pi]$ / $[0, 2\pi)$, shortest signed angle difference, and unwrapping of wrapped measurements
Tridiagonal Solver	Thomas algorithm — $O(n)$ factorization reused across right-hand sides for diagonally dominant / SPD tridiagonal systems
Cubic Spline	Vector-valued $C^2$ cubic spline (clamped / natural ends) fitted with one shared tridiagonal factorization
SE(3) Transform	Rigid transforms with twist/wrench adjoints and an accurate exp/log (linear-first $(v;\omega)$ ordering)
SE(2) Transform	Planar rigid transforms as unit complex rotations with twist/wrench adjoints, arc-exact exp/log and short-way pose error (linear-first $(v_x, v_y, \omega)$ ordering)