Module linear 

Dense linear algebra and the vector least-squares step.

The scalar root-finders live in solve; this is what the problems with more than one unknown need. Both are small and dense on purpose: a calibration Jacobian is one pillar per rung and a parametric curve fit is four to six parameters, so the matrices here are tens of entries and the cost is not where anything is slow.

Structs

Fitted 🔒

A converged fit: the parameters, the residual norm, and the work it took.

Enums

FitFailure 🔒

Why a least-squares fit produced no parameters.

Constants

FIT_ITERATION_CAP 🔒

The Levenberg-Marquardt cap. A four-to-six parameter fit from a sensible start converges in tens of steps; reaching this is a reported failure, not a silently returned iterate.

GRADIENT_TOLERANCE 🔒

First-order optimality: the fit has converged — after one final step — when the residual is this close to orthogonal to every Jacobian column — the largest |Jₐᵀr| / (‖Jₐ‖·‖r‖), the cosine MINPACK calls gtol.

Functions

inverse 🔒

The inverse of a square matrix by Gauss-Jordan elimination with partial pivoting, or None when it is singular to working precision.

levenberg_marquardt 🔒

Levenberg-Marquardt over a parameter vector.

norm2 🔒

The Euclidean norm of a residual vector.

normal_equations 🔒

JᵀJ and Jᵀr, both p-sized — the matrices this method inverts are the parameter count square, never the bond count. JᵀJ is symmetric, so one triangle is accumulated and mirrored.

stationary 🔒

Converged in the gradient (GRADIENT_TOLERANCE): at a minimum with a non-zero residual — every overdetermined fit — the residual is orthogonal to the Jacobian’s columns. A column that does not move the residual at all has nothing to say and is skipped rather than divided by.