make lsr function

[hokiespurs]

Generate a function "lsr.m" which which shares a similar syntax to nlinfit, but can perform:

• OLS
• WLS
• GLS
• Weighted/Unweighted Nonlinear Least Squares
• Weighted/Unweighted TLS
• Robust Least Squares.

LSR Function Format

function [beta,R,J,CovB,MSE,ErrorModelInfo] = lsr(X,Y,modelfun,beta0,options)
% Inputs:
%   - X              : Predictor variables
%   - Y              : Response values
%   - modelfun       : Model function handle @modelfun(beta,X)
%   - beta0          : Initial coefficient values
%   - options        : Structure with optional parameters
% 
% Outputs:
%   - beta           : Estimated regression coefficients
%   - R              : Residuals
%   - J              : Jacobian
%   - CovB           : Estimated Variance Covariance Matrix
%   - MSE            : Mean Squared Error (Computed Reference Variance)
%   - ErrorModelInfo : Information about error model 

Enhancements

• [x] TLS
• [x] optional explicit analytical jacobian (J,B)
• [x] handle linear least squares
• [x] automatically do chi2 test
• [x] option to not autoscale TLS covariance with So2
• [x] ability to add covariance of beta0

Maintain Capabilities

• [x] robust least squares
• [x] verbose output
• [x] optional stochastic model
• [x] finite difference Jacobian

Functions that will call it

• loess / lowess
• RANSAC

[hokiespurs]

• [x] addOptional for betacoef0 not working... needs to be input explicitly
• [x] replace R with V
• [x] add check for linearity using hessian
• [x] double check chi2 goodness of fit math

[hokiespurs]

Final Polishing of LSR.M

• [x] add Robust MSEthresh as parameter input
• [x] add maxrobustiter as parameter input
• [x] convert inv(A)*B to A\B
• [x] Finalize ErrorModelInfo Outputs
• [x] Finalize Nomenclature
• [x] Add H1 Header to function
• [x] Finalize Checks
• [x] Finalize Verbose Output
• [x] Document Code
• [x] Combine Robust for Nonlinear and Linear using anonymous function since the code is duplicated

Consolidate Checks to CheckLSR.M

• [x] Check Linear Unweighted
• [x] Check Linear Weighted
• [x] Check Linear Weighted and Beta0 As Observation
• [x] Check Nonlinear
• [x] Check Nonlinear Weighted
• [x] Check Robust Linear
• [x] Check Robust NonLinear
• [x] Check TLS

Generate Examples Script exampleLSR.m

• [x] Add makeNoisyData.m
• [x] different linear y=mx+b fits
• [x] different nonlinear fits
• [x] robust for linear with outliers
• [x] robust for nonlinear with outliers
• [x] chi2 goodness of fit
• [x] etc

[hokiespurs]

Documentation Layout

• Describe Motivation for writing the function
• Summary of types of least squares (Linear, Nonlinear, Total, Robust)
• Importance of reference variance and when to scale the covariance matrix
• Example Scripts
• Function Math Used Section
  • Define Variables
  • How linearity is automatically computed
  • Define Equations for:
  • Linear
  • Nonlinear
  • Robust
  • Total Least Squares
• Flowchart of when input warnings/errors are thrown

[hokiespurs]

ErrorModelInfo

• [x] rename it from errormodelinfo to modelinfo
• [x] change MSE to So2
• [x] change R to V
• [x] add betacoefiter and SO2iter (all iterations for nonlinear and robust)
• [x] fix covB
• [x] add TPUfunction with beta covariance built in, output [y, covY]
• [x] input from others

[hokiespurs]

finished draft of lsr, but its in general-purpoise-matlab