TOMLAB OPTIMIZATION ENVIRONMENT: StatLS

StatLS

Purpose

Compute parameter statistics.

Syntax

   LS = StatLS(x_k, r_k, J_k);

Input Parameters

 x_k     Optimal parameter vector, length n
 r_k     Residual vector, length m
 J_k     Jacobian matrix, length m by n

Output Parameters

         
 SSQ      Sum of squares: r_k'*r_k;
 Covar    Covariance matrix: Inverse of J' *diag(1./(r_k'*r_k)) * J
 sigma2   Estimate squared standard deviation of problem, 
          SSQ / Degrees of freedom, i.e. SSQ/(m-n);
 Corr     Correlation matrix: Normalized Covariance matrix
          Cov./(CovDiag*CovDiag'), where CovDiag = sqrt(diag(Cov));
 StdDev   Estimated standard deviation in parameters: CovDiag*sqrt(sigma2);
 x        =x_k, the input x
 ConfLim  95% Confidence limit (roughly) assuming normal distribution of errors
          ConfLim = 2*LS.StdDev;
 CoeffVar The coefficients of variation of estimates: StdDev./x_k

startup

stepexp