Add the option to export objects that are used to estimate the quality of a fit, such as:
Hessian at the solution point, or
Variance (vector) of the parameters at the solution point, or
Covariance matrix of the parameters at the solution point.
Note: For unconstrained problems this is quite straight-forward. The constrained case is somewhat more complex and
instruction and interpretation on how to assemble these objects needs research: case when at least one of the optimal parameter (value) is active at a bound
Interpretation / Questions
Covariance/variance of parameter at a solution point with active bound
Covariance/variance of parameter at a solution point when the problem is underdetermined
Covariance/variance of parameter at a solution point with active bound and the problem is underdetermined
Update: Export and assembly of covariance, variance and J^T J are already in bxnl, so we could backport to RALFit (unfortunately this does not include the active constraint case)
Idea
Add the option to export objects that are used to estimate the quality of a fit, such as:
Note: For unconstrained problems this is quite straight-forward. The constrained case is somewhat more complex and instruction and interpretation on how to assemble these objects needs research: case when at least one of the optimal parameter (value) is active at a bound
Interpretation / Questions
References
NAG: https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04ycf.html Ceres-solver: https://ceres-solver.googlesource.com/ceres-solver/+/refs/heads/master/include/ceres/covariance.h lm.m: https://people.duke.edu/~hpgavin/ce281/lm.pdf https://www8.cs.umu.se/kurser/5DA001/HT07/lectures/lsq-handouts.pdf