Non-Linear Optimization Numerical Update

This is the Non-Linear Optimization update where you are shown numerical indices of the fit, and an r² goodness of fit meter as an indicator of fit progress.

The numerical fit is governed by the options set in the current Fit Preferences.

If a fit consistently indicates that it is wrestling with one or more constraints, it may mean that the constraints need to be opened somewhat, or perhaps cautiously disabled.

When a numeric fit is initiated, a separate thread is used for the fitting. Responsiveness to intervention actions, such as stopping or aborting the fitting, should be immediate.

Fitting in Background

To have the fit performed in the background, simply minimize the fitting window. Since AutoSignal uses this separate and lower priority fitting thread, foreground performance should not suffer in any way.

Informational Elements

··Iteration - Indicates the current iteration in fitting.

··Constraints - Number of constraint violations occurring on the current iteration. This is an important indicator to watch. If a fit is spent mostly escaping constraint violations, it may suggest the need for more open constraint percents or better initial placement. Constraints are set in the Fit Preferences and when are created.

··Merit Function - The goodness of fit criterion that governs minimization. For least-squares, it will be the sum of squared residuals. For Robust Minimizations, it will be that robust procedure's merit function. The value will be the best merit function thus far achieved in the fit. A robust procedure is set in the Fit Preferences.

··Std Error - The best fit standard error thus far achieved. This will only be the standard error for the current iteration's parameters if such estimates are adopted.

··F-Stat - The best F statistic thus far achieved in the fit. This will only be the F-statistic for the current iteration's parameters if such estimates are adopted.

··r² - The r² coefficient of determination thus far achieved. This will only be the r² for the current iteration's parameters if such estimates are adopted. The r² value is also displayed graphically in the r² progress meter. An r² of 1.0 is a perfect fit; an r² of 0.0 is a complete lack of fit.

··Time - The total time thus far spent in fitting.

··Time/Iter - The average time per iteration.

··Fn Eval - The total number of function evaluations occurring in the fit. A single function evaluation consists of the computation of a given spectral component function and all associated partial derivatives.

··FnEval/Iter - The average number of function evaluations per iteration.

··Data Points - The total number of data points being fitted.

··Parameters - The total number of parameters fitted. This represents the size of matrix inverted with each iteration. A fit consisting of 35 parameters requires the inversion of a 35x35 matrix with each iteration.

R² Meter

The progress meter offers a graphical representation of the r² achieved. The r² bar is divided into five equal log sections.

Stop Current

This button will stop the fitting at its current iteration. It can be used when the fit is changing extremely slowly. Some fits may find themselves within a very narrow valley in parameter space, and even though convergence is not signaled, very little is to be gained by continuing the fit. The Stop Current button is only visible while a fit is underway.

Cancel

The Cancel button is available at the conclusion of a fit. When the estimates of one or more parameters go widely astray, the fitted result may be useless. This is especially possible if all constraints have been disabled. When a fit is canceled you are returned to the spectral procedure as if no fit had occurred.

Review Fit

The Review Fit option is available at the conclusion of a fit. It is used when you wish to proceed directly to AutoSignal's Non-Linear Optimization Review.