Curve-Fit Transition Functions¶
TableCurve 2D's built-in transition functions consist of a set of 29 total equations. There are 14 transition models with and without an intercept and a special impulse transition model. To make transition function fitting as flexible as possible, you are first presented with a transition configuration dialog which contains custom fit settings specifically for the built-in transition functions. You can choose only the symmetric or asymmetric transitions, one or both of the intercept and zero-intercept versions, as well as any one of the four Minimization Criteria available in the non-linear fitting engine. You can choose individual transition functions or you can have the AI Expert feature pick the settings for you based upon an analysis of the data profile. The non-linear fitting controls override the non-linear fit preferences in the Curve-Fit Preferences option. Your transition function customization will be automatically saved across sessions.
Also fitted with this option are all installed UDFs, and all active TCEX.DLL equations.
Symmetric Transition Functions¶
TableCurve 2D's symmetric transition functions include the Sigmoid, the Gaussian cumulative, the Lorentzian cumulative and the SDS (symmetric double sigmoidal) cumulative. The Lorentzian cumulative is the least sharp of TableCurve 2D's basic symmetric transitions and the Gaussian cumulative is the sharpest. The SDS cumulative has an additional width term enabling it to model most symmetric transitions, including those with a long straight line section.
Asymmetric Transition Functions¶
TableCurve 2D's asymmetric transition functions include the Logistic Dose Response model, the Log-Normal cumulative, the Extreme-Value cumulative, and the Weibull cumulative. Also available is the Pulse cumulative and the Pulse cumulative with a variable power term. Both fit transitions with a very rapid rise and much slower decay. The Cascade transition offers a similar profile, this based on formation in sequential first order kinetics. Unlike the sequential formation in the kinetics equation set which assumes the reaction begins at time X=0, the Cascade transition function includes a lag term. Also offered are two asymmetric sigmoids and an impulse transition which can model near instantaneous transitions within data whose Y-values are continuously increasing or decreasing with increasing X. The function set also includes the cumulative for the EMG(Exponentially-modified Gaussian).
Synthetic Functions¶
TableCurve 2D's built-in transition functions have all been constructed to be defined for all values of X, even if the native function has undefined regions or is undefined at certain parameter values. These synthetic functions will either return zero (for zero-intercept versions) or the intercept value (for intercept versions) when an undefined condition is present. This is especially useful with the Weibull and Pulse transitions. If you are fitting data that are at zero or a constant value until the transition profile begins, you need not remove any initial points. They can be fitted as a part of the actual model.
Negative Widths¶
Some transition functions produce a true reverse transition when the sign is changed on the width term. For these functions, TableCurve will use this mathematical symmetry to enable the fitting of a zero-intercept descending transition. For those transition functions which do not exhibit this property, descending transitions can only be fit with intercept forms.
AI Expert¶
When selecting this option, TableCurve 2D references raw data measurements of upper and lower baseline and asymmetry to determine which transition functions are most appropriate to the data as well as whether zero-intercept, intercept, or both versions should be fitted. The AI Expert option will only be effective if there is a full transition present so that accurate baselines can be estimated and only if there are sufficient points within the transition, since the asymmetry determination is made at the transition center.
Reading and Saving Transition Fitting Configurations¶
The most recent transition configuration is saved across sessions and presented each time this option is used. If you select the AI Expert and are not satisfied with the suggested fit, you can press Reset to restore the configuration present when first opening this dialog. If you will be fitting several types of specific transitions, you may want to save a configuration specific to each or to a given application or problem. The Save item will save all information shown in the dialog to a binary file with an [TRN] extension. The Read item can then be used to access this configuration whenever desired.
Nomenclature¶
During fitting, a function name with an underscore suffix, such as Sigmoid_, represents the zero-intercept version of the function. When the underscore is absent, the intercept version of the function is being referenced. In the Review, non-linear equations can be presented in either a full mathematical representation or in a symbolic notational format. Since some of the transition functions have rather long mathematical expressions, you may wish to use the notational format offered in the Preferences option in the main Edit menu or the File menu of the Curve-Fit graph.
Automated Fitting¶
Upon closing the transition configuration via the Fit button, TableCurve 2D's Automated Curve-Fit Processing begins and fits the transition functions as configured as well as any installed UDFs and TCEX.DLL functions. The non-linear fitting controls in the transition configuration will also apply to such UDFs and external functions.