Consider the scenario where the aim is to fit a lorenzian function to a 1D dataset but a constraint applied on the peak centre parameter. Assume the 1D dataset consists of data points , where is the ith x-value and is the ith observed value for that x-value. Write the lorentzian function as:
where he lorentzian fitting parameters here are
is the x-value of the ith data point and is the lorentzian calculated value at that data point.
We want to apply a constraint on the x0 parameter, i.e. the centre of the peak. For example, apply the constraint that should be in between and . If this is not satisfied we then add the following penalty function to if :
where is a constant (default 1000). The penalty function when takes the form:
.
If more than one constraint is defined, then for each violated constraint a penalty of the type defined above is added to the calculated fitting function.
Category: Concepts