Root-finding algorithm (e.g. fzero) on Additive Generalized Splines model

Dear community,

In principle a model that is based on splines has localized functions to describe the relationship between inputs and outputs. I understand it is easy to compute the output given the input but what if I need to reverse the question and given the output I need to find the input? Obs. my function is monotonic for the interval I am considering.

• Is it possible to implement a root-finding algorithm when I have a black-box model like splines to work with? Could you show an example? I have only applied this to parametric models before.

Thanks for your help!

[Vladimir Sovkov]

Find the function "fnzeros" in the Matlab documentation.

[Gustavo Lunardon Quillo]

Great! Thank you for your input.

Now, if I need to find the positions at which the splines have a nonzero value a any suggestion on how to proceed?

I tried: x = fnzeros(spline-a)

but it does not make operations with structs. Do I need to modify my spline or there is a way inside the fnzeros function?

[Steven Lord]

Can you show us the format in which the spline you created is stored? Different approaches may work if it's a struct array, a vector of breaks with an array of coefficients, a fit object from Curve Fitting Toolbox, etc.

[Gustavo Lunardon Quillo]

Could you please demonstrate how to do that applied to a spline created using the

• csapi MATLAB command (spline ppform)
• the spmak MATLAB command used in the documentation of fnzeros (could be useful to add a couple of lines in that direction in the documentation too) https://www.mathworks.com/help/curvefit/fnzeros.html

Thank you very much.

[Unai San Miguel]

Maybe this: |fnzeros(fncmb(spline, '-', a)|?