John D'Errico

I am NOT proposing anything. I merely tried to read the help for your own function, then tried to convince you that your code needs documentation when used in a way that your help says is possible. Here are a couple of lines, written by you!

% Usage 2: x = nsumk(1:5,2)
%
% n: vector

Exactly how should your code work? What is the behavior of your code when it is passed a vector input for n? You need to define that. And to this point, I have seen no definition, no explanation. I've seen multiple references to nchoosek, that your code is related in some way to nchoosek. Therefore I assumed that when I call it in a way that I would call nchoosek, I might get a similar result. If this is false, then you need to document your own code properly. I am not suggesting any new functionality for this code. Merely that you document the EXISTING functionality so that a person who might want to use it can do so.

Also, the help needs to be explicit about whether the pair of integers {2,3} is distinct from the pair {3,2}. I would argue that is an extremely important distinction. This code seems to count them both.

I wish I had written a paper on this topic years ago when I wrote the first version of this tool. I did not do so then, although I have given a few talks on the underlying modeling philosophy of these tools.

The basic idea is simply that of a least squares spline, augmented by a smoothness penalty like a smoothing spline. The smoothness penalty solves the problem of arbitrary (poor) knot selection in many cases.

General least squares splines are covered in depth in the literature, as are smoothing splines. For these fundamental ideas, de Boor is of course the classic reference, a book worth reading for any user of splines.

What the SLM tools add though is something that I've never really seen written about in the literature. This is the idea that intelligently chosen constraints on the curve shape can act as a strong, useful regularizer on your result. They allow you to build your own knowledge about a system into the model, using a simple vocabulary to describe the desired shape of that curve.

I wrote these tools after some years of seeing people using strange nonlinear regression models to fit curves, just because they needed a curve with a given shape. So the user picks some nonlinear sigmoidal form, a Gaussian, etc., for no better reason than that it fits some fundamental desired shape. And of course, nonlinear regression has its own problems, like poor starting values, lack of convergence, etc. Worse, the user finds that the curve shape they chose is not really the correct shape, so they end up with significant lack of fit. Once a viable tool becomes available to fit those curves, I find that far fewer people end up using nonlinear regression models for the wrong reasons.

There are a couple of files that discuss some of these ideas "slm_tutorial.html" and "shape prescriptive modeling.rtf" in the zip file, but that is all I can offer. We also suggested a citation format for tools from the file exchange, if you do need an explicit reference. You can find our recommendations here:

http://matlabwiki.mathworks.com/Citing_Files_from_the_File_Exchange

I wish I had written a paper on this topic years ago when I wrote the first version of this tool. I did not do so then, although I have given a few talks on the underlying modeling philosophy of these tools.

The basic idea is simply that of a least squares spline, augmented by a smoothness penalty like a smoothing spline. The smoothness penalty solves the problem of arbitrary (poor) knot selection in many cases.

General least squares splines are covered in depth in the literature, as are smoothing splines. For these fundamental ideas, de Boor is of course the classic reference, a book worth reading for any user of splines.

What the SLM tools add though is something that I've never really seen written about in the literature. This is the idea that intelligently chosen constraints on the curve shape can act as a strong, useful regularizer on your result. They allow you to build your own knowledge about a system into the model, using a simple vocabulary to describe the desired shape of that curve.

I wrote these tools after some years of seeing people using strange nonlinear regression models to fit curves, just because they needed a curve with a given shape. So the user picks some nonlinear sigmoidal form, a Gaussian, etc., for no better reason than that it fits some fundamental desired shape. And of course, nonlinear regression has its own problems, like poor starting values, lack of convergence, etc. Worse, the user finds that the curve shape they chose is not really the correct shape, so they end up with significant lack of fit. Once a viable tool becomes available to fit those curves, I find that far fewer people end up using nonlinear regression models for the wrong reasons.

There are a couple of files that discuss some of these ideas "slm_tutorial.html" and "shape prescriptive modeling.rtf" in the zip file, but that is all I can offer. We also suggested a citation format for tools from the file exchange, if you do need an explicit reference. You can find our recommendations here:

http://matlabwiki.mathworks.com/Citing_Files_from_the_File_Exchange

the new setting "'smoothness',[xsmooth ysmooth]" is a Godsend. Many Thanks