Mustafa - I'm glad you like it.
The initial knot placement is as you supply it, or if you supplied nothing, then the default is used. By default, the knots chosen are equally spaced from min(x) to max(x), with 6 knots in total, so there would be 4 interior knots to vary. The optimizer then varies only those interior knots.
There is no overt randomness in the optimization or the initial values though. For example:
x = rand(100);
y = exp(x);
clear functions
tic,slm = slmengine(x,y,'knots',6,'interiorknots','free');toc
Elapsed time is 1.369497 seconds.
tic,slm = slmengine(x,y,'knots',6,'interiorknots','free');toc
Elapsed time is 0.176209 seconds.
tic,slm = slmengine(x,y,'knots',6,'interiorknots','free');toc
Elapsed time is 0.127645 seconds.
tic,slm = slmengine(x,y,'knots',6,'interiorknots','free');toc
Elapsed time is 0.123504 seconds.
tic,slm = slmengine(x,y,'knots',6,'interiorknots','free');toc
Elapsed time is 0.121428 seconds.
tic,slm = slmengine(x,y,'knots',6,'interiorknots','free');toc
Elapsed time is 0.123522 seconds.
tic,slm = slmengine(x,y,'knots',6,'interiorknots','free');toc
Elapsed time is 0.126947 seconds.
The difference in time for the subsequent calls is small, but non-zero. That variability is purely due to your CPU as it is constantly running various other things in the background.
ALWAYS do such time tests multiple times, and ignore the first couple of calls from your sample, as the first time a function is called, MATLAB takes extra time to cache the JIT parsed code. Above, see that I did a clear functions first to clear the function cache. The first call was quite slow, then after the second call, the time needed was far less, and quite consistent.

I'm confused. If you found this page, you should be able to click on the "Download Submission" button. Once you have done that, unzip the file, and add the resulting directory to your search path using either addpath & savepath or pathtools.

Dear John
This is an amazing tool , thanks a lot, and definitely gonna be referenced in my journal. I have one question regarding piecewise linear fitting using free , 'interierknots' : I could not find how it initiate the first values of the knots to be optimized , and I am trying to figure this out in order to implement it on a microcontroller board , I would much appreciated if you could tell me, how the initial guesses were chosen based on the fmincon function so I can evaluate the complexity and how much time it will take on a printed board. Also when does the fitting stops, I noticed that the time it takes to reach to some certain fit varies every time ( for the same options ) which means the initial points differs , right ?
Regards,

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