Hello Jean,

I appreciate very much many of your fitting/interpolation examples. However, if I recall well I think that all of your examples were based on a single independent and a single dependent variable with many unknown parameters. If I was wrong, please excuse me.

On the other hand, I find almost impossible to solve in SMath a nonlinear (based on parameters) fitting problem with a single dependent variable and many independent ones. There are no similar functions like Mathcad mineer(), genfit() or LeastSquaresFit() which will solve the general nonlinear fitting problem with many independent variables.

Regards,
Radovan

Hello Jean,

Here is an example posted few times somewhere here in this Forum 6-7 years ago. It is still a univariate fitting problem, but nonlinear in parameters.I think these examples motivated Davide Carpi to make the NonlinearSolvers plugin. You can find there lots of similar discussion (from my side) where I constantly nagged about numerical solvers for nonlinear equations and optimization. There is no plugin solution in SMath yet concerning these problems.



NLMinimization-9c.sm (43kb) downloaded 27 time(s).

I simply do not know, for years now, how to solve in SMath the general nonlinear fitting problem y=f( X, b ), y - given vector of size n; X - given matrix of size n rows, m columns; b - unknown parameters of size m (m<n). Just pick whatever example you want with, say, n=10 and m=3 with an f( X,b ) function highly nonlinear in b parameters.

For example, like this one (also remained unsolved for me in SMath for years)

linfit_multiple-1.sm (23kb) downloaded 29 time(s).
linfit_multiple-1-1.sm (23kb) downloaded 19 time(s).

Regards,
Radovan

Edited by user 22 February 2019 12:28:49(UTC)  | Reason: Not specified

I don't know whether this counts as a reasonable fit, but at least you get a solution.


linfit_multiple-1_Kr.sm (163kb) downloaded 23 time(s).

Edit: second example shows the same MSE, and nearly the same b2 and b3.

Edited by user 22 February 2019 21:33:21(UTC)  | Reason: Not specified

Thank you Martin. It was a direct answer to my question - Fit() function from Maxima. Thank you for reminding us of this once more. Fortunately, we have Maxima plugin for nonlinear fitting (it slipped my mind) and I am glad that I was wrong. I also would have liked to be wrong by saying that this is the only function in SMath performing this task (maple plugin maybe?).

Regards,
Radovan

Edited by user 22 February 2019 22:55:24(UTC)  | Reason: Not specified

Thank you Alvaro,

You pointed out some issues with the maple module and using subpackeges.

BTW, could you remind me where can I find the Help for Maple V rev 5. I know I've used it but I forgot where it was.

Regards,
Radovan

... you can as well apply Medfit to the Y data.
It will have some smoothing effect on the bivariate,
considering enough data points are in cause.
Not 1/1 Mathcad, but very close.

Maths SlopeIntercept [Medfit].sm (14kb) downloaded 25 time(s).