Here is the problem I bumped into. I was just playing with Maxima package interpol and find out that it crashes SMath for cspline() and linearinterpol() functions when the Optimization is turned to None. I suppose that the charfun2() causes this problem, but do not know why. Please look at the example and try to turn the optimization to None for the red area. If the Symbolic optimization is on, then the error is issued. If I turned Optimization to None, then SMath crashes on my computer.

Regards,
Radovan

Edited by user 01 December 2013 13:08:57(UTC)  | Reason: Not specified

Hello Martin,

I am not sure if this particular problem (bug) might be somehow related to the relational operators in Smath and in Maxima (<= etc.). I remembered you mentioned this somewhere, but can not find it where it was at the moment.

Regards,
Radovan

Preview of partly problem solution. Back-translation of logical expressions is implemented and a the interpol results can be evaluated, plotted and numerically integrated. The plugin, however, does not yet wrap boolean expressions in charfun() when translating to Maxima, therefore such expressions cannot yet be integrated using Maxima's int() version.

It seems that expressions involving charfun() cannot be integrated symbolically using Maxima. Thus there might be a point of transforming boolean expressions to such with sign().

We upload the new plugin version as soon as it passes the regression test. Current state is too unstable.

If you are just up to numeric integration and differentiation of interpolated data, you could sample the interpolation and apply appropriate FIR kernels using uni's alglib functions. Works very well with Savitzky-Golay in matlab.

There should be no more crashes due to package interpol now.

You have to remove the suppression of charfun() (which I guess - if not bet - is still somewhere in your SMath sheet ;-)
Application and removal of type conversion functions like charfun() should be done in the translation process. This, however, is not yet implememted.

It might be a good idea to use the quadrature functions in Maxima for int() when numeric optimization is requested. This would, of course, require units preprocessing.

The latest Maxima 5.34.1 does not have numeric/interpol : tht's the first problem for all viewers.

Maxima cspline is an horrible monkey business probably incompatible with Smath, WHY ?
On the first count: Smath is not a 'scalar' system, only discrete.
Thus it might be impossible to built a scalar cspline that can be assigned as a function
as a function analytical up to the 2nd order derivative.
On the 2nd count: the former Maxima cspline is archaic in the displaying the segments,
just figure splining a data set of small 50 pairs. Again not exportable.

More confusing: Smath f(x) has linterp, ainterp [Akima spline], cinterp
these 3 are LOCAL interpolating functions, i.e: nothing else to do with
except populate data set for export.
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The Lagrange interpolation is totally useless. From a data set of length 'n' you can get
an nth order polynomial that will do exactly what your Lagrange interpolation does.
If your data set is like noisy or not so regular [they are always noisy or not very regular
from experimental sampling], the the polynomial fit can be or les order than the 'n' data.
Thus you benefit some smoothing. The polynomial fit need not be of integer monomials
x, x^2, x^3 ... the x's may be of decimal exponents, it may help the fit.

Polynomial fit is just few line of Smath simple coding.
A much, much, much more powerful fitter is the Padé rational fraction, in Mathcad 11, it works
by clicking the fingers. BTW, all [if not all] approximation of functions in computers
are Padé rational fractions [collected in Hart et al.]

jmgiraud@bell.net