1. If at least one of your data sets to be interpulated is on a grid, you can use numpy.ndimage.map function for fast interpolation for 2d (in fact for any dimensional) dataset. 2. Isn't there an analytic expression to average the expectration values of SH over all possible orientations between B and the crystal axis? My experience shows that some analytic work can save 99% of simulation time. Nadav Original Message From: numpydiscussionbounces@lists.sourceforge.net on behalf of Sebastian Zurek Sent: Sat 21Oct06 15:41 To: numpydiscussion@lists.sourceforge.net Cc: Subject: Re: [Numpydiscussion] Model and experiment fitting. Robert Kern napisal(a):
Your description is a bit vague.
Possibly by my weak English... I'll try to make myself clearer now. Do you mean that you have some model function f
that maps X values to Y values?
f(x) > y
My model is quantum energy operator  spin hamiltonian (SH) with some additional assumption about so called 'line shape', 'line widths',etc. It describes various electron interactions, visible in electron paramagnetic resonance (EPR, ESR) experiment. The simplest SH can be written in a form: H = m B g S (1) where m is a constant (bohr magneton), B is magnetic field (my xvariable), g is so called 'zeeman matrix' and S is total spin angular momentum operator. Summing it all together: the simple model is parametrized by:  line shape,  line width,  zeeman matrix (3x3 diagonal matrix  the spatial dependence),  total spin S. After SH (1) diagonalization one can obtain so called 'resonance fields' and 'resonance intensities'. After a convolution with appropriate line shape function which is parametrized by the line width one can finally get the simulated EPR spectrum (simDat=[[X1,...,Xn],[Y1,...,Yn]]). This is a roughly, schematic description, appropriate to EPR spectra of monocrystals. In my situation the problem is more sophisticated  I have polycrystaline (powders) data, and to obtain a simulated EPR powder spectrum I need to sum up the EPR spectra of monocrystals that come from many possible spatial orientations, and the resultant spectrum is an envelope of all the monocrystals spectra. There's no simple model function that maps X > Y.
If that is the case, is there some reason that you cannot run your simulation using the same X points as your experimental data?
I can only demand a X range and number of X values within the range, there's no possibility to find the Y(X) for a specified X. These limitations on one hand come from the external program I'm using to simulate the EPR spectra, on the other are a result of spatial averaging of EPR data for powders, where a lot of interpolations are involved.
OTOH, is there some other independent variable (say Z) that *is* common between your experimental and simulated data?
f(z) > (x, y)
This is probably the situation I'm in. These other variables are my model parameters, namely: line shapewidth, zeeman matrix... and they're commen between the experiment and the simulation. To make it clear. I've already solved the problem by a simple linear interpolation of simulated points within the narrow neighborhood of experimental data point. The simulation points are uniformly distributed along the Xrange, with a density I'm able to tune. It all works quite well but I'm founding it as a 'bruteforce' method and I wonder, if there's any more sophisticated and maybe already incorporated into any Python module method? Anyway, it looks like it's impossible to compare two discrete 2D data sets without any interpolations included... :] A. M. Archibald has proposed spline fitting, which I'll try. I'll also look at the Numerical Recipes discussion he has proposed. Sebastian  Using Tomcat but need to do more? Need to support web services, security? Get stuff done quickly with preintegrated technology to make your job easier Download IBM WebSphere Application Server v.1.0.1 based on Apache Geronimo http://sel.asus.falkag.net/sel?cmd=lnk&kid=120709&bid=263057&dat=121642 _______________________________________________ Numpydiscussion mailing list Numpydiscussion@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/numpydiscussion  Using Tomcat but need to do more? Need to support web services, security? Get stuff done quickly with preintegrated technology to make your job easier Download IBM WebSphere Application Server v.1.0.1 based on Apache Geronimo http://sel.asus.falkag.net/sel?cmd=lnk&kid=120709&bid=263057&dat=121642 _______________________________________________ Numpydiscussion mailing list Numpydiscussion@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/numpydiscussion
Nadav Horesh napisał(a):
1. If at least one of your data sets to be interpulated is on a grid, you can use numpy.ndimage.map function for fast interpolation for 2d (in fact for any dimensional) dataset.
I've already used a splines to interpolate a missing simulated points. That procedure works great and is very fast. But I'll check the numpy.ndimage  I haven't used it, yet.
2. Isn't there an analytic expression to average the expectration values of SH over all possible orientations between B and the crystal axis? My experience shows that some analytic work can save 99% of simulation time.
Well, the simulations are already very fast. The time consumption is approximately ~0.3s for a single powder spectrum (2.8GHz Pentium D). The calculations are held by an external, very fine EPR spectra simulation tool. The author must have incorporated into it a lot of rationalizations, but this is a binary tool (unfortunately) and I do not know, what exactly sits inside of it... All I know, is that the orientations are represented by a grid (with an increment step tunable by a user). From library documentation: "After having computed the spectrum for a number of orientations specified, the simulation function interpolates these spectra for additional orientations before summing up all spectra." The interpolation is accomplish with a splines. Thank you for your comment, best regards Sebastian  Using Tomcat but need to do more? Need to support web services, security? Get stuff done quickly with preintegrated technology to make your job easier Download IBM WebSphere Application Server v.1.0.1 based on Apache Geronimo http://sel.asus.falkag.net/sel?cmd=lnk&kid=120709&bid=263057&dat=121642 _______________________________________________ Numpydiscussion mailing list Numpydiscussion@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/numpydiscussion
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Nadav Horesh

Sebastian Żurek