Re: [Numpy-discussion] Model and experiment fitting.
Robert Kern napisał(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 x-variable), 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 shape-width, 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 X-range, with a density I'm able to tune. It all works quite well but I'm founding it as a 'brute-force' 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 pre-integrated technology to make your job easier Download IBM WebSphere Application Server v.1.0.1 based on Apache Geronimo http://sel.as-us.falkag.net/sel?cmd=lnkkid=120709bid=263057dat=121642 ___ Numpy-discussion mailing list Numpy-discussion@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/numpy-discussion
Re: [Numpy-discussion] Model and experiment fitting.
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: [EMAIL PROTECTED] on behalf of Sebastian Zurek Sent: Sat 21-Oct-06 15:41 To: numpy-discussion@lists.sourceforge.net Cc: Subject:Re: [Numpy-discussion] 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 x-variable), 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 shape-width, 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 X-range, with a density I'm able to tune. It all works quite well but I'm founding it as a 'brute-force' 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 pre-integrated technology to make your job easier Download IBM WebSphere Application Server v.1.0.1 based on Apache Geronimo http://sel.as-us.falkag.net/sel?cmd=lnkkid=120709bid=263057dat=121642 ___ Numpy-discussion mailing list Numpy-discussion@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/numpy-discussion winmail.dat- Using Tomcat but need to do more? Need to support web services, security? Get stuff done quickly with pre-integrated technology to make your job easier Download IBM WebSphere Application Server v.1.0.1 based on Apache Geronimo http://sel.as-us.falkag.net/sel?cmd=lnkkid=120709bid=263057dat=121642___ Numpy-discussion mailing list Numpy-discussion@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/numpy-discussion
Re: [Numpy-discussion] Model and experiment fitting.
Sebastian Żurek wrote: Hi! This is probably a silly question but I'm getting confused with a certain problem: a comparison between experimental data points (2D points set) and a model (2D points set - no analytical form). The physical model produces (by a sophisticated simulations done by an external program) some 2D points data and one of my task is to compare those calculated data with an experimental one. The experimental and modeled data have form of 2D curves, build of n 2D-points, i.e.: expDat=[[x1,x2,x3,..xn],[y1,y2,y3,...,yn]] simDat=[[X1,X2,X3,...,Xn],[Y1,Y2,Y3,...,Yn]] The task of determining, let's say, a root mean squarred error (RMSe) is trivial if x1==X1, x2==X2, etc. In general, which is a common situation xk differs from Xk (k=0..n) and one may not simply compare succeeding Yk and yk (k=0..n) to determine the goodness-of-fit. The distance h=Xk-X(k-1) is constant, but similar distance m(k)=xk-x(k-1) depends on k-th point and is not a constant value, although the data array lengths for simulation and experiment are the same. Your description is a bit vague. Do you mean that you have some model function f that maps X values to Y values? f(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? OTOH, is there some other independent variable (say Z) that *is* common between your experimental and simulated data? f(z) - (x, y) -- Robert Kern I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it as though it had an underlying truth. -- Umberto Eco - Using Tomcat but need to do more? Need to support web services, security? Get stuff done quickly with pre-integrated technology to make your job easier Download IBM WebSphere Application Server v.1.0.1 based on Apache Geronimo http://sel.as-us.falkag.net/sel?cmd=lnkkid=120709bid=263057dat=121642 ___ Numpy-discussion mailing list Numpy-discussion@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/numpy-discussion
Re: [Numpy-discussion] Model and experiment fitting.
On 20/10/06, Sebastian Żurek [EMAIL PROTECTED] wrote: Is there something like that in any numerical python modules (numpy, pylab) I could use? In scipy there are some very convenient spline fitting tools which will allow you to fit a nice smooth spline through the simulation data points (or near, if they have some uncertainty); you can then easily look at the RMS difference in the y values. You can also, less easily, look at the distance from the curve allowing for some uncertainty in the x values. I suppose you could also fit a curve through the experimental points and compare the two curves in some way. I can imagine, I can fit the data with some polynomial or whatever, and than compare the fitted data, but my goal is to operate on as raw data as it's possible. If you want to avoid using an a priori model, Numerical Recipes discuss some possible approaches (Do two-dimensional distributions differ? at http://www.nrbook.com/a/bookcpdf.html is one) but it's not clear how to turn the problem you describe into a solvable one - some assumption about how the models vary between sampled x values appears to be necessary, and that amounts to interpolation. A. M. Archibald - Using Tomcat but need to do more? Need to support web services, security? Get stuff done quickly with pre-integrated technology to make your job easier Download IBM WebSphere Application Server v.1.0.1 based on Apache Geronimo http://sel.as-us.falkag.net/sel?cmd=lnkkid=120709bid=263057dat=121642 ___ Numpy-discussion mailing list Numpy-discussion@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/numpy-discussion
