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PODifference between Levenberg-Marquardt-Algorithm and ODR
 

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  1. PODifference between Levenberg-Marquardt-Algorithm and ODR
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    <p>I was able to fit curves to a x/y dataset using <a href="http://lorentz.sourceforge.net/" rel="nofollow noreferrer">peak-o-mat</a>, as shown below. Thats a linear background and 10 lorentzian curves. <img src="https://i.stack.imgur.com/FKXNH.png" alt="Peak-o-mat results"></p> <p>Since I need to fit many similar curves I wrote a scripted fitting routine, using <a href="http://code.google.com/p/agpy/source/browse/trunk/mpfit/?r=399" rel="nofollow noreferrer">mpfit.py</a>, which is a Levenberg-Marquardt-Algorithm. However the fit takes longer and, in my opinion, is less accurate than the peak-o-mat result:</p> <p><strong>Starting values</strong> <img src="https://i.stack.imgur.com/yXS2D.png" alt="Starting values"></p> <p><strong>Fit result with fixed linear background</strong> (values for linear background taken from the peak-o-mat result) <img src="https://i.stack.imgur.com/dTbVr.png" alt="Fit fixed"></p> <p><strong>Fit result with all variables free</strong> <img src="https://i.stack.imgur.com/Zvs62.png" alt="Fit free"></p> <p>I believe the starting values are already very close, but even with the fixed linear background, the left lorentzian is clearly a degradation of the fit.</p> <p>The result is even worse for total free fit.</p> <p>Peak-o-mat appears to use <a href="http://www.scipy.org/doc/api_docs/SciPy.odr.odrpack.html" rel="nofollow noreferrer">scipy.odr.odrpack</a>. Now what is more likely:</p> <ol> <li>I did some implementation error? </li> <li>odrpack is more suitable for this particular problem?</li> </ol> <p>Fitting to a more simple problem (linear data with one peak in the middle) shows very good correlation between peak-o-mat and my script. Also I did not find a lot about ordpack.</p> <p><strong><em>Edit:</em></strong> It seems I could answer the question by myself, however the answer is a bit unsettling. Using scipy.odr (which allows fitting with odr or leastsq method) both give the result as peak-o-mat, even without constraints.</p> <p>The image below shows again the data, the start values (almost perfect) and then the odr and leastsq fits. The component curves are for the odr one</p> <p><img src="https://i.stack.imgur.com/y46w2.png" alt="scipy.odr"></p> <p>I will switch to odr, but this still leaves me upset. The methods (mpfit.py, scipy.optimize.leastsq, scipy.odr in leastsq mode) 'should' yield the same results.</p> <p>And for people stumbling upon this post: to do the odr fit an error must be specified for x and y values. If there is no error, use small values with sx &lt;&lt; sy. </p> <pre><code>linear = odr.Model(f) mydata = odr.RealData(x, y, sx = 1e-99, sy = 0.01) myodr = odr.ODR(mydata, linear, beta0 = beta0, maxit = 2000) myoutput1 = myodr.run() </code></pre>
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    1. COpeak-o-mat is open source, so you can in principle figure out how it does things.
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