[SciPy-user] optimize.leastsq confusing when it comes to errors

Pim Schellart P.Schellart@student.science.ru...
Thu Mar 26 16:40:16 CDT 2009


Dear Scipy users,

This is my first post to the list so please let me know if I am  
posting the question in the wrong place.
I need to fit several functions to a dataset and would love to use  
scipy for this, this would allow me to use Python for all my  
scientific work as this is the only task for which I still use gnuplot.
But I find the documentation on optimize.leastsq very confusing.
I can get the fit paramaters (using the example as a guide) but I also  
need the errors on the resulting parameters and basically all the  
information given by the default gnuplot fit command output, which is  
the following.

###################################################################
final sum of squares of residuals : 1588.68
rel. change during last iteration : -2.92059e-06

degrees of freedom    (FIT_NDF)                        : 27
rms of residuals      (FIT_STDFIT) = sqrt(WSSR/ndf)    : 7.67072
variance of residuals (reduced chisquare) = WSSR/ndf   : 58.84

Final set of parameters            Asymptotic Standard Error
=======================            ==========================

a               = 1.77246          +/- 1.984        (111.9%)
b               = 0.713972         +/- 0.06909      (9.677%)
c               = -0.207495        +/- 1.413        (681.2%)


correlation matrix of the fit parameters:

                a      b      c
a               1.000
b               0.004  1.000
c              -0.103 -0.088  1.000
###################################################################

Furthermore my datapoints have associated errors and these need to be  
taken into account in the fit.
How can I make sure this is done?
Is optimize.leastsq build to do this or should I use a different  
function.
It would be even better if the example in the tutorial is extended to  
include this information as I can imagine most real world applications  
need errors on both the input and the output.
Thank you very much in advance.

Kind regards,

Pim Schellart

P.S. I am aware of the gnuplot python module but I prefer scipy :)
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