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bestFit: a command-line tool for least-square fitting =
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url: http://emma.inrim.it:8080/gdurin/software/bestfit

bestFit is a simple python script to perform data fitting using nonlinear least-squares minimization. 
The routine is based on the scipy.optimize.leastsq method (see http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.leastsq.html#scipy.optimize.leastsq), which is a wrapper around MINPACK’s lmdif and lmder algorithms.

This is a command line tool, to keep everything easy and fast to use. 

INSTALLATION
See the included file INSTALL.txt

HOW TO USE IT
Make the bestFit.py executable (under Linux: chmod +x bestFit.py) and run it without any option. The output is the following:

Failed: Not enough input filenames specified

    bestFit v.0.1.2
    august 18 - 2011

    Usage summary: bestFit [OPTIONS]

    OPTIONS:
    -f, --filename   Filename of the data in form of columns
    -c, --cols          Columns to get the data (defaults: 0,1); a third number is used for errors' column
    -v, --vars         Variables (defaults: x,y)
    -r, --range       Range of the data to consider (i.e. 0:4; 0:-1 takes all)
    -p, --fitpars      Fitting Parameters names (separated by comas)
    -i, --initvals      Initial values of the parameters (separated by comas)
    -t, --theory       Theoretical function to best fit the data (between "...")
    -s, --sigma       Estimation of the error in the data (as a constant value)
    -d, --derivs      Use analytical derivatives
    --lin                 Use data in linear mode (default)
    --log                Use data il log mode (best for log-log data)
    --noplot           Don't show the plot output

    EXAMPLE
    bestfit -f mydata.dat -c 0,2 -r 10:-1 -v x,y -p a,b -i 1,1. -t "a+b*x"


TEST THE SCRIPT
To be sure that the script is working correctly, try one of the test fits included.

For instance, try to fit the eckerle4 data (see: http://www.itl.nist.gov/div898/strd/nls/data/eckerle4.shtml for details). 
This is a case considered of high difficulty.

On the command line copy the following line: 

./bestFit.py -f test/eckerle4/data.dat -p b1,b2,b3 -t "b1/b2*exp(-(x-b3)**2/(2.*b2**2))" -i 1.,10.,500. -c 1,0 -d

[Hint: make a soft link to bestFit.py in your local bin, such as
ln -s yourDirectory/bestFit.py /usr/local/bin/bestFit
and then move to the test/ecklerle4 directory so to simply use as:
bestFit -t data.dat ....
]

The results should be similar to my output:
================================================================================
Initial parameters =  (1.0, 10.0, 500.0)
initial cost = 7.2230265030e-01 (StD: 1.5023966794e-01)
optimized cost = 1.4635887487e-03 (StD: 6.7629245447e-03)
================================================================================
parameter            value         st. error    t-statistics
b1            1.5543826681   0.0154080427126   100.881253842
b2           4.08883191419   0.0468029694065   87.3626602338
b3           451.541218624   0.0468004675198   9648.22025407
================================================================================
Done in 18 iterations
Both actual and predicted relative reductions in the sum of squares
  are at most 0.000000
================================================================================
n. of data = 35
degree of freedom = 32
X^2_rel = 0.000046
pValue = 1.000000 (statistically significant if < 0.05)

In this run we have used the analytical derivatives with the "-d" option. Try now not to use it, so:
 
./bestFit.py -f test/eckerle4/data.dat -p b1,b2,b3 -t "b1/b2*exp(-(x-b3)**2/(2.*b2**2))" -i 1.,10.,500. -c 1,0 
================================================================================
Initial parameters =  (1.0, 10.0, 500.0)
initial cost = 7.2230265030e-01 (StD: 1.5023966794e-01)
optimized cost = 1.4635887487e-03 (StD: 6.7629245447e-03)
================================================================================
parameter            value         st. error    t-statistics
b1           1.55438266849   0.0154080427799   100.881253426
b2           4.08883191593   0.0468029705094   87.3626582123
b3           451.541218624   0.0468004675655   9648.22024464
================================================================================
Done in 63 iterations
Both actual and predicted relative reductions in the sum of squares
  are at most 0.000000
================================================================================
n. of data = 35
degree of freedom = 32
X^2_rel = 0.000046
pValue = 1.000000 (statistically significant if < 0.05)

If it is similar, your are done!