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Name

tablsqfit - general purpose least squares fitting program

Synopsis

tablsqfit in=table-file [parameter=value]

Description

tablsqfit takes a least squares fit (minimized ChiSquared) of a set of datapoints (x(i),y(i)) where a functional form y=f(x;a1,a2,...,an) is assumed. The functional form to be fitted has to be specified by name at this stage. A number of options are possible.

The inputfile is an ascii file in a tabular format, where on every line there must be an assigned column for the X- and Y-coordinates. An optional column can be assigned to the errors in Y (the DY-coordinates). If no DY-column is assigned, it is assumed that the errors in Y are all the same and equal to 1. Lines starting with the ’#’ symbol are comment lines. Certain models (see fit= below) allow multiple X or Y columns. For fit=line a proper goodness-of-fit is also computed in a second fit an error column (dycol=) is given.

For most linear functions the non-linear version of this program will also work fine, and has the added power that certain parameters can be fixed, and error estimates are returned. See tabnllsqfit(1NEMO) .

Parameters

The following parameters are recognized in any order if the keyword is also given:
in=in-file
(ascii) input file, a table of values from which data is taken. No default.
xcol=col,...
The column(s) from which the (independant) X-values are taken. The first column is called 1 by definition [default: 1].
ycol=col,...
The column(s) from which the (dependant) Y-values are taken [default: 2].
dxcol=int
Optional column from which the DX-values (errors in X) are taken. Currently only a straight line fit can use this option. See below.
dycol=int
Optional column from which the DY-values (errors in Y) are taken. The inverse square of the errors are uses as weights for those fits where these are used [default: none assigned].
xrange=xmin:xmax
Range in X-values for which the fit is done. If only one number is given, the other one is considered zero. [default: no entry, i.e. all].
fit=model
Model name what to fit. Currently implemented are line, plane, poly, ellipse, peak, zero, imageshift, area, gauss1d, and gauss2d. [default: line].
order=order
Highest order of the polynomial fit (fit=poly) or dimension of the hyper-plane fit (fit=plane). 0 would fit a constant. 0 and 1 would have the same meaning in both the plane and poly cases [Default: 0].
out=filename
Optional output filename (only active under certain options) where the data and residuals are stored. Column 1, 2 and 3 will contain the X, Y and residuals F(X)-Y respectively. A future release will also store the errors (if it was given, see keyword dycol above) in the 4th column. [default: empty, no output file created].
nsigma=sigma_factor
A positive number will delete points more than sigma_factor from the fit, and fit again. [Default: -1].
estimate=
Optional estimate for parameters of non-linear fits
nmax=max_lines
Maximum number of lines allocated if the input file was being read from a pipe. If not, the routine file_lines(3NEMO) is used to allocate space for the table. [Default: 10000].
mpfit=mode
The fitting mode in which mpfit(3NEMO) is used. 0=no errors. 1=only errors in X used (dxcol=), 2=only errors in Y used (dycol=), 3=errors in both X and Y used. See also linreg(1NEMO) .
tab=t|f
Output results in simple tabular format. Default: false.

Example

Here is an example of creating an on-the-fly table with a straight line, with some added noise and random weights between 1 and 2: 
% nemoinp 1:100 | tabmath - - "%1+rang(0,10),ranu(1,2)" seed=123 | tablsqfit
-
      a  =    0.974146       uncertainty:  0.039389 
      b  =    1.755022       uncertainty:  2.291149 
      x0 =   -1.801599       uncertainty:  2.353083
      y0 =    1.755022       uncertainty:  2.291149
      chi-squared:    12668.983284 
      goodness-of-fit:    1.000000 (no Y errors supplied [dycol=])
      r:  0.92923
      prob:  3.65557e-44
      z:  1.65272
The fitted line is written either as y=ax+b or alternatively with their (x0,y0) intercepts as x/x0 + y/y0=1.

See Also

tabhist(1NEMO) , tabmath(1NEMO) , gaussfit(1NEMO) , linreg(1NEMO) , tabnllsqfit(1NEMO) Numerical Recipies in C, Ch.14

mpfit: http://www.physics.wisc.edu/~craigm/idl/cmpfit.html (author: Craig B. Markwardt)

http://arxiv.org/abs/1008.4686: Data analysis recipes: Fitting a model to data P (Hogg, Bovy & Lang 2010)

Author

Peter Teuben

Files


~/src/kernel/tab    tablsqfit.c

Update History


 5-Aug-87    V1.0 created                         PJT
18-May-88    V1.4 various new options            PJT
31-May-88    V2.0 ’float’-> ’double’ for NumRec    PJT
14-nov-91    V2.4 ellips fit and various others     PJT
13-Mar-92    V2.5 added imageshift option        PJT
15-nov-93    V2.6 added nmax=                    PJT
13-jun-94    V2.7 code overhaul to add line/poly    PJT
8-jun-95     V2.8 added option fit=peak          PJT
26-jan-98    V2.9 added goodness-of-fit for fit=line     PJT
4-feb-98    V2.9a compute r (corr.coeff.) for line fit    PJT
14-aug-00    V3.0 added tab=                                PJT
8-aug-01    V3.1c added area, using natof, error in ellipse    PJT
24-feb-03    V3.4: added fit=zero    PJT
21-nov-05    V3.4b: added fit=gauss1d,gauss2d    PJT
9-dec-09    V4.0: added xcol= and mpfit=    PJT

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