gnuplot documentation

53 FIT gnuplot 4.3 59
the statistical assumptions may not be justified, or the model function may be too general, fitting
fluctuations in a particular sample in addition to the underlying trends. In the latter case, a simpler
function may be more appropriate.
You’ll have to get used to both fit and the kind of problems you apply it to before you can relate the
standard errors to some more practical estimates of parameter uncertainties or evaluate the significance
of the correlation matrix.
Note that fit, in common with most NLLS implementations, minimizes the weighted sum of squared
distances (y-f(x))**2. It does not provide any means to account for "errors" in the values of x, only in y.
Also, any "outliers" (data points outside the normal distribution of the model) will have an exaggerated
effect on the solution.
53.4 Control
There are a number of gnuplot variables that can be defined to affect fit. Those which can be defined
once gnuplot is running are listed under ’control variables’ while those defined before starting gnuplot
are listed under ’environment variables’.
53.4.1 Control variables
The default epsilon limit (1e-5) may be changed by declaring a value for
FIT_LIMIT
When the sum of squared residuals changes between two iteration steps by a factor less than this number
(epsilon), the fit is considered to have ’converged’.
The maximum number of iterations may be limited by declaring a value for
FIT_MAXITER
A value of 0 (or not defining it at all) means that there is no limit.
If you need even more control about the algorithm, and know the Marquardt-Levenberg algorithm well,
there are some more variables to influence it. The startup value of lambda is normally calculated
automatically from the ML-matrix, but if you want to, you may provide your own one with
FIT_START_LAMBDA
Specifying FIT START LAMBDA as zero or less will re-enable the automatic selection. The variable
FIT_LAMBDA_FACTOR
gives the factor by which lambda is increased or decreased whenever the chi-squared target function
increased or decreased significantly. Setting FIT LAMBDA FACTOR to zero re-enables the default
factor of 10.0.
Other variables with the FIT
user-defined variables.
prefix may be added to fit, so it is safer not to use that prefix for
The variables FIT SKIP and FIT INDEX were used by earlier releases of gnuplot with a ’fit’ patch
called gnufit and are no longer available. The datafile every modifier provides the functionality of
FIT SKIP. FIT INDEX was used for multi-branch fitting, but multi-branch fitting of one independent
variable is now done as a pseudo-3D fit in which the second independent variable and using are used to
specify the branch. See fit multi-branch (p. 60).
53.4.2 Environment variables
The environment variables must be defined before gnuplot is executed; how to do so depends on your
operating system.
FIT_LOG
changes the name (and/or path) of the file to which the fit log will be written from the default of "fit.log"
in the working directory. The default value can be overwritten using the command set fit logfile.