INCLAN Graphics: plot fit: Difference between revisions

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== Synopsis ==


Usage: plot fit ''x'' ''y'' ''s'' ''f1''...
'''plot fit''' ''x'' ''y'' ''σ'' ''f''<sub>1</sub>... (list mode)


List mode:
== Description ==
The command performs a linear least-squares fit of the basis functions  
 
given bythe vector expressions f1,... to the data points with x-coordinates,
Performs a linear least-squares fit of the basis functions given by the vector expressions ''f''<sub>1</sub>,... to the data points with ''x''-coordinates, ''y''-coordinates and errors given by the vector expressions ''x'', ''y'' and ''σ'', respectively. For ''m'' basis functions, ''f''<sub>1</sub>,... ,''f''<sub>m</sub>, the optimal linear combination,  
y-coordinates and errors given by the vector expressions x, y and s,
 
respectively. For m basis functions, f1,...,fm the optimal linear combination,
''y''(''x'') = ''a''<sub>1</sub>''f''<sub>1</sub>(''x'')+ +''a''<sub>m</sub>''f''<sub>m</sub>(''x'')
is determined by minimizing the chi^2 value. The optimal fit function is
 
added as another column to the list data. This command does not draw
is determined by minimizing
anything. The fit parameters, their standard deviations, and the
 
probability that this value of chi^2 would be exceeded by chance are
available through the intrinsic functions fitpar, fiterr, fitchisq
where i runs over the list data points. The optimal fit function y(x) is added as another column to the list data. This command does not draw anything. The fit parameters, a1,…,am, their standard deviations, 2, and the probability that this value of 2 would be exceeded by chance are available through the intrinsic functions fitpar, fiterr, fitchisq and fitprob, respectively. If the errors i of the data points are unknown, this can be indicated by setting to zero in the fit command.
and fitprob, respectively. If the errors of the data points are
dot x y1 # plot original data points
unkown, this can be indicated by setting s to zero in the fit command.
fit x log(y1) 0 1 x # logarithmic fit of ya1 exp(a2 x)
spline x exp(y2) # plot fitted curve

Revision as of 13:17, 13 August 2009

Synopsis

plot fit x y σ f1... (list mode)

Description

Performs a linear least-squares fit of the basis functions given by the vector expressions f1,... to the data points with x-coordinates, y-coordinates and errors given by the vector expressions x, y and σ, respectively. For m basis functions, f1,... ,fm, the optimal linear combination,

y(x) = a1f1(x)+ +amfm(x)

is determined by minimizing


where i runs over the list data points. The optimal fit function y(x) is added as another column to the list data. This command does not draw anything. The fit parameters, a1,…,am, their standard deviations, 2, and the probability that this value of 2 would be exceeded by chance are available through the intrinsic functions fitpar, fiterr, fitchisq and fitprob, respectively. If the errors i of the data points are unknown, this can be indicated by setting  to zero in the fit command. dot x y1 # plot original data points fit x log(y1) 0 1 x # logarithmic fit of ya1 exp(a2 x) spline x exp(y2) # plot fitted curve

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