INCLAN Graphics: plot fit: Difference between revisions
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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, | 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''(''x'') = ''a''<sub>1</sub>''f''<sub>1</sub>(''x'') + | ''y''(''x'') = ''a''<sub>1</sub>''f''<sub>1</sub>(''x'') + ... + ''a''<sub>m</sub>''f''<sub>m</sub>(''x'') | ||
is determined by minimizing | is determined by minimizing | ||
Revision as of 14:19, 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 ya1 exp(a2 x)
spline x exp(y2) # plot fitted curve