INCLAN Graphics: plot fit: Difference between revisions
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== Description == | == Description == | ||
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 | ||
χ<sup>2</sup>(''a''<sub>1</sub>, ..., ''a''<sub>''m''</sub>) = \sum_{''i''} ((''y''<sub>''i''</sub> - ''y''(''x''<sub>''i''</sub>)) / ''σ''<sub>''i''</sub>)<sup>2</sup> | |||
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, | 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, ''a''<sub>1</sub>,...,''a''<sub>m</sub>, their standard deviations, χ<sup>2</sup>, and the probability that this value of χ<sup>2</sup> would be exceeded by chance are available through the intrinsic functions '''fitpar''', '''fiterr''', '''fitchisq''' and '''fitprob''', respectively. If the errors ''σ''<sub>''i''</sub> of the data points are unknown, this can be indicated by setting ''σ'' to zero in the '''fit''' command. | ||
dot x y1 # plot original data points | |||
fit x log(y1) 0 1 x # logarithmic fit of | dot x y1 # plot original data points | ||
spline x exp(y2) # plot fitted curve | fit x log(y1) 0 1 x # logarithmic fit of ''y'' = ''a''<sub>1</sub> exp(-''a''<sub>2</sub>''x'') | ||
spline x exp(y2) # plot fitted curve | |||
Latest revision as of 15:05, 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
χ2(a1, ..., am) = \sum_{i} ((yi - y(xi)) / σi)2
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, χ2, and the probability that this value of χ2 would be exceeded by chance are available through the intrinsic functions fitpar, fiterr, fitchisq and fitprob, respectively. If the errors σi of the data points are unknown, this can be indicated by setting σ 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(-a2x) spline x exp(y2) # plot fitted curve