INCLAN Graphics: plot fit - Revision history

Admin at 13:05, 13 August 2009

2009-08-13T13:05:06Z

← Older revision		Revision as of 15:05, 13 August 2009
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	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>		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, ''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.		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.

Admin at 13:02, 13 August 2009

2009-08-13T13:02:41Z

← Older revision		Revision as of 15:02, 13 August 2009
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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'') + ... + ''a''<sub>m</sub>''f''<sub>m</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>		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, 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.		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 ~~ya1~~ exp(~~a2~~ x)		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

Admin at 12:31, 13 August 2009

2009-08-13T12:31:06Z

← Older revision		Revision as of 14:31, 13 August 2009
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	is determined by minimizing		is determined by minimizing

			χ<sup>2</sup>(''a''<sub>1</sub>, ..., ''a''<sub>m</sub>

	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.		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.

Admin at 12:19, 13 August 2009

2009-08-13T12:19:08Z

← Older revision		Revision as of 14:19, 13 August 2009
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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'') + ~~~~ + ''a''<sub>m</sub>''f''<sub>m</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

Admin at 12:18, 13 August 2009

2009-08-13T12:18:27Z

← Older revision		Revision as of 14:18, 13 August 2009
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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'')+ +''a''<sub>m</sub>''f''<sub>m</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

Admin at 12:17, 13 August 2009

2009-08-13T12:17:59Z

← Older revision		Revision as of 14:17, 13 August 2009
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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

Admin: 1 revision

2009-01-29T11:26:53Z

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← Older revision	Revision as of 13:26, 29 January 2009
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Admin: 1 revision

2009-01-28T23:35:39Z

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Usage: plot fit ''x'' ''y'' ''s'' ''f1''...

List mode:
The command performs a linear least-squares fit of the basis functions
given bythe vector expressions f1,... to the data points with x-coordinates,
y-coordinates and errors given by the vector expressions x, y and s,
respectively. For m basis functions, f1,...,fm the optimal linear combination,
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
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
and fitprob, respectively. If the errors of the data points are
unkown, this can be indicated by setting s to zero in the fit command.