sufr_fitting Module Reference

Procedures to fit functions to data. More...

Functions/Subroutines
subroutine, public	linear_fit_yerr (ndat, xdat, ydat, yerr, ncoef, fcoef, freecoef, ncov, covmat, chisq, myfunc)
	Fit the model coefficients using a chi^2 method.
subroutine, public	nonlin_fit_yerr (ny, ndat, xdat, ydat, yerr, ncoef, fcoef, freecoef, nmat, covmat, curvmat, chisq, iterstat, myfunc)
	Levenberg-Marquardt method to reduce the value of chi-squared of a fit of a set of data points with errors in Y to a non-linear function.
subroutine, public	nonlin_fit_example_myfunc (ny, xdat, ncoef, fcoef, ydat, dyda)
	Dummy example function myFunc for nonlin_fit_yerr(): return the value and partial derivatives.
pure subroutine, public	basefunc_polynomial (xval, ncoef, basefunc)
	User-provided base function to fit a polynomial to.

Detailed Description

Procedures to fit functions to data.

Function/Subroutine Documentation

basefunc_polynomial()

pure subroutine, public sufr_fitting::basefunc_polynomial	(	real(double), intent(in)	xval,
		integer, intent(in)	ncoef,
		real(double), dimension(ncoef), intent(out)	basefunc )

User-provided base function to fit a polynomial to.

Parameters

xVal	X value to evaluate yVal = basefunc_polynimial(xVal) for
nCoef	Number of coefficients for the base function
baseFunc	Base function i for coefficent i. For a polynomial, BF(i) = x**(i-1) (output)

Definition at line 585 of file fitting.f90.

References sufr_kinds::double.

linear_fit_yerr()

subroutine, public sufr_fitting::linear_fit_yerr	(	integer, intent(in)	ndat,
		real(double), dimension(ndat), intent(in)	xdat,
		real(double), dimension(ndat), intent(in)	ydat,
		real(double), dimension(ndat), intent(in)	yerr,
		integer, intent(in)	ncoef,
		real(double), dimension(ncoef), intent(inout)	fcoef,
		integer, dimension(ncoef), intent(in)	freecoef,
		integer, intent(in)	ncov,
		real(double), dimension(ncov,ncov), intent(out)	covmat,
		real(double), intent(out)	chisq,
		external	myfunc )

Fit the model coefficients using a chi^2 method.

Do a chi^2-minimisation fit of nDat data points xDat and yDat, the latter with errors yErr, to function func. The fit uses the nCoef coefficients stored in fCoef() that should be varied if the corresponding entry in freeCoef=1, fixed if =0.

The fitting function must be provided as the subroutine myFunc which returns a value y = myFunc(x, basefunc, nCoef), where y is a linear combination of x, i.e. y = SUM(i=1,nCoef) fCoef(i) * basefunc(i)(x). For example, for a polynomial, basefunc(i) = x**(i-1).

The routine returns the fit coefficients in fCoef(), the variance-covariance matrix in covMat sith size nCov, and the chi^2 value in chiSq.

Parameters

nDat	Number of data points
xDat	X values of the data (nDat)
yDat	Y values of the data (nDat)
yErr	Errors (standard deviations) of the y values (nDat)
nCoef	Number of coefficients of the fitting function
fCoef	Coefficients of the fitting function (nCoef) (output)
freeCoef	Fix coefficient coef(i) if freeCoef(i)=0, otherwise let if vary freely and fit it (nCoef)
nCov	Size of both dimensions of covMat()
covMat	Covariance matrix (nCov,nCov) (output)
chiSq	Chi^2 - chi squared (output)
myFunc	External subroutine that describes the model value of Y for given value X

Note

• Needs sort_var_covar_matrix() and solve_linear_equations_Gauss_Jordan()

See also

Numerical Recipes in Fortran 77, Sect.15.4

Definition at line 69 of file fitting.f90.

References sufr_kinds::double, sufr_system::quit_program_error(), and sufr_system::warn().

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nonlin_fit_example_myfunc()

subroutine, public sufr_fitting::nonlin_fit_example_myfunc	(	integer, intent(in)	ny,
		real(double), intent(in)	xdat,
		integer, intent(in)	ncoef,
		real(double), dimension(ncoef), intent(in)	fcoef,
		real(double), dimension(ny), intent(out)	ydat,
		real(double), dimension(ny,ncoef), intent(out)	dyda )

Dummy example function myFunc for nonlin_fit_yerr(): return the value and partial derivatives.

Parameters

nY	Number of Y values for each X value (normally 1, but e.g. 2 for a sky position with two coordinates)
xDat	Input X value for the current data point
nCoef	Number of coefficients
fCoef	Vector of coefficients that describe the function
yDat	Y values for the current data point (output)
dyda	Partial derivatives for yDat: 1: dy/dfCoef(1), ..., n: dy/dfCoef(n) (output)

Note

Write a subroutine with the same interface to use with nonlin_fit_yerr()

Definition at line 406 of file fitting.f90.

References sufr_kinds::double, sufr_system::quit_program_error(), sufr_system::swapdbl(), and sufr_system::warn().

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nonlin_fit_yerr()

subroutine, public sufr_fitting::nonlin_fit_yerr	(	integer, intent(in)	ny,
		integer, intent(in)	ndat,
		real(double), dimension(ndat), intent(in)	xdat,
		real(double), dimension(ny,ndat), intent(in)	ydat,
		real(double), dimension(ndat), intent(in)	yerr,
		integer, intent(in)	ncoef,
		real(double), dimension(ncoef), intent(inout)	fcoef,
		integer, dimension(ncoef), intent(in)	freecoef,
		integer, intent(in)	nmat,
		real(double), dimension(nmat,nmat), intent(out)	covmat,
		real(double), dimension(nmat,nmat), intent(out)	curvmat,
		real(double), intent(out)	chisq,
		real(double), intent(inout)	iterstat,
		external	myfunc )

Levenberg-Marquardt method to reduce the value of chi-squared of a fit of a set of data points with errors in Y to a non-linear function.

You will need to call this routine repeatedly, with different values for iterStat, until chiSq no longer decreases (significantly)

Parameters

nY	Number of Y values for each X value (normally 1, but e.g. 2 for a sky position with two coordinates)
nDat	Number of data points in X and Y
xDat	X data points to fit
yDat	Y data points to fit
yErr	Errors (standard deviations) for yDat
nCoef	Number of coefficients used to describe the non-linear function myFunc
fCoef	Coefficients for the non-linear function myFunc, updated after each call
freeCoef	Determines which coefficients for the non-linear function myFunc should be fitted for. Set freeCoef(i) = 0 in order to keep fCoef(i) fixed
nMat	Size of the matrices; > nCoef
covMat	Variance-covariance matrix - returned on last call with iterStat. Fixed parameters return zero (co)variances
curvMat	Hessian/curvature matrix - double partial derivative of chi squared to two coefficients fCoef
chiSq	Chi squared
iterStat	Iteration status; Set to <0 for initialisation in the first call, and let it vary in subsequent calls, until the fit converges. After that, set to 0 to return the variance-covariance and curvature matrices on the final call. IterStat decreases 10x if chiSq becomes smaller, and increases 10x otherwise.
myFunc	External subroutine that describes the model value of Y and partial derivatives dY/dXi for given value X and function coefficients fCoef

See also

Numerical Recipes in Fortran, 15.5: Modelling of Data / Non-linear models

Note

Uses sort_var_covar_matrix(), solve_linear_equations_Gauss_Jordan() and nonlin_fit_eval()

Definition at line 191 of file fitting.f90.

References sufr_numerics::deq0(), and sufr_kinds::double.

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