numOSL (version 2.0)

fitGrowth: Growth curve fitting

Description

Fitting growth curves using the Levenberg-Marquardt algorithm.

Usage

fitGrowth(Curvedata, model = "exp", origin = FALSE,  weight = TRUE, plot = TRUE)

Arguments

Curvedata

matrix(required): a three-column matrix (i.e., regenerative doses, standardised regenerative dose signals, and measurement errors of standardised regenerative dose signals)

model

character(with default): model used for growth curve fitting, see details

origin

logical(optional): force the fitted growth curve to pass the origin or not

weight

logical(with default): perform growth curve fitting using a weighted or an un-weighted procedure, see details

plot

logical(with default): plot output or not

Value

Return a list that contains the following elements:

LMpars

optimized parameters for the fitted growth curve

value

minimized objective for the fitted growth curve

fit.value

observed standardised regenerative dose signals and fitted counterparts

Details

In growth curve fitting using function fitGrowth, five models are available: (1) "line": a linear model, y=a*x+b; (2) "exp": a single saturation exponential model, y=a*[1-exp(-b*x)]+c; (3) "lexp": a single saturation exponential plus linear model, y=a*[1-exp(-b*x)]+c*x+d; (4) "dexp": a double saturation exponential model, y=a*[1-exp(-b*x)]+c*[1-exp(-d*x)]+e; (5) "gok": a general order kinetic model (Guralnik et al., 2015), y=a*[1-(1+b*c*x)^(-1/c)]+d. The fitting process is performed using the Levenberg-Marquardt algorithm (minpack: Fortran 90 source code by John Burkardt, freely available at http://people.sc.fsu.edu/~jburkardt/f_src/minpack/minpack.html). If weight=TRUE, a weighted procedure will be performed through weighting each data point by its inverse variance. User is advised to set argument plot=TRUE if possible to visualize the quality of fit.

References

Guralnik B, Li B, Jain M, Chen R, Paris RB, Murray AS, Li SH, Pagonis V, Valla PG, Herman F, 2015. Radiation-induced growth and isothermal decay of infrared-stimulated luminescence from feldspar. Radiation Measurements, 81: 224-231.

More JJ, 1978. "The Levenberg-Marquardt algorithm: implementation and theory" in Lecture Notes in Mathematics: Numerical Analysis, Springer-Verlag: Berlin. 105-116.

See Also

analyst; calED; fastED; calSARED; calSGCED

Examples

 Curvedata<-cbind(c(0, 18, 36, 54, 72, 0, 18),               
                  c(0.026, 1.55, 2.39, 3.46, 4.13, 0.023, 1.61),  
                  c(0.005, 0.11, 0.27, 0.22, 0.20, 0.008, 0.24)) 
 fitGrowth(Curvedata, model="gok", origin=FALSE, plot=TRUE)