diffractometry (version 0.1-10)

diffractogram: Complete analysis of diffractograms as described in Davies et al. (2008)

Description

Performs a complete analysis of x-ray diffractogram, i.e. calculation of the baseline and the peak intervals as well as decomposition of the peaks.

Usage

diffractogram(data, tau=2.5,gam=1, scl.factor=1.2, maxwdth=5, intnum=0, 
alpha=0.1, maxiter1=500, maxiter=10000, hmax=5, maxsolutions=3,
heterosk=TRUE, baselim=c(0.05,5), dispers=1)

Arguments

data

A diffractogram given as a matrix, where the first column gives the angles of diffraction in \(2\theta\) and the second column gives the corresponding photon counts. Angles of diffraction are taken to be equidistant.

tau

Value of Parameter tau used in the residual criterion.

gam

Factor which is used in the separation between peaks and baseline.

scl.factor

Factor which is used in the heteroscedastic residual criterion.

maxwdth

Maximum width of the peaks. By default set to 5 degrees.

intnum

Vector of numbers of intervals. If intnum = 0, all intervals are used

alpha

Test level for residual criterion

maxiter1

Number of attempts to fit a model with 1 component

maxiter

Number of attempts to fit a model with k > 1 components

hmax

Maximum number of components

maxsolutions

Number of solutions with k components

heterosk

If TRUE, the estimate of noise level given in baslfit is used (default); otherwise noise level is taken to be proportional to signal height

baselim

Limits for changes in the baseline estimate; first component is given in percent of the baseline height, second in counts per \(2\theta\)

dispers

Additional dispersion factor; not used if heterosk==T

Value

Returns a LIST with components

basl

Output of baselinefit

pks

Output of pkdecomp

Details

diffractogram first calls baselinefit with the specified parameters and then pkdecomp for the output of baselinefit. For further details, see the corresponding help pages.

References

P.L. Davies, U. Gather, M. Meise, D. Mergel, T. Mildenberger (2008): "Residual based localization and quantification of peaks in x-ray diffractograms", Annals of Applied Statistics, Vol. 2, No. 3, 861-886.. http://www.statistik.tu-dortmund.de/fileadmin/user_upload/Lehrstuehle/MSind/Publikationen/2008/2008_-_Davies_Gather_Meise_Mergel_Mildenberger_-_Residual_based_localization_and_quantification_of_peaks_in_x-ray_diffractograms.pdf

See Also

baselinefit, pkdecomp

Examples

# NOT RUN {
## Complete Analysis of a segment from indiumoxide data:
## Identification of baseline and peak as well as decomposition of the peaks  
## Plot shows baseline and decomposition of first found peak into two components 

set.seed(0)

par(mfrow=c(3,1))

data(indiumoxide)
indox<-indiumoxide[1901:2400,]

sol<-diffractogram(indox,maxsolutions=1,maxiter1=50,maxiter=250)

ind<-c(sol$bas$indlsep[1],sol$bas$indrsep[1])

plot(indox,xlab="",ylab="")
lines(indox[,1],sol$bas$baseline$basisl,col="red")
points(indox[ind[1]:ind[2],],col="blue")


plot(indox[ind[1]:ind[2],1], sol$bas$baseline$peaks[ind[1]:ind[2]],xlab="",ylab="")

lines(indox[ind[1]:ind[2],1],sol$pks[[2]]$fit,col="red")
plot(indox[ind[1]:ind[2],1],sol$pks[[2]]$fitpk[1,],ylim=c(0,1800),type="l",xlab="",ylab="")
lines(indox[ind[1]:ind[2],1],sol$pks[[2]]$fitpk[2,])



# }