nanop (version 2.0-1)

rss: Function to calculate the RSS between the simulated PDF or the total scattering structure function and target data

Description

Given a nanoparticle model and PDF or total scattering structure function data, this function calculates the PDF or total scattering structure function associated with the model. It then determines the residual sum of squares (RSS) between the simulated signals and the data.

Usage

rss(par, dataG=NA, dataS=NA, dataSAS=NA, part=NA, type="neutron",
    simPar=NA, PDF.fixed=list(), TotalScatt.fixed=list(), 
    parscale=NA, skel=NA, con=TRUE, oneDW=FALSE, 
    punish=FALSE, gammaR=NA, rvector=NA, fixed=NA,
    wG=0.03, wSAS=0.03, avRes=1, pareto=FALSE)

Value

If pareto=FALSE the R-factor: the square root of the sum of squared distances between the target data and simulated signal divided by a the sum of squared target data values. If pareto=TRUE a vector with R-factors as components.

Rdversion

1.1

Details

The following parameters may be fitted in rss (i.e., specified in par or skel): r, rsigma (sets standard deviation in the normal or log-normal distribution with mean value r), box, ellipse, bkg (background line that should be extracted from the SAS data), shell, rcore, scaleSq (scale factor for the total scattering function or the PDF), scaleSASq (scale factor for the total scattering function in SAS region or the gamma baseline term), pStack, pDimer, delta, sigma, latticep and latticepShell. For wurtzite structure to fit u parameter (second atom z-coordinate) third element in the vectors latticep and latticepShell may be specified.

Examples

part <- res_gQ <- res_gQ_WAS <- res_gQ_SAS <- list() 

## prepare polydisperse sample consisting of 30 particles:
size <- sort(rlnorm(30, meanlog = log(10), sdlog = log(1.1)))
base_Cu <- getBase("Cu")
Au <- createAtom("Au", base=base_Cu)

for(i in 1:30) {
  cat("r = ", size[i], "")
  part[[i]] <- simPart(atoms=list(Au), r=size[i], latticep=4.08, 
      rcenter=TRUE) 
  res_gQ_WAS[[i]] <- calcTotalScatt(part[[i]],minQ=.771, maxQ=20, 
      dr=0.01, dQ=0.02, sigma=c(0.02))							
  res_gQ_SAS[[i]] <- calcTotalScatt(part[[i]],minQ=.001, 
      dr=0.01, maxQ=.771, dQ=0.01, sigma=c(0.02))
  cat(i,"")
}

## calculate average values:
gQ_av_WAS <- 0
for(i in 1:length(res_gQ_WAS)) {
  gQ_av_WAS <- res_gQ_WAS[[i]]$gQ + gQ_av_WAS
}
gQ_av_WAS <- gQ_av_WAS/length(res_gQ_WAS)

gQ_av_SAS <- 0
for(i in 1:length(res_gQ_SAS)) {
  gQ_av_SAS <- res_gQ_SAS[[i]]$gQ + gQ_av_SAS
}
gQ_av_SAS <- gQ_av_SAS/length(res_gQ_SAS)

## calculate PDF and gamma baseline term
resSAS  <- calcQDepPDF(minR=0, maxR=30, dr=0.01, minQ=.001,
    maxQ=.771, verbose=100, 
    preTotalScat=list(Q=res_gQ_SAS[[1]]$Q,gQ=gQ_av_SAS))
  
mr <- which(res_gQ_WAS[[1]]$Q > 17)[1]
mxr <- which(res_gQ_WAS[[1]]$Q > 19)[1]
cuto <- res_gQ_WAS[[1]]$Q[mr:mxr][which(abs(gQ_av_WAS[mr:mxr])
    ==min(abs(gQ_av_WAS[mr:mxr]) ))[1] ]
resWAS <- calcQDepPDF(minR=0, maxR=30, dr=0.01, minQ=.771, 
    maxQ=cuto, verbose=100, 
    preTotalScat=list(Q=res_gQ_WAS[[1]]$Q,gQ=gQ_av_WAS))

## set boundaries for fitting procedure
iter_0 <- as.relistable(list(latticep=0, r=0, sigma=c(0), rsigma=0))
boundsL <- c(latticep=3.5,  r=10.0, sigma=c(.01), rsigma=1.1)
boundsU <- c(latticep=4.5,  r=14.0,  sigma=c(.03), rsigma=1.3)

## in order to estimate the parameters that were used to
## simulate the particles, the DEoptim package may be
## used. Install it, remove the comment symbols '#' below,
## and use a call like:
#library(DEoptim)

#resDE <- DEoptim(rss, lower = boundsL, upper = boundsU, 
#    oneDW=FALSE, type="neutron",                   
#    control=DEoptim.control(CR=0.85, F=0.7, NP=40, itermax=30, 
#        parallelType=1, packages = list("PerformanceAnalytics"),
#        parVar=list("rss", "simPart", "Unique", "calcPDF", 
#        "IqSASP", "GrSAS", "GrSASCS", "broadPDF", "termRip",
#        "getSymEl", "IqSAS", "displacePart", "calcTotalScatt")),       
#    dataS=NA, dataSAS=gQ_av_SAS, dataG=resWAS$gr, 
#    simPar = simPartPar(atoms=list(Au), rcenter=TRUE, 
#        move=TRUE, rot=FALSE),
#    gammaR = resSAS$gr, rvector = resSAS$r, skel=iter_0, 
#    PDF.fixed=PDFPar(minR=0, maxR=30, dr=.01, 
#        scatterLength=Au$scatterLength),
#    TotalScatt.fixed=TotalScattPar(minQ=0.771, maxQ=20, 
#        dQ=0.02, dQ_SAS=0.01, minQ_SAS=.001, maxQ_SAS=.771, 
#        scatterLength=Au$scatterLength, kind="fastHist", 
#        SASscale="normal", convolution = FALSE),
#    wG=1.0, wSAS=0.05, avRes=10, pareto=FALSE) 
#
## now resDE$optim contains estimates for the lattice parameter,
## particle radius, displacement variance sigma, and standard 
## deviation rsigma.
## show results:
#resDE$optim$bestmem

## package mco may be used to construct a Pareto front of 
## solutions. Note that calculations may take considerable time!

#library(mco)
#resMCO <- nsga2(rss, 4, 2, 
#    dataS=NA, dataSAS=gQ_av_SAS, dataG=resWAS$gr,  oneDW=FALSE,
#    simPar = simPartPar(rcenter=TRUE, move=TRUE, rot=FALSE),
#    gammaR = resSAS$gr, rvector = resSAS$r, skel=iter_0,
#    PDF.fixed=PDFPar(minR=0, maxR=30, dr=.01, 
#        scatterLength=scatterLength),
#    TotalScatt.fixed=TotalScattPar(minQ=0.771, maxQ=20, dQ_SAS=0.01, 
#        dQ=.02, minQ_SAS=.001, maxQ_SAS=.771, scatterLength=scatterLength,
#        kind="fastHist", SASscale="normal", convolution = FALSE),
#    wG=1.0, wSAS=0.2, avRes=10, pareto=TRUE,							 
#    constraints=NULL, cdim=0, popsize=40, generations=c(40), 
#    cprob=0.85, lower.bounds=boundsL, upper.bounds=boundsU)

## show results
#plot(resMCO, xlab="SAS(Q) residual", ylab="G(r) residual")			
#paretoSet(resMCO)