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216 lines
8.6 KiB
Plaintext
216 lines
8.6 KiB
Plaintext
##################################################
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################ EliminateKa2 ####################
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##################################################
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EliminateKa2 <- function(thth, intensity, lever = 2) {
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# Args: 2theta vector, numeric
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# intensity vector, numeric
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# parameter pairs, numeric between 1 and 6, default 2
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# "High-quality a2-free patterns can be obtained in most cases
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# using five (5) or seven (7) pairs of parameters."
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# "When the step-width is less than 0.01 degrees and the
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# 2theta angle is high, a large number of parameter pairs
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# should be used to get accurate results." {Dong1999a}
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### 1 2 3 4 5 6 - lever
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### 3 5 7 9 15 25 - corresponding parameter pairs
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#
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##### THIS FUNCTION USES THESE OTHER FUNCTIONS #####
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# REQUIRES: common.R :: as.radians() - converts degrees to radians
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# REQUIRES: stats::approx - linear interpolation
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####################################################
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# For test-purposes, use the following data
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# /home/taha/chepec/laboratory/XRD/0103-instrumentbroadening/100917Th2ThLong-counts.UXD
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##### STILL UNDER CONSTRUCTION ####
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##### STILL UNDER CONSTRUCTION ####
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startdatapoint <- 4
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# Ka1a Ka1b Ka2a Ka2b
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CuKa.data <- c(1.534753, 1.540596, 1.541058, 1.544410, 1.544721,
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3.69, 0.44, 0.60, 0.52, 0.62,
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1.60, 57.07, 7.64, 25.38, 8.31)
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CuKa <- data.frame(matrix(CuKa.data, ncol=3, byrow=F))
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names(CuKa) <- c("lambda", "w", "E")
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row.names(CuKa) <- c("Satellites", "Ka1a", "Ka1b", "Ka2a", "Ka2b")
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# The following lever arm weights are from Dong1999a
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weights <- list()
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# Three-bar weights
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weights[[1]] <- c(0.005134296, 0.491686047, 0.003179657)
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# Five-bar weights
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weights[[2]] <- c(0.002614410, 0.011928014, 0.480406967,
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0.002121807, 0.002928802)
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# Seven-bar weights
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weights[[3]] <- c(0.001580069, 0.003463773, 0.015533472, 0.422601977,
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0.053632977, 0.001572467, 0.001615265)
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# Nine-bar weights
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weights[[4]] <- c(0.001138001, 0.00195272, 0.004324464,
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0.019246541, 0.394175823, 0.079159001,
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-0.003591547, 0.002505604, 0.001089392)
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# 15-bar weights
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weights[[5]] <- c(0.000614225, 0.000810836, 0.001134775, 0.001723265, 0.002968405,
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0.006433676, 0.02575384, 0.345872599, 0.100578092, 0.014493969,
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-0.004176171, 0.000678688, 0.001610333, 0.000918077, 0.000585391)
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# 25-bar weights
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weights[[6]] <- c(0.000349669, 0.000408044, 0.000484578, 0.000587457, 0.000730087,
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0.000935685, 0.001247401, 0.001753233, 0.002657209, 0.004531817,
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0.009591103, 0.034998436, 0.2876498, 0.074964321, 0.065000871,
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0.016762729, -0.00306221, -0.002717412, -0.000902322, 0.000915701,
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0.001036484, 0.000808199, 0.000539899, 0.000398896, 0.000330325)
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# The following lever arm lengths are from Dong1999a
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lengths <- list()
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# Three-bar lengths
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lengths[[1]] <- c(0.998506815, 0.997503913, 0.996699460)
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# Five-bar lengths
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lengths[[2]] <- c(0.998471576, 0.997935524, 0.997503530,
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0.997163494, 0.996606519)
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# Seven-bar lengths
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lengths[[3]] <- c(0.998563433, 0.998204025, 0.997825027, 0.997522195,
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0.997297615, 0.996844235, 0.996516288)
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# Nine-bar lengths
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lengths[[4]] <- c(0.998609749, 0.998334027, 0.998054914,
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0.99776062, 0.997527844, 0.997327154,
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0.997028978, 0.996734639, 0.99646335)
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# 15-bar lengths
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lengths[[5]] <- c(0.998671599, 0.99850911, 0.998346447, 0.998183442, 0.998019704,
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0.997854063, 0.997680649, 0.997533314, 0.997377391, 0.997266106,
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0.997060614, 0.996888005, 0.996741151, 0.996583672, 0.996418168)
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# 25-bar lengths
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lengths[[6]] <- c(0.998706192, 0.998608958, 0.998511721, 0.998414475, 0.998317209,
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0.998219906, 0.998122538, 0.998025057, 0.997927367, 0.997829244,
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0.997730044, 0.997626987, 0.997535705, 0.997458223, 0.997346989,
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0.997277763, 0.997161452, 0.997057942, 0.996982688, 0.99686108,
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0.996769728, 0.996675255, 0.996578407, 0.996480641, 0.99638324)
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### --- Arguments check
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# Check that "lever" argument is within bounds
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if (lever > length(weights) || lever < 1) {
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# if not, fall back to the default value
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lever <- 2 # corresponds to 5 parameter pairs
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}
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### --- Arguments check
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# Check that vectors are of the same length
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if (!(length(thth) == length(intensity))) {
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# If not the same length, abort with error message
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stop("Arguments thth and intensity have different lengths!")
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}
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### --- Arguments check
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if (any(thth <= 0)) {
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stop("thth vector contains values less-than or equal to zero")
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}
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### --- Arguments check
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if (any(intensity < 0)) {
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stop("intensity vector contains values less than zero")
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}
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# THIS IS NECESSARY, but overlooked for the moment
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#int.p.start <- (1 / (1 + (CuKa["Ka2a", "E"] + CuKa["Ka2b", "E"]) /
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#(CuKa["Ka1a", "E"] + CuKa["Ka1b", "E"]))) * intensity[1:startdatapoint-1]
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# Redefine everything
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#thth <- thth[startdatapoint:length(thth)]
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#intensity <- intensity[startdatapoint:length(intensity)]
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# Convert from 2theta to theta scale for use in first step of calculations
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theta <- thth / 2
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sintheta <- sin(as.radians(theta))
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# Corresponds to equation 10 in Dong1999a
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# This is based on the assumption that we are supposed to get delta-thth values
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delta.thth.a <- matrix(0, length(theta), length(weights[[lever]]))
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for (j in 1:length(lengths[[lever]])) {
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delta.thth.a[,j] <- 2 * asin(as.radians((lengths[[lever]][j] * sintheta)))
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}
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# Add the calculated deltas to the recorded thth values
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# Corresponds to equation 10 in Dong1999a
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thth.a <- matrix(NA, dim(delta.thth.a)[1], dim(delta.thth.a)[2] + 1)
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# Flip the delta.thth.a matrix vertically (just for convenience)
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delta.thth.a <- delta.thth.a[,dim(delta.thth.a)[2]:1]
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for (j in 2:dim(thth.a)[2]) {
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thth.a[,1] <- thth
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thth.a[,j] <- thth + delta.thth.a[,j - 1]
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}
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# Intensities with interpolated intensities at the calculated 2theta values
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int.interp <- matrix(NA, dim(thth.a)[1], dim(thth.a)[2])
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for (j in 2:dim(int.interp)[2]) {
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int.interp[,1] <- intensity
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int.interp[,j] <- approx(thth, intensity, xout = thth.a[,j])$y
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}
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# So far, we have just replaced the old thth-scale with a new one,
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# and calculated the intensitites by linearly interpolating from the old intensities.
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# Intensities times lever weights, P(j) (this is what you will substract from int.interp)
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int.p <- matrix(NA, length(theta), length(weights[[lever]]))
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for (j in 1:length(lengths[[lever]])) {
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int.p[,j] <- weights[[lever]][j] * int.interp[,j + 1]
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}
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# Calculate intensities with Ka2 contribution stripped
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#int.stripped <- c(int.interp[,-1]) - rowSums(int.p)
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int.stripped <- thth - rowSums(int.p)
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#corr.tmp.df <- data.frame(thth = c(thth.a[,-1]), int.corr = int.stripped)
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corr.tmp.df <- data.frame(thth = thth, int.corr = int.stripped)
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corr.df <- corr.tmp.df[order(corr.tmp.df$thth), ]
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#row.names(corr.df) <- seq(1, length(corr.df$thth))
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# Make a dataframe of thth.a and int.a and order it by thth
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#df.a <- data.frame(thth = c(thth.a), intensity = c(int.a))
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#df.as <- df.a[order(df.a$thth), ]
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#row.names(df.as) <- seq(1,length(df.as$thth)) # fixes row names order
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# df.as is exactly as the original data, just with the correct number of
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# interpolated thth and intensity values included.
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return(corr.df)
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# Perhaps thth.a and int.p.terms are the new x and y
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# Intensities in summation term (this is the Ka2 correction)
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#int.p <- rowSums(int.p.terms)
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# Collapse the matrix thth.a into a single column
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#thth.ai <- matrix(NA, dim(thth.a)[1] * dim(thth.a)[2], 2)
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#thth.ai[,1] <- sort(c(thth.a))
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#thth.ai[,2] <- approx(thth, intensity, xout = thth.ai[,1])$y
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# Built-in functions in R to interpolate or extrapolate
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# stats::approx Linear interpolation
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# Hmisc::approxExtrap Linear extrapolation
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# go with linear functions for now, see how that works out
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# This is NOT necessary
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# This vector helps convert from lever to actual number of parameter pairs
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#parpairs <- numeric()
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#for (j in 1:length(weights)) {
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# parpairs[j] <- length(weights[[j]])
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#}
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##### STILL UNDER CONSTRUCTION ####
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}
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