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### This function is a component of astrochron: An R Package for Astrochronology
### Copyright (C) 2015 Stephen R. Meyers
###
###########################################################################
### detrend: linearly detrend data - (SRM: January 24, 2012; March 29, 2012;
### Oct. 11, 2012; Dec. 12, 2012;
### May 20, 2013; July 22, 2016;
### July 18, 2018)
###
###########################################################################
detrend <- function (dat,output=1,genplot=T,verbose=T)
{
if(verbose) cat("\n----- SUBTRACTING LINEAR TREND FROM STRATIGRAPHIC SERIES -----\n")
dat<-data.frame(dat)
### use least-squares fit to remove linear trend
lm.0 <- lm(dat[,2] ~ dat[,1])
if(verbose) cat(" * Slope=",lm.0$coeff[2],"\n")
if(verbose) cat(" * y-intercept=",lm.0$coeff[1],"\n")
y.predict <-predict(lm.0, se= TRUE)
out <- dat
out[2] <- dat[2] - y.predict$fit
if(genplot)
{
### plot linearly detrended data
par(mfrow=c(2,2))
plot(dat,cex=0.5, xlab="Location", ylab="Value", main="Data with Trend Line"); lines(dat[,1],y.predict$fit,col="red")
plot(out,cex=0.5, xlab="Location", ylab="Residual Value", main="Residuals from Trend Line"); lines(out)
### plot the denisty and the histogram together
hist(out[,2],freq=F, xlab="Residual Value", main="Distribution of Residual Values"); lines(density(out[,2], bw="nrd0"),col="red");grid()
### boxplot
boxplot(out[,2], ylab="Residual Value", main="Boxplot of Residual Values")
### Normal probabilty plot (Normal Q-Q Plot)
# qqnorm(out[,2]); qqline(out[,2], col="red")
}
if(output==1) return(out)
if(output==2) return(data.frame(cbind(dat[,1],y.predict$fit)))
### END function detrend
}
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