bin-boot_10.Rmd

---
title: "Composite curves and bootstrap C.I.'s via binning <br> (bin-boot.R)"
output:
  html_document:
    css: SI-md-08.css
    fig_caption: yes
    highlight: haddock
    number_sections: yes
    theme: united
    toc: yes
    toc_float: false
    collapsed: no
---

```{r bin-boot, echo=FALSE}
options(width = 105)
knitr::opts_chunk$set(dev='png', dpi=300, cache=TRUE)
pdf.options(useDingbats = TRUE)
```

# Introduction #

This script (`binboot-curve.R`) fits step-like composite curves, with bootstrapping by site confidence intervals, via binning.  As is the case with other analysis scripts, the script has two parts, a set-up portion that changes from analysis to analysis, and a computation part that does not change.  This version reads "presampled" data.

# Set up #

The variables `queryname`,  `basename` and `binname` are used to compose the path and filenames for the presampled data.

```{r pathnames}
# age-bin averages of influx data
# bootstrap-by-site confidence intervals

# names
queryname <- "v3i" # 
basename <- "nt2kb" 

# paths for input and output .csv files -- modify as appropriate
datapath <- "/Projects/GPWG/GPWGv3/GCDv3Data/v3i/"
sitelistpath <- "/Projects/GPWG/GPWGv3/GCDv3Data/v3i/v3i_sitelists/"
sitelist <- "v3i_nsa_globe"
outpath <- "/Projects/GPWG/GPWGv3/GCDv3Data/v3i/v3i_curves/"

# prebinning bin width
pbw <- 10

pbw_char <- as.character(pbw)
if (pbw < 10) pbw_char <- paste("0", pbw_char, sep="")
```

Set the number of bootstrap samples or replications:

```{r nreps}
# number of bootstrap samples/replications
nreps <- 200
```

Specifiy the age-bin centers, and spacing.  This version uses 20-year wide bins, with the first bin centered at -60 yr BP, or 2010 CE, and the last at 1950 yr BP, or 1 CE.

```{r age bins}
# age bin centers
abw <- 20 
abinbeg <- -60 
abinend <- 1950
```

Set array sizes for saving bootstrap results.

```{r otherSetup}
# array sizes
maxrecs <- 2000
maxreps <- 1000

# plotting set up
xmin <- 0; xmax <- 2020; ymin1 <- -1.0; ymax1 <- 1.0; ymin2 <- -0.5; ymax2 <- 1.0
xlim=c(xmin,xmax); ylim1=c(ymin1,ymax1); ylim2 <- c(ymin2,ymax2)
xlab="Year CE"; xminortick <- 50
ylab="Normalized Anomalies of Transformed Influx"

# plot output 
plotout <- "screen" # "pdf" # "png" # 
```

# Calculation preliminaries#

## Initial steps ##

Set various output paths and filenames.

```{r pathnames2}
# no changes below here

# prebinning file name
binname <- paste("bw", pbw_char, sep="")

# presampled/binned files
csvpath <- "/Projects/GPWG/GPWGv3/GCDv3Data/v3i/v3i_presamp_csv/"
csvname <- paste("_presamp_influx_",basename,"_",binname,".csv", sep="")

# site list file
sitelistfile <- paste(sitelistpath, sitelist, ".csv", sep="")
sitelistfile

# curve (output) path and file
curvecsvpath <- paste(datapath,queryname,"_curves/",sep="")

# if output folder does not exist, create it
dir.create(file.path(datapath, paste(queryname,"_curves/",sep="")), showWarnings=FALSE)
curvename <- paste(sitelist,"_binboot_",basename,"_",binname,"_abw",as.character(abw),"_",
  as.character(nreps), sep="")
curvefile <- paste(curvename, ".csv", sep="")
print(curvecsvpath)
print(curvename)
print(curvefile)
```

Code block to implement writing .pdf to file:

```{r pdf setup}
# .pdf plot of bootstrap iterations
if (plotout == "pdf") {
pdffile <- paste(curvename, ".pdf", sep="")
print(pdffile)
}
# .png plot of bootstrap iterations
if (plotout == "png") {
  pngfile <- paste(curvename, ".png", sep="")
  print(pngfile)
}
```

Read the list of sites to be processed.  Note that this is the site list may contain sites that after transforming and presampling may have no useful data.  Those sites are ignored when the data are read in.

```{r readsites}

# read the list of sites
sites <- read.csv(sitelistfile)
head(sites)
ns <- length(sites[,1]) #length(sites$ID_SITE)
ns
```
Define arrays for data, fitted values and statistics.

```{r arrayDefinition}
# arrays for data and fitted values
age <- matrix(NA, ncol=ns, nrow=maxrecs)
influx <- matrix(NA, ncol=ns, nrow=maxrecs)
nsamples <- rep(0, maxrecs)

# age bin centers
abinage <- seq(abinbeg, abinend, by=abw)
abinage
YearCE <- 1950 - abinage
YearCE

# generate YearCE with a 1/2 time-step (abw) offset so step-plot type "s" registers correctly
pltYearCE <- YearCE  +  (abw/2)
pltYearCE

# array for bootstrap results
min_age <- abinbeg-(abw/2); max_age <- abinend #+(abw/2)
nbins <- length(abinage)
yfit <- matrix(NA, nrow=nbins, ncol=maxreps)

# arrays for sample number tracking
ndec <- matrix(0, ncol=nbins, nrow=ns)
ndec_tot <- rep(0, nbins)
#xspan <- rep(0, ntarg)
ninwin <- matrix(0, ncol=nbins, nrow=ns)
ninwin_tot <- rep(0, nbins)
```

## Read data ##

Read and store data.  Note that sites without data, even if in the site list, are skipped using the `file.exists()` function.

```{r readData, results='hide'}
# read and store the presample (binned) files as matrices of ages and influx values
ii <- 0
for (i in 1:ns) {
  #i <- 1
  sitenum <- sites[i,1] # sites$ID_SITE[i]
  print(sitenum)
  siteidchar <- as.character(sitenum)
  if (sitenum >= 1) siteid <- paste("000", siteidchar, sep="")
  if (sitenum >= 10) siteid <- paste("00", siteidchar, sep="")
  if (sitenum >= 100) siteid <- paste("0", siteidchar, sep="")
  if (sitenum >= 1000) siteid <- paste(    siteidchar, sep="")
  
  inputfile <- paste(csvpath, siteid, csvname, sep="")
  print(inputfile)
  
  if (file.exists(inputfile)) {
    indata <- read.csv(inputfile)
    nsamp <-  length(indata$age) # 
    if (nsamp > 0) {
        ii <- ii+1
        age[1:nsamp,ii] <- indata$age # 
        influx[1:nsamp,ii] <- indata$norman # indata$zt # 
        nsamples[ii] <- nsamp
    }
  }
}
nsites <- ii
```

Number of sites with data.

```{r nsites}
# number of sites with data
nsites
```

As the presample files are read, individual files will be listed: 

```{r printExample, echo=FALSE}
cat(" [1] 1 \n [1] \"/Projects/GPWG/GPWGv3/GCDv3Data/v3i/v3i_presamp_csv/0001_presamp_influx_nt2kb_bw10.csv\" \n ... ")
```

Trim the input data to an appropriate range given the target ages, and censor (set to `NA`) any tranformed influx values greater than 10.

```{r trim}
# trim samples to age range
influx[age >= abinend+abw/2] <- NA
age[age >= abinend+abw/2] <- NA

# censor abs(influx) values > 10
influx[abs(influx) >= 10] <- NA
age[abs(influx) >= 10] <- NA
```

## Find number of sites and samples contributing to fitted values ##

The number of sites with samples (`ndec_tot`) and the number of samples (`ninwin_tot`) that contribute to each fitted value are calculated, along with the effective window width or "span". This code is clunky, but parallels that in the Fortran versions.

```{r ninwin}
# count number of sites that contributed to each fitted value
ptm <- proc.time()
for (i in 1:nbins) {
  
  for (j in 1:nsites) {
    for (k in 1:nsamples[j]) {
      if (!is.na(age[k,j])) {
        ii <- as.integer(ceiling((age[k,j]-abinbeg-(abw/2.0))/abw))+1
        #print (c(i,j,k,ii))
        if (ii > 0 && ii <= nbins) {ndec[j,ii] = 1}
        if (age[k,j] >= abinage[i]-(abw/2) && age[k,j] <= abinage[i]+(abw/2)) {ninwin[j,i] = 1}
      }
    }
  }
  ndec_tot[i] <- sum(ndec[,i])
  ninwin_tot[i] <- sum(ninwin[,i])
}
proc.time() - ptm
head(cbind(1950 - abinage, pltYearCE, abinage,ndec_tot,ninwin_tot))
tail(cbind(1950 - abinage, pltYearCE, abinage,ndec_tot,ninwin_tot))
```

# Curve-fitting and bootstrapping #

First, the overall composite curve, i.e. without bootstrapping, determined and saved for plotting over the individual bootstrap curves later (where "curves" here are stepped-line plots). Second, the `nreps` individual bootstrap samples are selected, and a composite curve fitted to each and saved. 

## Composite curve ##

The steps in getting this curve include:

1. Reshaping the data matrices (`age` and `influx`) into vectors
2. Binning the data and
3. calculating average values of the data for each bin.

The composite curve using all data is calculated as follows:  

```{r binning}
ptm <- proc.time()
# 1. reshape matrices into vectors 
x <- as.vector(age)
y <- as.vector(influx)
lfdata <- data.frame(x,y)
lfdata <- na.omit(lfdata)
lfdata <- lfdata[lfdata$x >= min_age & lfdata$x < max_age, ]
x <- lfdata$x; y <- lfdata$y

# average influx for each age bin

binnum <- as.integer(ceiling((x-abinbeg-(abw/2.0))/abw))+1
binave <- tapply(y, binnum, mean)
binaveage <- tapply(x, binnum, mean)
bin_fit_all <- binave
binsubs_all <- as.integer(unlist(dimnames(binave)))

# print results for debugging
#binnum; length(binnum)
#binave; length(binave)
#binaveage; length(binaveage)
#bin_fit_all; length(bin_fit_all)
#abinage; length(abinage) 
#pltYearCE; length(pltYearCE) 

head(cbind(1950 - binaveage, pltYearCE[binsubs_all], abinage[binsubs_all], bin_fit_all))
tail(cbind(1950 - binaveage, pltYearCE[binsubs_all], abinage[binsubs_all], bin_fit_all))
proc.time() - ptm
```

## Bootstrap-by-site confidence intervals ##

The bootstrap confidence intervals are obtained by sampling with replacement sites (as opposed to individual samples), fitting a composite curve using `locfit()`, and saving these.  The 95-percent confidence intervals are then determined for each target age using the `quantile()` function.

```{r boostrapping, results='hide'}
# Bootstrap samples

# Step 1 -- Set up to plot individual replications
if (plotout == "pdf") {pdf(file=paste(curvecsvpath,pdffile,sep=""))}
if (plotout == "png") {png(file=paste(curvecsvpath,pngfile,sep=""), res=150)}
plot(NULL, ylim=ylim2, xlim=xlim, ylab=ylab, xlab=xlab, cex.sub=0.8, sub=curvename, type="n")
axis(side = 1, at = seq(xmin-xminortick, xmax+xminortick, by = xminortick), labels = FALSE, tcl = -.25)
axis(side = 1, at = seq(xmin, xmax, by = xminortick*5), labels = FALSE, tcl = -.5) 

# for debugging step plots
# plot the bin averages -- note pltYearCE offset to center the plot steps
# points(1950 - x, y, pch=16, cex=0.5, col=rgb(0.5,0.5,0.5,0.70))
# lines(bin_fit_all ~ pltYearCE, type="s", col="red", lwd=2)
# points(1950 - abinage, bin_fit_all, col="blue", pch=16, cex=0.5)

set.seed(10) # do this to get the same sequence of random samples for each run

# Step 2 -- Do the bootstrap iterations, and plot each age-bin curve
ptm <- proc.time() # time the loop
for (i in 1:nreps) {
  print(i)
  randsitenum <- sample(seq(1:nsites), nsites, replace=TRUE)
  # print(head(randsitenum))
  x <- as.vector(age[,randsitenum])
  y <- as.vector(influx[,randsitenum])
  lfdata <- data.frame(x,y)
  lfdata <- na.omit(lfdata)
  lfdata <- lfdata[lfdata$x >= min_age & lfdata$x < max_age, ]
  x <- lfdata$x; y <- lfdata$y
  
  binnum <- as.integer(ceiling((x-abinbeg-(abw/2.0))/abw))+1
  binave <- tapply(y, binnum, mean)
  binaveage <- tapply(x, binnum, mean)
  binsubs <- as.integer(unlist(dimnames(binave)))
  #bin_fit <- binave[binsubs]
  yfit[binsubs,i] <- binave
  segments(pltYearCE-1.9*(abw/2), yfit[,i], pltYearCE-0.1*(abw/2), yfit[,i], lwd=0.6, col=rgb(0.3,0.3,0.3,0.25))
}
proc.time() - ptm # how long?

# Step 3 -- Plot the unresampled (initial) area averages
lines(pltYearCE[binsubs_all], bin_fit_all, type="s", lwd=1, col="red")
segments(pltYearCE[nbins]-abw, bin_fit_all[nbins], pltYearCE[nbins], bin_fit_all[nbins], lwd=1, col="red")
#points(pltYearCE[binsubs_all], bin_fit_all, pch="_", cex=0.8, col="blue")

# Step 4 -- Find and add bootstrap CIs
yfit975 <- apply(yfit, 1, function(x) quantile(x,prob=0.975, na.rm=T))
yfit025 <- apply(yfit, 1, function(x) quantile(x,prob=0.025, na.rm=T))
yfit50 <- apply(yfit, 1, function(x) quantile(x,prob=0.500, na.rm=T))

lines(pltYearCE, yfit975, type="s", lwd=0.5, col="red")
segments(pltYearCE[nbins]-abw, yfit975[nbins], pltYearCE[nbins], yfit975[nbins], lwd=1, col="red")
lines(pltYearCE, yfit025, type="s", lwd=0.5, col="red")
segments(pltYearCE[nbins]-abw, yfit025[nbins], pltYearCE[nbins], yfit025[nbins], lwd=1, col="red")

if (plotout == "pdf") {dev.off()}
if (plotout == "png") {dev.off()}
proc.time() - ptm
```


## Output ##

The fitted curves are written out in the usual way.

```{r output}
curveout <- data.frame(cbind(abinage, 1950-abinage, bin_fit_all, yfit975, yfit025, ndec_tot, ninwin_tot))
colnames(curveout) <- c("age", "YearCE", "bin_ave", "cu95", "cl95", "nsites", "ninwin")
outputfile <- paste(curvecsvpath, curvefile, sep="")
write.table(curveout, outputfile, col.names=TRUE, row.names=FALSE, sep=",")
```