% -*- TeX:Rnw:UTF-8 -*-
% ----------------------------------------------------------------
% .R knitr file  ************************************************
% ----------------------------------------------------------------
%%
<<echo=FALSE>>=
###############################################
##                                           ##
## (c) Andrej Blejec (andrej.blejec@nib.si)  ##
##                                           ##
###############################################
@
<<echo=FALSE,results='hide'>>=
options(width=60)
@
\clearpage
\subsection{Data}

<<>>=
exprs[1:5,1:5]   # exprsession data
pd[1:5,1:5]     # phenodata
pd <- pd[,c("variety","year","day","treat","rep")]
pd[1:5,1:5]
y <- t(as.matrix(exprs))
@

<<>>=
dim(exprs)
dim(pd)
pd <- pd[colnames(exprs),]
dim(pd)
all(rownames(pd)==colnames(exprs))
@

Factors:

<<>>=
names(pd)
str(pd)
summary(pd)
@

\clearpage
\subsection{Model design}



<<>>=
design <- with(pd, model.matrix(~ variety * day * treat))
head(design)
@

Explanation of coefficients

<<>>=
colnames(design)
comp <- c(
"C-WW-11vs0",
"F-WW-11vsC-WW-11",
"C-WW-34vsC-WW-11",
"C-WW-67vsC-WW-11",
"C-WS-11vsC-WW-11",
"(F-WW-34vsF-WW-11)vs(C-WW-34vsC-WW-11)",
"(F-WW-67vsF-WW-11)vs(C-WW-67vsC-WW-11)",
"(F-WS-11vsF-WW-11)vs(C-WS-11vsC-WW-11)",
"C-WS-34vsEC-34|S",
"C-WS-67vsEC-67|S",
"(F-WS-34vsF-WW-34)vs(C-WS-34vsC-WW-34)",
"(F-WS-67vsF-WW-67)vs(C-WS-67vsC-WW-67)"
)
cbind(colnames(design),comp)
comp <- gsub("-","",comp)
comp <- gsub("\\)vs\\(",") - (",comp)
comp <- gsub("vs",":",comp)
comps <- data.frame(colnames(design),comp)
comps

@


<<>>=
fit1 <- lmFit(exprs, design)
fit1 <- eBayes(fit1)
head(fit1[1:6,]$coefficients)
@


\clearpage
\subsubsection{Interaction plot}


<<>>=
predicted <- function(i, coef){
#tst(i)
#tst(coef)
nm <- colnames(coef)
if(length(i)==1) {
( nm0=nm[i])
( nm1=strsplit(nm0,":")[[1]])
( nm2=outer(nm1,nm1,paste,sep=":"))
( nm2=nm2[upper.tri(nm2)])
( nm3 <- c("(Intercept)",nm1,nm2,nm0))
( nm3 <- unique(nm3) )
(  coef[,nm3])
 nm3
 value <- sum(coef[,nm3])
 names(value) <- colnames(coef)[i]
 } else { value=sapply(i, predicted, coef=coef) }
 return(value)
}
coef <- fit1[1:6,]$coefficients
ncols <- ncol(coef)
for( i in 1:ncols) print(predicted(i,coef))
plot(1:ncols,sapply(1:ncols,predicted,coef),type="b",col=1:6,pch=16)
predicted(1:3,coef)

@


<<>>=
.testing <- TRUE
tst <- function(x) {
if(.testing) {
    cat("-->", deparse(substitute(x)),"\n")
     print(x)
     }
invisible(x)
}
coef <- fit1[1:6,]$coefficients[1:2,]
tst(coef)
.testing <- FALSE

@



<<>>=
# ver 6
.testing <- !TRUE
plot.interactions <- function(varname, phdata=pd, data=exprs, coef=NULL, coef.plt=FALSE, ylim=NULL, ...){
tst(dim(phdata))
tst(dim(data))
phdata <- phdata[colnames(data),]
days <- levels(factor(phdata$day))
ndays <- length(days)
ntreat <- length(levels(phdata$treat))
lv <- levels(phdata$variety)
nvar <- length(lv)
d <- 0.05
par(mfrow=c(1,length(lv)),mar=c(7,4,4,3))
# Factors
#
fct <- data.frame(f1=phdata$day,
                f2=phdata$treat,
                f3=phdata$variety,
                row.names=rownames(phdata)
                )
head(fct)
#
#for(i in 1:ncol(y)){
#    varname <- colnames(y)[i]
     y <-as.numeric(data[varname, ])
    if(is.null(ylim)) ylim <- range(y,na.rm=TRUE) else
    if(is.na(ylim)[1]) ylim <- range(data,na.rm=TRUE)
   for(var in levels(phdata$variety)){
    sel <- phdata$variety %in% var
    with(phdata[sel,],{
       interaction.plot(day,treat, y[sel], ylim=ylim,type="b",col=1:2, lty=2:1, pch=rep(16,2), ylab=c("Expression"), cex=1.5,lwd=2)
       tst(aggregate(y[sel],list(day,treat),mean))
    if(is.null(coef)) {
         rng <- (by(y[sel],list(treat,day),range))
         x0 <-  as.numeric(day)+(as.numeric(treat)-1.5)/7
         for(va in 1:nrow(rng))
           for(dy in 1:ncol(rng))
        segments(dy + (va-1.5)/7, rng[[va,dy]][1],
                 dy + (va-1.5)/7, rng[[va,dy]][2],
            lwd=1,
            col=va)
         points( x0, y[sel], pch=21, bg="white", col=as.numeric(treat))
    }
    if(any(diff(as.numeric(levels(day)))<0)) {
        abline(v=which(diff(as.numeric(levels(day)))<0)+0.5,col=8)

    }
    title(paste(varname,"\n", var))
    })
# coefficients plot
    if(!is.null(coef)){
    ind <- grep(lv[2],colnames(coef))
    tst(predicted((1:length(colnames(coef)))[-ind],coef))
    tst(predicted(ind,coef))
    tst(c((1:length(colnames(coef)))[-ind],ind))
    grind <- array(c((1:length(colnames(coef)))[-ind],ind), dim=c(ndays, ntreat, nvar),
       dimnames <- list(days,levels(phdata$treat),levels(phdata$var))
       )
    tst(grind)
    tst(with(fct,
    grind[levels(f1)[1],levels(f2)[1],levels(f3)[1]]))
      #ind <- grep(lv[2],colnames(coef))
      if(var!=lv[2]) ind <- -ind
       #abline(h=sum(cf[c(1)]),xpd=NA,col=1)
       #abline(h=sum(cf[c(1,3)]),xpd=NA,col=2)
       #tst(ind)
       cf <- coef[,ind]
       cF <- cf
       cc <- coef[-ind]
       if(var==lv[2]) { cf <- coef[,ind]+coef[,-ind]
       #tst(colnames(coef)[ind])
       #tst(colnames(coef)[-ind])
          names(cf) <- colnames(coef)[ind]
          coefs <- data.frame(cC=coef[-ind], cF.model=coef[ind], cF.plus.C = coef[-ind]+coef[ind])
          rownames(coefs) <- colnames(coef)[-ind]
          }
       abline(h=cf[1],col=8,lwd=1)
       lwda <- 2
##
### First level
#
       if(var!=lv[2]) {
if(FALSE){

       arrows(0.95,min(exprs),0.95,cf[1],col=1,length=0.08,lwd=3)
       for(ii in 2:ndays){
       e <- cf[1]
#              points(ii-d,e,col=ii)
       arrows(ii-d,e,ii-d,e+cf[ii],col=ii,length=0.08,lwd=lwda)
       #abline(h=sum(cf[c(1,4)]),xpd=NA,col=3)
#       e <- cf[1]
#              points(3,e,col=3)
#       arrows(3,e,3,e+cf[3],col=3,length=0.08, lwd=lwda)
#       #abline(h=sum(cf[c(1,5)]),xpd=NA, col=4)
        }
       ii <- ndays+1
       e <- cf[1]
              points(1,e,col=ii)
       arrows(1,e,1,e+cf[ii],col=ii,length=0.08, lwd=lwda)
       lines(1:ndays,cf[1]+cf[ii]+c(0,cf[2:ndays]),col=2,type="b",lwd=1,lty=3)
       #abline(h=sum(cf[c(1,3,5,9)]),xpd=NA, col=5)
              for(jj in 2:ndays){
       e <- sum(cf[c(1,jj,(ndays+1))])
       arrows(jj+d,e,jj+d,e + cf[ndays+jj],col=ndays+jj,length=0.08, lwd=lwda)
       }
       #
}
         eind <- grind[ ,1,1]  #c(1,3,4)
                  tst(eind)
         cl <- 0
         esF <- predicted(eind,coef)
         es <- esF-coef[,eind]
#         lines(1:ndays,es,col=7,lwd=3)
#         lines(1:ndays,esF,col=7,lwd=3)
#         lines(1:ndays,es,col=8,type="b",lwd=1,lty=3)
#
         arrows(1:ndays-d,es,1:ndays-d,esF,col=cl+1:ndays,length=0.08, lwd=lwda)
                #
         eind <- grind[ ,2,1]  #c(5,9,10)
                  tst(eind)
         cl <- ndays
         esF <- predicted(eind,coef)
         es <- esF-coef[,eind]
#         lines(1:ndays,es,col=7,lwd=3)
#         lines(1:ndays,esF,col=7,lwd=3)
delta <- c(coef[,eind[1]],rep(0,length(eind)-1))
         lines(1:ndays,delta+es,col=2,type="b",lwd=1,lty=3)
#
         arrows(1:ndays+d,es,1:ndays+d,esF,col=cl+1:ndays,length=0.08, lwd=lwda)
       cfs <- 1:(ndays*ntreat)
       ltext <- paste(sprintf("% .1f",cf[cfs]),"|",names(cf)[cfs])
       legend("topleft",col=cfs,lwd=2,legend=ltext, bty="n",cex=0.75)
       } else {
#
### second level
#
if(FALSE){
         cF <- coef[,ind]
         abline(h=cc[1], col=8)
# expected for C
#         lines(1:ndays,cc[1]+cF[1]+c(0,cc[2:ndays]),col=8,type="b",lwd=1,lty=3)
#
         e <- cc[1]
         points(0.95,e,col=1)
         arrows(0.95,e,0.95,e+cF[1],col=1,length=0.08, lwd=lwda)
         for(ii in 2:ndays){
         e <- sum(cc[c(1,ii)])+cF[1]
#         points(ii-d,e,col=ii)
#         arrows(ii-d,e,ii-d,e+cF[ii],col=ii,length=0.08, lwd=lwda)
#         e <- sum(cc[c(1,3)])+cF[1]
#         points(3,e,col=3)
#         arrows(3,e,3,e+cF[3],col=3,length=0.08, lwd=lwda)
         }
         eind <- grind[ ,1,2]  #c(2,6,7)
                  tst(eind)
                  esF <- predicted(eind,coef)
         es <- esF-coef[,eind]
         lines(1:ndays,es,col=7,lwd=3)
         lines(1:ndays,esF,col=7,lwd=3)
         lines(1:ndays,es,col=8,type="b",lwd=1,lty=3)
#
         arrows(1:ndays,es,1:ndays,esF,col=1:ndays,length=0.08, lwd=lwda)
#

         ii <- ndays+1
         e <- cc[1]+cF[1]
#         points(1,e,col=ii,cex=2)
#         arrows(1,e,1,e+cf[ii],col=ii,length=0.08, lwd=lwda)
           es <- predicted(8,coef)-coef[,8]+c(0,coef[,c(9,10)])
           es <- predicted(2,coef)+coef[,5]+c(0,coef[,c(3,4)])
           lines(1:ndays,es,col=7,lwd=1,lty=4,type="b")
           es <- es+c(0,coef[,c(9,10)])
           lines(1:ndays,es,col=7+1,lwd=1,lty=4,type="b")
                      es <- es+c(0,coef[,c(6,7)])
           lines(1:ndays,es,col=7+1+1,lwd=1,lty=4,type="b")
                      es <- es+c(0,coef[,c(9,10)])
           lines(1:ndays,es,col=7+1+1+1,lwd=2,lty=4,type="b")
           esF <- predicted(c(8,11,12),coef)
           es <- esF-coef[c(8,11,12)]
      #  lines(1:ndays,cf[1]+cf[ii]+c(0,cf[2:ndays]),col=2,lwd=1,lty=2)
      lines(1:ndays,es,col=2,lwd=1,lty=3,type="b")
#      lines(1:ndays,esF,col=7,lwd=1,lty=4,type="b")

#      eC <- predicted(c(5,9,10),coef)
#      lines(1:ndays,eC-eC[1]+es[1],col=8,lwd=1,lty=2,type="b")
#      es <- eC-eC[1]+es[1]
     for(jj in 1:ndays){
       tst(jj)
#       e <- sum(cf[c(1,jj,(ndays+1))])
       e <- predicted(abs(ind[ndays+jj]), coef)
tst(e)
       arrows(jj+d,es[jj],jj+d,e,col=ndays+jj,length=0.08, lwd=lwda)
       }
       }

         eind <- grind[ ,1,2]  # c(2,6,7)
         tst(eind)
         cl <- 0
         esF <- predicted(eind,coef)
         es <- esF-coef[,eind]
#         lines(1:ndays,es,col=7,lwd=3)
#         lines(1:ndays,esF,col=7,lwd=3)
abline(h=predicted(1,coef),lwd=0.5,col=8)
delta <- c(coef[,eind[1]],rep(0,length(eind)-1))
         lines(1:ndays,delta+es,col=8,type="b",lwd=1,lty=3)
#
         arrows(1:ndays-d,es,1:ndays-d,esF,col=cl+1:ndays,length=0.08, lwd=lwda)
                #
         eind <- grind[ ,2,2]  #c(8,11,12)
         cl <- ndays
         esF <- predicted(eind,coef)
         es <- esF-coef[,eind]
#         lines(1:ndays,es,col=7,lwd=3)
#         lines(1:ndays,esF,col=7,lwd=3)
         lines(1:ndays,es,col=2,type="b",lwd=1,lty=3)
#
         arrows(1:ndays+d,es,1:ndays+d,esF,col=cl+1:ndays,length=0.08, lwd=lwda)

         cfs <- 1:(ndays*ntreat)
       ltext <- paste(sprintf("% .1f",cF[cfs]),"|",names(cF)[cfs])
       legend("topleft",col=cfs,lwd=2,legend=ltext, bty="n",cex=0.75)
        }
       #abline(h=sum(cf[c(1,4,5,10)]),xpd=NA, col=6)
#       e <- sum(cf[c(1,3,4)])
#              points(3,e,col=6)
#       arrows(3,e,3,e+cf[6],col=6,length=0.08, lwd=lwda)

      }
    }
#
################        arrows(3+2*d,predicted(12,coef)-coef[12],3+2*d,predicted(6,coef),lwd=4,col=7)
#ind <- c(8,11,12)
#indc <- c(5,9,10)
#for(i in 1:3){
#    tst(predicted(ind[i],coef))
#    tst(predicted(indc[i],coef))
#    arrows(i+2*d,predicted(ind[i],coef)-coef[ind[i]],
#    i+2*d,predicted(ind[i],coef),lwd=4,col=7)
#    }
###############
#abline(h=c(4,4.06))
    if(coef.plt) {
      par(mfrow=c(6,7),mar=c(1,1,2,2),new=TRUE)
      with(coefs, {
      xlim <- range(c(cC[-1], cF[-1]))
      plot(cC[-1],cF[-1],col=2:nrow(coefs),
      xlim = xlim,
      ylim = xlim,
      pty = "s",
       pch=16,new=TRUE,axes=FALSE, asp=1)
      axis(3)
      axis(4)
      mtext("C", side=1, cex=0.7, line=0)
      mtext("F", side=2, cex=0.7, las = 2,line=0.3)
      abline(h=0,v=0,lwd=0.5,col=8)
      box()
      #abline(c(0,1),col=8)
      }
      )
    }
    invisible(coefs)
}
varname <- rownames(exprs)[10]#[13]
t(fit1[varname,]$coefficients)
coef=fit1[varname,]$coefficients
bla <- plot.interactions(varname, coef=fit1[varname,]$coefficients,
   coef.plt=TRUE)
#bla
#predicted(1, coef)
#predicted(1:12,coef)
cbind(t(coef),1:ncol(coef))

@

Inspect the varietyF:day67

<<>>=
varname <- "Vitvi14g01639"
bla <- plot.interactions(varname, coef=fit1[varname,]$coefficients,
   coef.plt=TRUE)
bla
@

Graphical interpretation of coefficients:

<<>>=
varname <- rownames(exprs)[13]
coef=fit1[varname,]$coefficients
coefs <- plot.interactions(varname, coef=fit1[varname,]$coefficients,
   coef.plt=TRUE)
coefs
@


Plot coefficients

<<>>=
par(mfrow=c(1,2),mar=c(4,5,3,3))
with(coefs, plot(cC, cF.plus.C, col=1:nrow(coefs), pch=16))
abline(h=0,v=0,col=8)
abline(c(0,1),col=8)
with(coefs, plot(cC[-1], cF.plus.C[-1], col=2:nrow(coefs), pch=16))
abline(h=0,v=0,col=8)
@

Combined plot
<<>>=
plot.interactions(varname, coef=fit1[varname,]$coefficients,
 coef.plt = TRUE )
@

<<>>=
plot.interactions(varname)
@

\subsection{Top tables}
<<>>=
tt <- topTable(fit1)
tt
@

Top table for difference of variety reaction to stress in day 67

<<>>=
comps[12,]
tt <- topTable(fit1,coef=12)
head(tt)
@



<<>>=
varname <- rownames(tt)[1]
fit1[varname,]$coefficients
plot.interactions(varname)
plot.interactions(varname, coef=fit1[varname,]$coefficients, coef.plt=TRUE)

@

<<>>=
varname <- rownames(tt)[2]
fit1[varname,]$coefficients
plot.interactions(varname)
plot.interactions(varname, coef=fit1[varname,]$coefficients, coef.plt=TRUE)
@

<<>>=
varname <- rownames(tt)[3]
fit1[varname,]$coefficients
plot.interactions(varname)
plot.interactions(varname, coef=fit1[varname,]$coefficients, coef.plt=TRUE)
@

<<>>=
par(mfrow=c(3,3),mar=c(4,4,2,0.5))
select <- 2:6
for(i in 1:9){
varname <- rownames(tt)[i]
coef <- fit1[varname,]$coefficients
ind <- grep("F",colnames(coef))
coef[-ind]
coef[ind]
plot(coef[-ind][select],coef[ind][select],col=select,
   pch=16,
   xlab="C",ylab="F",
   ylim=c(-2,2),
   xlim=c(-2,2),
   type="n"
   )
rect(-3,-1,3,1, col=rgb(.95,.95,.95,.80),border=NA)
rect(-1,-3,1,3, col=rgb(.95,.95,.95,.80),border=NA)

points(coef[-ind][select],coef[ind][select],col=select,
   pch=16,
      cex=c(1,1,1,1,2)*1.5
      )
title(varname)
if(i==1)legend("topright",bty="n",col=select,pch=rep(16,5) ,legend=colnames(coef)[-ind][select], cex=.7,pt.cex=1)
abline(v=0,h=0,col=8,lwd=0.5)
box()
#polygon(c(-2,-1,-1, 1, 1, 2, 2, 1, 1,-1,-1,-2,-2),
#        c(-1,-1,-2,-2,-1,-1, 1, 1, 2, 2, 1, 1,-1),
#        col=rgb(.95,.95,.95,.50))


#abline(h=-1:1,v=-1:1, col=8)
#abline(h=0,v=0)
}
@

<<>>=
par(mfrow=c(3,3),mar=c(4,4,2,0.5))
select <- 1:6
for(i in 1:9){
varname <- rownames(tt)[i]
coef <- fit1[varname,]$coefficients
ind <- grep("F",colnames(coef))
coef[-ind]
coef[ind]
plot(coef[-ind][select],coef[ind][select],col=select,
   pch=16,
   xlab="C",ylab="F",
#   ylim=c(-2,2),
#   xlim=c(-2,2),
   type="n"
   )
rect(-10,-1,10,1, col=rgb(.95,.95,.95,.90),border=NA)
rect(-1,-10,1,10, col=rgb(.95,.95,.95,.90),border=NA)
box()
points(coef[-ind][select],coef[ind][select],col=select,
   pch=16,
      cex=c(1,1,1,1,2)*1.5
      )
title(varname)
if(i==1)legend("topright",bty="n",col=select,pch=rep(16,5) ,legend=colnames(coef)[-ind][select], cex=.7,pt.cex=1.5)
abline(v=0,h=0,col=8,lwd=0.5)
#polygon(c(-2,-1,-1, 1, 1, 2, 2, 1, 1,-1,-1,-2,-2),
#        c(-1,-1,-2,-2,-1,-1, 1, 1, 2, 2, 1, 1,-1),
#        col=rgb(.95,.95,.95,.50))


#abline(h=-1:1,v=-1:1, col=8)
#abline(h=0,v=0)
}
@
\clearpage
\section{Coefficients}

Model design
<<>>=
design <- with(pd, model.matrix(~ variety * day * treat))
head(design)
@
Linear models
<<>>=
fit1 <- lmFit(exprs, design)
fit1 <- eBayes(fit1)
head(fit1[1:6,]$coefficients)
@

<<>>=
which <- ncol(fit1$coefficients)
cname <- colnames(fit1$coefficients)[which]
cnames <- colnames(fit1$coefficients)
ind <- grep("varietyF",cnames)
cname <- cnames[-ind]

@

\clearpage

Expressions in \code{exprs}, phenodata in \code{pd}.

<<>>=
alpha <- 0.01
maxnames <- 10
out <- ""
cnames <- colnames(fit1$coefficients)
which <- 2
for(which in 2:ncol(fit1[1:6,]$coefficients)){
  cname <- cnames[which]
  out <- paste(out,
  "\\clearpage\n\\subsection{",cname," }\n")
  #comps[8,]
  tt <- topTable(fit1,coef=which, number=Inf)

  cat("\n----------  ",cname, alpha,"\n")
  filter <- tt$adj.P.Val < alpha
  print(table(filter))
  cat("\n\n")
  head(tt)
  varnames <- rownames(tt)[filter][1:min(maxnames,sum(filter))]
  varnames
#  varname <- varnames[1]
  for ( varname in varnames)
  out <- paste(out,knit_child("20aa_interaction-plots.rnw",quiet=TRUE))
}
@
\Sexpr{out}

<<>>=
which <- ncol(fit1$coefficients)
cname <- colnames(fit1$coefficients)[which]
cname

@

\clearpage
\subsection{\Sexpr{cname} }
%Top table  of difference of F reaction to stress in day 67 (compared to C).

<<>>=
which <- ncol(fit1[1:6,]$coefficients)
which
#comps[8,]
tt <- topTable(fit1,coef=which, number=Inf)
alpha <- 0.05
table(tt$adj.P.Val < alpha)
head(tt)

@

Expressions in \code{exprs}, phenodata in \code{pd}

<<result="hide">>=
out <- ""
filter <- tt$adj.P.Val < alpha
for ( varname in rownames(tt)[filter])
out <- paste(out,knit_child("20aa_interaction-plots.rnw",quiet=TRUE))
@
\Sexpr{out}