source("gradientDescents.R")

rosen <- function(x,...) {
  100 * ((x[2] - x[1]^2)^2) + (1.0 - x[1])^2
}

rosenGrad <- function(x,...) {
  g1 <- -400 * (x[2] - x[1]^2) * x[1] - 2 * (1 - x[1])
  g2 <-  200 * (x[2] - x[1]^2)
  matrix(c(g1,g2))
}

f<-rosen
df <- rosenGrad

xs <- seq(-1,2,len=30)
ys <- seq(-1,2,len=30)
p <- expand.grid(xs,ys)
fx <- NULL
for (i in 1:nrow(p)) {
  fx <- c(fx,f(t(p[i,]),center,S))
}
fx <- matrix(fx,length(xs),length(ys))
contour(xs,ys,fx,drawlabels=FALSE,levels=1.6^c(0:10))

loc <- 1
while (!is.null(loc)) {

  cat("Click left button to start search. To stop, click right.\n");
  loc <- locator(1)
  if (!is.null(loc)) {
    firstx <- matrix(c(loc$x, loc$y))

    resultSCG <- scg(firstx, f, df, xtracep=TRUE,
                     xPrecision=1.e-10, fPrecision=1.e-10, nIterations=2000)
    resultSteepest <- steepest(firstx,f,df,stepsize=0.0001,xtracep=TRUE,
                               xPrecision=1.e-10, fPrecision=1.e-10,
                               nIterations=2000)

    contour(xs,ys,fx,drawlabels=FALSE,levels=1.6^c(0:10))
    
    fsearch <- c()
    r <- resultSteepest
    for (i in ncol(r$xtrace)) {
      x <- r$xtrace[,i]
      fsearch <- c(fsearch,f(x,center,S))
    }
    lines(r$xtrace[1,],r$xtrace[2,],col=2)
    points(r$xtrace[1,],r$xtrace[2,],col=2)

    r <- resultSCG
    fsearch <- c()
    for (i in ncol(r$xtrace)) {
      x <- r$xtrace[,i]
      fsearch <- c(fsearch,f(x,center,S))
    }
    lines(r$xtrace[1,],r$xtrace[2,],col=4)
    points(r$xtrace[1,],r$xtrace[2,],col=4)

    text(0.7,-0.5,paste(ncol(resultSteepest$xtrace),"steps for Steepest Descent"),pos=4,col=2)
    text(0.7,-0.8,paste(ncol(resultSCG$xtrace),"steps for SCG"),pos=4,col=4)


}
  
}