source("gradientDescents.R")

  
parabola <- function(x,xmin,s) {
  d <- x - xmin
  t(d) %*% s %*% d / 20 + sin(x*2)
}
parabolaGrad <- function(x,xmin,s) {
  d <- x - xmin
  2 * s %*% d / 20 + 2*cos(x*2)
}

f <- parabola
df <- parabolaGrad
center <- 5
S <- 3

xs <- seq(0,10,len=100)
fx <- NULL
fg <- NULL
for (x in xs)  {
  fx <- c(fx,f(x,center,S))
  fg <- c(fg,df(x,center,S))
}
plot(xs,fx,type="l");

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 <- loc$x
    
    resultSCG <- scg(firstx, f, df, center, S, xPrecision=0.001, xtracep=TRUE)
print(resultSCG$x)
    resultSteepest <- steepest(firstx,f,df,center,S,stepsize=0.1,
                               xPrecision=0.001, xtracep=TRUE)

    plot(xs,fx,type="l")

    ## first steepest
    fsearch <- c()
    r <- resultSteepest
    for (x in r$xtrace)
      fsearch <- c(fsearch,f(x,center,S))
    lines(r$xtrace,fsearch,col=2)
    points(r$xtrace,fsearch,col=2)

    r <- resultSCG
    fsearch <- c()
    for (x in r$xtrace)
      fsearch <- c(fsearch,f(x,center,S))
    lines(r$xtrace,fsearch,col=4)
    points(r$xtrace,fsearch,col=4)

    text(2,3,paste(length(resultSteepest$xtrace),"steps for Steepest Descent"),pos=4,col=2)
    text(2,2.5,paste(length(resultSCG$xtrace),"steps for SCG"),pos=4,col=4)

}
  
}