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126 lines
3.7 KiB
126 lines
3.7 KiB
library(ggplot2)
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library(gganimate)
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library(patchwork)
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gradient <- function(f, x, d){
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return((f(x + d) - f(x - d)) / (2*d))
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}
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gradient.ascent.move <- function(f, x, d, mu){
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return(x + mu * gradient(f, x, d))
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}
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func.g <- function(x) x
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func.k <- function(x) sin(x)
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func.h <- function(x) x * sin(x)
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func.l <- function(x) 2 + cos(x) + sin(2*x)
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gradient.ascent.iterate <- function(f, x, d, mu, n){
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if(n == 1) {
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return(gradient.ascent.move(f, x, d, mu))
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}
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return(gradient.ascent.niter(f
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,gradient.descent.move(f, x, d, mu)
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,d
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,mu
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,n-1
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))
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}
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gradient.ascent.iterverb <- function(f, x, d, mu, n, xs=numeric()){
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next_x <- gradient.ascent.move(f, x, d, mu)
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xs[length(xs)+1] <- next_x
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if(n == 1) {
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return(xs)
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}
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return(gradient.ascent.iterverb(f, next_x, d, mu, n-1, xs))
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}
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trace.ascent <- function(f, x, d, eta, n, xs) {
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df_dc = data.frame(x=numeric()
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,y=numeric()
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,i=integer()
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,start_x=character()
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,eta=numeric())
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for(start in x) {
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for(e in eta) {
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first_it <- TRUE
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if(first_it == TRUE) {
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df_dc <- rbind(df_dc, data.frame(x=c(start)
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,y=c(f(start))
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,i=c(0)
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,start_x=c(as.character(start))
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,eta=c(e)
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))
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first_it <- FALSE
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}
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xf <- gradient.ascent.iterverb(f, start, d, e, n)
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df_dc <- rbind(df_dc, data.frame(x=xf
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,y=f(xf)
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,i=1:length(xf)
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,start_x=rep(as.character(start), length(xf))
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,eta=e)
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)
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}
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}
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return(df_dc)
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}
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plot.ascent <- function(f, x, d, eta, n, xs) {
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df_dc = trace.ascent(f, x, d, eta, n, xs)
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func_str = deparse(substitute(f))
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df_f <- data.frame(x=xs, y=f(xs))
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p1 <- ggplot(df_f, aes(x=x, y=y)) +
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geom_line() +
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geom_point(aes(colour=start_x
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,size=i
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)
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,data=df_dc) +
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labs(size="iteration"
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,alpha="iteration"
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,color="start x"
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,y=sprintf("%s(x)", func_str)) +
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facet_grid(eta ~ ., labeller=label_both)
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p2 <- ggplot(df_dc, aes(x=i, y=y)) +
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geom_line(aes(colour=start_x), show.legend=FALSE) +
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labs(x="iteration"
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,y=sprintf("%s(x)", func_str)) +
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facet_grid(eta ~ ., labeller=label_both)
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p <- (p1 | p2) +
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plot_annotation(title=sprintf("function: %s", func_str)) +
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plot_layout(guides="collect"
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,widths=10
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,heights=2)
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return(p)
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}
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animate.ascent <- function(f, x, d, eta, n, xs) {
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df_dc = trace.ascent(f, x, d, eta, n, xs)
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func_str <- deparse(substitute(f))
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df_f <- data.frame(x=xs, y=f(xs))
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p <- ggplot(df_f, aes(x=x, y=y)) +
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geom_line() +
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geom_point(aes(colour=start_x), size=2.5, data=df_dc) +
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labs(color="start x", y=sprintf("%s(x)", func_str)) +
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facet_grid(eta ~ ., labeller=label_both) +
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ggtitle(sprintf("function: %s", func_str))
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anim <- p + transition_reveal(i)
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return(anim)
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}
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