init

ue02/a1/a/gradient_ascent.R

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