arma-thesis

commit 44f6b8d5132e91241c4224797879aded4d50b1e3
parent 7f3ce758b5c2491677f2e204a0b7df9c772fa234
Author: Ivan Gankevich <igankevich@ya.ru>
Date:   Wed, 20 Jun 2018 12:18:29 +0300

Add Stokes wave ACF.

Diffstat:
R/common.R
 | 
47
+++++++++++++++++++++++++++++++++++++----------
arma-slides.org
 | 
15
+++++++++------

2 files changed, 46 insertions(+), 16 deletions(-)
diff --git a/R/common.R b/R/common.R
@@ -20,16 +20,7 @@ arma.qqplot_grid_adj <- function (dir, params, titles, adj, ...) {
   }
 }
 
-arma.wavy_plot <- function (data, t, ...) {
-	slice <- data[data$t == t,]
-	x <- unique(slice$x)
-	y <- unique(slice$y)
-	z <- with(slice, {
-		n <- sqrt(length(z))
-		out <- matrix(nrow=n, ncol=n)
-		out[cbind(x, y)] <- z
-		out
-	})
+arma.wavy_plot_matrix <- function (x, y, z, t, ...) {
 	nrz <- nrow(z)
 	ncz <- ncol(z)
 	# Create a function interpolating colors in the range of specified colors
@@ -44,6 +35,42 @@ arma.wavy_plot <- function (data, t, ...) {
 	persp(x, y, z, phi=30, theta=30, col=color[facetcol], ...)
 }
 
+arma.to_matrix <- function (data, t) {
+	slice <- data[data$t == t,]
+	x <- unique(slice$x)
+	y <- unique(slice$y)
+	z <- with(slice, {
+		n <- sqrt(length(z))
+		out <- matrix(nrow=n, ncol=n)
+		out[cbind(x, y)] <- z
+		out
+	})
+	list(x=x,y=y,z=z)
+}
+
+arma.wavy_plot <- function (data, t, ...) {
+	with(arma.to_matrix(data, t), arma.wavy_plot_matrix(x, y, z, ...))
+}
+
+arma.acf_plot <- function (data, t, ...) {
+	ifft <- function (arr) { fft(arr, inverse=TRUE) }
+	with(
+		arma.to_matrix(data, t),
+		function () {
+			# compute ACF using Wiener---Khinchin theorem
+			n <- nrow(z)*ncol(z)
+			z <- Re(ifft(abs(fft(z))^2))/n/n
+			# slice 1/4th of the matrix
+			n1 <- floor(nrow(z)/2)
+			n2 <- floor(ncol(z)/2)
+			x <- x[1:n1]
+			y <- y[1:n2]
+			z <- z[1:n1,1:n2]
+			arma.wavy_plot_matrix(x, y, z, ...)
+		}
+	)()
+}
+
 arma.skew_normal_1_plot <- function(x, params) {
   data <- mapply(
     function (s, k) arma.skew_normal_1(x, s, k),
diff --git a/arma-slides.org b/arma-slides.org
@@ -282,20 +282,23 @@ arma.wavy_plot(df, 0, zlim=c(-0.05,0.05), expand=0.5, border=NA)
 source(file.path("R", "common.R"))
 par(mar=c(0,0.5,0,0))
 df <- data.frame(t=rep(NA,0), x=rep(NA,0), y=rep(NA,0), z=rep(NA,0))
-n <- 20
+n <- 40
+alpha <- 0.5
 grid <- seq(1, n)
-alpha <- 2.31906
-beta <- -5.49873
-gamm <- 0.0680413
+k <- 0.77341
+t <- 0
+omega <- 0.3
+a <- 1.5
 for (i in grid) {
 	for (j in grid) {
     x <- i/(n-1)
     y <- j/(n-1)
-		z <- gamm * exp(-alpha*(x+y)) * cos(beta*x) * cos(beta*y)
+    theta <- k*(x + y) - omega*t
+		z <- a * exp(-alpha*(x+y)) * (cos(theta) + 0.5*k*a*cos(2*theta) + (3/8)*(k*a*k*a)*cos(3*theta))
 		df[nrow(df) + 1,] <- c(0,i,j,z)
 	}
 }
-arma.wavy_plot(df, 0, zlim=c(-0.05,0.05), expand=0.5, border=NA)
+arma.acf_plot(df, 0, zlim=c(0,1.0), expand=0.5, border=NA)
 #+end_src
 
 #+caption: Волна Стокса