Two-dimentional gaussian surface

## Settings for RMarkdown http://yihui.name/knitr/options#chunk_options
opts_chunk$set(comment = "", warning = FALSE, message = FALSE, tidy = FALSE, 
    echo = TRUE, fig.width = 7, fig.height = 7)
options(width = 116, scipen = 10)

setwd("~/statistics/Rmedstats/")

Reference

• Wikipedia: Gaussian function
• http://en.wikipedia.org/wiki/Gaussian_function#Two-dimensional_Gaussian_function

Define symmetric two-dimentional gaussian function

\(f(x,y) = a * exp(- \frac {(x^2 + y^2)} {b})\)

##
f.2d.gaussian <- function(a, b, x, y) {
    a * exp(-(x^2 + y^2) / b)
}

Create vector for X and Y axes

axis.vector <- seq(from = -3, to = 3, by = 0.1)

Create Z axis value for each X, Y combination

Constants: a = 1, b = 1

z.axis.vector <- outer(X = axis.vector, Y = axis.vector, function(X,Y) f.2d.gaussian(a = 1, b = 1, x = X, y = Y))

Graphing with persp

persp(x = axis.vector,
      y = axis.vector,
      z = z.axis.vector,
      theta = 30, phi = 30, expand = 0.6, shade = 0.3)

Define the function at sugakuart.com and graph

http://sugakuart.com/products09.html

\(f(x,y) = a * exp(- \frac {{(x - y)}^2} {b})\)

f.sugakuart.com <- function(a, b, x, y) {
    a * exp(- (x - y)^2 / b)
}

z.axis.vector.2 <- outer(X = axis.vector, Y = axis.vector, function(X,Y) f.sugakuart.com(a = 1, b = 1, x = X, y = Y))

persp(x = axis.vector,
      y = axis.vector,
      z = z.axis.vector.2,
      theta = 120, phi = 15, expand = 0.6, shade = 0.3)

From different angles

layout(matrix(1:9, ncol = 3, byrow = T))
par(mar = c(0,0,0,0))

for(i in seq(0, 360, length.out = 9)) {
    persp(x = axis.vector,
          y = axis.vector,
          z = z.axis.vector.2,
          theta = i, phi = 15, expand = 0.6, shade = 0.3)
}