maximple: Graphical representation of a toy example of simulated...

In mcsm: Functions for Monte Carlo Methods with R

Description

For the toy function h(x)=(cos(50*x)+sin(20*x))^2, this function represents simulated annealing sequences converging to a local or global maxima as paths on top of the function h itself. The simulated annealing parameters ratemp and powemp can be changed, as well as the stopping rule tolerance.

Usage

maximple(tolerance = 10^(-5), ratemp = 5, powemp = 2)

Arguments

tolerance	maximal difference in the target value needed to stop the simulated annealing algorithm
ratemp	scale factor of temp that determines the scale of the random walk
powemp	power of 1/(1+t) used to set the temperature schedule

Value

The value of this function is a list, with components

x	coordinates of the successive values of the random walk produced by the simulated annealing algorithm
y	corresponding values of h(x), of the same length as x

Author(s)

Christian P. Robert and George Casella

References

From Chapter 5 of EnteR Monte Carlo Statistical Methods

See Also

dyadic

Examples

# Section 5.2.2, artificial function example 5.8

h=function(x){(cos(50*x)+sin(20*x))^2}
par(mar=c(4,4,1,1),mfrow=c(2,2))
for (tt in 1:4){

  curve(h,from=0,to=1,n=10001,col="grey",lwd=2)
  sam=maximple()
  xgo=sam$x
  hgo=sam$y
  lines(xgo,hgo,col="steelblue4",lwd=2)
  points(xgo,hgo,col="steelblue4",cex=.5,pch=19)
  }

Example output

Loading required package: MASS
Loading required package: coda

mcsm documentation built on May 2, 2019, 10:16 a.m.