DATA605-Discussion-10

Exercise 13 Write a program to compute \(u^{(n)}\) given u and P. Use this program to compute \(u^{(10)}\) for the Land of Oz example, with u = (0, 1, 0), and with u = (1/3, 1/3, 1/3).

library(expm)

## Warning: package 'expm' was built under R version 3.6.3

## Loading required package: Matrix

## 
## Attaching package: 'expm'

## The following object is masked from 'package:Matrix':
## 
##     expm

compute_un <- function(n,u,P){
  
  Pn <- P %^% n #find p^n
  
  out <- u %*% Pn  #find uP^n

  return(out)
}

#set up the transition max for oz
oz <- matrix(c(0.5,0.25,0.25,0.5,0,0.5,0.25,0.25,0.5),nrow = 3,byrow=T)

u1 <- c(0,1,0)
u2 <- c(0.33,0.33,0.33)

#for u1
round(compute_un(10,u1,oz),2)

##      [,1] [,2] [,3]
## [1,]  0.4  0.2  0.4

#for u2
round(compute_un(10,u2,oz),2)

##      [,1] [,2] [,3]
## [1,]  0.4  0.2  0.4