A<-matrix(c(0,0,0,0,0,322.8,0.966,0,0,0,0,0,0.013,0.01,0.125,0,0,3.348,0.07,0,0.125,0.238,0,30.17,0.08,0,0.038,0.245,0.167,0.862,0,0,0,0.023,0.75,0), nr = 6, byrow = TRUE)
A
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 0.000 0.00 0.000 0.000 0.000 322.800
## [2,] 0.966 0.00 0.000 0.000 0.000 0.000
## [3,] 0.013 0.01 0.125 0.000 0.000 3.348
## [4,] 0.070 0.00 0.125 0.238 0.000 30.170
## [5,] 0.080 0.00 0.038 0.245 0.167 0.862
## [6,] 0.000 0.00 0.000 0.023 0.750 0.000
nt<-matrix(c(200,150,140,130,110,100), ncol = 1)
nt
## [,1]
## [1,] 200
## [2,] 150
## [3,] 140
## [4,] 130
## [5,] 110
## [6,] 100
nt1= A %*% nt
nt1
## [,1]
## [1,] 32280.00
## [2,] 193.20
## [3,] 356.40
## [4,] 3079.44
## [5,] 157.74
## [6,] 85.49
years=10
n.projections <- matrix(0, nrow = nrow(A), ncol = years + 1)
n.projections
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11]
## [1,] 0 0 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0 0 0
n.projections[, 1] <- nt
n.projections
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11]
## [1,] 200 0 0 0 0 0 0 0 0 0 0
## [2,] 150 0 0 0 0 0 0 0 0 0 0
## [3,] 140 0 0 0 0 0 0 0 0 0 0
## [4,] 130 0 0 0 0 0 0 0 0 0 0
## [5,] 110 0 0 0 0 0 0 0 0 0 0
## [6,] 100 0 0 0 0 0 0 0 0 0 0
for (i in 1:years) n.projections[, i + 1] <- A %*% n.projections[,i]
n.projections
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 200 32280.00 27596.1720 61051.848 877049.340 1120833.933 3133801.25
## [2,] 150 193.20 31182.4800 26657.902 58976.085 847229.662 1082725.58
## [3,] 140 356.40 752.3425 1397.832 10331.516 24907.848 58659.61
## [4,] 130 3079.44 5616.2900 9068.568 88578.730 188523.632 419336.34
## [5,] 110 157.74 3450.4410 4351.529 10227.829 96959.438 161362.18
## [6,] 100 85.49 189.1321 2717.005 3472.224 9708.182 77055.62
## [,8] [,9] [,10] [,11]
## [1,] 24873554.9 42179105.0 128396663 734523107
## [2,] 3027252.0 24027854.0 40745015 124031177
## [3,] 316881.3 830709.9 2224143 9972913
## [4,] 2651268.7 6353965.4 16569014 81860270
## [5,] 449040.0 2839110.8 5779617 17342314
## [6,] 130666.4 397759.2 2275474 4715800
lambda<-array(0,10)
for(i in 1:10){lambda[i]<-colSums(n.projections)[i+1]/colSums(n.projections)[i]}
lambda
## [1] 43.556952 1.902698 1.530012 9.963788 2.182038 2.155852 6.375237
## [8] 2.436622 2.557663 4.961712