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iterate-matrix-example

library(greta.dynamics)
#> Loading required package: greta
#> 
#> Attaching package: 'greta'
#> The following objects are masked from 'package:stats':
#> 
#>     binomial, cov2cor, poisson
#> The following objects are masked from 'package:base':
#> 
#>     %*%, apply, backsolve, beta, chol2inv, colMeans, colSums, diag,
#>     eigen, forwardsolve, gamma, identity, rowMeans, rowSums, sweep,
#>     tapply
greta_sitrep()
#> ℹ checking if python available
#> ✔ python (v3.10) available
#> 
#> ℹ checking if TensorFlow available
#> ✔ TensorFlow (v2.15.0) available
#> 
#> ℹ checking if TensorFlow Probability available
#> ✔ TensorFlow Probability (v0.23.0) available
#> 
#> ℹ checking if greta conda environment available
#> ✔ greta conda environment available
#> 
#> ℹ greta is ready to use!
# simulate from a probabilistic 4-stage transition matrix model
k <- 4

# component variables
# survival probability for all stages
survival <- uniform(0, 1, dim = k)
# conditional (on survival) probability of staying in a stage
stasis <- c(uniform(0, 1, dim = k - 1), 1)
# marginal probability of staying/progressing
stay <- survival * stasis
progress <- (survival * (1 - stay))[1:(k - 1)]
# recruitment rate for the largest two stages
recruit <- exponential(c(3, 5))
# combine into a matrix:
tmat <- zeros(k, k)
diag(tmat) <- stay
progress_idx <- row(tmat) - col(tmat) == 1
tmat[progress_idx] <- progress
tmat[1, k - (1:0)] <- recruit
# analyse this to get the intrinsic growth rate and stable state
iterations <- iterate_matrix(tmat)
iterations$lambda
#> greta array <operation>
#> 
#>      [,1]
#> [1,]  ?
#> 
iterations$stable_distribution
#> greta array <operation>
#>      [,1]
#> [1,]  ?  
#> [2,]  ?  
#> [3,]  ?  
#> [4,]  ?
#> 
iterations$all_states
#> greta array <operation>
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,]  ?    ?    ?    ?    ?    ?    ?    ?    ?    ?     ?     ?     ?     ?   
#> [2,]  ?    ?    ?    ?    ?    ?    ?    ?    ?    ?     ?     ?     ?     ?   
#> [3,]  ?    ?    ?    ?    ?    ?    ?    ?    ?    ?     ?     ?     ?     ?   
#> [4,]  ?    ?    ?    ?    ?    ?    ?    ?    ?    ?     ?     ?     ?     ?   
#>      [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#> [2,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#> [3,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#> [4,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#>      [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#> [2,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#> [3,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#> [4,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#>      [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#> [2,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#> [3,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#> [4,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#>      [,51] [,52] [,53] [,54] [,55] [,56] [,57] [,58] [,59] [,60] [,61] [,62]
#> [1,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#> [2,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#> [3,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#> [4,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#>      [,63] [,64] [,65] [,66] [,67] [,68] [,69] [,70] [,71] [,72] [,73] [,74]
#> [1,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#> [2,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#> [3,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#> [4,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#>      [,75] [,76] [,77] [,78] [,79] [,80] [,81] [,82] [,83] [,84] [,85] [,86]
#> [1,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#> [2,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#> [3,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#> [4,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#>      [,87] [,88] [,89] [,90] [,91] [,92] [,93] [,94] [,95] [,96] [,97] [,98]
#> [1,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#> [2,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#> [3,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#> [4,]  ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?     ?   
#>      [,99] [,100]
#> [1,]  ?     ?    
#> [2,]  ?     ?    
#> [3,]  ?     ?    
#> [4,]  ?     ?
#> 
#> ℹ 390 more values
#> Use `print(n = ...)` to see more values
# Can also do this simultaneously for a collection of transition matrices
k <- 2
n <- 10
survival <- uniform(0, 1, dim = c(n, k))
stasis <- cbind(uniform(0, 1, dim = n), rep(1, n))
stay <- survival * stasis
progress <- (survival * (1 - stasis))[, 1]
recruit_rate <- 1 / seq(0.1, 5, length.out = n)
recruit <- exponential(recruit_rate, dim = n)
tmats <- zeros(10, 2, 2)
tmats[, 1, 1] <- stasis[, 1]
tmats[, 2, 2] <- stasis[, 2]
tmats[, 2, 1] <- progress
tmats[, 1, 2] <- recruit
iterations <- iterate_matrix(tmats)
iterations$lambda
#> greta array <operation>
#> 
#>       [,1]
#>  [1,]  ?  
#>  [2,]  ?  
#>  [3,]  ?  
#>  [4,]  ?  
#>  [5,]  ?  
#>  [6,]  ?  
#>  [7,]  ?  
#>  [8,]  ?  
#>  [9,]  ?  
#> [10,]  ?
#> 
iterations$stable_distribution
#> greta array <operation>
#> , , 1
#> 
#>       [,1] [,2]
#>  [1,]  ?    ?  
#>  [2,]  ?    ?  
#>  [3,]  ?    ?  
#>  [4,]  ?    ?  
#>  [5,]  ?    ?  
#>  [6,]  ?    ?  
#>  [7,]  ?    ?  
#>  [8,]  ?    ?  
#>  [9,]  ?    ?  
#> [10,]  ?    ?
#> 
#> ℹ 10 more values
#> Use `print(n = ...)` to see more values
dim(iterations$all_states)
#> [1]  10   2 100
iterations$all_states[, , 1]
#> greta array <operation>
#> 
#> , , 1
#> 
#>       [,1] [,2]
#>  [1,]  ?    ?  
#>  [2,]  ?    ?  
#>  [3,]  ?    ?  
#>  [4,]  ?    ?  
#>  [5,]  ?    ?  
#>  [6,]  ?    ?  
#>  [7,]  ?    ?  
#>  [8,]  ?    ?  
#>  [9,]  ?    ?  
#> [10,]  ?    ?
#> 
#> ℹ 10 more values
#> Use `print(n = ...)` to see more values
iterations$all_states[, , 100]
#> greta array <operation>
#> 
#> , , 1
#> 
#>       [,1] [,2]
#>  [1,]  ?    ?  
#>  [2,]  ?    ?  
#>  [3,]  ?    ?  
#>  [4,]  ?    ?  
#>  [5,]  ?    ?  
#>  [6,]  ?    ?  
#>  [7,]  ?    ?  
#>  [8,]  ?    ?  
#>  [9,]  ?    ?  
#> [10,]  ?    ?
#> 
#> ℹ 10 more values
#> Use `print(n = ...)` to see more values

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