In brouwern/popcycles: What the Package Does (One Line, Title Case)

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

library(popcycles)

Introduction

Not yet updated. Probably doesn't make much sense without the text from the books.

Examples from Caswell Chapter 13 Periodic Matrix Models Section 13.2.1 Period matrix models for annuals Example 13.4 A model for winter annual plants

From Watkinson 1981

#### Subcomponent matrices
b11 <- 0.3
b21 <- 0.1
b22 <- 0.6
b32 <- 0.2
Bm <- matrix(data = c(b11, 0.0,
                     b21, b22,
                     0.0, b32), byrow = TRUE,nrow = 3)

c11 <- 1
c12 <- 10
c13 <- 100
Cm <- c(c11, c12, c13)

d11 <- d21 <- 0.5
Dm <- matrix(data = c(d11,
                     d21), nrow = 2)

f11 <- 0.05
f22 <- 0.1
Fm <- matrix(data = c(f11, 0.0,
                     0.0,  f22), byrow = TRUE, nrow = 2)

#multiply all subcomponents
Fm%*%Dm%*%Cm%*%Bm


#Build a full matrix
mfull <-matrix(
c(0  ,0  ,0  ,0  ,0  ,0  ,f11,0  ,
  0  ,0  ,0  ,0  ,0  ,0  ,0  ,f22,
  b11,0  ,0  ,0  ,0  ,0  ,0  ,0  ,
  b21,b22,0  ,0  ,0  ,0  ,0  ,0  ,
  0  ,b32,0  ,0  ,0  ,0  ,0  ,0  ,
  0  ,0  ,c11,c12,c13,0  ,0  ,0  ,
  0  ,0  ,0  ,0  ,0  ,d11,0  ,0  ,
  0  ,0  ,0  ,0  ,0  ,d21,0  ,0
   ), byrow = TRUE, nrow = 8)


#build design matrices
MB <-matrix(
  c(0  ,0  ,0  ,0  ,0  ,0  ,0  ,0  ,
    0  ,0  ,0  ,0  ,0  ,0  ,0  ,0  ,
    1  ,0  ,0  ,0  ,0  ,0  ,0  ,0  ,
    1  ,1  ,0  ,0  ,0  ,0  ,0  ,0  ,
    0  ,1  ,0  ,0  ,0  ,0  ,0  ,0  ,
    0  ,0  ,0  ,0  ,0  ,0  ,0  ,0  ,
    0  ,0  ,0  ,0  ,0  ,0  ,0  ,0  ,
    0  ,0  ,0  ,0  ,0  ,0  ,0  ,0
  ), byrow = TRUE, nrow = 8)

MC <-matrix(
  c(0  ,0  ,0  ,0  ,0  ,0  ,0  ,0  ,
    0  ,0  ,0  ,0  ,0  ,0  ,0  ,0  ,
    0  ,0  ,0  ,0  ,0  ,0  ,0  ,0  ,
    0  ,0  ,0  ,0  ,0  ,0  ,0  ,0  ,
    0  ,0  ,0  ,0  ,0  ,0  ,0  ,0  ,
    0  ,0  ,1  ,1  ,1  ,0  ,0  ,0  ,
    0  ,0  ,0  ,0  ,0  ,0  ,0  ,0  ,
    0  ,0  ,0  ,0  ,0  ,0  ,0  ,0
  ), byrow = TRUE, nrow = 8)


#compare submatrices to full matrix*design matrix
Cm%*%Bm
(mfull*MC)%*%(mfull*MB)