I have the following data. The data has 2 groups (G) each with 2 individuals (n_i).
rm(list=ls()); set.seed(1234)
G=2 ; # Suppose 2 groups
n_i<-2 # There are two individuals per group
nTot<-4 # In total we have 4 individuals
z_ij<-runif(nTot, 0, 5)
T_ij<- runif(nTot, 5, 10)
Data<-round(data.frame(id=rep(1:nTot), group=rep(1:G, rep(2,G) ),z_ij, T_ij),1)
Data
id group z_ij T_ij
1 1 1 0.6 9.3
2 2 1 3.1 8.2
3 3 2 3.0 5.0
4 4 2 3.1 6.2
For every individual(row), I have the following function f(x,y)= xy\exp(x y z[id])
where upper limit in integrating for x
is Tij[id]
.
I would like a code in R that can compute the following integral
Group 1:
Group 2
My attempt which yields an error Error in integrate(function(y) as.numeric(sapply(split(sapply(1:nTot, : evaluation of function gave a result of wrong lengt
GroupInt<-rep(NA,G)
for(i in 1:G) ## s<-3
{
GroupInt[i]<- integrate( function(y)
as.numeric( sapply( split( sapply( 1:nTot, function(id) integrate(function(x)
x*y*exp( x y Data$z_ij[id] ), 0, Data$T_ij[id] )$value ), Data$group),prod) )[i] ,
0 , 5 )$value
}
CodePudding user response:
set.seed(1234)
G <- 2 ; # Suppose 2 groups
n_i <- 2 # There are two individuals per group
nTot <- 4 # In total we have 4 individuals
z_ij <- runif(nTot, 0, 5)
T_ij <- runif(nTot, 5, 10)
Data <- round(data.frame(id = rep(1:nTot), group = rep(1:G, rep(2,G)), z_ij, T_ij), 1)
# function for the inner integral
fInner <- function(df) {
Vectorize({function(y) {
prod(
sapply(
seq_along(df),
function(i) integrate(function(x) x*y*exp(x y df$z_ij[i]), 0, df$T_ij[i])$value
)
)
}})
}
GroupInt <- sapply(1:G, function(grp) integrate(fInner(subset(Data, group == grp, select = c("z_ij", "T_ij"))), 0, 5)$value)
GroupInt
#> [1] 2.173417e 16 1.534357e 14
# compare to the analytical solution
fAnal <- function(df) {
exp(sum(df$z_ij))*(41*exp(10) - 1)*prod(exp(df$T_ij)*(df$T_ij - 1) 1)/4
}
GroupInt2 <- sapply(1:G, function(grp) fAnal(subset(Data, group == grp, select = c("z_ij", "T_ij"))))
GroupInt2
#> [1] 2.173417e 16 1.534357e 14
all.equal(GroupInt, GroupInt2)
#> [1] TRUE