Nothing
##==============================================================================
## Ascendency function
##==============================================================================
Ascendfun <- function(Tij,irow,icol) {
FlowFrom <- colSums(Tij)
FlowTo <- rowSums(Tij)
# Sum of all flows, including externals
Throughput <- sum(Tij)
Asc <- 0 # The ascendency of network
Overh <- 0 # The overhead of network
Cap <- 0 # The capacity of network
for (i in irow) {
for (j in icol){
if (Tij[i,j]>0) {
Asc <- Asc + Tij[i,j]*log2(Tij[i,j]*Throughput/FlowTo[i]/FlowFrom[j])
# Overh <- Overh - Tij[i,j]*log2(Tij[i,j]*Tij[i,j] /FlowTo[i]/FlowFrom[j])
Cap <- Cap - Tij[i,j]*log2(Tij[i,j]/Throughput)
}
}
}
Overh <- Cap-Asc
return (c(Asc,Overh,Cap))
}
##==============================================================================
##
## THE ASCENDENCY SUITE
##
## Calculates Ascendency, Overhead and Capacity
## for list of rows (irow) and columns (icol) in Tij
##==============================================================================
AscInd <- function (Flow = NULL, # from-to
Tij = t(Flow), # to-from
Import =NULL, # flow from external (colNr Tij)
Export =NULL, # flow to external (colNr Tij)
Dissipation=NULL) # external dissipation flow
{
N <- InternalNetwork (Tij,Import,Export)
# number of columns and rows for total flows (Tij)
ncTij <- ncol(Tij)
nrTij <- nrow(Tij)
# THROUGHPUT = Sum of all flows, including externals
Throughput <- sum(Tij)
Ascend <- matrix (nrow=5,ncol=4)
colnames(Ascend) <- c("Ascendency","Overhead","Capacity","ACratio")
rownames(Ascend) <- c("Total","Internal","Import","Export","Dissipation")
# ascendency for the entire network (nrTij: number of rows in Tij)
Ascend[1,1:3] <- Ascendfun(Tij,1:nrTij,1:ncTij)
# ascendency for the internal network (iN: indices to internal rows in Tij)
Ascend[2,1:3] <- Ascendfun(Tij,N$iN,N$jN)
# ascendency for the import (Import: index to external column in Tij)
Ascend[3,1:3] <- Ascendfun(Tij,1:nrTij,N$import)
# ascendency for the export
Export1 <- setdiff(N$export,Dissipation) # true export flow
Ascend[4,1:3] <- Ascendfun(Tij,Export1,1:ncTij)
# ascendency for the dissipation
Ascend[5,1:3] <- Ascendfun(Tij,Dissipation,1:ncTij)
# Ascendency - Capacity Ratio
Ascend[,4] <- Ascend[,1]/ Ascend[,3]
return(Ascend)
}
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