findFeasibleMatrix {systemicrisk}

Finds a Nonnegative Matrix Satisfying Row and Column Sums

Description

Given row and column sums and a matrix p which indicates which elements of the matrix can be present, this function computes a nonnegative matrix that match these row and column sums. If this is not possible then the function returns an error message.

Usage

findFeasibleMatrix(r, c, p, eps = 1e-09)

Arguments

r

vector of row sums (nonnegative

c

vector of column sums (nonnegative)

p

matrix of probabilities (must be in [0,1]), matching the dimensions of r and c. Values of p=0 are interpreted that the corresponding matrix elements have to be 0. Note: p=1 does not force the corresponding matrix element to exist.

eps

row and col sums can at most be different by eps. Default 1e-9.

Details

The function transforms the problem into a Maximum Flow problem of a graph and uses the Edmonds-Karps algorithm to solve it. If the error message "Could not find feasible matrix." is produced then this could be due to p imposing disconnected components in the graph implied by row and column sums that are not compatible with the row and column sums..

Value

A feasible matrix.

Examples

p=matrix(c(1,0,0,1),nrow=2)
findFeasibleMatrix(c(1,1),c(1,1),p=p)

n <- 4
M <- matrix(nrow=n,ncol=n,rexp(n*n)*(runif(n*n)>0.6))
M
r <- rowSums(M)
c <- colSums(M)
Mnew <- findFeasibleMatrix(r=r,c=c,p=(M>0)*0.5)
Mnew
rowSums(M);rowSums(Mnew)
colSums(M);colSums(Mnew)