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#' @title Inbreeding coefficients
#'
#' @description Calculates inbreeding coefficients for all animals in the pedigree.
#'
#' @param ped : \code{data.frame} with integer columns corresponding to ID, SIRE, DAM. Missing value is 0.
#'
#' @return Vector of inbreeding coefficients
#'
#' @examples
#' ped = data.frame(ID=1:7, SIRE=c(0,0,1,1,3,1,5), DAM=c(0,0,0,2,4,4,6))
#' inbreed(ped)
#'
#' @export
inbreed <- function(ped) {
message("Estimating inbreeding coefficients based on Meuwissen and Luo (1992)")
N = nrow(ped)
if(ped[1,1]!=1) stop("The first ID is not equal to 1.")
if(any(ped[,1] - c(0,ped[-N,1])!=1)) stop("IDs are not sequential.")
F = L = POINT = rep(0, N)
D = rep(1, N)
ped$P1 = apply(ped[,2:3], 1, FUN=max)
ped$P2 = apply(ped[,2:3], 1, FUN=min)
for(I in 1:N)
{
P1 = ped$P1[I]
P2 = ped$P2[I]
if(P2==0) {
if(P1 > 0) D[I] = (3-F[P1])/4
F[I] = 0
} else if(P1==ped$P1[I-1] & P2==ped$P2[I-1]) {
D[I] = D[I-1]
F[I] = F[I-1]
} else {
D[I] = (2-F[P1]-F[P2])/4
FI = -1
L[I] = 1
J = I
while(J!=0)
{
K = J
R = L[K]/2
KS = ped$P1[K]
KD = ped$P2[K]
if(KS > 0) {
while(POINT[K] > KS) K = POINT[K]
L[KS] = L[KS] + R
if(KS!=POINT[K]) {
POINT[KS] = POINT[K]
POINT[K] = KS
}
if(KD > 0) {
while(POINT[K] > KD) K = POINT[K]
L[KD] = L[KD] + R
if(KD!=POINT[K]) {
POINT[KD] = POINT[K]
POINT[K] = KD
}
}
}
FI = FI + L[J]^2*D[J]
L[J] = 0
K = J
J = POINT[J]
POINT[K] = 0
}
F[I] = FI
}
}
return(F)
}
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