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## compar.lynch.R (2002-08-28)
## Lynch's Comparative Method
## Copyright 2002 Julien Claude
## This file is part of the R-package `ape'.
## See the file ../COPYING for licensing issues.
compar.lynch <- function(x, G, eps = 1e-4)
{
if (is.vector(x) || is.data.frame(x)) x <- as.matrix(x)
alea <- runif(1, 0, 1)
z <- as.vector(x)
uz <- apply(x, 2, mean)
vcvz <- var(x)
vz <- diag(vcvz)
nsp <- nrow(x)
k <- ncol(x)
X1 <- matrix(0, k, k)
diag(X1) <- 1
I <- matrix(0, nsp, nsp)
diag(I) <- 1
vara <- trvare <- matrix(NA, k, k)
nsp1 <- rep(1, nsp)
X <- X1 %x% nsp1
compteur <- 0
vara <- A0 <- alea * vcvz
vare <- E0 <- (1 - alea) * vcvz
newu <- u0 <- uz
Ginv <- solve(G)
V0 <- vcvz %x% G
a0 <- e0 <- matrix(0, nsp, k)
a1 <- e1 <- matrix(1, nsp, k)
while (any(abs((rbind(a1, e1) - rbind(a0, e0))) > eps)) {
a1 <- a0
e1 <- e0
compteur <- compteur + 1
Rinv <- solve(E0 %x% I)
Dinv <- solve(A0 %x% G)
info <- solve(Rinv + Dinv)
newa <- solve(Rinv + Dinv) %*% Rinv %*% (z - X %*% u0)
newe <- z - X %*% u0 - newa
e0 <- mnewe <- matrix(newe, nsp, k)
a0 <- mnewa <- matrix(newa, nsp, k)
for (i in 1:k) {
for (j in 1:k) {
trvare[i, j] <- sum(diag(info[(((i - 1) * nsp) + 1):(i * nsp),
(((j - 1) * nsp) + 1):(j * nsp)]))}
}
vare <- ((nsp - 1) * var(mnewe) + trvare) / nsp
for (i in 1:k) {
for (j in 1:k) {
vara[i, j] <- (t(mnewa[, i]) %*% Ginv %*% mnewa[, j] +
sum(diag(Ginv %*%
info[(((i - 1) * nsp) + 1):(i * nsp),
(((j - 1) * nsp) + 1):(j * nsp)]))) / nsp
}
}
newu <- apply(x - mnewa, 2, mean)
V <- vara %x% G + vare %x% I
p <- (2 * pi)^(-nsp) * det(V)^(-0.5) *
exp(-0.5 * t(z - (X %*% newu)) %*% solve(V) %*% (z - (X %*% newu)))
E0 <- vare
A0 <- vara
u0 <- newu
}
dimnames(vare) <- dimnames(vara)
list(vare = vare, vara = vara, A = mnewa, E = mnewe, u = newu, lik = log(p))
}
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