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evec = matrix(
c( -0.5, 0.6906786606674509, 0.15153543380548623, 0.5,
0.5, -0.15153543380548576, 0.6906786606674498, 0.5,
-0.5, -0.6906786606674498, -0.15153543380548617, 0.5,
0.5, 0.15153543380548554, -0.6906786606674503, 0.5),
nrow=4,ncol=4,byrow=T)
ievc = matrix(
c( -0.5, 0.5, -0.5, 0.5,
0.6906786606674505, -0.15153543380548617, -0.6906786606674507, 0.15153543380548645,
0.15153543380548568, 0.6906786606674509, -0.15153543380548584, -0.6906786606674509,
0.5, 0.5, 0.5, 0.5),
nrow=4,ncol=4,byrow=T)
make.expDt = function(t) {
matrix(
c(exp(-2*t), 0, 0, 0,
0, exp(-1*t)*cos(1*t), exp(-1*t)*sin(1*t), 0,
0, -exp(-1*t)*sin(1*t), exp(-1*t)*cos(1*t), 0,
0, 0, 0, 1),
nrow=4,ncol=4,byrow=T)
}
q.circulant = matrix(
c(-1, 1, 0, 0,
0, -1, 1, 0,
0, 0, -1, 1,
1, 0, 0, -1),
nrow=4,ncol=4,byrow=T)
test.1 = evec %*% make.expDt(0.1) %*% ievc # Schur decomposition (method used in BEAGLE)
Evec = eigen(q.circulant)$vectors # Complex eigendecomposition
Ievc = solve(Evec)
make2.expDt = function(t) {
diag(exp(eigen(q.circulant)$values * t))
}
test.2 = Evec %*% make2.expDt(0.1) %*% Ievc # Should (and does) equal test.1
out.1 = t(make.expDt(0.1)) %*% t(evec) # Should be intermediate result
out.2 = t(ievc) %*% out.1 # Should (and does) equal t(test.1)
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