See comments in-line:
On 01/10/11 23:26, Antoine wrote:
Dear Rolf,
I tryed to follow your advices but the results I am getting seems still
strange to me. See below an example of a matrix:
datamat<- matrix(c(2.2, 0.4, 0.4, 2.8), 2, 2)
plot(ellipse(datamat),type='l')
eigenval<- eigen(datamat)$values
eigenvect<- eigen(datamat)$vectors
eigenscl<- eigenvect * sqrt(eigenval) * (qchisq(0.95,2))# One solution to
get rescale
This is wrong because you are multiplying the i-th row of ``eigenvect''
the square root of the i-th eigenvalue. The *columns* of ``eigenvect''
are the eigenvectors. So you need to multiply the j-th column by
the square root of the j-th eigenvalue.
v1<- (eigenvect[,1])*(sqrt(eigenval[1]))*(qchisq(0.95,2))#or directly
rescale the vectors needed
v2<- (eigenvect[,2])*(sqrt(eigenval[2]))*(qchisq(0.95,2))
The foregoing is correct except that you need to take the square
root of the chi-squared quantile.
#Or
v1<- eigenscl[1,]
v2<- eigenscl[2,]
segments(-v1[1],-v1[2],v1[1],v1[2])
segments(-v2[1],-v2[2],v2[1],v2[2])
The vectors don't seem to be scaled properly and I don't see what I am doing
wrong. Any ideas?
Here is correct code:
require(ellipse)
S <- matrix(c(2.2, 0.4, 0.4, 2.8), 2, 2)
# Note the ``asp=1'' which makes orthogonal lines
# look orthogonal:
plot(ellipse(S),type='l',asp=1)
E <- eigen(S)
Val <- E$values
Vec <- E$vectors
v1 <- sqrt(Val[1]*qchisq(0.95,2))*Vec[,1]
v2 <- sqrt(Val[2]*qchisq(0.95,2))*Vec[,2]
segments(-v1[1],-v1[2],v1[1],v1[2])
segments(-v2[1],-v2[2],v2[1],v2[2])
cheers,
Rolf Turner
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