ProjectMatrix {evolqg}

Project Covariance Matrix

Description

This function projects a given covariance matrix into the basis provided by an eigentensor decomposition.

Usage

ProjectMatrix(matrix, etd)

Arguments

matrix

A symmetric covariance matrix for k traits

etd

Eigentensor decomposition of m covariance matrices for k traits (obtained from EigenTensorDecomposition)

Value

Vector of scores of given covariance matrix onto eigentensor basis.

Author(s)

Guilherme Garcia, Diogo Melo

References

Basser P. J., Pajevic S. 2007. Spectral decomposition of a 4th-order covariance tensor: Applications to diffusion tensor MRI. Signal Processing. 87:220-236.

Hine E., Chenoweth S. F., Rundle H. D., Blows M. W. 2009. Characterizing the evolution of genetic variance using genetic covariance tensors. Philosophical transactions of the Royal Society of London. Series B, Biological sciences. 364:1567-78.

See Also

EigenTensorDecomposition, RevertMatrix

Examples

# this function is useful for projecting posterior samples for a set of 
# covariance matrices onto the eigentensor decomposition done 
# on their estimated means

data(dentus)

dentus.models <- dlply(dentus, .(species), lm, 
                       formula = cbind(humerus, ulna, femur, tibia) ~ 1)

dentus.matrices <- llply(dentus.models, BayesianCalculateMatrix, samples = 100)

dentus.post.vcv <- laply(dentus.matrices, function (L) L $ Ps)
dentus.post.vcv <- aperm(dentus.post.vcv, c(3, 4, 1, 2))

dentus.mean.vcv <- aaply(dentus.post.vcv, 3, MeanMatrix)
dentus.mean.vcv <- aperm(dentus.mean.vcv, c(2, 3, 1))

dentus.mean.etd <- EigenTensorDecomposition(dentus.mean.vcv)
dentus.mean.proj <- data.frame('species' = LETTERS [1:5], dentus.mean.etd $ projection)

dentus.post.proj <- adply(dentus.post.vcv, c(3, 4), ProjectMatrix, etd = dentus.mean.etd)
colnames(dentus.post.proj) [1:2] <- c('species', 'sample')
levels(dentus.post.proj $ species) <- LETTERS[1:5]

require(ggplot2)
ggplot() +
  geom_point(aes(x = ET1, y = ET2, color = species), 
     data = dentus.mean.proj, shape = '+', size = 8) +
  geom_point(aes(x = ET1, y = ET2, color = species), 
     data = dentus.post.proj, shape = '+', size = 3) +
  theme_bw()