RevertMatrix function

Revert Matrix

Constructs a covariance matrix based on scores over covariance matrix eigentensors.

RevertMatrix(values, etd, scaled = TRUE)

Arguments

• values: vector of values to build matrix, each value corresponding to a score on the ordered set of eigentensors (up to the maximum number of eigentensors on the target decomposition); if there are less values than eigentensors provided in etd (see below), the function will assume zero as the value for the score in remaining eigentensors
• etd: Eigentensor decomposition of m covariance matrices for k traits (obtained from EigenTensorDecomposition)
• scaled: should we treat each score as a value given in standard deviations for each eigentensor? Defaults to TRUE

Returns

A symmetric covariance matrix with k traits

Examples

## we can use RevertMatrix to represent eigentensors using SRD to compare two matrices
## which differ with respect to their projections on a single directions

data(dentus)

dentus.vcv <- daply (dentus, .(species), function(x) cov(x[,-5]))

dentus.vcv <- aperm(dentus.vcv, c(2, 3, 1))

dentus.etd <- EigenTensorDecomposition(dentus.vcv, TRUE)

## calling RevertMatrix with a single value will use this value as the score
## on the first eigentensor and use zero as the value of remaining scores

low.et1 <- RevertMatrix(-1.96, dentus.etd, TRUE)
upp.et1 <- RevertMatrix(1.96, dentus.etd, TRUE)

srd.et1 <- SRD(low.et1, upp.et1)
 
plot(srd.et1)

## we can also look at the second eigentensor, by providing each call 
## of RevertMatrix with a vector of two values, the first being zero

low.et2 <- RevertMatrix(c(0, -1.96), dentus.etd, TRUE)
upp.et2 <- RevertMatrix(c(0, 1.96), dentus.etd, TRUE)

srd.et2 <- SRD(low.et2, upp.et2)
 
plot(srd.et2)

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.