Convert CoDA covariance matricies between representations

ilrvar, clrvar, and varmat (variation matrix). ilrvar2phi calculates phi statistics (for proportionality) from an ILR covariance matrix as described in Lovell (2015).

ilrvar2phi(Sigma, V)

ilrvar2ilrvar(Sigma, V1, V2)

ilrvar2clrvar(Sigma, V)

clrvar2ilrvar(Sigma, V)

clrvar2varmat(Sigma)

ilrvar2varmat(Sigma, V)

alrvar2clrvar(Sigma, d1)

clrvar2alrvar(Sigma, d2)

alrvar2alrvar(Sigma, d1, d2)

alrvar2ilrvar(Sigma, d1, V2)

ilrvar2alrvar(Sigma, V1, d2)

alrvar2varmat(Sigma, d1)

Arguments

Sigma	covariance matrix in specified transformed space
V	ILR contrast matrix (i.e., transformation matrix of ILR)
V1	ILR contrast matrix of basis Sigma is already in
V2	ILR contrast matrix of basis Sigma is desired in
d1	alr reference element Sigma is already expressed with respec to
d2	alr reference element Sigma is to be expressed with respect to

Value

matrix

Examples

x <- matrix(runif(30),  10, 3)
x <- miniclo(x)
x.ilr <- ilr(x)
V <- create_default_ilr_base(3)
Sigma <- cov(x.ilr)
Sigma.clr <- ilrvar2clrvar(Sigma, V)
clrvar2ilrvar(Sigma.clr, V)
#>           [,1]      [,2]
#> [1,]  1.621652 -1.330676
#> [2,] -1.330676  1.476700
clrvar2varmat(Sigma.clr)
ilrvar2varmat(Sigma, V)
ilrvar2phi(Sigma,V)
#>          [,1]      [,2]      [,3]
#> [1,] 0.000000 5.3306740 3.2433035
#> [2,] 5.330674 0.0000000 0.7210786
#> [3,] 3.243303 0.7210786 0.0000000