R: Unique parametrisations for matrices.

parametricMat {compositions} | R Documentation

## Unique parametrisations for matrices.

### Description

Helper functions to parametrize positive semidefinite matrices in multivariate variogram models.

### Usage

    parametricRank1Mat(p)
    parametricPosdefMat(p)
    parameterRank1Mat(A)
    parameterPosdefMat(A)
    parametricRank1ClrMat(p)
    parametricPosdefClrMat(p)
    parameterRank1ClrMat(A)
    parameterPosdefClrMat(A)

### Arguments

`A` | a positiv definit matrix of the given type
`p` | a vector of parameters describing the matrix, as returned by the parameter functions.

### Details

The rank 1 matrix is parametrised by the first eigenvector scaled by the square root of the eigenvalue. The positiv semidefinit matrix the entries of a upper right triangular matrix R with `t(R)%*%R==A`. The clr matrices are work with the parameters of the corresponding ilr matrix.

### Value

A or p, depending on what is not given.

### Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

### See Also

`vgram2lrvgram`, `CompLinModCoReg`, `vgmFit`

### Examples

    parametricRank1Mat(c(0,0,2))
    parametricPosdefMat(c(0,0,1,0,0,0))
    parameterRank1Mat(matrix(1,nr=3,nc=3))
    parameterPosdefMat(diag(5))

[Package compositions version 1.40-5 Index]