parametricMat {compositions}

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))