rgr (version 1.1.15)

orthonorm: Computation of an Orthonormal Basis Matrix

Description

Computes an othonormal basis matrix to be used for the back-transformation of ilr-based data and statistics to clr-based data and statistics.

Usage

orthonorm(p)

Arguments

p

the dimension of the p-space, the number of original variables.

Value

V

the p by (p-1) orthormal basis matrix.

References

Filzmoser, P., Hron, K., Reimann, C. and Garrett, R., 2009. Robust factor analysis for compositional data. Computers & Geosciences, 35(9):1854-1861.

See Also

ilr, clr, gx.mva.closed, gx.robmva.closed, gx.md.gait.closed

Examples

# NOT RUN {
## Make test data available
data(sind.mat2open)

## Compute and display clr transformed data
prmatrix(clr(sind.mat2open))

## Compute and display ilr transformed data
sind.ilr <-ilr(sind.mat2open)
prmatrix(sind.ilr)

## Compute and display orthonormal basis matrix
## sind.mat2open is a 25 by 6 matrix (data set)
V <- orthonorm(6)
prmatrix(V)

## Back-transform ilr transformed data to clr form and display
temp <- sind.ilr %*% t(V)
dimnames(temp)[[2]] <- dimnames(sind.mat2open)[[2]]
prmatrix(temp)

## Clean-up
rm(sind.ilr)
rm(V)
rm(temp)
# }