[R] R-code to generate random rotation matrix for rotation testing

Martin Krautschke m.krautschke at gmx.at
Mon Dec 27 22:47:26 CET 2010

Dear list,

I am looking for an implementation of random rotation matrix generation in R to do a rotation test: I want to use the matrices to create random multivariate normal matrices with common covariance structure and mean based on an observed data matrix.

The rRotationMatrix-function in the mixAK-package is an option, but as far as I can tell I need to draw rotation matrices with determinant -1 as well. Roast and Romer in the limma-bioconductor package appear to have implemented something similar, which seems not to be general enough for my purposes, however. Inspired by the code in the ffmanova-rotationtest function I thought of the following, but it appears to me that there only the covariance, not the mean, is preserved:

# a given Y has independent, multivariate normal rows
Y <- rmvnorm(4,mean=1:10,sigma=diag(1:10)+3)

# Generation of a set of random matrices Z
for (i in 1:10) {
 # R is random matrix of independent standard-normal entries
 R <- matrix(rnorm(16),ncol=4)
 R <- qr.Q(qr(R, LAPACK = TRUE))
 # Z shall be a random matrix with the same mean and covariance structure as Y
 Z <- crossprod(R,Y)

A suggestion for the procedure exists (in Dorum et al. http://www.bepress.com/sagmb/vol8/iss1/art34/ , end of chapter 2.1), but a hint to a (fast) implementation would be greatly appreciated.

Best regards and a happy new year,
Martin Krautschke

Martin Krautschke
Student at University of Vienna

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