rorth: Random Orthogonal Matrix Creation Uniform WRT the Haar Measure.
Description
A function to create a random orthogonal matrix uniformly distributed with respect to the Haar measure.
Usage
rorth(k)
Arguments
k
the desired numer of columns (=rows) of the orthogonal matrix.
Value
An orthogonal k times k matrix
Details
The function fills a kxk matrix with N(0,1) random variables and perfroms then a QR decompoistion using qr. If the diagonal elements of R are all positive the resulting orthogonal matrix Q is uniform distributed wrt to the Haar measure. Note that the function currently does not check if
all diagonal measurements are indeed positive (however this will happen with probability 1 in theory).
References
Stewart, G.W. (1980), The efficient generation of random orthogonal matrices with an application to condition estimators, SIAM Journal on Numerical Analysis, 17, 403--409. <doi:10.1137/0717034>.