rorth: Random Orthogonal Matrix Creation Uniform WRT the Haar...
In ICtest: Estimating and Testing the Number of Interesting Components in Linear Dimension Reduction
rorth R Documentation
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.
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).
Value
An orthogonal k times k matrix
Author(s)
Klaus Nordhausen
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>.
Examples
Orth <- rorth(4)
crossprod(Orth)
tcrossprod(Orth)
ICtest documentation built on May 18, 2022, 9:05 a.m.
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| rorth | R Documentation |
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. |
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).
Value
An orthogonal k times k matrix
Author(s)
Klaus Nordhausen
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>.
Examples
Orth <- rorth(4) crossprod(Orth) tcrossprod(Orth)
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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