NAME

rq_decompose - Decompose a matrix M into the product of a right triangular matrix and an

SYNOPSIS

#include "n/n_qr.h"

Example compile flags (system dependent):
  -DLINUX_X86_64 -DLINUX_X86_64_OPTERON  -DGNU_COMPILER 
   -I/home/kobus/include
   -L/home/kobus/misc/load/linux_x86_64_opteron -L/usr/lib/x86_64-linux-gnu
  -lKJB                               -lfftw3  -lgsl -lgslcblas -ljpeg  -lSVM -lstdc++                    -lpthread -lSLATEC -lg2c    -lacml -lacml_mv -lblas -lg2c      -lncursesw 


int rq_decompose
(
	const Matrix *mp,
	Matrix **R_mpp,
	Matrix **Q_mpp
);

DESCRIPTION

orthogonal matrix.

RETURNS

NO_ERROR on success, and ERROR on failure, with an appropriate error message being set.

NOTE

The result is obtained directly from the result of qr_decompose(). Let S be an antidiagonal matrix of all 1's, which reverses the order of rows of columns of the matrix it multiplies (depending on if it is left or right multiplied). The dimension of S is implied from the dimension of the other multiplicand. Note that S * S = I and S = S'. As we see below, the RQ decomposition of M can by computed from the QR decomposition of M' * S: | M'* S = Q * R QR decomposition

   M' * S = Q * S * S * R     since (S * S) = I
   S * M  = R' * S * S * Q'   transpose both sides
   M = S * R' * S * S * Q'    algebra
   M = (R_new) * (Q_new)      since (S * R' * S) is upper triangular

NOTE This routine requires that that the LAPACK library is available. If this file was compiled without the presence of that library, then this routine will return ERROR.

DISCLAIMER

This software is not adequatedly tested. It is recomended that results are checked independantly where appropriate.

AUTHOR

Kyle Simek

DOCUMENTER

Kobus Barnard