org.netlib.lapack
Class DLATRZ

java.lang.Object
  org.netlib.lapack.DLATRZ

public class DLATRZ
extends java.lang.Object

DLATRZ is a simplified interface to the JLAPACK routine dlatrz.
This interface converts Java-style 2D row-major arrays into
the 1D column-major linearized arrays expected by the lower
level JLAPACK routines.  Using this interface also allows you
to omit offset and leading dimension arguments.  However, because
of these conversions, these routines will be slower than the low
level ones.  Following is the description from the original Fortran
source.  Contact seymour@cs.utk.edu with any questions.

 *     ..
 *
 *  Purpose
 *  =======
 *
 *  DLATRZ factors the M-by-(M+L) real upper trapezoidal matrix
 *  [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R  0 ) * Z, by means
 *  of orthogonal transformations.  Z is an (M+L)-by-(M+L) orthogonal
 *  matrix and, R and A1 are M-by-M upper triangular matrices.
 *
 *  Arguments
 *  =========
 *
 *  M       (input) INTEGER
 *          The number of rows of the matrix A.  M >= 0.
 *
 *  N       (input) INTEGER
 *          The number of columns of the matrix A.  N >= 0.
 *
 *  L       (input) INTEGER
 *          The number of columns of the matrix A containing the
 *          meaningful part of the Householder vectors. N-M >= L >= 0.
 *
 *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
 *          On entry, the leading M-by-N upper trapezoidal part of the
 *          array A must contain the matrix to be factorized.
 *          On exit, the leading M-by-M upper triangular part of A
 *          contains the upper triangular matrix R, and elements N-L+1 to
 *          N of the first M rows of A, with the array TAU, represent the
 *          orthogonal matrix Z as a product of M elementary reflectors.

 *
 *  LDA     (input) INTEGER
 *          The leading dimension of the array A.  LDA >= max(1,M).
 *
 *  TAU     (output) DOUBLE PRECISION array, dimension (M)
 *          The scalar factors of the elementary reflectors.
 *
 *  WORK    (workspace) DOUBLE PRECISION array, dimension (M)
 *
 *  Further Details
 *  ===============
 *
 *  Based on contributions by
 *    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

 *
 *  The factorization is obtained by Householder's method.  The kth
 *  transformation matrix, Z( k ), which is used to introduce zeros into

 *  the ( m - k + 1 )th row of A, is given in the form
 *
 *     Z( k ) = ( I     0   ),
 *              ( 0  T( k ) )
 *
 *  where
 *
 *     T( k ) = I - tau*u( k )*u( k )',   u( k ) = (   1    ),
 *                                                 (   0    )
 *                                                 ( z( k ) )
 *
 *  tau is a scalar and z( k ) is an l element vector. tau and z( k )
 *  are chosen to annihilate the elements of the kth row of A2.
 *
 *  The scalar tau is returned in the kth element of TAU and the vector
 *  u( k ) in the kth row of A2, such that the elements of z( k ) are
 *  in  a( k, l + 1 ), ..., a( k, n ). The elements of R are returned in

 *  the upper triangular part of A1.
 *
 *  Z is given by
 *
 *     Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).
 *
 *  =====================================================================
 *
 *     .. Parameters ..

Constructor Summary

DLATRZ()

Method Summary

static void

DLATRZ(int m, int n, int l, double[][] a, double[] tau, double[] work)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

DLATRZ

public DLATRZ()

Method Detail

DLATRZ

public static void DLATRZ(int m,
                          int n,
                          int l,
                          double[][] a,
                          double[] tau,
                          double[] work)