qrsol.src

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/*
** qrsol.src - Procedures related to the QR decomposition.
** (C) Copyright 1988-1998 by Aptech Systems, Inc.
** All Rights Reserved.
**
** This Software Product is PROPRIETARY SOURCE CODE OF APTECH
** SYSTEMS, INC.    This File Header must accompany all files using
** any portion, in whole or in part, of this Source Code.   In
** addition, the right to create such files is strictly limited by
** Section 2.A. of the GAUSS Applications License Agreement
** accompanying this Software Product.
**
** If you wish to distribute any portion of the proprietary Source
** Code, in whole or in part, you must first obtain written
** permission from Aptech Systems.
**
** These functions require GAUSS 3.1.1
**
**  Format                   Purpose                             Line
** ------------------------------------------------------------------
**   x = QRSOL(b,R);        QR Solve where R is upper triangular   26
**   x = QRTSOL(b,L);       QR Solve where L is lower triangular   59
*/

/*
**> qrsol
**
**  Purpose:    Computes the solution of R x = b where R is an
**              upper triangular matrix.
**
**  Format:     x = qrsol(b,R);
**
**  Input:      R    PxP upper triangular matrix.
**
**              b    PxK matrix.
**
**  Output:     x    PxK matrix.
**
**  Remarks:    qrsol applies a backsolve to
**
**                    R x = b
**
**              to solve for x.  Generally R will be the R matrix from
**              a qr factorization.  It may be used, however, in any
**              situation where R is upper triangular.
**              If b has more than one column, each column will be
**              solved for separately, i.e., qrsol will apply a back-
**              solve to R x[.,i] = b[.,i].
**
**   See Also: qqr, qr, qtyr, qrtsol
**
*/

proc qrsol(b,r);
    retp(utrisol(b,r));
endp;

/*
**> qrtsol
**
**  Purpose:    Computes the solution of L x = b where L is a
**              lower triangular matrix.
**
**  Format:     x = qrtsol(b,L);
**
**  Input:      L    PxP lower triangular matrix.
**
**              b    PxK matrix.
**
**  Output:     x    PxK matrix.
**
**  Remarks:    qrtsol applies a forward solve to
**
**                    L x = b
**
**              to solve for x.  Generally L will be the R' matrix from
**              a QR factorization.  It may be used, however, in any
**              situation where L is lower triangular.
**              If b has more than one column, each column will be
**              solved for separately, i.e., qrtsol will apply a forward
**              solve to L x[.,i] = b[.,i].
**
**  See Also: qqr, qr, qtyr, qrsol
**
*/

proc qrtsol(b,rt);
     retp(ltrisol(b,rt));
endp;