[BACK]Return to dgerq2.f CVS log [TXT] [DIR] Up to [local] / rpl / lapack / lapack

Diff for /rpl/lapack/lapack/dgerq2.f between versions 1.9 and 1.10

version 1.9, 2011/07/22 07:38:05 version 1.10, 2011/11/21 20:42:51
Line 1 Line 1
   *> \brief \b DGERQ2
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DGERQ2 + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgerq2.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgerq2.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgerq2.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DGERQ2( M, N, A, LDA, TAU, WORK, INFO )
   * 
   *       .. Scalar Arguments ..
   *       INTEGER            INFO, LDA, M, N
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DGERQ2 computes an RQ factorization of a real m by n matrix A:
   *> A = R * Q.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] M
   *> \verbatim
   *>          M is INTEGER
   *>          The number of rows of the matrix A.  M >= 0.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The number of columns of the matrix A.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in,out] A
   *> \verbatim
   *>          A is DOUBLE PRECISION array, dimension (LDA,N)
   *>          On entry, the m by n matrix A.
   *>          On exit, if m <= n, the upper triangle of the subarray
   *>          A(1:m,n-m+1:n) contains the m by m upper triangular matrix R;
   *>          if m >= n, the elements on and above the (m-n)-th subdiagonal
   *>          contain the m by n upper trapezoidal matrix R; the remaining
   *>          elements, with the array TAU, represent the orthogonal matrix
   *>          Q as a product of elementary reflectors (see Further
   *>          Details).
   *> \endverbatim
   *>
   *> \param[in] LDA
   *> \verbatim
   *>          LDA is INTEGER
   *>          The leading dimension of the array A.  LDA >= max(1,M).
   *> \endverbatim
   *>
   *> \param[out] TAU
   *> \verbatim
   *>          TAU is DOUBLE PRECISION array, dimension (min(M,N))
   *>          The scalar factors of the elementary reflectors (see Further
   *>          Details).
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is DOUBLE PRECISION array, dimension (M)
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>          = 0: successful exit
   *>          < 0: if INFO = -i, the i-th argument had an illegal value
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup doubleGEcomputational
   *
   *> \par Further Details:
   *  =====================
   *>
   *> \verbatim
   *>
   *>  The matrix Q is represented as a product of elementary reflectors
   *>
   *>     Q = H(1) H(2) . . . H(k), where k = min(m,n).
   *>
   *>  Each H(i) has the form
   *>
   *>     H(i) = I - tau * v * v**T
   *>
   *>  where tau is a real scalar, and v is a real vector with
   *>  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
   *>  A(m-k+i,1:n-k+i-1), and tau in TAU(i).
   *> \endverbatim
   *>
   *  =====================================================================
       SUBROUTINE DGERQ2( M, N, A, LDA, TAU, WORK, INFO )        SUBROUTINE DGERQ2( M, N, A, LDA, TAU, WORK, INFO )
 *  *
 *  -- LAPACK routine (version 3.3.1) --  *  -- LAPACK computational routine (version 3.4.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *  -- April 2011                                                      --  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, M, N        INTEGER            INFO, LDA, M, N
Line 12 Line 135
       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )        DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DGERQ2 computes an RQ factorization of a real m by n matrix A:  
 *  A = R * Q.  
 *  
 *  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.  
 *  
 *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)  
 *          On entry, the m by n matrix A.  
 *          On exit, if m <= n, the upper triangle of the subarray  
 *          A(1:m,n-m+1:n) contains the m by m upper triangular matrix R;  
 *          if m >= n, the elements on and above the (m-n)-th subdiagonal  
 *          contain the m by n upper trapezoidal matrix R; the remaining  
 *          elements, with the array TAU, represent the orthogonal matrix  
 *          Q as a product of elementary reflectors (see Further  
 *          Details).  
 *  
 *  LDA     (input) INTEGER  
 *          The leading dimension of the array A.  LDA >= max(1,M).  
 *  
 *  TAU     (output) DOUBLE PRECISION array, dimension (min(M,N))  
 *          The scalar factors of the elementary reflectors (see Further  
 *          Details).  
 *  
 *  WORK    (workspace) DOUBLE PRECISION array, dimension (M)  
 *  
 *  INFO    (output) INTEGER  
 *          = 0: successful exit  
 *          < 0: if INFO = -i, the i-th argument had an illegal value  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  The matrix Q is represented as a product of elementary reflectors  
 *  
 *     Q = H(1) H(2) . . . H(k), where k = min(m,n).  
 *  
 *  Each H(i) has the form  
 *  
 *     H(i) = I - tau * v * v**T  
 *  
 *  where tau is a real scalar, and v is a real vector with  
 *  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in  
 *  A(m-k+i,1:n-k+i-1), and tau in TAU(i).  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.9  
changed lines
  Added in v.1.10

CVSweb interface <joel.bertrand@systella.fr>