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version 1.7, 2010/12/21 13:53:35 version 1.8, 2011/11/21 20:43:00
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   *> \brief \b DORMBR
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DORMBR + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dormbr.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dormbr.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dormbr.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
   *                          LDC, WORK, LWORK, INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          SIDE, TRANS, VECT
   *       INTEGER            INFO, K, LDA, LDC, LWORK, M, N
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> If VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C
   *> with
   *>                 SIDE = 'L'     SIDE = 'R'
   *> TRANS = 'N':      Q * C          C * Q
   *> TRANS = 'T':      Q**T * C       C * Q**T
   *>
   *> If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C
   *> with
   *>                 SIDE = 'L'     SIDE = 'R'
   *> TRANS = 'N':      P * C          C * P
   *> TRANS = 'T':      P**T * C       C * P**T
   *>
   *> Here Q and P**T are the orthogonal matrices determined by DGEBRD when
   *> reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and
   *> P**T are defined as products of elementary reflectors H(i) and G(i)
   *> respectively.
   *>
   *> Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
   *> order of the orthogonal matrix Q or P**T that is applied.
   *>
   *> If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
   *> if nq >= k, Q = H(1) H(2) . . . H(k);
   *> if nq < k, Q = H(1) H(2) . . . H(nq-1).
   *>
   *> If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
   *> if k < nq, P = G(1) G(2) . . . G(k);
   *> if k >= nq, P = G(1) G(2) . . . G(nq-1).
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] VECT
   *> \verbatim
   *>          VECT is CHARACTER*1
   *>          = 'Q': apply Q or Q**T;
   *>          = 'P': apply P or P**T.
   *> \endverbatim
   *>
   *> \param[in] SIDE
   *> \verbatim
   *>          SIDE is CHARACTER*1
   *>          = 'L': apply Q, Q**T, P or P**T from the Left;
   *>          = 'R': apply Q, Q**T, P or P**T from the Right.
   *> \endverbatim
   *>
   *> \param[in] TRANS
   *> \verbatim
   *>          TRANS is CHARACTER*1
   *>          = 'N':  No transpose, apply Q  or P;
   *>          = 'T':  Transpose, apply Q**T or P**T.
   *> \endverbatim
   *>
   *> \param[in] M
   *> \verbatim
   *>          M is INTEGER
   *>          The number of rows of the matrix C. M >= 0.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The number of columns of the matrix C. N >= 0.
   *> \endverbatim
   *>
   *> \param[in] K
   *> \verbatim
   *>          K is INTEGER
   *>          If VECT = 'Q', the number of columns in the original
   *>          matrix reduced by DGEBRD.
   *>          If VECT = 'P', the number of rows in the original
   *>          matrix reduced by DGEBRD.
   *>          K >= 0.
   *> \endverbatim
   *>
   *> \param[in] A
   *> \verbatim
   *>          A is DOUBLE PRECISION array, dimension
   *>                                (LDA,min(nq,K)) if VECT = 'Q'
   *>                                (LDA,nq)        if VECT = 'P'
   *>          The vectors which define the elementary reflectors H(i) and
   *>          G(i), whose products determine the matrices Q and P, as
   *>          returned by DGEBRD.
   *> \endverbatim
   *>
   *> \param[in] LDA
   *> \verbatim
   *>          LDA is INTEGER
   *>          The leading dimension of the array A.
   *>          If VECT = 'Q', LDA >= max(1,nq);
   *>          if VECT = 'P', LDA >= max(1,min(nq,K)).
   *> \endverbatim
   *>
   *> \param[in] TAU
   *> \verbatim
   *>          TAU is DOUBLE PRECISION array, dimension (min(nq,K))
   *>          TAU(i) must contain the scalar factor of the elementary
   *>          reflector H(i) or G(i) which determines Q or P, as returned
   *>          by DGEBRD in the array argument TAUQ or TAUP.
   *> \endverbatim
   *>
   *> \param[in,out] C
   *> \verbatim
   *>          C is DOUBLE PRECISION array, dimension (LDC,N)
   *>          On entry, the M-by-N matrix C.
   *>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q
   *>          or P*C or P**T*C or C*P or C*P**T.
   *> \endverbatim
   *>
   *> \param[in] LDC
   *> \verbatim
   *>          LDC is INTEGER
   *>          The leading dimension of the array C. LDC >= max(1,M).
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
   *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
   *> \endverbatim
   *>
   *> \param[in] LWORK
   *> \verbatim
   *>          LWORK is INTEGER
   *>          The dimension of the array WORK.
   *>          If SIDE = 'L', LWORK >= max(1,N);
   *>          if SIDE = 'R', LWORK >= max(1,M).
   *>          For optimum performance LWORK >= N*NB if SIDE = 'L', and
   *>          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
   *>          blocksize.
   *>
   *>          If LWORK = -1, then a workspace query is assumed; the routine
   *>          only calculates the optimal size of the WORK array, returns
   *>          this value as the first entry of the WORK array, and no error
   *>          message related to LWORK is issued by XERBLA.
   *> \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 doubleOTHERcomputational
   *
   *  =====================================================================
       SUBROUTINE DORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,        SUBROUTINE DORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
      $                   LDC, WORK, LWORK, INFO )       $                   LDC, WORK, LWORK, INFO )
 *  *
 *  -- LAPACK routine (version 3.2) --  *  -- 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..--
 *     November 2006  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          SIDE, TRANS, VECT        CHARACTER          SIDE, TRANS, VECT
Line 14 Line 208
       DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )        DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  If VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C  
 *  with  
 *                  SIDE = 'L'     SIDE = 'R'  
 *  TRANS = 'N':      Q * C          C * Q  
 *  TRANS = 'T':      Q**T * C       C * Q**T  
 *  
 *  If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C  
 *  with  
 *                  SIDE = 'L'     SIDE = 'R'  
 *  TRANS = 'N':      P * C          C * P  
 *  TRANS = 'T':      P**T * C       C * P**T  
 *  
 *  Here Q and P**T are the orthogonal matrices determined by DGEBRD when  
 *  reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and  
 *  P**T are defined as products of elementary reflectors H(i) and G(i)  
 *  respectively.  
 *  
 *  Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the  
 *  order of the orthogonal matrix Q or P**T that is applied.  
 *  
 *  If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:  
 *  if nq >= k, Q = H(1) H(2) . . . H(k);  
 *  if nq < k, Q = H(1) H(2) . . . H(nq-1).  
 *  
 *  If VECT = 'P', A is assumed to have been a K-by-NQ matrix:  
 *  if k < nq, P = G(1) G(2) . . . G(k);  
 *  if k >= nq, P = G(1) G(2) . . . G(nq-1).  
 *  
 *  Arguments  
 *  =========  
 *  
 *  VECT    (input) CHARACTER*1  
 *          = 'Q': apply Q or Q**T;  
 *          = 'P': apply P or P**T.  
 *  
 *  SIDE    (input) CHARACTER*1  
 *          = 'L': apply Q, Q**T, P or P**T from the Left;  
 *          = 'R': apply Q, Q**T, P or P**T from the Right.  
 *  
 *  TRANS   (input) CHARACTER*1  
 *          = 'N':  No transpose, apply Q  or P;  
 *          = 'T':  Transpose, apply Q**T or P**T.  
 *  
 *  M       (input) INTEGER  
 *          The number of rows of the matrix C. M >= 0.  
 *  
 *  N       (input) INTEGER  
 *          The number of columns of the matrix C. N >= 0.  
 *  
 *  K       (input) INTEGER  
 *          If VECT = 'Q', the number of columns in the original  
 *          matrix reduced by DGEBRD.  
 *          If VECT = 'P', the number of rows in the original  
 *          matrix reduced by DGEBRD.  
 *          K >= 0.  
 *  
 *  A       (input) DOUBLE PRECISION array, dimension  
 *                                (LDA,min(nq,K)) if VECT = 'Q'  
 *                                (LDA,nq)        if VECT = 'P'  
 *          The vectors which define the elementary reflectors H(i) and  
 *          G(i), whose products determine the matrices Q and P, as  
 *          returned by DGEBRD.  
 *  
 *  LDA     (input) INTEGER  
 *          The leading dimension of the array A.  
 *          If VECT = 'Q', LDA >= max(1,nq);  
 *          if VECT = 'P', LDA >= max(1,min(nq,K)).  
 *  
 *  TAU     (input) DOUBLE PRECISION array, dimension (min(nq,K))  
 *          TAU(i) must contain the scalar factor of the elementary  
 *          reflector H(i) or G(i) which determines Q or P, as returned  
 *          by DGEBRD in the array argument TAUQ or TAUP.  
 *  
 *  C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)  
 *          On entry, the M-by-N matrix C.  
 *          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q  
 *          or P*C or P**T*C or C*P or C*P**T.  
 *  
 *  LDC     (input) INTEGER  
 *          The leading dimension of the array C. LDC >= max(1,M).  
 *  
 *  WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))  
 *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.  
 *  
 *  LWORK   (input) INTEGER  
 *          The dimension of the array WORK.  
 *          If SIDE = 'L', LWORK >= max(1,N);  
 *          if SIDE = 'R', LWORK >= max(1,M).  
 *          For optimum performance LWORK >= N*NB if SIDE = 'L', and  
 *          LWORK >= M*NB if SIDE = 'R', where NB is the optimal  
 *          blocksize.  
 *  
 *          If LWORK = -1, then a workspace query is assumed; the routine  
 *          only calculates the optimal size of the WORK array, returns  
 *          this value as the first entry of the WORK array, and no error  
 *          message related to LWORK is issued by XERBLA.  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:  successful exit  
 *          < 0:  if INFO = -i, the i-th argument had an illegal value  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Local Scalars ..  *     .. Local Scalars ..
Removed from v.1.7  
changed lines
  Added in v.1.8

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