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version 1.7, 2010/12/21 13:53:34 version 1.9, 2011/11/21 20:43:00
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   *> \brief \b DORGBR
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DORGBR + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorgbr.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorgbr.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorgbr.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          VECT
   *       INTEGER            INFO, K, LDA, LWORK, M, N
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DORGBR generates one of the real orthogonal matrices Q or P**T
   *> 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) or G(i) respectively.
   *>
   *> If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
   *> is of order M:
   *> if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n
   *> columns of Q, where m >= n >= k;
   *> if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an
   *> M-by-M matrix.
   *>
   *> If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T
   *> is of order N:
   *> if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m
   *> rows of P**T, where n >= m >= k;
   *> if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as
   *> an N-by-N matrix.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] VECT
   *> \verbatim
   *>          VECT is CHARACTER*1
   *>          Specifies whether the matrix Q or the matrix P**T is
   *>          required, as defined in the transformation applied by DGEBRD:
   *>          = 'Q':  generate Q;
   *>          = 'P':  generate P**T.
   *> \endverbatim
   *>
   *> \param[in] M
   *> \verbatim
   *>          M is INTEGER
   *>          The number of rows of the matrix Q or P**T to be returned.
   *>          M >= 0.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The number of columns of the matrix Q or P**T to be returned.
   *>          N >= 0.
   *>          If VECT = 'Q', M >= N >= min(M,K);
   *>          if VECT = 'P', N >= M >= min(N,K).
   *> \endverbatim
   *>
   *> \param[in] K
   *> \verbatim
   *>          K is INTEGER
   *>          If VECT = 'Q', the number of columns in the original M-by-K
   *>          matrix reduced by DGEBRD.
   *>          If VECT = 'P', the number of rows in the original K-by-N
   *>          matrix reduced by DGEBRD.
   *>          K >= 0.
   *> \endverbatim
   *>
   *> \param[in,out] A
   *> \verbatim
   *>          A is DOUBLE PRECISION array, dimension (LDA,N)
   *>          On entry, the vectors which define the elementary reflectors,
   *>          as returned by DGEBRD.
   *>          On exit, the M-by-N matrix Q or P**T.
   *> \endverbatim
   *>
   *> \param[in] LDA
   *> \verbatim
   *>          LDA is INTEGER
   *>          The leading dimension of the array A. LDA >= max(1,M).
   *> \endverbatim
   *>
   *> \param[in] TAU
   *> \verbatim
   *>          TAU is DOUBLE PRECISION array, dimension
   *>                                (min(M,K)) if VECT = 'Q'
   *>                                (min(N,K)) if VECT = 'P'
   *>          TAU(i) must contain the scalar factor of the elementary
   *>          reflector H(i) or G(i), which determines Q or P**T, as
   *>          returned by DGEBRD in its array argument TAUQ or TAUP.
   *> \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. LWORK >= max(1,min(M,N)).
   *>          For optimum performance LWORK >= min(M,N)*NB, 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 doubleGBcomputational
   *
   *  =====================================================================
       SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )        SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, 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          VECT        CHARACTER          VECT
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       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )        DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DORGBR generates one of the real orthogonal matrices Q or P**T  
 *  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) or G(i) respectively.  
 *  
 *  If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q  
 *  is of order M:  
 *  if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n  
 *  columns of Q, where m >= n >= k;  
 *  if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an  
 *  M-by-M matrix.  
 *  
 *  If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T  
 *  is of order N:  
 *  if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m  
 *  rows of P**T, where n >= m >= k;  
 *  if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as  
 *  an N-by-N matrix.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  VECT    (input) CHARACTER*1  
 *          Specifies whether the matrix Q or the matrix P**T is  
 *          required, as defined in the transformation applied by DGEBRD:  
 *          = 'Q':  generate Q;  
 *          = 'P':  generate P**T.  
 *  
 *  M       (input) INTEGER  
 *          The number of rows of the matrix Q or P**T to be returned.  
 *          M >= 0.  
 *  
 *  N       (input) INTEGER  
 *          The number of columns of the matrix Q or P**T to be returned.  
 *          N >= 0.  
 *          If VECT = 'Q', M >= N >= min(M,K);  
 *          if VECT = 'P', N >= M >= min(N,K).  
 *  
 *  K       (input) INTEGER  
 *          If VECT = 'Q', the number of columns in the original M-by-K  
 *          matrix reduced by DGEBRD.  
 *          If VECT = 'P', the number of rows in the original K-by-N  
 *          matrix reduced by DGEBRD.  
 *          K >= 0.  
 *  
 *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)  
 *          On entry, the vectors which define the elementary reflectors,  
 *          as returned by DGEBRD.  
 *          On exit, the M-by-N matrix Q or P**T.  
 *  
 *  LDA     (input) INTEGER  
 *          The leading dimension of the array A. LDA >= max(1,M).  
 *  
 *  TAU     (input) DOUBLE PRECISION array, dimension  
 *                                (min(M,K)) if VECT = 'Q'  
 *                                (min(N,K)) if VECT = 'P'  
 *          TAU(i) must contain the scalar factor of the elementary  
 *          reflector H(i) or G(i), which determines Q or P**T, as  
 *          returned by DGEBRD in its array argument TAUQ or TAUP.  
 *  
 *  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. LWORK >= max(1,min(M,N)).  
 *          For optimum performance LWORK >= min(M,N)*NB, 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  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Line 139 Line 216
       END IF        END IF
 *  *
       IF( INFO.EQ.0 ) THEN        IF( INFO.EQ.0 ) THEN
            WORK( 1 ) = 1
          IF( WANTQ ) THEN           IF( WANTQ ) THEN
             NB = ILAENV( 1, 'DORGQR', ' ', M, N, K, -1 )              IF( M.GE.K ) THEN
                  CALL DORGQR( M, N, K, A, LDA, TAU, WORK, -1, IINFO )
               ELSE
                  IF( M.GT.1 ) THEN
                     CALL DORGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK,
        $                         -1, IINFO )
                  END IF
               END IF
          ELSE           ELSE
             NB = ILAENV( 1, 'DORGLQ', ' ', M, N, K, -1 )              IF( K.LT.N ) THEN
                  CALL DORGLQ( M, N, K, A, LDA, TAU, WORK, -1, IINFO )
               ELSE
                  IF( N.GT.1 ) THEN
                     CALL DORGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
        $                         -1, IINFO )
                  END IF
               END IF
          END IF           END IF
          LWKOPT = MAX( 1, MN )*NB           LWKOPT = WORK( 1 )
          WORK( 1 ) = LWKOPT  
       END IF        END IF
 *  *
       IF( INFO.NE.0 ) THEN        IF( INFO.NE.0 ) THEN
Line 201 Line 292
          END IF           END IF
       ELSE        ELSE
 *  *
 *        Form P', determined by a call to DGEBRD to reduce a k-by-n  *        Form P**T, determined by a call to DGEBRD to reduce a k-by-n
 *        matrix  *        matrix
 *  *
          IF( K.LT.N ) THEN           IF( K.LT.N ) THEN
Line 215 Line 306
 *           If k >= n, assume m = n  *           If k >= n, assume m = n
 *  *
 *           Shift the vectors which define the elementary reflectors one  *           Shift the vectors which define the elementary reflectors one
 *           row downward, and set the first row and column of P' to  *           row downward, and set the first row and column of P**T to
 *           those of the unit matrix  *           those of the unit matrix
 *  *
             A( 1, 1 ) = ONE              A( 1, 1 ) = ONE
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    60       CONTINUE     60       CONTINUE
             IF( N.GT.1 ) THEN              IF( N.GT.1 ) THEN
 *  *
 *              Form P'(2:n,2:n)  *              Form P**T(2:n,2:n)
 *  *
                CALL DORGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,                 CALL DORGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
      $                      LWORK, IINFO )       $                      LWORK, IINFO )
Removed from v.1.7  
changed lines
  Added in v.1.9

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