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version 1.6, 2010/08/13 21:03:52 version 1.14, 2014/01/27 09:28:22
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   *> \brief \b DLARZB applies a block reflector or its transpose to a general matrix.
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DLARZB + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarzb.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarzb.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarzb.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
   *                          LDV, T, LDT, C, LDC, WORK, LDWORK )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          DIRECT, SIDE, STOREV, TRANS
   *       INTEGER            K, L, LDC, LDT, LDV, LDWORK, M, N
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   C( LDC, * ), T( LDT, * ), V( LDV, * ),
   *      $                   WORK( LDWORK, * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DLARZB applies a real block reflector H or its transpose H**T to
   *> a real distributed M-by-N  C from the left or the right.
   *>
   *> Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] SIDE
   *> \verbatim
   *>          SIDE is CHARACTER*1
   *>          = 'L': apply H or H**T from the Left
   *>          = 'R': apply H or H**T from the Right
   *> \endverbatim
   *>
   *> \param[in] TRANS
   *> \verbatim
   *>          TRANS is CHARACTER*1
   *>          = 'N': apply H (No transpose)
   *>          = 'C': apply H**T (Transpose)
   *> \endverbatim
   *>
   *> \param[in] DIRECT
   *> \verbatim
   *>          DIRECT is CHARACTER*1
   *>          Indicates how H is formed from a product of elementary
   *>          reflectors
   *>          = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet)
   *>          = 'B': H = H(k) . . . H(2) H(1) (Backward)
   *> \endverbatim
   *>
   *> \param[in] STOREV
   *> \verbatim
   *>          STOREV is CHARACTER*1
   *>          Indicates how the vectors which define the elementary
   *>          reflectors are stored:
   *>          = 'C': Columnwise                        (not supported yet)
   *>          = 'R': Rowwise
   *> \endverbatim
   *>
   *> \param[in] M
   *> \verbatim
   *>          M is INTEGER
   *>          The number of rows of the matrix C.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The number of columns of the matrix C.
   *> \endverbatim
   *>
   *> \param[in] K
   *> \verbatim
   *>          K is INTEGER
   *>          The order of the matrix T (= the number of elementary
   *>          reflectors whose product defines the block reflector).
   *> \endverbatim
   *>
   *> \param[in] L
   *> \verbatim
   *>          L is INTEGER
   *>          The number of columns of the matrix V containing the
   *>          meaningful part of the Householder reflectors.
   *>          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
   *> \endverbatim
   *>
   *> \param[in] V
   *> \verbatim
   *>          V is DOUBLE PRECISION array, dimension (LDV,NV).
   *>          If STOREV = 'C', NV = K; if STOREV = 'R', NV = L.
   *> \endverbatim
   *>
   *> \param[in] LDV
   *> \verbatim
   *>          LDV is INTEGER
   *>          The leading dimension of the array V.
   *>          If STOREV = 'C', LDV >= L; if STOREV = 'R', LDV >= K.
   *> \endverbatim
   *>
   *> \param[in] T
   *> \verbatim
   *>          T is DOUBLE PRECISION array, dimension (LDT,K)
   *>          The triangular K-by-K matrix T in the representation of the
   *>          block reflector.
   *> \endverbatim
   *>
   *> \param[in] LDT
   *> \verbatim
   *>          LDT is INTEGER
   *>          The leading dimension of the array T. LDT >= K.
   *> \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 H*C or H**T*C or C*H or C*H**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 (LDWORK,K)
   *> \endverbatim
   *>
   *> \param[in] LDWORK
   *> \verbatim
   *>          LDWORK is INTEGER
   *>          The leading dimension of the array WORK.
   *>          If SIDE = 'L', LDWORK >= max(1,N);
   *>          if SIDE = 'R', LDWORK >= max(1,M).
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date September 2012
   *
   *> \ingroup doubleOTHERcomputational
   *
   *> \par Contributors:
   *  ==================
   *>
   *>    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
   *
   *> \par Further Details:
   *  =====================
   *>
   *> \verbatim
   *> \endverbatim
   *>
   *  =====================================================================
       SUBROUTINE DLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,        SUBROUTINE DLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
      $                   LDV, T, LDT, C, LDC, WORK, LDWORK )       $                   LDV, T, LDT, C, LDC, WORK, LDWORK )
 *  *
 *  -- LAPACK routine (version 3.2) --  *  -- LAPACK computational routine (version 3.4.2) --
 *  -- 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  *     September 2012
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          DIRECT, SIDE, STOREV, TRANS        CHARACTER          DIRECT, SIDE, STOREV, TRANS
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      $                   WORK( LDWORK, * )       $                   WORK( LDWORK, * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DLARZB applies a real block reflector H or its transpose H**T to  
 *  a real distributed M-by-N  C from the left or the right.  
 *  
 *  Currently, only STOREV = 'R' and DIRECT = 'B' are supported.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  SIDE    (input) CHARACTER*1  
 *          = 'L': apply H or H' from the Left  
 *          = 'R': apply H or H' from the Right  
 *  
 *  TRANS   (input) CHARACTER*1  
 *          = 'N': apply H (No transpose)  
 *          = 'C': apply H' (Transpose)  
 *  
 *  DIRECT  (input) CHARACTER*1  
 *          Indicates how H is formed from a product of elementary  
 *          reflectors  
 *          = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet)  
 *          = 'B': H = H(k) . . . H(2) H(1) (Backward)  
 *  
 *  STOREV  (input) CHARACTER*1  
 *          Indicates how the vectors which define the elementary  
 *          reflectors are stored:  
 *          = 'C': Columnwise                        (not supported yet)  
 *          = 'R': Rowwise  
 *  
 *  M       (input) INTEGER  
 *          The number of rows of the matrix C.  
 *  
 *  N       (input) INTEGER  
 *          The number of columns of the matrix C.  
 *  
 *  K       (input) INTEGER  
 *          The order of the matrix T (= the number of elementary  
 *          reflectors whose product defines the block reflector).  
 *  
 *  L       (input) INTEGER  
 *          The number of columns of the matrix V containing the  
 *          meaningful part of the Householder reflectors.  
 *          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.  
 *  
 *  V       (input) DOUBLE PRECISION array, dimension (LDV,NV).  
 *          If STOREV = 'C', NV = K; if STOREV = 'R', NV = L.  
 *  
 *  LDV     (input) INTEGER  
 *          The leading dimension of the array V.  
 *          If STOREV = 'C', LDV >= L; if STOREV = 'R', LDV >= K.  
 *  
 *  T       (input) DOUBLE PRECISION array, dimension (LDT,K)  
 *          The triangular K-by-K matrix T in the representation of the  
 *          block reflector.  
 *  
 *  LDT     (input) INTEGER  
 *          The leading dimension of the array T. LDT >= K.  
 *  
 *  C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)  
 *          On entry, the M-by-N matrix C.  
 *          On exit, C is overwritten by H*C or H'*C or C*H or C*H'.  
 *  
 *  LDC     (input) INTEGER  
 *          The leading dimension of the array C. LDC >= max(1,M).  
 *  
 *  WORK    (workspace) DOUBLE PRECISION array, dimension (LDWORK,K)  
 *  
 *  LDWORK  (input) INTEGER  
 *          The leading dimension of the array WORK.  
 *          If SIDE = 'L', LDWORK >= max(1,N);  
 *          if SIDE = 'R', LDWORK >= max(1,M).  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  Based on contributions by  
 *    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
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 *  *
       IF( LSAME( SIDE, 'L' ) ) THEN        IF( LSAME( SIDE, 'L' ) ) THEN
 *  *
 *        Form  H * C  or  H' * C  *        Form  H * C  or  H**T * C
 *  *
 *        W( 1:n, 1:k ) = C( 1:k, 1:n )'  *        W( 1:n, 1:k ) = C( 1:k, 1:n )**T
 *  *
          DO 10 J = 1, K           DO 10 J = 1, K
             CALL DCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 )              CALL DCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 )
    10    CONTINUE     10    CONTINUE
 *  *
 *        W( 1:n, 1:k ) = W( 1:n, 1:k ) + ...  *        W( 1:n, 1:k ) = W( 1:n, 1:k ) + ...
 *                        C( m-l+1:m, 1:n )' * V( 1:k, 1:l )'  *                        C( m-l+1:m, 1:n )**T * V( 1:k, 1:l )**T
 *  *
          IF( L.GT.0 )           IF( L.GT.0 )
      $      CALL DGEMM( 'Transpose', 'Transpose', N, K, L, ONE,       $      CALL DGEMM( 'Transpose', 'Transpose', N, K, L, ONE,
      $                  C( M-L+1, 1 ), LDC, V, LDV, ONE, WORK, LDWORK )       $                  C( M-L+1, 1 ), LDC, V, LDV, ONE, WORK, LDWORK )
 *  *
 *        W( 1:n, 1:k ) = W( 1:n, 1:k ) * T'  or  W( 1:m, 1:k ) * T  *        W( 1:n, 1:k ) = W( 1:n, 1:k ) * T**T  or  W( 1:m, 1:k ) * T
 *  *
          CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, ONE, T,           CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, ONE, T,
      $               LDT, WORK, LDWORK )       $               LDT, WORK, LDWORK )
 *  *
 *        C( 1:k, 1:n ) = C( 1:k, 1:n ) - W( 1:n, 1:k )'  *        C( 1:k, 1:n ) = C( 1:k, 1:n ) - W( 1:n, 1:k )**T
 *  *
          DO 30 J = 1, N           DO 30 J = 1, N
             DO 20 I = 1, K              DO 20 I = 1, K
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    30    CONTINUE     30    CONTINUE
 *  *
 *        C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...  *        C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
 *                            V( 1:k, 1:l )' * W( 1:n, 1:k )'  *                            V( 1:k, 1:l )**T * W( 1:n, 1:k )**T
 *  *
          IF( L.GT.0 )           IF( L.GT.0 )
      $      CALL DGEMM( 'Transpose', 'Transpose', L, N, K, -ONE, V, LDV,       $      CALL DGEMM( 'Transpose', 'Transpose', L, N, K, -ONE, V, LDV,
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 *  *
       ELSE IF( LSAME( SIDE, 'R' ) ) THEN        ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *  *
 *        Form  C * H  or  C * H'  *        Form  C * H  or  C * H**T
 *  *
 *        W( 1:m, 1:k ) = C( 1:m, 1:k )  *        W( 1:m, 1:k ) = C( 1:m, 1:k )
 *  *
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    40    CONTINUE     40    CONTINUE
 *  *
 *        W( 1:m, 1:k ) = W( 1:m, 1:k ) + ...  *        W( 1:m, 1:k ) = W( 1:m, 1:k ) + ...
 *                        C( 1:m, n-l+1:n ) * V( 1:k, 1:l )'  *                        C( 1:m, n-l+1:n ) * V( 1:k, 1:l )**T
 *  *
          IF( L.GT.0 )           IF( L.GT.0 )
      $      CALL DGEMM( 'No transpose', 'Transpose', M, K, L, ONE,       $      CALL DGEMM( 'No transpose', 'Transpose', M, K, L, ONE,
      $                  C( 1, N-L+1 ), LDC, V, LDV, ONE, WORK, LDWORK )       $                  C( 1, N-L+1 ), LDC, V, LDV, ONE, WORK, LDWORK )
 *  *
 *        W( 1:m, 1:k ) = W( 1:m, 1:k ) * T  or  W( 1:m, 1:k ) * T'  *        W( 1:m, 1:k ) = W( 1:m, 1:k ) * T  or  W( 1:m, 1:k ) * T**T
 *  *
          CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, ONE, T,           CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, ONE, T,
      $               LDT, WORK, LDWORK )       $               LDT, WORK, LDWORK )
Removed from v.1.6  
changed lines
  Added in v.1.14

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