zlarzb.f

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*> \brief \b ZLARZB applies a block reflector or its conjugate-transpose to a general matrix.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
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*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE ZLARZB( 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 ..
*       COMPLEX*16         C( LDC, * ), T( LDT, * ), V( LDV, * ),
*      $                   WORK( LDWORK, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZLARZB applies a complex block reflector H or its transpose H**H
*> to a complex 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**H from the Left
*>          = 'R': apply H or H**H from the Right
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*>          TRANS is CHARACTER*1
*>          = 'N': apply H (No transpose)
*>          = 'C': apply H**H (Conjugate 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 array, dimension (LDC,N)
*>          On entry, the M-by-N matrix C.
*>          On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H.
*> \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 COMPLEX*16 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 December 2016
*
*> \ingroup complex16OTHERcomputational
*
*> \par Contributors:
*  ==================
*>
*>    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
*
*> \par Further Details:
*  =====================
*>
*> \verbatim
*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE zlarzb( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
     $                   LDV, T, LDT, C, LDC, WORK, LDWORK )
*
*  -- LAPACK computational routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      CHARACTER          DIRECT, SIDE, STOREV, TRANS
      INTEGER            K, L, LDC, LDT, LDV, LDWORK, M, N
*     ..
*     .. Array Arguments ..
      COMPLEX*16         C( ldc, * ), T( ldt, * ), V( ldv, * ),
     $                   work( ldwork, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX*16         ONE
      parameter( one = ( 1.0d+0, 0.0d+0 ) )
*     ..
*     .. Local Scalars ..
      CHARACTER          TRANST
      INTEGER            I, INFO, J
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla, zcopy, zgemm, zlacgv, ztrmm
*     ..
*     .. Executable Statements ..
*
*     Quick return if possible
*
      IF( m.LE.0 .OR. n.LE.0 )
     $   RETURN
*
*     Check for currently supported options
*
      info = 0
      IF( .NOT.lsame( direct, 'B' ) ) THEN
         info = -3
      ELSE IF( .NOT.lsame( storev, 'R' ) ) THEN
         info = -4
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'ZLARZB', -info )
         RETURN
      END IF
*
      IF( lsame( trans, 'N' ) ) THEN
         transt = 'C'
      ELSE
         transt = 'N'
      END IF
*
      IF( lsame( side, 'L' ) ) THEN
*
*        Form  H * C  or  H**H * C
*
*        W( 1:n, 1:k ) = C( 1:k, 1:n )**H
*
         DO 10 j = 1, k
            CALL zcopy( n, c( j, 1 ), ldc, work( 1, j ), 1 )
   10    CONTINUE
*
*        W( 1:n, 1:k ) = W( 1:n, 1:k ) + ...
*                        C( m-l+1:m, 1:n )**H * V( 1:k, 1:l )**T
*
         IF( l.GT.0 )
     $      CALL zgemm( 'Transpose', 'Conjugate transpose', n, k, l,
     $                  one, c( m-l+1, 1 ), ldc, v, ldv, one, work,
     $                  ldwork )
*
*        W( 1:n, 1:k ) = W( 1:n, 1:k ) * T**T  or  W( 1:m, 1:k ) * T
*
         CALL ztrmm( 'Right', 'Lower', transt, 'Non-unit', n, k, one, t,
     $               ldt, work, ldwork )
*
*        C( 1:k, 1:n ) = C( 1:k, 1:n ) - W( 1:n, 1:k )**H
*
         DO 30 j = 1, n
            DO 20 i = 1, k
               c( i, j ) = c( i, j ) - work( j, i )
   20       CONTINUE
   30    CONTINUE
*
*        C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
*                            V( 1:k, 1:l )**H * W( 1:n, 1:k )**H
*
         IF( l.GT.0 )
     $      CALL zgemm( 'Transpose', 'Transpose', l, n, k, -one, v, ldv,
     $                  work, ldwork, one, c( m-l+1, 1 ), ldc )
*
      ELSE IF( lsame( side, 'R' ) ) THEN
*
*        Form  C * H  or  C * H**H
*
*        W( 1:m, 1:k ) = C( 1:m, 1:k )
*
         DO 40 j = 1, k
            CALL zcopy( m, c( 1, j ), 1, work( 1, j ), 1 )
   40    CONTINUE
*
*        W( 1:m, 1:k ) = W( 1:m, 1:k ) + ...
*                        C( 1:m, n-l+1:n ) * V( 1:k, 1:l )**H
*
         IF( l.GT.0 )
     $      CALL zgemm( 'No transpose', 'Transpose', m, k, l, one,
     $                  c( 1, n-l+1 ), ldc, v, ldv, one, work, ldwork )
*
*        W( 1:m, 1:k ) = W( 1:m, 1:k ) * conjg( T )  or
*                        W( 1:m, 1:k ) * T**H
*
         DO 50 j = 1, k
            CALL zlacgv( k-j+1, t( j, j ), 1 )
   50    CONTINUE
         CALL ztrmm( 'Right', 'Lower', trans, 'Non-unit', m, k, one, t,
     $               ldt, work, ldwork )
         DO 60 j = 1, k
            CALL zlacgv( k-j+1, t( j, j ), 1 )
   60    CONTINUE
*
*        C( 1:m, 1:k ) = C( 1:m, 1:k ) - W( 1:m, 1:k )
*
         DO 80 j = 1, k
            DO 70 i = 1, m
               c( i, j ) = c( i, j ) - work( i, j )
   70       CONTINUE
   80    CONTINUE
*
*        C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
*                            W( 1:m, 1:k ) * conjg( V( 1:k, 1:l ) )
*
         DO 90 j = 1, l
            CALL zlacgv( k, v( 1, j ), 1 )
   90    CONTINUE
         IF( l.GT.0 )
     $      CALL zgemm( 'No transpose', 'No transpose', m, l, k, -one,
     $                  work, ldwork, v, ldv, one, c( 1, n-l+1 ), ldc )
         DO 100 j = 1, l
            CALL zlacgv( k, v( 1, j ), 1 )
  100    CONTINUE
*
      END IF
*
      RETURN
*
*     End of ZLARZB
*
      END