clarzb.f

          SUBROUTINE CLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
         $                   LDV, T, LDT, C, LDC, WORK, LDWORK )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          DIRECT, SIDE, STOREV, TRANS
          INTEGER            K, L, LDC, LDT, LDV, LDWORK, M, N
    *     ..
    *     .. Array Arguments ..
          COMPLEX            C( LDC, * ), T( LDT, * ), V( LDV, * ),
         $                   WORK( LDWORK, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CLARZB 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.
    *
    *  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' (Conjugate 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) COMPLEX 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) COMPLEX 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) COMPLEX 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) COMPLEX 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 ..
          COMPLEX            ONE
          PARAMETER          ( ONE = ( 1.0E+0, 0.0E+0 ) )
    *     ..
    *     .. Local Scalars ..
          CHARACTER          TRANST
          INTEGER            I, INFO, J
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           CCOPY, CGEMM, CLACGV, CTRMM, XERBLA
    *     ..
    *     .. 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( 'CLARZB', -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' * C
    *
    *        W( 1:n, 1:k ) = conjg( C( 1:k, 1:n )' )
    *
             DO 10 J = 1, K
                CALL CCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 )
       10    CONTINUE
    *
    *        W( 1:n, 1:k ) = W( 1:n, 1:k ) + ...
    *                        conjg( C( m-l+1:m, 1:n )' ) * V( 1:k, 1:l )'
    *
             IF( L.GT.0 )
         $      CALL CGEMM( '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'  or  W( 1:m, 1:k ) * T
    *
             CALL CTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, ONE, T,
         $               LDT, WORK, LDWORK )
    *
    *        C( 1:k, 1:n ) = C( 1:k, 1:n ) - conjg( W( 1:n, 1:k )' )
    *
             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 ) - ...
    *                    conjg( V( 1:k, 1:l )' ) * conjg( W( 1:n, 1:k )' )
    *
             IF( L.GT.0 )
         $      CALL CGEMM( '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'
    *
    *        W( 1:m, 1:k ) = C( 1:m, 1:k )
    *
             DO 40 J = 1, K
                CALL CCOPY( 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 ) * conjg( V( 1:k, 1:l )' )
    *
             IF( L.GT.0 )
         $      CALL CGEMM( '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 ) * conjg( T' )
    *
             DO 50 J = 1, K
                CALL CLACGV( K-J+1, T( J, J ), 1 )
       50    CONTINUE
             CALL CTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, ONE, T,
         $               LDT, WORK, LDWORK )
             DO 60 J = 1, K
                CALL CLACGV( 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 CLACGV( K, V( 1, J ), 1 )
       90    CONTINUE
             IF( L.GT.0 )
         $      CALL CGEMM( '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 CLACGV( K, V( 1, J ), 1 )
      100    CONTINUE
    *
          END IF
    *
          RETURN
    *
    *     End of CLARZB
    *
          END