clarzt.f

          SUBROUTINE CLARZT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          DIRECT, STOREV
          INTEGER            K, LDT, LDV, N
    *     ..
    *     .. Array Arguments ..
          COMPLEX            T( LDT, * ), TAU( * ), V( LDV, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CLARZT forms the triangular factor T of a complex block reflector
    *  H of order > n, which is defined as a product of k elementary
    *  reflectors.
    *
    *  If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;
    *
    *  If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.
    *
    *  If STOREV = 'C', the vector which defines the elementary reflector
    *  H(i) is stored in the i-th column of the array V, and
    *
    *     H  =  I - V * T * V'
    *
    *  If STOREV = 'R', the vector which defines the elementary reflector
    *  H(i) is stored in the i-th row of the array V, and
    *
    *     H  =  I - V' * T * V
    *
    *  Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
    *
    *  Arguments
    *  =========
    *
    *  DIRECT  (input) CHARACTER*1
    *          Specifies the order in which the elementary reflectors are
    *          multiplied to form the block reflector:
    *          = '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
    *          Specifies how the vectors which define the elementary
    *          reflectors are stored (see also Further Details):
    *          = 'C': columnwise                        (not supported yet)
    *          = 'R': rowwise
    *
    *  N       (input) INTEGER
    *          The order of the block reflector H. N >= 0.
    *
    *  K       (input) INTEGER
    *          The order of the triangular factor T (= the number of
    *          elementary reflectors). K >= 1.
    *
    *  V       (input/output) COMPLEX array, dimension
    *                               (LDV,K) if STOREV = 'C'
    *                               (LDV,N) if STOREV = 'R'
    *          The matrix V. See further details.
    *
    *  LDV     (input) INTEGER
    *          The leading dimension of the array V.
    *          If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.
    *
    *  TAU     (input) COMPLEX array, dimension (K)
    *          TAU(i) must contain the scalar factor of the elementary
    *          reflector H(i).
    *
    *  T       (output) COMPLEX array, dimension (LDT,K)
    *          The k by k triangular factor T of the block reflector.
    *          If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is
    *          lower triangular. The rest of the array is not used.
    *
    *  LDT     (input) INTEGER
    *          The leading dimension of the array T. LDT >= K.
    *
    *  Further Details
    *  ===============
    *
    *  Based on contributions by
    *    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
    *
    *  The shape of the matrix V and the storage of the vectors which define
    *  the H(i) is best illustrated by the following example with n = 5 and
    *  k = 3. The elements equal to 1 are not stored; the corresponding
    *  array elements are modified but restored on exit. The rest of the
    *  array is not used.
    *
    *  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':
    *
    *                                              ______V_____
    *         ( v1 v2 v3 )                        /            \
    *         ( v1 v2 v3 )                      ( v1 v1 v1 v1 v1 . . . . 1 )
    *     V = ( v1 v2 v3 )                      ( v2 v2 v2 v2 v2 . . . 1   )
    *         ( v1 v2 v3 )                      ( v3 v3 v3 v3 v3 . . 1     )
    *         ( v1 v2 v3 )
    *            .  .  .
    *            .  .  .
    *            1  .  .
    *               1  .
    *                  1
    *
    *  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':
    *
    *                                                        ______V_____
    *            1                                          /            \
    *            .  1                           ( 1 . . . . v1 v1 v1 v1 v1 )
    *            .  .  1                        ( . 1 . . . v2 v2 v2 v2 v2 )
    *            .  .  .                        ( . . 1 . . v3 v3 v3 v3 v3 )
    *            .  .  .
    *         ( v1 v2 v3 )
    *         ( v1 v2 v3 )
    *     V = ( v1 v2 v3 )
    *         ( v1 v2 v3 )
    *         ( v1 v2 v3 )
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          COMPLEX            ZERO
          PARAMETER          ( ZERO = ( 0.0E+0, 0.0E+0 ) )
    *     ..
    *     .. Local Scalars ..
          INTEGER            I, INFO, J
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           CGEMV, CLACGV, CTRMV, XERBLA
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. Executable Statements ..
    *
    *     Check for currently supported options
    *
          INFO = 0
          IF( .NOT.LSAME( DIRECT, 'B' ) ) THEN
             INFO = -1
          ELSE IF( .NOT.LSAME( STOREV, 'R' ) ) THEN
             INFO = -2
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'CLARZT', -INFO )
             RETURN
          END IF
    *
          DO 20 I = K, 1, -1
             IF( TAU( I ).EQ.ZERO ) THEN
    *
    *           H(i)  =  I
    *
                DO 10 J = I, K
                   T( J, I ) = ZERO
       10       CONTINUE
             ELSE
    *
    *           general case
    *
                IF( I.LT.K ) THEN
    *
    *              T(i+1:k,i) = - tau(i) * V(i+1:k,1:n) * V(i,1:n)'
    *
                   CALL CLACGV( N, V( I, 1 ), LDV )
                   CALL CGEMV( 'No transpose', K-I, N, -TAU( I ),
         $                     V( I+1, 1 ), LDV, V( I, 1 ), LDV, ZERO,
         $                     T( I+1, I ), 1 )
                   CALL CLACGV( N, V( I, 1 ), LDV )
    *
    *              T(i+1:k,i) = T(i+1:k,i+1:k) * T(i+1:k,i)
    *
                   CALL CTRMV( 'Lower', 'No transpose', 'Non-unit', K-I,
         $                     T( I+1, I+1 ), LDT, T( I+1, I ), 1 )
                END IF
                T( I, I ) = TAU( I )
             END IF
       20 CONTINUE
          RETURN
    *
    *     End of CLARZT
    *
          END