      SUBROUTINE DLARZT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
*
*  -- LAPACK routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     June 30, 1999
*
*     .. Scalar Arguments ..
      CHARACTER          DIRECT, STOREV
      INTEGER            K, LDT, LDV, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   T( LDT, * ), TAU( * ), V( LDV, * )
*     ..
*
*  Purpose
*  =======
*
*  DLARZT forms the triangular factor T of a real 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (K)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i).
*
*  T       (output) DOUBLE PRECISION 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 ..
      DOUBLE PRECISION   ZERO
      PARAMETER          ( ZERO = 0.0D+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, INFO, J
*     ..
*     .. External Subroutines ..
      EXTERNAL           DGEMV, DTRMV, 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( 'DLARZT', -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 DGEMV( 'No transpose', K-I, N, -TAU( I ),
     $                     V( I+1, 1 ), LDV, V( I, 1 ), LDV, ZERO,
     $                     T( I+1, I ), 1 )
*
*              T(i+1:k,i) = T(i+1:k,i+1:k) * T(i+1:k,i)
*
               CALL DTRMV( '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 DLARZT
*
      END
