clarft.f

          SUBROUTINE CLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
    *
    *  -- LAPACK auxiliary 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
    *  =======
    *
    *  CLARFT 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
    *
    *  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)
    *          = '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
    *          = '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
    *  ===============
    *
    *  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 = (  1       )                 V = (  1 v1 v1 v1 v1 )
    *                   ( v1  1    )                     (     1 v2 v2 v2 )
    *                   ( v1 v2  1 )                     (        1 v3 v3 )
    *                   ( v1 v2 v3 )
    *                   ( v1 v2 v3 )
    *
    *  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':
    *
    *               V = ( v1 v2 v3 )                 V = ( v1 v1  1       )
    *                   ( v1 v2 v3 )                     ( v2 v2 v2  1    )
    *                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
    *                   (     1 v3 )
    *                   (        1 )
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          COMPLEX            ONE, ZERO
          PARAMETER          ( ONE = ( 1.0E+0, 0.0E+0 ),
         $                   ZERO = ( 0.0E+0, 0.0E+0 ) )
    *     ..
    *     .. Local Scalars ..
          INTEGER            I, J
          COMPLEX            VII
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           CGEMV, CLACGV, CTRMV
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. Executable Statements ..
    *
    *     Quick return if possible
    *
          IF( N.EQ.0 )
         $   RETURN
    *
          IF( LSAME( DIRECT, 'F' ) ) THEN
             DO 20 I = 1, K
                IF( TAU( I ).EQ.ZERO ) THEN
    *
    *              H(i)  =  I
    *
                   DO 10 J = 1, I
                      T( J, I ) = ZERO
       10          CONTINUE
                ELSE
    *
    *              general case
    *
                   VII = V( I, I )
                   V( I, I ) = ONE
                   IF( LSAME( STOREV, 'C' ) ) THEN
    *
    *                 T(1:i-1,i) := - tau(i) * V(i:n,1:i-1)' * V(i:n,i)
    *
                      CALL CGEMV( 'Conjugate transpose', N-I+1, I-1,
         $                        -TAU( I ), V( I, 1 ), LDV, V( I, I ), 1,
         $                        ZERO, T( 1, I ), 1 )
                   ELSE
    *
    *                 T(1:i-1,i) := - tau(i) * V(1:i-1,i:n) * V(i,i:n)'
    *
                      IF( I.LT.N )
         $               CALL CLACGV( N-I, V( I, I+1 ), LDV )
                      CALL CGEMV( 'No transpose', I-1, N-I+1, -TAU( I ),
         $                        V( 1, I ), LDV, V( I, I ), LDV, ZERO,
         $                        T( 1, I ), 1 )
                      IF( I.LT.N )
         $               CALL CLACGV( N-I, V( I, I+1 ), LDV )
                   END IF
                   V( I, I ) = VII
    *
    *              T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i)
    *
                   CALL CTRMV( 'Upper', 'No transpose', 'Non-unit', I-1, T,
         $                     LDT, T( 1, I ), 1 )
                   T( I, I ) = TAU( I )
                END IF
       20    CONTINUE
          ELSE
             DO 40 I = K, 1, -1
                IF( TAU( I ).EQ.ZERO ) THEN
    *
    *              H(i)  =  I
    *
                   DO 30 J = I, K
                      T( J, I ) = ZERO
       30          CONTINUE
                ELSE
    *
    *              general case
    *
                   IF( I.LT.K ) THEN
                      IF( LSAME( STOREV, 'C' ) ) THEN
                         VII = V( N-K+I, I )
                         V( N-K+I, I ) = ONE
    *
    *                    T(i+1:k,i) :=
    *                            - tau(i) * V(1:n-k+i,i+1:k)' * V(1:n-k+i,i)
    *
                         CALL CGEMV( 'Conjugate transpose', N-K+I, K-I,
         $                           -TAU( I ), V( 1, I+1 ), LDV, V( 1, I ),
         $                           1, ZERO, T( I+1, I ), 1 )
                         V( N-K+I, I ) = VII
                      ELSE
                         VII = V( I, N-K+I )
                         V( I, N-K+I ) = ONE
    *
    *                    T(i+1:k,i) :=
    *                            - tau(i) * V(i+1:k,1:n-k+i) * V(i,1:n-k+i)'
    *
                         CALL CLACGV( N-K+I-1, V( I, 1 ), LDV )
                         CALL CGEMV( 'No transpose', K-I, N-K+I, -TAU( I ),
         $                           V( I+1, 1 ), LDV, V( I, 1 ), LDV, ZERO,
         $                           T( I+1, I ), 1 )
                         CALL CLACGV( N-K+I-1, V( I, 1 ), LDV )
                         V( I, N-K+I ) = VII
                      END IF
    *
    *                 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
       40    CONTINUE
          END IF
          RETURN
    *
    *     End of CLARFT
    *
          END