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Mise à jour globale de Lapack 3.2.2.

    1:       SUBROUTINE DLARZT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
    2: *
    3: *  -- LAPACK routine (version 3.2) --
    4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    6: *     November 2006
    7: *
    8: *     .. Scalar Arguments ..
    9:       CHARACTER          DIRECT, STOREV
   10:       INTEGER            K, LDT, LDV, N
   11: *     ..
   12: *     .. Array Arguments ..
   13:       DOUBLE PRECISION   T( LDT, * ), TAU( * ), V( LDV, * )
   14: *     ..
   15: *
   16: *  Purpose
   17: *  =======
   18: *
   19: *  DLARZT forms the triangular factor T of a real block reflector
   20: *  H of order > n, which is defined as a product of k elementary
   21: *  reflectors.
   22: *
   23: *  If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;
   24: *
   25: *  If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.
   26: *
   27: *  If STOREV = 'C', the vector which defines the elementary reflector
   28: *  H(i) is stored in the i-th column of the array V, and
   29: *
   30: *     H  =  I - V * T * V'
   31: *
   32: *  If STOREV = 'R', the vector which defines the elementary reflector
   33: *  H(i) is stored in the i-th row of the array V, and
   34: *
   35: *     H  =  I - V' * T * V
   36: *
   37: *  Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
   38: *
   39: *  Arguments
   40: *  =========
   41: *
   42: *  DIRECT  (input) CHARACTER*1
   43: *          Specifies the order in which the elementary reflectors are
   44: *          multiplied to form the block reflector:
   45: *          = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet)
   46: *          = 'B': H = H(k) . . . H(2) H(1) (Backward)
   47: *
   48: *  STOREV  (input) CHARACTER*1
   49: *          Specifies how the vectors which define the elementary
   50: *          reflectors are stored (see also Further Details):
   51: *          = 'C': columnwise                        (not supported yet)
   52: *          = 'R': rowwise
   53: *
   54: *  N       (input) INTEGER
   55: *          The order of the block reflector H. N >= 0.
   56: *
   57: *  K       (input) INTEGER
   58: *          The order of the triangular factor T (= the number of
   59: *          elementary reflectors). K >= 1.
   60: *
   61: *  V       (input/output) DOUBLE PRECISION array, dimension
   62: *                               (LDV,K) if STOREV = 'C'
   63: *                               (LDV,N) if STOREV = 'R'
   64: *          The matrix V. See further details.
   65: *
   66: *  LDV     (input) INTEGER
   67: *          The leading dimension of the array V.
   68: *          If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.
   69: *
   70: *  TAU     (input) DOUBLE PRECISION array, dimension (K)
   71: *          TAU(i) must contain the scalar factor of the elementary
   72: *          reflector H(i).
   73: *
   74: *  T       (output) DOUBLE PRECISION array, dimension (LDT,K)
   75: *          The k by k triangular factor T of the block reflector.
   76: *          If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is
   77: *          lower triangular. The rest of the array is not used.
   78: *
   79: *  LDT     (input) INTEGER
   80: *          The leading dimension of the array T. LDT >= K.
   81: *
   82: *  Further Details
   83: *  ===============
   84: *
   85: *  Based on contributions by
   86: *    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
   87: *
   88: *  The shape of the matrix V and the storage of the vectors which define
   89: *  the H(i) is best illustrated by the following example with n = 5 and
   90: *  k = 3. The elements equal to 1 are not stored; the corresponding
   91: *  array elements are modified but restored on exit. The rest of the
   92: *  array is not used.
   93: *
   94: *  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':
   95: *
   96: *                                              ______V_____
   97: *         ( v1 v2 v3 )                        /            \
   98: *         ( v1 v2 v3 )                      ( v1 v1 v1 v1 v1 . . . . 1 )
   99: *     V = ( v1 v2 v3 )                      ( v2 v2 v2 v2 v2 . . . 1   )
  100: *         ( v1 v2 v3 )                      ( v3 v3 v3 v3 v3 . . 1     )
  101: *         ( v1 v2 v3 )
  102: *            .  .  .
  103: *            .  .  .
  104: *            1  .  .
  105: *               1  .
  106: *                  1
  107: *
  108: *  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':
  109: *
  110: *                                                        ______V_____
  111: *            1                                          /            \
  112: *            .  1                           ( 1 . . . . v1 v1 v1 v1 v1 )
  113: *            .  .  1                        ( . 1 . . . v2 v2 v2 v2 v2 )
  114: *            .  .  .                        ( . . 1 . . v3 v3 v3 v3 v3 )
  115: *            .  .  .
  116: *         ( v1 v2 v3 )
  117: *         ( v1 v2 v3 )
  118: *     V = ( v1 v2 v3 )
  119: *         ( v1 v2 v3 )
  120: *         ( v1 v2 v3 )
  121: *
  122: *  =====================================================================
  123: *
  124: *     .. Parameters ..
  125:       DOUBLE PRECISION   ZERO
  126:       PARAMETER          ( ZERO = 0.0D+0 )
  127: *     ..
  128: *     .. Local Scalars ..
  129:       INTEGER            I, INFO, J
  130: *     ..
  131: *     .. External Subroutines ..
  132:       EXTERNAL           DGEMV, DTRMV, XERBLA
  133: *     ..
  134: *     .. External Functions ..
  135:       LOGICAL            LSAME
  136:       EXTERNAL           LSAME
  137: *     ..
  138: *     .. Executable Statements ..
  139: *
  140: *     Check for currently supported options
  141: *
  142:       INFO = 0
  143:       IF( .NOT.LSAME( DIRECT, 'B' ) ) THEN
  144:          INFO = -1
  145:       ELSE IF( .NOT.LSAME( STOREV, 'R' ) ) THEN
  146:          INFO = -2
  147:       END IF
  148:       IF( INFO.NE.0 ) THEN
  149:          CALL XERBLA( 'DLARZT', -INFO )
  150:          RETURN
  151:       END IF
  152: *
  153:       DO 20 I = K, 1, -1
  154:          IF( TAU( I ).EQ.ZERO ) THEN
  155: *
  156: *           H(i)  =  I
  157: *
  158:             DO 10 J = I, K
  159:                T( J, I ) = ZERO
  160:    10       CONTINUE
  161:          ELSE
  162: *
  163: *           general case
  164: *
  165:             IF( I.LT.K ) THEN
  166: *
  167: *              T(i+1:k,i) = - tau(i) * V(i+1:k,1:n) * V(i,1:n)'
  168: *
  169:                CALL DGEMV( 'No transpose', K-I, N, -TAU( I ),
  170:      $                     V( I+1, 1 ), LDV, V( I, 1 ), LDV, ZERO,
  171:      $                     T( I+1, I ), 1 )
  172: *
  173: *              T(i+1:k,i) = T(i+1:k,i+1:k) * T(i+1:k,i)
  174: *
  175:                CALL DTRMV( 'Lower', 'No transpose', 'Non-unit', K-I,
  176:      $                     T( I+1, I+1 ), LDT, T( I+1, I ), 1 )
  177:             END IF
  178:             T( I, I ) = TAU( I )
  179:          END IF
  180:    20 CONTINUE
  181:       RETURN
  182: *
  183: *     End of DLARZT
  184: *
  185:       END