slarzt.f(3)

NAME
slarzt.f -

SYNOPSIS

  Functions/Subroutines
subroutine slarzt (DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
SLARZT forms the triangular factor T of a block reflector H = I - vtvH.

Function/Subroutine Documentation

  subroutine slarzt (characterDIRECT, characterSTOREV, integerN, integerK, real, dimension( ldv, * )V, integerLDV, real, dimension( * )TAU, real, dimension( ldt, * )T, integerLDT)

Purpose:

     SLARZT 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**T
     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 * T * V
     Currently, only STOREV = 'R' and DIRECT = 'B' are supported.

Parameters:
    DIRECT

              DIRECT is 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

              STOREV is 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

              N is INTEGER
              The order of the block reflector H. N >= 0.

    K

              K is INTEGER
              The order of the triangular factor T (= the number of
              elementary reflectors). K >= 1.

    V

              V is REAL array, dimension
                                   (LDV,K) if STOREV = 'C'
                                   (LDV,N) if STOREV = 'R'
              The matrix V. See further details.

    LDV

              LDV is INTEGER
              The leading dimension of the array V.
              If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.

    TAU

              TAU is REAL array, dimension (K)
              TAU(i) must contain the scalar factor of the elementary
              reflector H(i).

    T

              T is REAL 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

              LDT is INTEGER
              The leading dimension of the array T. LDT >= K.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    September 2012

Contributors:
    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

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_____
             ( 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 )

Definition at line 186 of file slarzt.f.

Author

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