clarft.f(3)

NAME
clarft.f -

SYNOPSIS

  Functions/Subroutines

subroutine clarft (DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
CLARFT forms the triangular factor T of a block reflector H = I - vtvH

Function/Subroutine Documentation

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

CLARFT forms the triangular factor T of a block reflector H = I - vtvH

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**H

     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**H * T * V

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)
              = '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
              = '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 COMPLEX 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 COMPLEX array, dimension (K)
              TAU(i) must contain the scalar factor of the elementary
              reflector H(i).

    T

              T is 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

              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

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.

      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 )

Definition at line 164 of file clarft.f.

Author

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