SRC/zlarft.f(3)            Library Functions Manual            SRC/zlarft.f(3)

NAME
       SRC/zlarft.f

SYNOPSIS
   Functions/Subroutines
       recursive subroutine zlarft (direct, storev, n, k, v, ldv, tau, t, ldt)
           ZLARFT forms the triangular factor T of a block reflector H = I -
           vtvH

Function/Subroutine Documentation
   recursive subroutine zlarft (character direct, character storev, integer n,
       integer k, complex*16, dimension( ldv, * ) v, integer ldv, complex*16,
       dimension( * ) tau, complex*16, dimension( ldt, * ) t, integer ldt)
       ZLARFT forms the triangular factor T of a block reflector H = I - vtvH

       Purpose:


           !>
           !> ZLARFT 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*16 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*16 array, dimension (K)
           !>          TAU(i) must contain the scalar factor of the elementary
           !>          reflector H(i).
           !>

           T

           !>          T is COMPLEX*16 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.

       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 162 of file zlarft.f.

Author
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LAPACK                          Version 3.12.0                 SRC/zlarft.f(3)