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

NAME
       SRC/zlarfb.f

SYNOPSIS
   Functions/Subroutines
       subroutine zlarfb (side, trans, direct, storev, m, n, k, v, ldv, t,
           ldt, c, ldc, work, ldwork)
           ZLARFB applies a block reflector or its conjugate-transpose to a
           general rectangular matrix.

Function/Subroutine Documentation
   subroutine zlarfb (character side, character trans, character direct,
       character storev, integer m, integer n, integer k, complex*16,
       dimension( ldv, * ) v, integer ldv, complex*16, dimension( ldt, * ) t,
       integer ldt, complex*16, dimension( ldc, * ) c, integer ldc,
       complex*16, dimension( ldwork, * ) work, integer ldwork)
       ZLARFB applies a block reflector or its conjugate-transpose to a
       general rectangular matrix.

       Purpose:


           !>
           !> ZLARFB applies a complex block reflector H or its transpose H**H to a
           !> complex M-by-N matrix C, from either the left or the right.
           !>

       Parameters
           SIDE

           !>          SIDE is CHARACTER*1
           !>          = 'L': apply H or H**H from the Left
           !>          = 'R': apply H or H**H from the Right
           !>

           TRANS

           !>          TRANS is CHARACTER*1
           !>          = 'N': apply H (No transpose)
           !>          = 'C': apply H**H (Conjugate transpose)
           !>

           DIRECT

           !>          DIRECT is CHARACTER*1
           !>          Indicates how H is formed from a product of elementary
           !>          reflectors
           !>          = 'F': H = H(1) H(2) . . . H(k) (Forward)
           !>          = 'B': H = H(k) . . . H(2) H(1) (Backward)
           !>

           STOREV

           !>          STOREV is CHARACTER*1
           !>          Indicates how the vectors which define the elementary
           !>          reflectors are stored:
           !>          = 'C': Columnwise
           !>          = 'R': Rowwise
           !>

           M

           !>          M is INTEGER
           !>          The number of rows of the matrix C.
           !>

           N

           !>          N is INTEGER
           !>          The number of columns of the matrix C.
           !>

           K

           !>          K is INTEGER
           !>          The order of the matrix T (= the number of elementary
           !>          reflectors whose product defines the block reflector).
           !>          If SIDE = 'L', M >= K >= 0;
           !>          if SIDE = 'R', N >= K >= 0.
           !>

           V

           !>          V is COMPLEX*16 array, dimension
           !>                                (LDV,K) if STOREV = 'C'
           !>                                (LDV,M) if STOREV = 'R' and SIDE = 'L'
           !>                                (LDV,N) if STOREV = 'R' and SIDE = 'R'
           !>          See Further Details.
           !>

           LDV

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

           T

           !>          T is COMPLEX*16 array, dimension (LDT,K)
           !>          The triangular K-by-K matrix T in the representation of the
           !>          block reflector.
           !>

           LDT

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

           C

           !>          C is COMPLEX*16 array, dimension (LDC,N)
           !>          On entry, the M-by-N matrix C.
           !>          On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H.
           !>

           LDC

           !>          LDC is INTEGER
           !>          The leading dimension of the array C. LDC >= max(1,M).
           !>

           WORK

           !>          WORK is COMPLEX*16 array, dimension (LDWORK,K)
           !>

           LDWORK

           !>          LDWORK is INTEGER
           !>          The leading dimension of the array WORK.
           !>          If SIDE = 'L', LDWORK >= max(1,N);
           !>          if SIDE = 'R', LDWORK >= max(1,M).
           !>

       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 triangular part of V (including its diagonal) is not
           !>  referenced.
           !>
           !>  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 194 of file zlarfb.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                 SRC/zlarfb.f(3)