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/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/zlarfb.f(3) Library Functions Manual /home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/zlarfb.f(3)

NAME

/home/abuild/rpmbuild/BUILD/lapack-3.12.0/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 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 = (  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 195 of file zlarfb.f.

Author

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Version 3.12.0 LAPACK