# zlarfb.f - Man Page

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

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

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zlarfb(3) is an alias of zlarfb.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK