# clarfb.f man page

clarfb.f —

## Synopsis

### Functions/Subroutines

subroutineclarfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)CLARFBapplies a block reflector or its conjugate-transpose to a general rectangular matrix.

## Function/Subroutine Documentation

### subroutine clarfb (characterSIDE, characterTRANS, characterDIRECT, characterSTOREV, integerM, integerN, integerK, complex, dimension( ldv, * )V, integerLDV, complex, dimension( ldt, * )T, integerLDT, complex, dimension( ldc, * )C, integerLDC, complex, dimension( ldwork, * )WORK, integerLDWORK)

**CLARFB** applies a block reflector or its conjugate-transpose to a general rectangular matrix.

**Purpose:**

```
CLARFB 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).
```

*V*

```
V is COMPLEX array, dimension
(LDV,K) if STOREV = 'C'
(LDV,M) if STOREV = 'R' and SIDE = 'L'
(LDV,N) if STOREV = 'R' and SIDE = 'R'
The matrix V. 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 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 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 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.

**Date:**

June 2013

**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 clarfb.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

clarfb(3) is an alias of clarfb.f(3).