# dtprfb.f - Man Page

SRC/dtprfb.f

## Synopsis

### Functions/Subroutines

subroutine dtprfb (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, a, lda, b, ldb, work, ldwork)
DTPRFB applies a real 'triangular-pentagonal' block reflector to a real matrix, which is composed of two blocks.

## Function/Subroutine Documentation

### subroutine dtprfb (character side, character trans, character direct, character storev, integer m, integer n, integer k, integer l, double precision, dimension( ldv, * ) v, integer ldv, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( ldwork, * ) work, integer ldwork)

DTPRFB applies a real 'triangular-pentagonal' block reflector to a real matrix, which is composed of two blocks.

Purpose:

``` DTPRFB applies a real 'triangular-pentagonal' block reflector H or its
transpose H**T to a real matrix C, which is composed of two
blocks A and B, either from the left or right.```
Parameters

SIDE

```          SIDE is CHARACTER*1
= 'L': apply H or H**T from the Left
= 'R': apply H or H**T from the Right```

TRANS

```          TRANS is CHARACTER*1
= 'N': apply H (No transpose)
= 'T': apply H**T (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': Columns
= 'R': Rows```

M

```          M is INTEGER
The number of rows of the matrix B.
M >= 0.```

N

```          N is INTEGER
The number of columns of the matrix B.
N >= 0.```

K

```          K is INTEGER
The order of the matrix T, i.e. the number of elementary
reflectors whose product defines the block reflector.
K >= 0.```

L

```          L is INTEGER
The order of the trapezoidal part of V.
K >= L >= 0.  See Further Details.```

V

```          V is DOUBLE PRECISION array, dimension
(LDV,K) if STOREV = 'C'
(LDV,M) if STOREV = 'R' and SIDE = 'L'
(LDV,N) if STOREV = 'R' and SIDE = 'R'
The pentagonal matrix V, which contains the elementary reflectors
H(1), H(2), ..., H(K).  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 DOUBLE PRECISION 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.```

A

```          A is DOUBLE PRECISION array, dimension
(LDA,N) if SIDE = 'L' or (LDA,K) if SIDE = 'R'
On entry, the K-by-N or M-by-K matrix A.
On exit, A is overwritten by the corresponding block of
H*C or H**T*C or C*H or C*H**T.  See Further Details.```

LDA

```          LDA is INTEGER
The leading dimension of the array A.
If SIDE = 'L', LDA >= max(1,K);
If SIDE = 'R', LDA >= max(1,M).```

B

```          B is DOUBLE PRECISION array, dimension (LDB,N)
On entry, the M-by-N matrix B.
On exit, B is overwritten by the corresponding block of
H*C or H**T*C or C*H or C*H**T.  See Further Details.```

LDB

```          LDB is INTEGER
The leading dimension of the array B.
LDB >= max(1,M).```

WORK

```          WORK is DOUBLE PRECISION array, dimension
(LDWORK,N) if SIDE = 'L',
(LDWORK,K) if SIDE = 'R'.```

LDWORK

```          LDWORK is INTEGER
The leading dimension of the array WORK.
If SIDE = 'L', LDWORK >= K;
if SIDE = 'R', LDWORK >= M.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Further Details:

```  The matrix C is a composite matrix formed from blocks A and B.
The block B is of size M-by-N; if SIDE = 'R', A is of size M-by-K,
and if SIDE = 'L', A is of size K-by-N.

If SIDE = 'R' and DIRECT = 'F', C = [A B].

If SIDE = 'L' and DIRECT = 'F', C = [A]
[B].

If SIDE = 'R' and DIRECT = 'B', C = [B A].

If SIDE = 'L' and DIRECT = 'B', C = [B]
[A].

The pentagonal matrix V is composed of a rectangular block V1 and a
trapezoidal block V2.  The size of the trapezoidal block is determined by
the parameter L, where 0<=L<=K.  If L=K, the V2 block of V is triangular;
if L=0, there is no trapezoidal block, thus V = V1 is rectangular.

If DIRECT = 'F' and STOREV = 'C':  V = [V1]
[V2]
- V2 is upper trapezoidal (first L rows of K-by-K upper triangular)

If DIRECT = 'F' and STOREV = 'R':  V = [V1 V2]

- V2 is lower trapezoidal (first L columns of K-by-K lower triangular)

If DIRECT = 'B' and STOREV = 'C':  V = [V2]
[V1]
- V2 is lower trapezoidal (last L rows of K-by-K lower triangular)

If DIRECT = 'B' and STOREV = 'R':  V = [V2 V1]

- V2 is upper trapezoidal (last L columns of K-by-K upper triangular)

If STOREV = 'C' and SIDE = 'L', V is M-by-K with V2 L-by-K.

If STOREV = 'C' and SIDE = 'R', V is N-by-K with V2 L-by-K.

If STOREV = 'R' and SIDE = 'L', V is K-by-M with V2 K-by-L.

If STOREV = 'R' and SIDE = 'R', V is K-by-N with V2 K-by-L.```

Definition at line 249 of file dtprfb.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

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