---
name: "ztprfb.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/ztprfb.f"
---

# ztprfb.f(3)

## NAME

SRC/ztprfb.f

## SYNOPSIS

### Functions/Subroutines

subroutine **ztprfb** (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, a, lda, b, ldb, work, ldwork)\
 **ZTPRFB** applies a complex *triangular-pentagonal"*block*reflector*to*a*complex*matrix,*which*is*composed*of*two*blocks.*

## Function/Subroutine Documentation

### subroutine ztprfb (character side, character trans, character direct, character storev, integer m, integer n, integer k, integer l, complex\*16, dimension( ldv, \* ) v, integer ldv, complex\*16, dimension( ldt, \* ) t, integer ldt, complex\*16, dimension( lda, \* ) a, integer lda, complex\*16, dimension( ldb, \* ) b, integer ldb, complex\*16, dimension( ldwork, \* ) work, integer ldwork)

**ZTPRFB** applies a complex "triangular-pentagonal" block reflector to a complex matrix, which is composed of two blocks.

**Purpose:**

```
!>
!> ZTPRFB applies a complex  block reflector H or its
!> conjugate transpose H**H to a complex 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**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': 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 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'
!>          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 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.
!>
```

*A*

```
!>          A is COMPLEX*16 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**H*C or C*H or C*H**H.  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 COMPLEX*16 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**H*C or C*H or C*H**H.  See Further Details.
!>
```

*LDB*

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

*WORK*

```
!>          WORK is COMPLEX*16 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

Univ. of Colorado Denver

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 **ztprfb.f**.

## Author

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