---
name: "dtpqrt2.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/dtpqrt2.f"
---

# dtpqrt2.f(3)

## NAME

SRC/dtpqrt2.f

## SYNOPSIS

### Functions/Subroutines

subroutine **dtpqrt2** (m, n, l, a, lda, b, ldb, t, ldt, info)\
 **DTPQRT2** computes a QR factorization of a real or complex *triangular-pentagonal"*matrix,*which*is*composed*of*a*triangular*block*and*a*pentagonal*block,*using*the*compact*WY*representation*for*Q.

## Function/Subroutine Documentation

### subroutine dtpqrt2 (integer m, integer n, integer l, double precision, dimension( lda, \* ) a, integer lda, double precision, dimension( ldb, \* ) b, integer ldb, double precision, dimension( ldt, \* ) t, integer ldt, integer info)

**DTPQRT2** computes a QR factorization of a real or complex "triangular-pentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.

**Purpose:**

```
!>
!> DTPQRT2 computes a QR factorization of a real
!> matrix C, which is composed of a triangular block A and pentagonal block B,
!> using the compact WY representation for Q.
!>
```

**Parameters**

*M*

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

*N*

```
!>          N is INTEGER
!>          The number of columns of the matrix B, and the order of
!>          the triangular matrix A.
!>          N >= 0.
!>
```

*L*

```
!>          L is INTEGER
!>          The number of rows of the upper trapezoidal part of B.
!>          MIN(M,N) >= L >= 0.  See Further Details.
!>
```

*A*

```
!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          On entry, the upper triangular N-by-N matrix A.
!>          On exit, the elements on and above the diagonal of the array
!>          contain the upper triangular matrix R.
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>
```

*B*

```
!>          B is DOUBLE PRECISION array, dimension (LDB,N)
!>          On entry, the pentagonal M-by-N matrix B.  The first M-L rows
!>          are rectangular, and the last L rows are upper trapezoidal.
!>          On exit, B contains the pentagonal matrix V.  See Further Details.
!>
```

*LDB*

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

*T*

```
!>          T is DOUBLE PRECISION array, dimension (LDT,N)
!>          The N-by-N upper triangular factor T of the block reflector.
!>          See Further Details.
!>
```

*LDT*

```
!>          LDT is INTEGER
!>          The leading dimension of the array T.  LDT >= max(1,N)
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -i, the i-th argument had an illegal value
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

```
!>
!>  The input matrix C is a (N+M)-by-N matrix
!>
!>               C = [ A ]
!>                   [ B ]
!>
!>  where A is an upper triangular N-by-N matrix, and B is M-by-N pentagonal
!>  matrix consisting of a (M-L)-by-N rectangular matrix B1 on top of a L-by-N
!>  upper trapezoidal matrix B2:
!>
!>               B = [ B1 ]  <- (M-L)-by-N rectangular
!>                   [ B2 ]  <-     L-by-N upper trapezoidal.
!>
!>  The upper trapezoidal matrix B2 consists of the first L rows of a
!>  N-by-N upper triangular matrix, where 0 <= L <= MIN(M,N).  If L=0,
!>  B is rectangular M-by-N; if M=L=N, B is upper triangular.
!>
!>  The matrix W stores the elementary reflectors H(i) in the i-th column
!>  below the diagonal (of A) in the (N+M)-by-N input matrix C
!>
!>               C = [ A ]  <- upper triangular N-by-N
!>                   [ B ]  <- M-by-N pentagonal
!>
!>  so that W can be represented as
!>
!>               W = [ I ]  <- identity, N-by-N
!>                   [ V ]  <- M-by-N, same form as B.
!>
!>  Thus, all of information needed for W is contained on exit in B, which
!>  we call V above.  Note that V has the same form as B; that is,
!>
!>               V = [ V1 ] <- (M-L)-by-N rectangular
!>                   [ V2 ] <-     L-by-N upper trapezoidal.
!>
!>  The columns of V represent the vectors which define the H(i)'s.
!>  The (M+N)-by-(M+N) block reflector H is then given by
!>
!>               H = I - W * T * W**T
!>
!>  where W^H is the conjugate transpose of W and T is the upper triangular
!>  factor of the block reflector.
!>
```

Definition at line **172** of file **dtpqrt2.f**.

## Author

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