---
name: "ctpqrt.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/ctpqrt.f"
---

# ctpqrt.f(3)

## NAME

SRC/ctpqrt.f

## SYNOPSIS

### Functions/Subroutines

subroutine **ctpqrt** (m, n, l, nb, a, lda, b, ldb, t, ldt, work, info)\
 **CTPQRT**

## Function/Subroutine Documentation

### subroutine ctpqrt (integer m, integer n, integer l, integer nb, complex, dimension( lda, \* ) a, integer lda, complex, dimension( ldb, \* ) b, integer ldb, complex, dimension( ldt, \* ) t, integer ldt, complex, dimension( \* ) work, integer info)

**CTPQRT**

**Purpose:**

```
!>
!> CTPQRT computes a blocked QR factorization of a complex
!>  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 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.
!>
```

*NB*

```
!>          NB is INTEGER
!>          The block size to be used in the blocked QR.  N >= NB >= 1.
!>
```

*A*

```
!>          A is COMPLEX 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 COMPLEX 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 COMPLEX array, dimension (LDT,N)
!>          The upper triangular block reflectors stored in compact form
!>          as a sequence of upper triangular blocks.  See Further Details.
!>
```

*LDT*

```
!>          LDT is INTEGER
!>          The leading dimension of the array T.  LDT >= NB.
!>
```

*WORK*

```
!>          WORK is COMPLEX array, dimension (NB*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 number of blocks is B = ceiling(N/NB), where each
!>  block is of order NB except for the last block, which is of order
!>  IB = N - (B-1)*NB.  For each of the B blocks, a upper triangular block
!>  reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB
!>  for the last block) T's are stored in the NB-by-N matrix T as
!>
!>               T = [T1 T2 ... TB].
!>
```

Definition at line **187** of file **ctpqrt.f**.

## Author

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