---
name: "ztzrqf.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/ztzrqf.f"
---

# ztzrqf.f(3)

## NAME

SRC/DEPRECATED/ztzrqf.f

## SYNOPSIS

### Functions/Subroutines

subroutine **ztzrqf** (m, n, a, lda, tau, info)\
 **ZTZRQF**

## Function/Subroutine Documentation

### subroutine ztzrqf (integer m, integer n, complex\*16, dimension( lda, \* ) a, integer lda, complex\*16, dimension( \* ) tau, integer info)

**ZTZRQF**

**Purpose:**

```
!>
!> This routine is deprecated and has been replaced by routine ZTZRZF.
!>
!> ZTZRQF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A
!> to upper triangular form by means of unitary transformations.
!>
!> The upper trapezoidal matrix A is factored as
!>
!>    A = ( R  0 ) * Z,
!>
!> where Z is an N-by-N unitary matrix and R is an M-by-M upper
!> triangular matrix.
!>
```

**Parameters**

*M*

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

*N*

```
!>          N is INTEGER
!>          The number of columns of the matrix A.  N >= M.
!>
```

*A*

```
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, the leading M-by-N upper trapezoidal part of the
!>          array A must contain the matrix to be factorized.
!>          On exit, the leading M-by-M upper triangular part of A
!>          contains the upper triangular matrix R, and elements M+1 to
!>          N of the first M rows of A, with the array TAU, represent the
!>          unitary matrix Z as a product of M elementary reflectors.
!>
```

*LDA*

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

*TAU*

```
!>          TAU is COMPLEX*16 array, dimension (M)
!>          The scalar factors of the elementary reflectors.
!>
```

*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  factorization is obtained by Householder's method.  The kth
!>  transformation matrix, Z( k ), whose conjugate transpose is used to
!>  introduce zeros into the (m - k + 1)th row of A, is given in the form
!>
!>     Z( k ) = ( I     0   ),
!>              ( 0  T( k ) )
!>
!>  where
!>
!>     T( k ) = I - tau*u( k )*u( k )**H,   u( k ) = (   1    ),
!>                                                   (   0    )
!>                                                   ( z( k ) )
!>
!>  tau is a scalar and z( k ) is an ( n - m ) element vector.
!>  tau and z( k ) are chosen to annihilate the elements of the kth row
!>  of X.
!>
!>  The scalar tau is returned in the kth element of TAU and the vector
!>  u( k ) in the kth row of A, such that the elements of z( k ) are
!>  in  a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in
!>  the upper triangular part of A.
!>
!>  Z is given by
!>
!>     Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).
!>
```

Definition at line **137** of file **ztzrqf.f**.

## Author

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