---
name: "stzrzf.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/stzrzf.f"
---

# stzrzf.f(3)

## NAME

SRC/stzrzf.f

## SYNOPSIS

### Functions/Subroutines

subroutine **stzrzf** (m, n, a, lda, tau, work, lwork, info)\
 **STZRZF**

## Function/Subroutine Documentation

### subroutine stzrzf (integer m, integer n, real, dimension( lda, \* ) a, integer lda, real, dimension( \* ) tau, real, dimension( \* ) work, integer lwork, integer info)

**STZRZF**

**Purpose:**

```
!>
!> STZRZF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A
!> to upper triangular form by means of orthogonal transformations.
!>
!> The upper trapezoidal matrix A is factored as
!>
!>    A = ( R  0 ) * Z,
!>
!> where Z is an N-by-N orthogonal 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 REAL 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
!>          orthogonal 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 REAL array, dimension (M)
!>          The scalar factors of the elementary reflectors.
!>
```

*WORK*

```
!>          WORK is REAL array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!>
```

*LWORK*

```
!>          LWORK is INTEGER
!>          The dimension of the array WORK.  LWORK >= max(1,M).
!>          For optimum performance LWORK >= M*NB, where NB is
!>          the optimal blocksize.
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the optimal size of the WORK array, returns
!>          this value as the first entry of the WORK array, and no error
!>          message related to LWORK is issued by XERBLA.
!>
```

*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.

**Contributors:**

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

**Further Details:**

```
!>
!>  The N-by-N matrix Z can be computed by
!>
!>     Z =  Z(1)*Z(2)* ... *Z(M)
!>
!>  where each N-by-N Z(k) is given by
!>
!>     Z(k) = I - tau(k)*v(k)*v(k)**T
!>
!>  with v(k) is the kth row vector of the M-by-N matrix
!>
!>     V = ( I   A(:,M+1:N) )
!>
!>  I is the M-by-M identity matrix, A(:,M+1:N)
!>  is the output stored in A on exit from STZRZF,
!>  and tau(k) is the kth element of the array TAU.
!>
!>
```

Definition at line **150** of file **stzrzf.f**.

## Author

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