---
name: "srqt02.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/srqt02.f"
---

# srqt02.f(3)

## NAME

TESTING/LIN/srqt02.f

## SYNOPSIS

### Functions/Subroutines

subroutine **srqt02** (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork, result)\
 **SRQT02**

## Function/Subroutine Documentation

### subroutine srqt02 (integer m, integer n, integer k, real, dimension( lda, \* ) a, real, dimension( lda, \* ) af, real, dimension( lda, \* ) q, real, dimension( lda, \* ) r, integer lda, real, dimension( \* ) tau, real, dimension( lwork ) work, integer lwork, real, dimension( \* ) rwork, real, dimension( \* ) result)

**SRQT02**

**Purpose:**

```
!>
!> SRQT02 tests SORGRQ, which generates an m-by-n matrix Q with
!> orthonormal rows that is defined as the product of k elementary
!> reflectors.
!>
!> Given the RQ factorization of an m-by-n matrix A, SRQT02 generates
!> the orthogonal matrix Q defined by the factorization of the last k
!> rows of A; it compares R(m-k+1:m,n-m+1:n) with
!> A(m-k+1:m,1:n)*Q(n-m+1:n,1:n)', and checks that the rows of Q are
!> orthonormal.
!>
```

**Parameters**

*M*

```
!>          M is INTEGER
!>          The number of rows of the matrix Q to be generated.  M >= 0.
!>
```

*N*

```
!>          N is INTEGER
!>          The number of columns of the matrix Q to be generated.
!>          N >= M >= 0.
!>
```

*K*

```
!>          K is INTEGER
!>          The number of elementary reflectors whose product defines the
!>          matrix Q. M >= K >= 0.
!>
```

*A*

```
!>          A is REAL array, dimension (LDA,N)
!>          The m-by-n matrix A which was factorized by SRQT01.
!>
```

*AF*

```
!>          AF is REAL array, dimension (LDA,N)
!>          Details of the RQ factorization of A, as returned by SGERQF.
!>          See SGERQF for further details.
!>
```

*Q*

```
!>          Q is REAL array, dimension (LDA,N)
!>
```

*R*

```
!>          R is REAL array, dimension (LDA,M)
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the arrays A, AF, Q and L. LDA >= N.
!>
```

*TAU*

```
!>          TAU is REAL array, dimension (M)
!>          The scalar factors of the elementary reflectors corresponding
!>          to the RQ factorization in AF.
!>
```

*WORK*

```
!>          WORK is REAL array, dimension (LWORK)
!>
```

*LWORK*

```
!>          LWORK is INTEGER
!>          The dimension of the array WORK.
!>
```

*RWORK*

```
!>          RWORK is REAL array, dimension (M)
!>
```

*RESULT*

```
!>          RESULT is REAL array, dimension (2)
!>          The test ratios:
!>          RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS )
!>          RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **134** of file **srqt02.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.