---
name: "crqt01.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/crqt01.f"
---

# crqt01.f(3)

## NAME

TESTING/LIN/crqt01.f

## SYNOPSIS

### Functions/Subroutines

subroutine **crqt01** (m, n, a, af, q, r, lda, tau, work, lwork, rwork, result)\
 **CRQT01**

## Function/Subroutine Documentation

### subroutine crqt01 (integer m, integer n, complex, dimension( lda, \* ) a, complex, dimension( lda, \* ) af, complex, dimension( lda, \* ) q, complex, dimension( lda, \* ) r, integer lda, complex, dimension( \* ) tau, complex, dimension( lwork ) work, integer lwork, real, dimension( \* ) rwork, real, dimension( \* ) result)

**CRQT01**

**Purpose:**

```
!>
!> CRQT01 tests CGERQF, which computes the RQ factorization of an m-by-n
!> matrix A, and partially tests CUNGRQ which forms the n-by-n
!> orthogonal matrix Q.
!>
!> CRQT01 compares R with A*Q', and checks that Q is orthogonal.
!>
```

**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 >= 0.
!>
```

*A*

```
!>          A is COMPLEX array, dimension (LDA,N)
!>          The m-by-n matrix A.
!>
```

*AF*

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

*Q*

```
!>          Q is COMPLEX array, dimension (LDA,N)
!>          The n-by-n orthogonal matrix Q.
!>
```

*R*

```
!>          R is COMPLEX array, dimension (LDA,max(M,N))
!>
```

*LDA*

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

*TAU*

```
!>          TAU is COMPLEX array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors, as returned
!>          by CGERQF.
!>
```

*WORK*

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

*LWORK*

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

*RWORK*

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

*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 **124** of file **crqt01.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.