---
name: "zqrt02.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/zqrt02.f"
---

# zqrt02.f(3)

## NAME

TESTING/LIN/zqrt02.f

## SYNOPSIS

### Functions/Subroutines

subroutine **zqrt02** (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork, result)\
 **ZQRT02**

## Function/Subroutine Documentation

### subroutine zqrt02 (integer m, integer n, integer k, complex\*16, dimension( lda, \* ) a, complex\*16, dimension( lda, \* ) af, complex\*16, dimension( lda, \* ) q, complex\*16, dimension( lda, \* ) r, integer lda, complex\*16, dimension( \* ) tau, complex\*16, dimension( lwork ) work, integer lwork, double precision, dimension( \* ) rwork, double precision, dimension( \* ) result)

**ZQRT02**

**Purpose:**

```
!>
!> ZQRT02 tests ZUNGQR, which generates an m-by-n matrix Q with
!> orthonormal columns that is defined as the product of k elementary
!> reflectors.
!>
!> Given the QR factorization of an m-by-n matrix A, ZQRT02 generates
!> the orthogonal matrix Q defined by the factorization of the first k
!> columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k),
!> and checks that the columns 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.
!>          M >= N >= 0.
!>
```

*K*

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

*A*

```
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          The m-by-n matrix A which was factorized by ZQRT01.
!>
```

*AF*

```
!>          AF is COMPLEX*16 array, dimension (LDA,N)
!>          Details of the QR factorization of A, as returned by ZGEQRF.
!>          See ZGEQRF for further details.
!>
```

*Q*

```
!>          Q is COMPLEX*16 array, dimension (LDA,N)
!>
```

*R*

```
!>          R is COMPLEX*16 array, dimension (LDA,N)
!>
```

*LDA*

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

*TAU*

```
!>          TAU is COMPLEX*16 array, dimension (N)
!>          The scalar factors of the elementary reflectors corresponding
!>          to the QR factorization in AF.
!>
```

*WORK*

```
!>          WORK is COMPLEX*16 array, dimension (LWORK)
!>
```

*LWORK*

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

*RWORK*

```
!>          RWORK is DOUBLE PRECISION array, dimension (M)
!>
```

*RESULT*

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

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **133** of file **zqrt02.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.