---
name: "zlqt02"
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/zlqt02.f"
---

# zlqt02(3)

Part of [zlqt02.f(3)](/zlqt02.f/3.md).

## NAME

TESTING/LIN/zlqt02.f

## SYNOPSIS

### Functions/Subroutines

subroutine **zlqt02** (m, n, k, a, af, q, l, lda, tau, work, lwork, rwork, result)\
 **ZLQT02**

## Function/Subroutine Documentation

### subroutine zlqt02 (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, \* ) l, integer lda, complex\*16, dimension( \* ) tau, complex\*16, dimension( lwork ) work, integer lwork, double precision, dimension( \* ) rwork, double precision, dimension( \* ) result)

**ZLQT02**

**Purpose:**

```
!>
!> ZLQT02 tests ZUNGLQ, which generates an m-by-n matrix Q with
!> orthonormal rows that is defined as the product of k elementary
!> reflectors.
!>
!> Given the LQ factorization of an m-by-n matrix A, ZLQT02 generates
!> the orthogonal matrix Q defined by the factorization of the first k
!> rows of A; it compares L(1:k,1:m) with A(1:k,1:n)*Q(1:m,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 COMPLEX*16 array, dimension (LDA,N)
!>          The m-by-n matrix A which was factorized by ZLQT01.
!>
```

*AF*

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

*Q*

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

*L*

```
!>          L is COMPLEX*16 array, dimension (LDA,M)
!>
```

*LDA*

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

*TAU*

```
!>          TAU is COMPLEX*16 array, dimension (M)
!>          The scalar factors of the elementary reflectors corresponding
!>          to the LQ 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( L - 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 **133** of file **zlqt02.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.