---
name: "cqlt02.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/cqlt02.f"
---

# cqlt02.f(3)

## NAME

TESTING/LIN/cqlt02.f

## SYNOPSIS

### Functions/Subroutines

subroutine **cqlt02** (m, n, k, a, af, q, l, lda, tau, work, lwork, rwork, result)\
 **CQLT02**

## Function/Subroutine Documentation

### subroutine cqlt02 (integer m, integer n, integer k, complex, dimension( lda, \* ) a, complex, dimension( lda, \* ) af, complex, dimension( lda, \* ) q, complex, dimension( lda, \* ) l, integer lda, complex, dimension( \* ) tau, complex, dimension( lwork ) work, integer lwork, real, dimension( \* ) rwork, real, dimension( \* ) result)

**CQLT02**

**Purpose:**

```
!>
!> CQLT02 tests CUNGQL, which generates an m-by-n matrix Q with
!> orthonormal columns that is defined as the product of k elementary
!> reflectors.
!>
!> Given the QL factorization of an m-by-n matrix A, CQLT02 generates
!> the orthogonal matrix Q defined by the factorization of the last k
!> columns of A; it compares L(m-n+1:m,n-k+1:n) with
!> Q(1:m,m-n+1:m)'*A(1:m,n-k+1:n), 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 array, dimension (LDA,N)
!>          The m-by-n matrix A which was factorized by CQLT01.
!>
```

*AF*

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

*Q*

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

*L*

```
!>          L is COMPLEX array, dimension (LDA,N)
!>
```

*LDA*

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

*TAU*

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

*WORK*

```
!>          WORK is COMPLEX 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( L - 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 **134** of file **cqlt02.f**.

## Author

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