---
name: "zqrt03.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/zqrt03.f"
---

# zqrt03.f(3)

## NAME

TESTING/LIN/zqrt03.f

## SYNOPSIS

### Functions/Subroutines

subroutine **zqrt03** (m, n, k, af, c, cc, q, lda, tau, work, lwork, rwork, result)\
 **ZQRT03**

## Function/Subroutine Documentation

### subroutine zqrt03 (integer m, integer n, integer k, complex\*16, dimension( lda, \* ) af, complex\*16, dimension( lda, \* ) c, complex\*16, dimension( lda, \* ) cc, complex\*16, dimension( lda, \* ) q, integer lda, complex\*16, dimension( \* ) tau, complex\*16, dimension( lwork ) work, integer lwork, double precision, dimension( \* ) rwork, double precision, dimension( \* ) result)

**ZQRT03**

**Purpose:**

```
!>
!> ZQRT03 tests ZUNMQR, which computes Q*C, Q'*C, C*Q or C*Q'.
!>
!> ZQRT03 compares the results of a call to ZUNMQR with the results of
!> forming Q explicitly by a call to ZUNGQR and then performing matrix
!> multiplication by a call to ZGEMM.
!>
```

**Parameters**

*M*

```
!>          M is INTEGER
!>          The order of the orthogonal matrix Q.  M >= 0.
!>
```

*N*

```
!>          N is INTEGER
!>          The number of rows or columns of the matrix C; C is m-by-n if
!>          Q is applied from the left, or n-by-m if Q is applied from
!>          the right.  N >= 0.
!>
```

*K*

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

*AF*

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

*C*

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

*CC*

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

*Q*

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

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the arrays AF, C, CC, and Q.
!>
```

*TAU*

```
!>          TAU is COMPLEX*16 array, dimension (min(M,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 length of WORK.  LWORK must be at least M, and should be
!>          M*NB, where NB is the blocksize for this environment.
!>
```

*RWORK*

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

*RESULT*

```
!>          RESULT is DOUBLE PRECISION array, dimension (4)
!>          The test ratios compare two techniques for multiplying a
!>          random matrix C by an m-by-m orthogonal matrix Q.
!>          RESULT(1) = norm( Q*C - Q*C )  / ( M * norm(C) * EPS )
!>          RESULT(2) = norm( C*Q - C*Q )  / ( M * norm(C) * EPS )
!>          RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS )
!>          RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS )
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **134** of file **zqrt03.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.