# zrqt03.f - Man Page

TESTING/LIN/zrqt03.f

## Synopsis

### Functions/Subroutines

subroutine zrqt03 (m, n, k, af, c, cc, q, lda, tau, work, lwork, rwork, result)
ZRQT03

## Function/Subroutine Documentation

### subroutine zrqt03 (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)

ZRQT03

Purpose:

``` ZRQT03 tests ZUNMRQ, which computes Q*C, Q'*C, C*Q or C*Q'.

ZRQT03 compares the results of a call to ZUNMRQ with the results of
forming Q explicitly by a call to ZUNGRQ and then performing matrix
multiplication by a call to ZGEMM.```
Parameters

M

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

N

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

K

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

AF

```          AF is COMPLEX*16 array, dimension (LDA,N)
Details of the RQ factorization of an m-by-n matrix, as
returned by ZGERQF. See CGERQF 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,N)`

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 RQ 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 n-by-n orthogonal matrix Q.
RESULT(1) = norm( Q*C - Q*C )  / ( N * norm(C) * EPS )
RESULT(2) = norm( C*Q - C*Q )  / ( N * norm(C) * EPS )
RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS )
RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS )```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 134 of file zrqt03.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zrqt03(3) is an alias of zrqt03.f(3).

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK