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*> \brief \b ZRQT03
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition
* ==========
*
* SUBROUTINE ZRQT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
*
* .. Scalar Arguments ..
* INTEGER K, LDA, LWORK, M, N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION RESULT( * ), RWORK( * )
* COMPLEX*16 AF( LDA, * ), C( LDA, * ), CC( LDA, * ),
* $ Q( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
* Purpose
* =======
*
*>\details \b Purpose:
*>\verbatim
*>
*> 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.
*>
*>\endverbatim
*
* Arguments
* =========
*
*> \param[in] M
*> \verbatim
*> 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.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the orthogonal matrix Q. N >= 0.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*> K is INTEGER
*> The number of elementary reflectors whose product defines the
*> orthogonal matrix Q. N >= K >= 0.
*> \endverbatim
*>
*> \param[in] AF
*> \verbatim
*> 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.
*> \endverbatim
*>
*> \param[out] C
*> \verbatim
*> C is COMPLEX*16 array, dimension (LDA,N)
*> \endverbatim
*>
*> \param[out] CC
*> \verbatim
*> CC is COMPLEX*16 array, dimension (LDA,N)
*> \endverbatim
*>
*> \param[out] Q
*> \verbatim
*> Q is COMPLEX*16 array, dimension (LDA,N)
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the arrays AF, C, CC, and Q.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is COMPLEX*16 array, dimension (min(M,N))
*> The scalar factors of the elementary reflectors corresponding
*> to the RQ factorization in AF.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX*16 array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> 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.
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (M)
*> \endverbatim
*>
*> \param[out] RESULT
*> \verbatim
*> 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 )
*> \endverbatim
*>
*
* Authors
* =======
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup complex16_lin
*
* =====================================================================
SUBROUTINE ZRQT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
$ RWORK, RESULT )
*
* -- LAPACK test routine (version 3.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
INTEGER K, LDA, LWORK, M, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION RESULT( * ), RWORK( * )
COMPLEX*16 AF( LDA, * ), C( LDA, * ), CC( LDA, * ),
$ Q( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
COMPLEX*16 ROGUE
PARAMETER ( ROGUE = ( -1.0D+10, -1.0D+10 ) )
* ..
* .. Local Scalars ..
CHARACTER SIDE, TRANS
INTEGER INFO, ISIDE, ITRANS, J, MC, MINMN, NC
DOUBLE PRECISION CNORM, EPS, RESID
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION DLAMCH, ZLANGE
EXTERNAL LSAME, DLAMCH, ZLANGE
* ..
* .. External Subroutines ..
EXTERNAL ZGEMM, ZLACPY, ZLARNV, ZLASET, ZUNGRQ, ZUNMRQ
* ..
* .. Local Arrays ..
INTEGER ISEED( 4 )
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, DCMPLX, MAX, MIN
* ..
* .. Scalars in Common ..
CHARACTER*32 SRNAMT
* ..
* .. Common blocks ..
COMMON / SRNAMC / SRNAMT
* ..
* .. Data statements ..
DATA ISEED / 1988, 1989, 1990, 1991 /
* ..
* .. Executable Statements ..
*
EPS = DLAMCH( 'Epsilon' )
MINMN = MIN( M, N )
*
* Quick return if possible
*
IF( MINMN.EQ.0 ) THEN
RESULT( 1 ) = ZERO
RESULT( 2 ) = ZERO
RESULT( 3 ) = ZERO
RESULT( 4 ) = ZERO
RETURN
END IF
*
* Copy the last k rows of the factorization to the array Q
*
CALL ZLASET( 'Full', N, N, ROGUE, ROGUE, Q, LDA )
IF( K.GT.0 .AND. N.GT.K )
$ CALL ZLACPY( 'Full', K, N-K, AF( M-K+1, 1 ), LDA,
$ Q( N-K+1, 1 ), LDA )
IF( K.GT.1 )
$ CALL ZLACPY( 'Lower', K-1, K-1, AF( M-K+2, N-K+1 ), LDA,
$ Q( N-K+2, N-K+1 ), LDA )
*
* Generate the n-by-n matrix Q
*
SRNAMT = 'ZUNGRQ'
CALL ZUNGRQ( N, N, K, Q, LDA, TAU( MINMN-K+1 ), WORK, LWORK,
$ INFO )
*
DO 30 ISIDE = 1, 2
IF( ISIDE.EQ.1 ) THEN
SIDE = 'L'
MC = N
NC = M
ELSE
SIDE = 'R'
MC = M
NC = N
END IF
*
* Generate MC by NC matrix C
*
DO 10 J = 1, NC
CALL ZLARNV( 2, ISEED, MC, C( 1, J ) )
10 CONTINUE
CNORM = ZLANGE( '1', MC, NC, C, LDA, RWORK )
IF( CNORM.EQ.ZERO )
$ CNORM = ONE
*
DO 20 ITRANS = 1, 2
IF( ITRANS.EQ.1 ) THEN
TRANS = 'N'
ELSE
TRANS = 'C'
END IF
*
* Copy C
*
CALL ZLACPY( 'Full', MC, NC, C, LDA, CC, LDA )
*
* Apply Q or Q' to C
*
SRNAMT = 'ZUNMRQ'
IF( K.GT.0 )
$ CALL ZUNMRQ( SIDE, TRANS, MC, NC, K, AF( M-K+1, 1 ), LDA,
$ TAU( MINMN-K+1 ), CC, LDA, WORK, LWORK,
$ INFO )
*
* Form explicit product and subtract
*
IF( LSAME( SIDE, 'L' ) ) THEN
CALL ZGEMM( TRANS, 'No transpose', MC, NC, MC,
$ DCMPLX( -ONE ), Q, LDA, C, LDA,
$ DCMPLX( ONE ), CC, LDA )
ELSE
CALL ZGEMM( 'No transpose', TRANS, MC, NC, NC,
$ DCMPLX( -ONE ), C, LDA, Q, LDA,
$ DCMPLX( ONE ), CC, LDA )
END IF
*
* Compute error in the difference
*
RESID = ZLANGE( '1', MC, NC, CC, LDA, RWORK )
RESULT( ( ISIDE-1 )*2+ITRANS ) = RESID /
$ ( DBLE( MAX( 1, N ) )*CNORM*EPS )
*
20 CONTINUE
30 CONTINUE
*
RETURN
*
* End of ZRQT03
*
END
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