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*> \brief \b CQRT02
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE CQRT02( M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
*
* .. Scalar Arguments ..
* INTEGER K, LDA, LWORK, M, N
* ..
* .. Array Arguments ..
* REAL RESULT( * ), RWORK( * )
* COMPLEX A( LDA, * ), AF( LDA, * ), Q( LDA, * ),
* $ R( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CQRT02 tests CUNGQR, which generates an m-by-n matrix Q with
*> orthonormal columns that is defined as the product of k elementary
*> reflectors.
*>
*> Given the QR factorization of an m-by-n matrix A, CQRT02 generates
*> the orthogonal matrix Q defined by the factorization of the first k
*> columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k),
*> and checks that the columns of Q are orthonormal.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix Q to be generated. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix Q to be generated.
*> M >= N >= 0.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*> K is INTEGER
*> The number of elementary reflectors whose product defines the
*> matrix Q. N >= K >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is COMPLEX array, dimension (LDA,N)
*> The m-by-n matrix A which was factorized by CQRT01.
*> \endverbatim
*>
*> \param[in] AF
*> \verbatim
*> AF is COMPLEX array, dimension (LDA,N)
*> Details of the QR factorization of A, as returned by CGEQRF.
*> See CGEQRF for further details.
*> \endverbatim
*>
*> \param[out] Q
*> \verbatim
*> Q is COMPLEX array, dimension (LDA,N)
*> \endverbatim
*>
*> \param[out] R
*> \verbatim
*> R is COMPLEX array, dimension (LDA,N)
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the arrays A, AF, Q and R. LDA >= M.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is COMPLEX array, dimension (N)
*> The scalar factors of the elementary reflectors corresponding
*> to the QR factorization in AF.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The dimension of the array WORK.
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is REAL array, dimension (M)
*> \endverbatim
*>
*> \param[out] RESULT
*> \verbatim
*> RESULT is REAL array, dimension (2)
*> The test ratios:
*> RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
*> RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex_lin
*
* =====================================================================
SUBROUTINE CQRT02( M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK,
$ RWORK, RESULT )
*
* -- LAPACK test routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER K, LDA, LWORK, M, N
* ..
* .. Array Arguments ..
REAL RESULT( * ), RWORK( * )
COMPLEX A( LDA, * ), AF( LDA, * ), Q( LDA, * ),
$ R( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
COMPLEX ROGUE
PARAMETER ( ROGUE = ( -1.0E+10, -1.0E+10 ) )
* ..
* .. Local Scalars ..
INTEGER INFO
REAL ANORM, EPS, RESID
* ..
* .. External Functions ..
REAL CLANGE, CLANSY, SLAMCH
EXTERNAL CLANGE, CLANSY, SLAMCH
* ..
* .. External Subroutines ..
EXTERNAL CGEMM, CHERK, CLACPY, CLASET, CUNGQR
* ..
* .. Intrinsic Functions ..
INTRINSIC CMPLX, MAX, REAL
* ..
* .. Scalars in Common ..
CHARACTER*32 SRNAMT
* ..
* .. Common blocks ..
COMMON / SRNAMC / SRNAMT
* ..
* .. Executable Statements ..
*
EPS = SLAMCH( 'Epsilon' )
*
* Copy the first k columns of the factorization to the array Q
*
CALL CLASET( 'Full', M, N, ROGUE, ROGUE, Q, LDA )
CALL CLACPY( 'Lower', M-1, K, AF( 2, 1 ), LDA, Q( 2, 1 ), LDA )
*
* Generate the first n columns of the matrix Q
*
SRNAMT = 'CUNGQR'
CALL CUNGQR( M, N, K, Q, LDA, TAU, WORK, LWORK, INFO )
*
* Copy R(1:n,1:k)
*
CALL CLASET( 'Full', N, K, CMPLX( ZERO ), CMPLX( ZERO ), R, LDA )
CALL CLACPY( 'Upper', N, K, AF, LDA, R, LDA )
*
* Compute R(1:n,1:k) - Q(1:m,1:n)' * A(1:m,1:k)
*
CALL CGEMM( 'Conjugate transpose', 'No transpose', N, K, M,
$ CMPLX( -ONE ), Q, LDA, A, LDA, CMPLX( ONE ), R, LDA )
*
* Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) .
*
ANORM = CLANGE( '1', M, K, A, LDA, RWORK )
RESID = CLANGE( '1', N, K, R, LDA, RWORK )
IF( ANORM.GT.ZERO ) THEN
RESULT( 1 ) = ( ( RESID / REAL( MAX( 1, M ) ) ) / ANORM ) / EPS
ELSE
RESULT( 1 ) = ZERO
END IF
*
* Compute I - Q'*Q
*
CALL CLASET( 'Full', N, N, CMPLX( ZERO ), CMPLX( ONE ), R, LDA )
CALL CHERK( 'Upper', 'Conjugate transpose', N, M, -ONE, Q, LDA,
$ ONE, R, LDA )
*
* Compute norm( I - Q'*Q ) / ( M * EPS ) .
*
RESID = CLANSY( '1', 'Upper', N, R, LDA, RWORK )
*
RESULT( 2 ) = ( RESID / REAL( MAX( 1, M ) ) ) / EPS
*
RETURN
*
* End of CQRT02
*
END
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