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*> \brief \b SQRT01
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE SQRT01( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
*
* .. Scalar Arguments ..
* INTEGER LDA, LWORK, M, N
* ..
* .. Array Arguments ..
* REAL A( LDA, * ), AF( LDA, * ), Q( LDA, * ),
* $ R( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
* $ WORK( LWORK )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SQRT01 tests SGEQRF, which computes the QR factorization of an m-by-n
*> matrix A, and partially tests SORGQR which forms the m-by-m
*> orthogonal matrix Q.
*>
*> SQRT01 compares R with Q'*A, and checks that Q is orthogonal.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix A. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is REAL array, dimension (LDA,N)
*> The m-by-n matrix A.
*> \endverbatim
*>
*> \param[out] AF
*> \verbatim
*> AF is REAL array, dimension (LDA,N)
*> Details of the QR factorization of A, as returned by SGEQRF.
*> See SGEQRF for further details.
*> \endverbatim
*>
*> \param[out] Q
*> \verbatim
*> Q is REAL array, dimension (LDA,M)
*> The m-by-m orthogonal matrix Q.
*> \endverbatim
*>
*> \param[out] R
*> \verbatim
*> R is REAL array, dimension (LDA,max(M,N))
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the arrays A, AF, Q and R.
*> LDA >= max(M,N).
*> \endverbatim
*>
*> \param[out] TAU
*> \verbatim
*> TAU is REAL array, dimension (min(M,N))
*> The scalar factors of the elementary reflectors, as returned
*> by SGEQRF.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is REAL 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.
*
*> \date November 2011
*
*> \ingroup single_lin
*
* =====================================================================
SUBROUTINE SQRT01( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK,
$ RWORK, RESULT )
*
* -- LAPACK test routine (version 3.4.0) --
* -- 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 LDA, LWORK, M, N
* ..
* .. Array Arguments ..
REAL A( LDA, * ), AF( LDA, * ), Q( LDA, * ),
$ R( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
$ WORK( LWORK )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
REAL ROGUE
PARAMETER ( ROGUE = -1.0E+10 )
* ..
* .. Local Scalars ..
INTEGER INFO, MINMN
REAL ANORM, EPS, RESID
* ..
* .. External Functions ..
REAL SLAMCH, SLANGE, SLANSY
EXTERNAL SLAMCH, SLANGE, SLANSY
* ..
* .. External Subroutines ..
EXTERNAL SGEMM, SGEQRF, SLACPY, SLASET, SORGQR, SSYRK
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN, REAL
* ..
* .. Scalars in Common ..
CHARACTER*32 SRNAMT
* ..
* .. Common blocks ..
COMMON / SRNAMC / SRNAMT
* ..
* .. Executable Statements ..
*
MINMN = MIN( M, N )
EPS = SLAMCH( 'Epsilon' )
*
* Copy the matrix A to the array AF.
*
CALL SLACPY( 'Full', M, N, A, LDA, AF, LDA )
*
* Factorize the matrix A in the array AF.
*
SRNAMT = 'SGEQRF'
CALL SGEQRF( M, N, AF, LDA, TAU, WORK, LWORK, INFO )
*
* Copy details of Q
*
CALL SLASET( 'Full', M, M, ROGUE, ROGUE, Q, LDA )
CALL SLACPY( 'Lower', M-1, N, AF( 2, 1 ), LDA, Q( 2, 1 ), LDA )
*
* Generate the m-by-m matrix Q
*
SRNAMT = 'SORGQR'
CALL SORGQR( M, M, MINMN, Q, LDA, TAU, WORK, LWORK, INFO )
*
* Copy R
*
CALL SLASET( 'Full', M, N, ZERO, ZERO, R, LDA )
CALL SLACPY( 'Upper', M, N, AF, LDA, R, LDA )
*
* Compute R - Q'*A
*
CALL SGEMM( 'Transpose', 'No transpose', M, N, M, -ONE, Q, LDA, A,
$ LDA, ONE, R, LDA )
*
* Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) .
*
ANORM = SLANGE( '1', M, N, A, LDA, RWORK )
RESID = SLANGE( '1', M, N, 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 SLASET( 'Full', M, M, ZERO, ONE, R, LDA )
CALL SSYRK( 'Upper', 'Transpose', M, M, -ONE, Q, LDA, ONE, R,
$ LDA )
*
* Compute norm( I - Q'*Q ) / ( M * EPS ) .
*
RESID = SLANSY( '1', 'Upper', M, R, LDA, RWORK )
*
RESULT( 2 ) = ( RESID / REAL( MAX( 1, M ) ) ) / EPS
*
RETURN
*
* End of SQRT01
*
END
|
