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*> \brief \b SGET04
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE SGET04( N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID )
*
* .. Scalar Arguments ..
* INTEGER LDX, LDXACT, N, NRHS
* REAL RCOND, RESID
* ..
* .. Array Arguments ..
* REAL X( LDX, * ), XACT( LDXACT, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SGET04 computes the difference between a computed solution and the
*> true solution to a system of linear equations.
*>
*> RESID = ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS ),
*> where RCOND is the reciprocal of the condition number and EPS is the
*> machine epsilon.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of rows of the matrices X and XACT. N >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*> NRHS is INTEGER
*> The number of columns of the matrices X and XACT. NRHS >= 0.
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*> X is REAL array, dimension (LDX,NRHS)
*> The computed solution vectors. Each vector is stored as a
*> column of the matrix X.
*> \endverbatim
*>
*> \param[in] LDX
*> \verbatim
*> LDX is INTEGER
*> The leading dimension of the array X. LDX >= max(1,N).
*> \endverbatim
*>
*> \param[in] XACT
*> \verbatim
*> XACT is REAL array, dimension( LDX, NRHS )
*> The exact solution vectors. Each vector is stored as a
*> column of the matrix XACT.
*> \endverbatim
*>
*> \param[in] LDXACT
*> \verbatim
*> LDXACT is INTEGER
*> The leading dimension of the array XACT. LDXACT >= max(1,N).
*> \endverbatim
*>
*> \param[in] RCOND
*> \verbatim
*> RCOND is REAL
*> The reciprocal of the condition number of the coefficient
*> matrix in the system of equations.
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*> RESID is REAL
*> The maximum over the NRHS solution vectors of
*> ( norm(X-XACT) * RCOND ) / ( norm(XACT) * 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 SGET04( N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID )
*
* -- 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 LDX, LDXACT, N, NRHS
REAL RCOND, RESID
* ..
* .. Array Arguments ..
REAL X( LDX, * ), XACT( LDXACT, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO
PARAMETER ( ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
INTEGER I, IX, J
REAL DIFFNM, EPS, XNORM
* ..
* .. External Functions ..
INTEGER ISAMAX
REAL SLAMCH
EXTERNAL ISAMAX, SLAMCH
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX
* ..
* .. Executable Statements ..
*
* Quick exit if N = 0 or NRHS = 0.
*
IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
RESID = ZERO
RETURN
END IF
*
* Exit with RESID = 1/EPS if RCOND is invalid.
*
EPS = SLAMCH( 'Epsilon' )
IF( RCOND.LT.ZERO ) THEN
RESID = 1.0 / EPS
RETURN
END IF
*
* Compute the maximum of
* norm(X - XACT) / ( norm(XACT) * EPS )
* over all the vectors X and XACT .
*
RESID = ZERO
DO 20 J = 1, NRHS
IX = ISAMAX( N, XACT( 1, J ), 1 )
XNORM = ABS( XACT( IX, J ) )
DIFFNM = ZERO
DO 10 I = 1, N
DIFFNM = MAX( DIFFNM, ABS( X( I, J )-XACT( I, J ) ) )
10 CONTINUE
IF( XNORM.LE.ZERO ) THEN
IF( DIFFNM.GT.ZERO )
$ RESID = 1.0 / EPS
ELSE
RESID = MAX( RESID, ( DIFFNM / XNORM )*RCOND )
END IF
20 CONTINUE
IF( RESID*EPS.LT.1.0 )
$ RESID = RESID / EPS
*
RETURN
*
* End of SGET04
*
END
|
