177 lines
4.5 KiB
Fortran
177 lines
4.5 KiB
Fortran
*> \brief \b DGET04
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE DGET04( N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* INTEGER LDX, LDXACT, N, NRHS
|
|
* DOUBLE PRECISION RCOND, RESID
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* DOUBLE PRECISION X( LDX, * ), XACT( LDXACT, * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> DGET04 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION
|
|
*> The reciprocal of the condition number of the coefficient
|
|
*> matrix in the system of equations.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] RESID
|
|
*> \verbatim
|
|
*> RESID is DOUBLE PRECISION
|
|
*> 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.
|
|
*
|
|
*> \ingroup double_lin
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE DGET04( N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID )
|
|
*
|
|
* -- 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 LDX, LDXACT, N, NRHS
|
|
DOUBLE PRECISION RCOND, RESID
|
|
* ..
|
|
* .. Array Arguments ..
|
|
DOUBLE PRECISION X( LDX, * ), XACT( LDXACT, * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
DOUBLE PRECISION ZERO
|
|
PARAMETER ( ZERO = 0.0D+0 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
INTEGER I, IX, J
|
|
DOUBLE PRECISION DIFFNM, EPS, XNORM
|
|
* ..
|
|
* .. External Functions ..
|
|
INTEGER IDAMAX
|
|
DOUBLE PRECISION DLAMCH
|
|
EXTERNAL IDAMAX, DLAMCH
|
|
* ..
|
|
* .. 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 = DLAMCH( 'Epsilon' )
|
|
IF( RCOND.LT.ZERO ) THEN
|
|
RESID = 1.0D0 / 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 = IDAMAX( 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 = 1.0D0 / EPS
|
|
ELSE
|
|
RESID = MAX( RESID, ( DIFFNM / XNORM )*RCOND )
|
|
END IF
|
|
20 CONTINUE
|
|
IF( RESID*EPS.LT.1.0D0 )
|
|
$ RESID = RESID / EPS
|
|
*
|
|
RETURN
|
|
*
|
|
* End of DGET04
|
|
*
|
|
END
|