180 lines
4.6 KiB
Fortran
180 lines
4.6 KiB
Fortran
*> \brief \b DGET04
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE DGET04( N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID )
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*
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* .. Scalar Arguments ..
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* INTEGER LDX, LDXACT, N, NRHS
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* DOUBLE PRECISION RCOND, RESID
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION X( LDX, * ), XACT( LDXACT, * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> DGET04 computes the difference between a computed solution and the
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*> true solution to a system of linear equations.
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*>
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*> RESID = ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS ),
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*> where RCOND is the reciprocal of the condition number and EPS is the
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*> machine epsilon.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of rows of the matrices X and XACT. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] NRHS
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*> \verbatim
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*> NRHS is INTEGER
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*> The number of columns of the matrices X and XACT. NRHS >= 0.
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*> \endverbatim
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*>
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*> \param[in] X
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*> \verbatim
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*> X is DOUBLE PRECISION array, dimension (LDX,NRHS)
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*> The computed solution vectors. Each vector is stored as a
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*> column of the matrix X.
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*> \endverbatim
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*>
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*> \param[in] LDX
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*> \verbatim
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*> LDX is INTEGER
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*> The leading dimension of the array X. LDX >= max(1,N).
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*> \endverbatim
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*>
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*> \param[in] XACT
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*> \verbatim
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*> XACT is DOUBLE PRECISION array, dimension( LDX, NRHS )
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*> The exact solution vectors. Each vector is stored as a
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*> column of the matrix XACT.
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*> \endverbatim
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*>
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*> \param[in] LDXACT
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*> \verbatim
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*> LDXACT is INTEGER
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*> The leading dimension of the array XACT. LDXACT >= max(1,N).
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*> \endverbatim
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*>
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*> \param[in] RCOND
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*> \verbatim
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*> RCOND is DOUBLE PRECISION
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*> The reciprocal of the condition number of the coefficient
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*> matrix in the system of equations.
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*> \endverbatim
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*>
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*> \param[out] RESID
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*> \verbatim
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*> RESID is DOUBLE PRECISION
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*> The maximum over the NRHS solution vectors of
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*> ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS )
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date December 2016
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*
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*> \ingroup double_lin
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*
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* =====================================================================
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SUBROUTINE DGET04( N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID )
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*
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* -- LAPACK test routine (version 3.7.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* December 2016
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*
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* .. Scalar Arguments ..
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INTEGER LDX, LDXACT, N, NRHS
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DOUBLE PRECISION RCOND, RESID
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION X( LDX, * ), XACT( LDXACT, * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO
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PARAMETER ( ZERO = 0.0D+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, IX, J
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DOUBLE PRECISION DIFFNM, EPS, XNORM
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* ..
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* .. External Functions ..
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INTEGER IDAMAX
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DOUBLE PRECISION DLAMCH
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EXTERNAL IDAMAX, DLAMCH
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX
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* ..
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* .. Executable Statements ..
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*
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* Quick exit if N = 0 or NRHS = 0.
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*
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IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
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RESID = ZERO
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RETURN
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END IF
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*
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* Exit with RESID = 1/EPS if RCOND is invalid.
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*
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EPS = DLAMCH( 'Epsilon' )
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IF( RCOND.LT.ZERO ) THEN
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RESID = 1.0D0 / EPS
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RETURN
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END IF
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*
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* Compute the maximum of
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* norm(X - XACT) / ( norm(XACT) * EPS )
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* over all the vectors X and XACT .
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*
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RESID = ZERO
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DO 20 J = 1, NRHS
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IX = IDAMAX( N, XACT( 1, J ), 1 )
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XNORM = ABS( XACT( IX, J ) )
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DIFFNM = ZERO
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DO 10 I = 1, N
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DIFFNM = MAX( DIFFNM, ABS( X( I, J )-XACT( I, J ) ) )
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10 CONTINUE
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IF( XNORM.LE.ZERO ) THEN
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IF( DIFFNM.GT.ZERO )
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$ RESID = 1.0D0 / EPS
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ELSE
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RESID = MAX( RESID, ( DIFFNM / XNORM )*RCOND )
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END IF
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20 CONTINUE
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IF( RESID*EPS.LT.1.0D0 )
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$ RESID = RESID / EPS
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*
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RETURN
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*
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* End of DGET04
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*
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END
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