*> \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