*> \brief \b DPTT02 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DPTT02( N, NRHS, D, E, X, LDX, B, LDB, RESID ) * * .. Scalar Arguments .. * INTEGER LDB, LDX, N, NRHS * DOUBLE PRECISION RESID * .. * .. Array Arguments .. * DOUBLE PRECISION B( LDB, * ), D( * ), E( * ), X( LDX, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DPTT02 computes the residual for the solution to a symmetric *> tridiagonal system of equations: *> RESID = norm(B - A*X) / (norm(A) * norm(X) * EPS), *> where EPS is the machine epsilon. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGTER *> The order of the matrix A. *> \endverbatim *> *> \param[in] NRHS *> \verbatim *> NRHS is INTEGER *> The number of right hand sides, i.e., the number of columns *> of the matrices B and X. NRHS >= 0. *> \endverbatim *> *> \param[in] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> The n diagonal elements of the tridiagonal matrix A. *> \endverbatim *> *> \param[in] E *> \verbatim *> E is DOUBLE PRECISION array, dimension (N-1) *> The (n-1) subdiagonal elements of the tridiagonal matrix A. *> \endverbatim *> *> \param[in] X *> \verbatim *> X is DOUBLE PRECISION array, dimension (LDX,NRHS) *> The n by nrhs matrix of solution vectors X. *> \endverbatim *> *> \param[in] LDX *> \verbatim *> LDX is INTEGER *> The leading dimension of the array X. LDX >= max(1,N). *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is DOUBLE PRECISION array, dimension (LDB,NRHS) *> On entry, the n by nrhs matrix of right hand side vectors B. *> On exit, B is overwritten with the difference B - A*X. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,N). *> \endverbatim *> *> \param[out] RESID *> \verbatim *> RESID is DOUBLE PRECISION *> norm(B - A*X) / (norm(A) * norm(X) * EPS) *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup double_lin * * ===================================================================== SUBROUTINE DPTT02( N, NRHS, D, E, X, LDX, B, LDB, 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 LDB, LDX, N, NRHS DOUBLE PRECISION RESID * .. * .. Array Arguments .. DOUBLE PRECISION B( LDB, * ), D( * ), E( * ), X( LDX, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER J DOUBLE PRECISION ANORM, BNORM, EPS, XNORM * .. * .. External Functions .. DOUBLE PRECISION DASUM, DLAMCH, DLANST EXTERNAL DASUM, DLAMCH, DLANST * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. External Subroutines .. EXTERNAL DLAPTM * .. * .. Executable Statements .. * * Quick return if possible * IF( N.LE.0 ) THEN RESID = ZERO RETURN END IF * * Compute the 1-norm of the tridiagonal matrix A. * ANORM = DLANST( '1', N, D, E ) * * Exit with RESID = 1/EPS if ANORM = 0. * EPS = DLAMCH( 'Epsilon' ) IF( ANORM.LE.ZERO ) THEN RESID = ONE / EPS RETURN END IF * * Compute B - A*X. * CALL DLAPTM( N, NRHS, -ONE, D, E, X, LDX, ONE, B, LDB ) * * Compute the maximum over the number of right hand sides of * norm(B - A*X) / ( norm(A) * norm(X) * EPS ). * RESID = ZERO DO 10 J = 1, NRHS BNORM = DASUM( N, B( 1, J ), 1 ) XNORM = DASUM( N, X( 1, J ), 1 ) IF( XNORM.LE.ZERO ) THEN RESID = ONE / EPS ELSE RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS ) END IF 10 CONTINUE * RETURN * * End of DPTT02 * END