*> \brief \b DPBT02 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DPBT02( UPLO, N, KD, NRHS, A, LDA, X, LDX, B, LDB, * RWORK, RESID ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER KD, LDA, LDB, LDX, N, NRHS * DOUBLE PRECISION RESID * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), B( LDB, * ), RWORK( * ), * $ X( LDX, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DPBT02 computes the residual for a solution of a symmetric banded *> system of equations A*x = b: *> RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS) *> where EPS is the machine precision. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies whether the upper or lower triangular part of the *> symmetric matrix A is stored: *> = 'U': Upper triangular *> = 'L': Lower triangular *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of rows and columns of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] KD *> \verbatim *> KD is INTEGER *> The number of super-diagonals of the matrix A if UPLO = 'U', *> or the number of sub-diagonals if UPLO = 'L'. KD >= 0. *> \endverbatim *> *> \param[in] NRHS *> \verbatim *> NRHS is INTEGER *> The number of right hand sides. NRHS >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> The original symmetric band matrix A. If UPLO = 'U', the *> upper triangular part of A is stored as a band matrix; if *> UPLO = 'L', the lower triangular part of A is stored. The *> columns of the appropriate triangle are stored in the columns *> of A and the diagonals of the triangle are stored in the rows *> of A. See DPBTRF for further details. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER. *> The leading dimension of the array A. LDA >= max(1,KD+1). *> \endverbatim *> *> \param[in] X *> \verbatim *> X is DOUBLE PRECISION array, dimension (LDX,NRHS) *> The computed solution vectors for the system of linear *> equations. *> \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 right hand side vectors for the system of *> linear equations. *> 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] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, dimension (N) *> \endverbatim *> *> \param[out] RESID *> \verbatim *> RESID is DOUBLE PRECISION *> The maximum over the number of right hand sides of *> 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. * *> \date December 2016 * *> \ingroup double_lin * * ===================================================================== SUBROUTINE DPBT02( UPLO, N, KD, NRHS, A, LDA, X, LDX, B, LDB, $ RWORK, RESID ) * * -- LAPACK test routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER KD, LDA, LDB, LDX, N, NRHS DOUBLE PRECISION RESID * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), B( LDB, * ), RWORK( * ), $ X( LDX, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. INTEGER J DOUBLE PRECISION ANORM, BNORM, EPS, XNORM * .. * .. External Functions .. DOUBLE PRECISION DASUM, DLAMCH, DLANSB EXTERNAL DASUM, DLAMCH, DLANSB * .. * .. External Subroutines .. EXTERNAL DSBMV * .. * .. Intrinsic Functions .. INTRINSIC 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 ANORM = 0. * EPS = DLAMCH( 'Epsilon' ) ANORM = DLANSB( '1', UPLO, N, KD, A, LDA, RWORK ) IF( ANORM.LE.ZERO ) THEN RESID = ONE / EPS RETURN END IF * * Compute B - A*X * DO 10 J = 1, NRHS CALL DSBMV( UPLO, N, KD, -ONE, A, LDA, X( 1, J ), 1, ONE, $ B( 1, J ), 1 ) 10 CONTINUE * * Compute the maximum over the number of right hand sides of * norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) * RESID = ZERO DO 20 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 20 CONTINUE * RETURN * * End of DPBT02 * END