*> \brief \b CPTT02 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE CPTT02( UPLO, N, NRHS, D, E, X, LDX, B, LDB, RESID ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER LDB, LDX, N, NRHS * REAL RESID * .. * .. Array Arguments .. * REAL D( * ) * COMPLEX B( LDB, * ), E( * ), X( LDX, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CPTT02 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] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies whether the superdiagonal or the subdiagonal of the *> tridiagonal matrix A is stored. *> = 'U': E is the superdiagonal of A *> = 'L': E is the subdiagonal of A *> \endverbatim *> *> \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 REAL array, dimension (N) *> The n diagonal elements of the tridiagonal matrix A. *> \endverbatim *> *> \param[in] E *> \verbatim *> E is COMPLEX array, dimension (N-1) *> The (n-1) subdiagonal elements of the tridiagonal matrix A. *> \endverbatim *> *> \param[in] X *> \verbatim *> X is COMPLEX 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 COMPLEX 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 REAL *> 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 complex_lin * * ===================================================================== SUBROUTINE CPTT02( UPLO, N, NRHS, D, E, X, LDX, B, LDB, 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 LDB, LDX, N, NRHS REAL RESID * .. * .. Array Arguments .. REAL D( * ) COMPLEX B( LDB, * ), E( * ), X( LDX, * ) * .. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. INTEGER J REAL ANORM, BNORM, EPS, XNORM * .. * .. External Functions .. REAL CLANHT, SCASUM, SLAMCH EXTERNAL CLANHT, SCASUM, SLAMCH * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. External Subroutines .. EXTERNAL CLAPTM * .. * .. 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 = CLANHT( '1', N, D, E ) * * Exit with RESID = 1/EPS if ANORM = 0. * EPS = SLAMCH( 'Epsilon' ) IF( ANORM.LE.ZERO ) THEN RESID = ONE / EPS RETURN END IF * * Compute B - A*X. * CALL CLAPTM( UPLO, 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 = SCASUM( N, B( 1, J ), 1 ) XNORM = SCASUM( 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 CPTT02 * END