*> \brief \b SGTT02 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SGTT02( TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB, * RESID ) * * .. Scalar Arguments .. * CHARACTER TRANS * INTEGER LDB, LDX, N, NRHS * REAL RESID * .. * .. Array Arguments .. * REAL B( LDB, * ), D( * ), DL( * ), DU( * ), * $ X( LDX, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SGTT02 computes the residual for the solution to a tridiagonal *> system of equations: *> RESID = norm(B - op(A)*X) / (norm(op(A)) * norm(X) * EPS), *> where EPS is the machine epsilon. *> The norm used is the 1-norm. *> \endverbatim * * Arguments: * ========== * *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER *> Specifies the form of the residual. *> = 'N': B - A * X (No transpose) *> = 'T': B - A**T * X (Transpose) *> = 'C': B - A**H * X (Conjugate transpose = Transpose) *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGTER *> The order of the matrix A. N >= 0. *> \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] DL *> \verbatim *> DL is REAL array, dimension (N-1) *> The (n-1) sub-diagonal elements of A. *> \endverbatim *> *> \param[in] D *> \verbatim *> D is REAL array, dimension (N) *> The diagonal elements of A. *> \endverbatim *> *> \param[in] DU *> \verbatim *> DU is REAL array, dimension (N-1) *> The (n-1) super-diagonal elements of A. *> \endverbatim *> *> \param[in] X *> \verbatim *> X is REAL array, dimension (LDX,NRHS) *> The computed 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 REAL 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 - op(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 - op(A)*X) / (norm(op(A)) * norm(X) * EPS) *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup single_lin * * ===================================================================== SUBROUTINE SGTT02( TRANS, N, NRHS, DL, D, DU, 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 .. CHARACTER TRANS INTEGER LDB, LDX, N, NRHS REAL RESID * .. * .. Array Arguments .. REAL B( LDB, * ), D( * ), DL( * ), DU( * ), $ 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 .. LOGICAL LSAME REAL SASUM, SLAMCH, SLANGT EXTERNAL LSAME, SASUM, SLAMCH, SLANGT * .. * .. External Subroutines .. EXTERNAL SLAGTM * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Quick exit if N = 0 or NRHS = 0 * RESID = ZERO IF( N.LE.0 .OR. NRHS.EQ.0 ) $ RETURN * * Compute the maximum over the number of right hand sides of * norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ). * IF( LSAME( TRANS, 'N' ) ) THEN ANORM = SLANGT( '1', N, DL, D, DU ) ELSE ANORM = SLANGT( 'I', N, DL, D, DU ) END IF * * Exit with RESID = 1/EPS if ANORM = 0. * EPS = SLAMCH( 'Epsilon' ) IF( ANORM.LE.ZERO ) THEN RESID = ONE / EPS RETURN END IF * * Compute B - op(A)*X and store in B. * CALL SLAGTM( TRANS, N, NRHS, -ONE, DL, D, DU, X, LDX, ONE, B, $ LDB ) * DO 10 J = 1, NRHS BNORM = SASUM( N, B( 1, J ), 1 ) XNORM = SASUM( 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 SGTT02 * END