SUBROUTINE DPTT02( N, NRHS, D, E, X, LDX, B, LDB, RESID ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER LDB, LDX, N, NRHS DOUBLE PRECISION RESID * .. * .. Array Arguments .. DOUBLE PRECISION B( LDB, * ), D( * ), E( * ), X( LDX, * ) * .. * * Purpose * ======= * * 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. * * Arguments * ========= * * N (input) INTEGTER * The order of the matrix A. * * NRHS (input) INTEGER * The number of right hand sides, i.e., the number of columns * of the matrices B and X. NRHS >= 0. * * D (input) DOUBLE PRECISION array, dimension (N) * The n diagonal elements of the tridiagonal matrix A. * * E (input) DOUBLE PRECISION array, dimension (N-1) * The (n-1) subdiagonal elements of the tridiagonal matrix A. * * X (input) DOUBLE PRECISION array, dimension (LDX,NRHS) * The n by nrhs matrix of solution vectors X. * * LDX (input) INTEGER * The leading dimension of the array X. LDX >= max(1,N). * * B (input/output) 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. * * LDB (input) INTEGER * The leading dimension of the array B. LDB >= max(1,N). * * RESID (output) DOUBLE PRECISION * norm(B - A*X) / (norm(A) * norm(X) * EPS) * * ===================================================================== * * .. 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