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SUBROUTINE DGTT02( TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB,
$ RWORK, RESID ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER TRANS INTEGER LDB, LDX, N, NRHS DOUBLE PRECISION RESID * .. * .. Array Arguments .. DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ), $ RWORK( * ), X( LDX, * ) * .. * * Purpose * ======= * * DGTT02 computes the residual for the solution to a tridiagonal * system of equations: * RESID = norm(B - op(A)*X) / (norm(A) * norm(X) * EPS), * where EPS is the machine epsilon. * * Arguments * ========= * * TRANS (input) CHARACTER * Specifies the form of the residual. * = 'N': B - A * X (No transpose) * = 'T': B - A'* X (Transpose) * = 'C': B - A'* X (Conjugate transpose = Transpose) * * N (input) INTEGTER * The order of the matrix A. N >= 0. * * NRHS (input) INTEGER * The number of right hand sides, i.e., the number of columns * of the matrices B and X. NRHS >= 0. * * DL (input) DOUBLE PRECISION array, dimension (N-1) * The (n-1) sub-diagonal elements of A. * * D (input) DOUBLE PRECISION array, dimension (N) * The diagonal elements of A. * * DU (input) DOUBLE PRECISION array, dimension (N-1) * The (n-1) super-diagonal elements of A. * * X (input) DOUBLE PRECISION array, dimension (LDX,NRHS) * The computed 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 right hand side vectors for the system of * linear equations. * On exit, B is overwritten with the difference B - op(A)*X. * * LDB (input) INTEGER * The leading dimension of the array B. LDB >= max(1,N). * * RWORK (workspace) DOUBLE PRECISION array, dimension (N) * * RESID (output) DOUBLE PRECISION * norm(B - op(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 .. LOGICAL LSAME DOUBLE PRECISION DASUM, DLAMCH, DLANGT EXTERNAL LSAME, DASUM, DLAMCH, DLANGT * .. * .. External Subroutines .. EXTERNAL DLAGTM * .. * .. 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(A) * norm(X) * EPS ). * IF( LSAME( TRANS, 'N' ) ) THEN ANORM = DLANGT( '1', N, DL, D, DU ) ELSE ANORM = DLANGT( 'I', N, DL, D, DU ) END IF * * Exit with RESID = 1/EPS if ANORM = 0. * EPS = DLAMCH( 'Epsilon' ) IF( ANORM.LE.ZERO ) THEN RESID = ONE / EPS RETURN END IF * * Compute B - op(A)*X. * CALL DLAGTM( TRANS, N, NRHS, -ONE, DL, D, DU, X, LDX, ONE, B, $ LDB ) * 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 DGTT02 * END |