SUBROUTINE DTBT06( RCOND, RCONDC, UPLO, DIAG, N, KD, AB, LDAB, \$ WORK, RAT ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER DIAG, UPLO INTEGER KD, LDAB, N DOUBLE PRECISION RAT, RCOND, RCONDC * .. * .. Array Arguments .. DOUBLE PRECISION AB( LDAB, * ), WORK( * ) * .. * * Purpose * ======= * * DTBT06 computes a test ratio comparing RCOND (the reciprocal * condition number of a triangular matrix A) and RCONDC, the estimate * computed by DTBCON. Information about the triangular matrix A is * used if one estimate is zero and the other is non-zero to decide if * underflow in the estimate is justified. * * Arguments * ========= * * RCOND (input) DOUBLE PRECISION * The estimate of the reciprocal condition number obtained by * forming the explicit inverse of the matrix A and computing * RCOND = 1/( norm(A) * norm(inv(A)) ). * * RCONDC (input) DOUBLE PRECISION * The estimate of the reciprocal condition number computed by * DTBCON. * * UPLO (input) CHARACTER * Specifies whether the matrix A is upper or lower triangular. * = 'U': Upper triangular * = 'L': Lower triangular * * DIAG (input) CHARACTER * Specifies whether or not the matrix A is unit triangular. * = 'N': Non-unit triangular * = 'U': Unit triangular * * N (input) INTEGER * The order of the matrix A. N >= 0. * * KD (input) INTEGER * The number of superdiagonals or subdiagonals of the * triangular band matrix A. KD >= 0. * * AB (input) DOUBLE PRECISION array, dimension (LDAB,N) * The upper or lower triangular band matrix A, stored in the * first kd+1 rows of the array. The j-th column of A is stored * in the j-th column of the array AB as follows: * if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). * * LDAB (input) INTEGER * The leading dimension of the array AB. LDAB >= KD+1. * * WORK (workspace) DOUBLE PRECISION array, dimension (N) * * RAT (output) DOUBLE PRECISION * The test ratio. If both RCOND and RCONDC are nonzero, * RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1. * If RAT = 0, the two estimates are exactly the same. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. DOUBLE PRECISION ANORM, BIGNUM, EPS, RMAX, RMIN, SMLNUM * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, DLANTB EXTERNAL DLAMCH, DLANTB * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. External Subroutines .. EXTERNAL DLABAD * .. * .. Executable Statements .. * EPS = DLAMCH( 'Epsilon' ) RMAX = MAX( RCOND, RCONDC ) RMIN = MIN( RCOND, RCONDC ) * * Do the easy cases first. * IF( RMIN.LT.ZERO ) THEN * * Invalid value for RCOND or RCONDC, return 1/EPS. * RAT = ONE / EPS * ELSE IF( RMIN.GT.ZERO ) THEN * * Both estimates are positive, return RMAX/RMIN - 1. * RAT = RMAX / RMIN - ONE * ELSE IF( RMAX.EQ.ZERO ) THEN * * Both estimates zero. * RAT = ZERO * ELSE * * One estimate is zero, the other is non-zero. If the matrix is * ill-conditioned, return the nonzero estimate multiplied by * 1/EPS; if the matrix is badly scaled, return the nonzero * estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum * element in absolute value in A. * SMLNUM = DLAMCH( 'Safe minimum' ) BIGNUM = ONE / SMLNUM CALL DLABAD( SMLNUM, BIGNUM ) ANORM = DLANTB( 'M', UPLO, DIAG, N, KD, AB, LDAB, WORK ) * RAT = RMAX*( MIN( BIGNUM / MAX( ONE, ANORM ), ONE / EPS ) ) END IF * RETURN * * End of DTBT06 * END