*> \brief \b STPT06 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE STPT06( RCOND, RCONDC, UPLO, DIAG, N, AP, WORK, RAT ) * * .. Scalar Arguments .. * CHARACTER DIAG, UPLO * INTEGER N * REAL RAT, RCOND, RCONDC * .. * .. Array Arguments .. * REAL AP( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> STPT06 computes a test ratio comparing RCOND (the reciprocal *> condition number of a triangular matrix A) and RCONDC, the estimate *> computed by STPCON. 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. *> \endverbatim * * Arguments: * ========== * *> \param[in] RCOND *> \verbatim *> RCOND is REAL *> 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)) ). *> \endverbatim *> *> \param[in] RCONDC *> \verbatim *> RCONDC is REAL *> The estimate of the reciprocal condition number computed by *> STPCON. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER *> Specifies whether the matrix A is upper or lower triangular. *> = 'U': Upper triangular *> = 'L': Lower triangular *> \endverbatim *> *> \param[in] DIAG *> \verbatim *> DIAG is CHARACTER *> Specifies whether or not the matrix A is unit triangular. *> = 'N': Non-unit triangular *> = 'U': Unit triangular *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] AP *> \verbatim *> AP is REAL array, dimension (N*(N+1)/2) *> The upper or lower triangular matrix A, packed columnwise in *> a linear array. The j-th column of A is stored in the array *> AP as follows: *> if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', *> AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is REAL array, dimension (N) *> \endverbatim *> *> \param[out] RAT *> \verbatim *> RAT is REAL *> 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. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup single_lin * * ===================================================================== SUBROUTINE STPT06( RCOND, RCONDC, UPLO, DIAG, N, AP, WORK, RAT ) * * -- 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 DIAG, UPLO INTEGER N REAL RAT, RCOND, RCONDC * .. * .. Array Arguments .. REAL AP( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) * .. * .. Local Scalars .. REAL ANORM, BIGNUM, EPS, RMAX, RMIN, SMLNUM * .. * .. External Functions .. REAL SLAMCH, SLANTP EXTERNAL SLAMCH, SLANTP * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. External Subroutines .. EXTERNAL SLABAD * .. * .. Executable Statements .. * EPS = SLAMCH( '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 = SLAMCH( 'Safe minimum' ) BIGNUM = ONE / SMLNUM CALL SLABAD( SMLNUM, BIGNUM ) ANORM = SLANTP( 'M', UPLO, DIAG, N, AP, WORK ) * RAT = RMAX*( MIN( BIGNUM / MAX( ONE, ANORM ), ONE / EPS ) ) END IF * RETURN * * End of STPT06 * END