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*> \brief \b STBT06
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE STBT06( RCOND, RCONDC, UPLO, DIAG, N, KD, AB, LDAB,
* WORK, RAT )
*
* .. Scalar Arguments ..
* CHARACTER DIAG, UPLO
* INTEGER KD, LDAB, N
* REAL RAT, RCOND, RCONDC
* ..
* .. Array Arguments ..
* REAL AB( LDAB, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> STBT06 computes a test ratio comparing RCOND (the reciprocal
*> condition number of a triangular matrix A) and RCONDC, the estimate
*> computed by STBCON. 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
*> STBCON.
*> \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] KD
*> \verbatim
*> KD is INTEGER
*> The number of superdiagonals or subdiagonals of the
*> triangular band matrix A. KD >= 0.
*> \endverbatim
*>
*> \param[in] AB
*> \verbatim
*> AB is REAL 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).
*> \endverbatim
*>
*> \param[in] LDAB
*> \verbatim
*> LDAB is INTEGER
*> The leading dimension of the array AB. LDAB >= KD+1.
*> \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 STBT06( RCOND, RCONDC, UPLO, DIAG, N, KD, AB, LDAB,
$ 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 KD, LDAB, N
REAL RAT, RCOND, RCONDC
* ..
* .. Array Arguments ..
REAL AB( LDAB, * ), 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, SLANTB
EXTERNAL SLAMCH, SLANTB
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. 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
ANORM = SLANTB( 'M', UPLO, DIAG, N, KD, AB, LDAB, WORK )
*
RAT = RMAX*( MIN( BIGNUM / MAX( ONE, ANORM ), ONE / EPS ) )
END IF
*
RETURN
*
* End of STBT06
*
END
|
