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*> \brief \b ZTRT06
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZTRT06( RCOND, RCONDC, UPLO, DIAG, N, A, LDA, RWORK,
* RAT )
*
* .. Scalar Arguments ..
* CHARACTER DIAG, UPLO
* INTEGER LDA, N
* DOUBLE PRECISION RAT, RCOND, RCONDC
* ..
* .. Array Arguments ..
* DOUBLE PRECISION RWORK( * )
* COMPLEX*16 A( LDA, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZTRT06 computes a test ratio comparing RCOND (the reciprocal
*> condition number of a triangular matrix A) and RCONDC, the estimate
*> computed by ZTRCON. 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 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)) ).
*> \endverbatim
*>
*> \param[in] RCONDC
*> \verbatim
*> RCONDC is DOUBLE PRECISION
*> The estimate of the reciprocal condition number computed by
*> ZTRCON.
*> \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] A
*> \verbatim
*> A is COMPLEX*16 array, dimension (LDA,N)
*> The triangular matrix A. If UPLO = 'U', the leading n by n
*> upper triangular part of the array A contains the upper
*> triangular matrix, and the strictly lower triangular part of
*> A is not referenced. If UPLO = 'L', the leading n by n lower
*> triangular part of the array A contains the lower triangular
*> matrix, and the strictly upper triangular part of A is not
*> referenced. If DIAG = 'U', the diagonal elements of A are
*> also not referenced and are assumed to be 1.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
*>
*> \param[out] RAT
*> \verbatim
*> RAT is 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.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup complex16_lin
*
* =====================================================================
SUBROUTINE ZTRT06( RCOND, RCONDC, UPLO, DIAG, N, A, LDA, RWORK,
$ RAT )
*
* -- LAPACK test routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
CHARACTER DIAG, UPLO
INTEGER LDA, N
DOUBLE PRECISION RAT, RCOND, RCONDC
* ..
* .. Array Arguments ..
DOUBLE PRECISION RWORK( * )
COMPLEX*16 A( LDA, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
DOUBLE PRECISION ANORM, BIGNUM, EPS, RMAX, RMIN
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, ZLANTR
EXTERNAL DLAMCH, ZLANTR
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. 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.
*
BIGNUM = ONE / DLAMCH( 'Safe minimum' )
ANORM = ZLANTR( 'M', UPLO, DIAG, N, N, A, LDA, RWORK )
*
RAT = RMAX*( MIN( BIGNUM / MAX( ONE, ANORM ), ONE / EPS ) )
END IF
*
RETURN
*
* End of ZTRT06
*
END
|
