You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
197 lines
5.5 KiB
197 lines
5.5 KiB
*> \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.
|
|
*
|
|
*> \ingroup complex16_lin
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE ZTRT06( RCOND, RCONDC, UPLO, DIAG, N, A, LDA, RWORK,
|
|
$ 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 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
|
|
|