dtrt06.f

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*> \brief \b DTRT06
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
*  Definition:
*  ===========
*
*       SUBROUTINE DTRT06( RCOND, RCONDC, UPLO, DIAG, N, A, LDA, WORK,
*                          RAT )
* 
*       .. Scalar Arguments ..
*       CHARACTER          DIAG, UPLO
*       INTEGER            LDA, N
*       DOUBLE PRECISION   RAT, RCOND, RCONDC
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   A( LDA, * ), WORK( * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DTRT06 computes a test ratio comparing RCOND (the reciprocal
*> condition number of a triangular matrix A) and RCONDC, the estimate
*> computed by DTRCON.  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
*>          DTRCON.
*> \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 DOUBLE PRECISION 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] WORK
*> \verbatim
*>          WORK 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 November 2011
*
*> \ingroup double_lin
*
*  =====================================================================
      SUBROUTINE dtrt06( RCOND, RCONDC, UPLO, DIAG, N, A, LDA, WORK,
     $                   rat )
*
*  -- LAPACK test routine (version 3.4.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. Scalar Arguments ..
      CHARACTER          DIAG, UPLO
      INTEGER            LDA, N
      DOUBLE PRECISION   RAT, RCOND, RCONDC
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( lda, * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. 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, DLANTR
      EXTERNAL           dlamch, dlantr
*     ..
*     .. 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 = dlantr( 'M', uplo, diag, n, n, a, lda, work )
*
         rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
      END IF
*
      RETURN
*
*     End of DTRT06
*
      END