LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dtrt06.f
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00001 *> \brief \b DTRT06
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *  Definition:
00009 *  ===========
00010 *
00011 *       SUBROUTINE DTRT06( RCOND, RCONDC, UPLO, DIAG, N, A, LDA, WORK,
00012 *                          RAT )
00013 * 
00014 *       .. Scalar Arguments ..
00015 *       CHARACTER          DIAG, UPLO
00016 *       INTEGER            LDA, N
00017 *       DOUBLE PRECISION   RAT, RCOND, RCONDC
00018 *       ..
00019 *       .. Array Arguments ..
00020 *       DOUBLE PRECISION   A( LDA, * ), WORK( * )
00021 *       ..
00022 *  
00023 *
00024 *> \par Purpose:
00025 *  =============
00026 *>
00027 *> \verbatim
00028 *>
00029 *> DTRT06 computes a test ratio comparing RCOND (the reciprocal
00030 *> condition number of a triangular matrix A) and RCONDC, the estimate
00031 *> computed by DTRCON.  Information about the triangular matrix A is
00032 *> used if one estimate is zero and the other is non-zero to decide if
00033 *> underflow in the estimate is justified.
00034 *> \endverbatim
00035 *
00036 *  Arguments:
00037 *  ==========
00038 *
00039 *> \param[in] RCOND
00040 *> \verbatim
00041 *>          RCOND is DOUBLE PRECISION
00042 *>          The estimate of the reciprocal condition number obtained by
00043 *>          forming the explicit inverse of the matrix A and computing
00044 *>          RCOND = 1/( norm(A) * norm(inv(A)) ).
00045 *> \endverbatim
00046 *>
00047 *> \param[in] RCONDC
00048 *> \verbatim
00049 *>          RCONDC is DOUBLE PRECISION
00050 *>          The estimate of the reciprocal condition number computed by
00051 *>          DTRCON.
00052 *> \endverbatim
00053 *>
00054 *> \param[in] UPLO
00055 *> \verbatim
00056 *>          UPLO is CHARACTER
00057 *>          Specifies whether the matrix A is upper or lower triangular.
00058 *>          = 'U':  Upper triangular
00059 *>          = 'L':  Lower triangular
00060 *> \endverbatim
00061 *>
00062 *> \param[in] DIAG
00063 *> \verbatim
00064 *>          DIAG is CHARACTER
00065 *>          Specifies whether or not the matrix A is unit triangular.
00066 *>          = 'N':  Non-unit triangular
00067 *>          = 'U':  Unit triangular
00068 *> \endverbatim
00069 *>
00070 *> \param[in] N
00071 *> \verbatim
00072 *>          N is INTEGER
00073 *>          The order of the matrix A.  N >= 0.
00074 *> \endverbatim
00075 *>
00076 *> \param[in] A
00077 *> \verbatim
00078 *>          A is DOUBLE PRECISION array, dimension (LDA,N)
00079 *>          The triangular matrix A.  If UPLO = 'U', the leading n by n
00080 *>          upper triangular part of the array A contains the upper
00081 *>          triangular matrix, and the strictly lower triangular part of
00082 *>          A is not referenced.  If UPLO = 'L', the leading n by n lower
00083 *>          triangular part of the array A contains the lower triangular
00084 *>          matrix, and the strictly upper triangular part of A is not
00085 *>          referenced.  If DIAG = 'U', the diagonal elements of A are
00086 *>          also not referenced and are assumed to be 1.
00087 *> \endverbatim
00088 *>
00089 *> \param[in] LDA
00090 *> \verbatim
00091 *>          LDA is INTEGER
00092 *>          The leading dimension of the array A.  LDA >= max(1,N).
00093 *> \endverbatim
00094 *>
00095 *> \param[out] WORK
00096 *> \verbatim
00097 *>          WORK is DOUBLE PRECISION array, dimension (N)
00098 *> \endverbatim
00099 *>
00100 *> \param[out] RAT
00101 *> \verbatim
00102 *>          RAT is DOUBLE PRECISION
00103 *>          The test ratio.  If both RCOND and RCONDC are nonzero,
00104 *>             RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
00105 *>          If RAT = 0, the two estimates are exactly the same.
00106 *> \endverbatim
00107 *
00108 *  Authors:
00109 *  ========
00110 *
00111 *> \author Univ. of Tennessee 
00112 *> \author Univ. of California Berkeley 
00113 *> \author Univ. of Colorado Denver 
00114 *> \author NAG Ltd. 
00115 *
00116 *> \date November 2011
00117 *
00118 *> \ingroup double_lin
00119 *
00120 *  =====================================================================
00121       SUBROUTINE DTRT06( RCOND, RCONDC, UPLO, DIAG, N, A, LDA, WORK,
00122      $                   RAT )
00123 *
00124 *  -- LAPACK test routine (version 3.4.0) --
00125 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00126 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00127 *     November 2011
00128 *
00129 *     .. Scalar Arguments ..
00130       CHARACTER          DIAG, UPLO
00131       INTEGER            LDA, N
00132       DOUBLE PRECISION   RAT, RCOND, RCONDC
00133 *     ..
00134 *     .. Array Arguments ..
00135       DOUBLE PRECISION   A( LDA, * ), WORK( * )
00136 *     ..
00137 *
00138 *  =====================================================================
00139 *
00140 *     .. Parameters ..
00141       DOUBLE PRECISION   ZERO, ONE
00142       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
00143 *     ..
00144 *     .. Local Scalars ..
00145       DOUBLE PRECISION   ANORM, BIGNUM, EPS, RMAX, RMIN, SMLNUM
00146 *     ..
00147 *     .. External Functions ..
00148       DOUBLE PRECISION   DLAMCH, DLANTR
00149       EXTERNAL           DLAMCH, DLANTR
00150 *     ..
00151 *     .. Intrinsic Functions ..
00152       INTRINSIC          MAX, MIN
00153 *     ..
00154 *     .. External Subroutines ..
00155       EXTERNAL           DLABAD
00156 *     ..
00157 *     .. Executable Statements ..
00158 *
00159       EPS = DLAMCH( 'Epsilon' )
00160       RMAX = MAX( RCOND, RCONDC )
00161       RMIN = MIN( RCOND, RCONDC )
00162 *
00163 *     Do the easy cases first.
00164 *
00165       IF( RMIN.LT.ZERO ) THEN
00166 *
00167 *        Invalid value for RCOND or RCONDC, return 1/EPS.
00168 *
00169          RAT = ONE / EPS
00170 *
00171       ELSE IF( RMIN.GT.ZERO ) THEN
00172 *
00173 *        Both estimates are positive, return RMAX/RMIN - 1.
00174 *
00175          RAT = RMAX / RMIN - ONE
00176 *
00177       ELSE IF( RMAX.EQ.ZERO ) THEN
00178 *
00179 *        Both estimates zero.
00180 *
00181          RAT = ZERO
00182 *
00183       ELSE
00184 *
00185 *        One estimate is zero, the other is non-zero.  If the matrix is
00186 *        ill-conditioned, return the nonzero estimate multiplied by
00187 *        1/EPS; if the matrix is badly scaled, return the nonzero
00188 *        estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
00189 *        element in absolute value in A.
00190 *
00191          SMLNUM = DLAMCH( 'Safe minimum' )
00192          BIGNUM = ONE / SMLNUM
00193          CALL DLABAD( SMLNUM, BIGNUM )
00194          ANORM = DLANTR( 'M', UPLO, DIAG, N, N, A, LDA, WORK )
00195 *
00196          RAT = RMAX*( MIN( BIGNUM / MAX( ONE, ANORM ), ONE / EPS ) )
00197       END IF
00198 *
00199       RETURN
00200 *
00201 *     End of DTRT06
00202 *
00203       END
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