LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dtpt06.f
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00001 *> \brief \b DTPT06
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 DTPT06( RCOND, RCONDC, UPLO, DIAG, N, AP, WORK, RAT )
00012 * 
00013 *       .. Scalar Arguments ..
00014 *       CHARACTER          DIAG, UPLO
00015 *       INTEGER            N
00016 *       DOUBLE PRECISION   RAT, RCOND, RCONDC
00017 *       ..
00018 *       .. Array Arguments ..
00019 *       DOUBLE PRECISION   AP( * ), WORK( * )
00020 *       ..
00021 *  
00022 *
00023 *> \par Purpose:
00024 *  =============
00025 *>
00026 *> \verbatim
00027 *>
00028 *> DTPT06 computes a test ratio comparing RCOND (the reciprocal
00029 *> condition number of a triangular matrix A) and RCONDC, the estimate
00030 *> computed by DTPCON.  Information about the triangular matrix A is
00031 *> used if one estimate is zero and the other is non-zero to decide if
00032 *> underflow in the estimate is justified.
00033 *> \endverbatim
00034 *
00035 *  Arguments:
00036 *  ==========
00037 *
00038 *> \param[in] RCOND
00039 *> \verbatim
00040 *>          RCOND is DOUBLE PRECISION
00041 *>          The estimate of the reciprocal condition number obtained by
00042 *>          forming the explicit inverse of the matrix A and computing
00043 *>          RCOND = 1/( norm(A) * norm(inv(A)) ).
00044 *> \endverbatim
00045 *>
00046 *> \param[in] RCONDC
00047 *> \verbatim
00048 *>          RCONDC is DOUBLE PRECISION
00049 *>          The estimate of the reciprocal condition number computed by
00050 *>          DTPCON.
00051 *> \endverbatim
00052 *>
00053 *> \param[in] UPLO
00054 *> \verbatim
00055 *>          UPLO is CHARACTER
00056 *>          Specifies whether the matrix A is upper or lower triangular.
00057 *>          = 'U':  Upper triangular
00058 *>          = 'L':  Lower triangular
00059 *> \endverbatim
00060 *>
00061 *> \param[in] DIAG
00062 *> \verbatim
00063 *>          DIAG is CHARACTER
00064 *>          Specifies whether or not the matrix A is unit triangular.
00065 *>          = 'N':  Non-unit triangular
00066 *>          = 'U':  Unit triangular
00067 *> \endverbatim
00068 *>
00069 *> \param[in] N
00070 *> \verbatim
00071 *>          N is INTEGER
00072 *>          The order of the matrix A.  N >= 0.
00073 *> \endverbatim
00074 *>
00075 *> \param[in] AP
00076 *> \verbatim
00077 *>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
00078 *>          The upper or lower triangular matrix A, packed columnwise in
00079 *>          a linear array.  The j-th column of A is stored in the array
00080 *>          AP as follows:
00081 *>          if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
00082 *>          if UPLO = 'L',
00083 *>             AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
00084 *> \endverbatim
00085 *>
00086 *> \param[out] WORK
00087 *> \verbatim
00088 *>          WORK is DOUBLE PRECISION array, dimension (N)
00089 *> \endverbatim
00090 *>
00091 *> \param[out] RAT
00092 *> \verbatim
00093 *>          RAT is DOUBLE PRECISION
00094 *>          The test ratio.  If both RCOND and RCONDC are nonzero,
00095 *>             RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
00096 *>          If RAT = 0, the two estimates are exactly the same.
00097 *> \endverbatim
00098 *
00099 *  Authors:
00100 *  ========
00101 *
00102 *> \author Univ. of Tennessee 
00103 *> \author Univ. of California Berkeley 
00104 *> \author Univ. of Colorado Denver 
00105 *> \author NAG Ltd. 
00106 *
00107 *> \date November 2011
00108 *
00109 *> \ingroup double_lin
00110 *
00111 *  =====================================================================
00112       SUBROUTINE DTPT06( RCOND, RCONDC, UPLO, DIAG, N, AP, WORK, RAT )
00113 *
00114 *  -- LAPACK test routine (version 3.4.0) --
00115 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00116 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00117 *     November 2011
00118 *
00119 *     .. Scalar Arguments ..
00120       CHARACTER          DIAG, UPLO
00121       INTEGER            N
00122       DOUBLE PRECISION   RAT, RCOND, RCONDC
00123 *     ..
00124 *     .. Array Arguments ..
00125       DOUBLE PRECISION   AP( * ), WORK( * )
00126 *     ..
00127 *
00128 *  =====================================================================
00129 *
00130 *     .. Parameters ..
00131       DOUBLE PRECISION   ZERO, ONE
00132       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
00133 *     ..
00134 *     .. Local Scalars ..
00135       DOUBLE PRECISION   ANORM, BIGNUM, EPS, RMAX, RMIN, SMLNUM
00136 *     ..
00137 *     .. External Functions ..
00138       DOUBLE PRECISION   DLAMCH, DLANTP
00139       EXTERNAL           DLAMCH, DLANTP
00140 *     ..
00141 *     .. Intrinsic Functions ..
00142       INTRINSIC          MAX, MIN
00143 *     ..
00144 *     .. External Subroutines ..
00145       EXTERNAL           DLABAD
00146 *     ..
00147 *     .. Executable Statements ..
00148 *
00149       EPS = DLAMCH( 'Epsilon' )
00150       RMAX = MAX( RCOND, RCONDC )
00151       RMIN = MIN( RCOND, RCONDC )
00152 *
00153 *     Do the easy cases first.
00154 *
00155       IF( RMIN.LT.ZERO ) THEN
00156 *
00157 *        Invalid value for RCOND or RCONDC, return 1/EPS.
00158 *
00159          RAT = ONE / EPS
00160 *
00161       ELSE IF( RMIN.GT.ZERO ) THEN
00162 *
00163 *        Both estimates are positive, return RMAX/RMIN - 1.
00164 *
00165          RAT = RMAX / RMIN - ONE
00166 *
00167       ELSE IF( RMAX.EQ.ZERO ) THEN
00168 *
00169 *        Both estimates zero.
00170 *
00171          RAT = ZERO
00172 *
00173       ELSE
00174 *
00175 *        One estimate is zero, the other is non-zero.  If the matrix is
00176 *        ill-conditioned, return the nonzero estimate multiplied by
00177 *        1/EPS; if the matrix is badly scaled, return the nonzero
00178 *        estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
00179 *        element in absolute value in A.
00180 *
00181          SMLNUM = DLAMCH( 'Safe minimum' )
00182          BIGNUM = ONE / SMLNUM
00183          CALL DLABAD( SMLNUM, BIGNUM )
00184          ANORM = DLANTP( 'M', UPLO, DIAG, N, AP, WORK )
00185 *
00186          RAT = RMAX*( MIN( BIGNUM / MAX( ONE, ANORM ), ONE / EPS ) )
00187       END IF
00188 *
00189       RETURN
00190 *
00191 *     End of DTPT06
00192 *
00193       END
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