LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
ctpt06.f
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00001 *> \brief \b CTPT06
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 CTPT06( RCOND, RCONDC, UPLO, DIAG, N, AP, RWORK, RAT )
00012 * 
00013 *       .. Scalar Arguments ..
00014 *       CHARACTER          DIAG, UPLO
00015 *       INTEGER            N
00016 *       REAL               RAT, RCOND, RCONDC
00017 *       ..
00018 *       .. Array Arguments ..
00019 *       REAL               RWORK( * )
00020 *       COMPLEX            AP( * )
00021 *       ..
00022 *  
00023 *
00024 *> \par Purpose:
00025 *  =============
00026 *>
00027 *> \verbatim
00028 *>
00029 *> CTPT06 computes a test ratio comparing RCOND (the reciprocal
00030 *> condition number of the triangular matrix A) and RCONDC, the estimate
00031 *> computed by CTPCON.  Information about the triangular matrix is used
00032 *> 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 REAL
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 REAL
00050 *>          The estimate of the reciprocal condition number computed by
00051 *>          CTPCON.
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] AP
00077 *> \verbatim
00078 *>          AP is COMPLEX array, dimension (N*(N+1)/2)
00079 *>          The upper or lower triangular matrix A, packed columnwise in
00080 *>          a linear array.  The j-th column of A is stored in the array
00081 *>          AP as follows:
00082 *>          if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
00083 *>          if UPLO = 'L',
00084 *>             AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
00085 *> \endverbatim
00086 *>
00087 *> \param[out] RWORK
00088 *> \verbatim
00089 *>          RWORK is REAL array, dimension (N)
00090 *> \endverbatim
00091 *>
00092 *> \param[out] RAT
00093 *> \verbatim
00094 *>          RAT is REAL
00095 *>          The test ratio.  If both RCOND and RCONDC are nonzero,
00096 *>             RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
00097 *>          If RAT = 0, the two estimates are exactly the same.
00098 *> \endverbatim
00099 *
00100 *  Authors:
00101 *  ========
00102 *
00103 *> \author Univ. of Tennessee 
00104 *> \author Univ. of California Berkeley 
00105 *> \author Univ. of Colorado Denver 
00106 *> \author NAG Ltd. 
00107 *
00108 *> \date November 2011
00109 *
00110 *> \ingroup complex_lin
00111 *
00112 *  =====================================================================
00113       SUBROUTINE CTPT06( RCOND, RCONDC, UPLO, DIAG, N, AP, RWORK, RAT )
00114 *
00115 *  -- LAPACK test routine (version 3.4.0) --
00116 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00117 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00118 *     November 2011
00119 *
00120 *     .. Scalar Arguments ..
00121       CHARACTER          DIAG, UPLO
00122       INTEGER            N
00123       REAL               RAT, RCOND, RCONDC
00124 *     ..
00125 *     .. Array Arguments ..
00126       REAL               RWORK( * )
00127       COMPLEX            AP( * )
00128 *     ..
00129 *
00130 *  =====================================================================
00131 *
00132 *     .. Parameters ..
00133       REAL               ZERO, ONE
00134       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
00135 *     ..
00136 *     .. Local Scalars ..
00137       REAL               ANORM, BIGNUM, EPS, RMAX, RMIN
00138 *     ..
00139 *     .. External Functions ..
00140       REAL               CLANTP, SLAMCH
00141       EXTERNAL           CLANTP, SLAMCH
00142 *     ..
00143 *     .. Intrinsic Functions ..
00144       INTRINSIC          MAX, MIN
00145 *     ..
00146 *     .. Executable Statements ..
00147 *
00148       EPS = SLAMCH( 'Epsilon' )
00149       RMAX = MAX( RCOND, RCONDC )
00150       RMIN = MIN( RCOND, RCONDC )
00151 *
00152 *     Do the easy cases first.
00153 *
00154       IF( RMIN.LT.ZERO ) THEN
00155 *
00156 *        Invalid value for RCOND or RCONDC, return 1/EPS.
00157 *
00158          RAT = ONE / EPS
00159 *
00160       ELSE IF( RMIN.GT.ZERO ) THEN
00161 *
00162 *        Both estimates are positive, return RMAX/RMIN - 1.
00163 *
00164          RAT = RMAX / RMIN - ONE
00165 *
00166       ELSE IF( RMAX.EQ.ZERO ) THEN
00167 *
00168 *        Both estimates zero.
00169 *
00170          RAT = ZERO
00171 *
00172       ELSE
00173 *
00174 *        One estimate is zero, the other is non-zero.  If the matrix is
00175 *        ill-conditioned, return the nonzero estimate multiplied by
00176 *        1/EPS; if the matrix is badly scaled, return the nonzero
00177 *        estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
00178 *        element in absolute value in A.
00179 *
00180          BIGNUM = ONE / SLAMCH( 'Safe minimum' )
00181          ANORM = CLANTP( 'M', UPLO, DIAG, N, AP, RWORK )
00182 *
00183          RAT = RMAX*( MIN( BIGNUM / MAX( ONE, ANORM ), ONE / EPS ) )
00184       END IF
00185 *
00186       RETURN
00187 *
00188 *     End of CTPT06
00189 *
00190       END
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