LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dtbt06.f
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00001 *> \brief \b DTBT06
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 DTBT06( RCOND, RCONDC, UPLO, DIAG, N, KD, AB, LDAB,
00012 *                          WORK, RAT )
00013 * 
00014 *       .. Scalar Arguments ..
00015 *       CHARACTER          DIAG, UPLO
00016 *       INTEGER            KD, LDAB, N
00017 *       DOUBLE PRECISION   RAT, RCOND, RCONDC
00018 *       ..
00019 *       .. Array Arguments ..
00020 *       DOUBLE PRECISION   AB( LDAB, * ), WORK( * )
00021 *       ..
00022 *  
00023 *
00024 *> \par Purpose:
00025 *  =============
00026 *>
00027 *> \verbatim
00028 *>
00029 *> DTBT06 computes a test ratio comparing RCOND (the reciprocal
00030 *> condition number of a triangular matrix A) and RCONDC, the estimate
00031 *> computed by DTBCON.  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 *>          DTBCON.
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] KD
00077 *> \verbatim
00078 *>          KD is INTEGER
00079 *>          The number of superdiagonals or subdiagonals of the
00080 *>          triangular band matrix A.  KD >= 0.
00081 *> \endverbatim
00082 *>
00083 *> \param[in] AB
00084 *> \verbatim
00085 *>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
00086 *>          The upper or lower triangular band matrix A, stored in the
00087 *>          first kd+1 rows of the array. The j-th column of A is stored
00088 *>          in the j-th column of the array AB as follows:
00089 *>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
00090 *>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
00091 *> \endverbatim
00092 *>
00093 *> \param[in] LDAB
00094 *> \verbatim
00095 *>          LDAB is INTEGER
00096 *>          The leading dimension of the array AB.  LDAB >= KD+1.
00097 *> \endverbatim
00098 *>
00099 *> \param[out] WORK
00100 *> \verbatim
00101 *>          WORK is DOUBLE PRECISION array, dimension (N)
00102 *> \endverbatim
00103 *>
00104 *> \param[out] RAT
00105 *> \verbatim
00106 *>          RAT is DOUBLE PRECISION
00107 *>          The test ratio.  If both RCOND and RCONDC are nonzero,
00108 *>             RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
00109 *>          If RAT = 0, the two estimates are exactly the same.
00110 *> \endverbatim
00111 *
00112 *  Authors:
00113 *  ========
00114 *
00115 *> \author Univ. of Tennessee 
00116 *> \author Univ. of California Berkeley 
00117 *> \author Univ. of Colorado Denver 
00118 *> \author NAG Ltd. 
00119 *
00120 *> \date November 2011
00121 *
00122 *> \ingroup double_lin
00123 *
00124 *  =====================================================================
00125       SUBROUTINE DTBT06( RCOND, RCONDC, UPLO, DIAG, N, KD, AB, LDAB,
00126      $                   WORK, RAT )
00127 *
00128 *  -- LAPACK test routine (version 3.4.0) --
00129 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00130 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00131 *     November 2011
00132 *
00133 *     .. Scalar Arguments ..
00134       CHARACTER          DIAG, UPLO
00135       INTEGER            KD, LDAB, N
00136       DOUBLE PRECISION   RAT, RCOND, RCONDC
00137 *     ..
00138 *     .. Array Arguments ..
00139       DOUBLE PRECISION   AB( LDAB, * ), WORK( * )
00140 *     ..
00141 *
00142 *  =====================================================================
00143 *
00144 *     .. Parameters ..
00145       DOUBLE PRECISION   ZERO, ONE
00146       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
00147 *     ..
00148 *     .. Local Scalars ..
00149       DOUBLE PRECISION   ANORM, BIGNUM, EPS, RMAX, RMIN, SMLNUM
00150 *     ..
00151 *     .. External Functions ..
00152       DOUBLE PRECISION   DLAMCH, DLANTB
00153       EXTERNAL           DLAMCH, DLANTB
00154 *     ..
00155 *     .. Intrinsic Functions ..
00156       INTRINSIC          MAX, MIN
00157 *     ..
00158 *     .. External Subroutines ..
00159       EXTERNAL           DLABAD
00160 *     ..
00161 *     .. Executable Statements ..
00162 *
00163       EPS = DLAMCH( 'Epsilon' )
00164       RMAX = MAX( RCOND, RCONDC )
00165       RMIN = MIN( RCOND, RCONDC )
00166 *
00167 *     Do the easy cases first.
00168 *
00169       IF( RMIN.LT.ZERO ) THEN
00170 *
00171 *        Invalid value for RCOND or RCONDC, return 1/EPS.
00172 *
00173          RAT = ONE / EPS
00174 *
00175       ELSE IF( RMIN.GT.ZERO ) THEN
00176 *
00177 *        Both estimates are positive, return RMAX/RMIN - 1.
00178 *
00179          RAT = RMAX / RMIN - ONE
00180 *
00181       ELSE IF( RMAX.EQ.ZERO ) THEN
00182 *
00183 *        Both estimates zero.
00184 *
00185          RAT = ZERO
00186 *
00187       ELSE
00188 *
00189 *        One estimate is zero, the other is non-zero.  If the matrix is
00190 *        ill-conditioned, return the nonzero estimate multiplied by
00191 *        1/EPS; if the matrix is badly scaled, return the nonzero
00192 *        estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
00193 *        element in absolute value in A.
00194 *
00195          SMLNUM = DLAMCH( 'Safe minimum' )
00196          BIGNUM = ONE / SMLNUM
00197          CALL DLABAD( SMLNUM, BIGNUM )
00198          ANORM = DLANTB( 'M', UPLO, DIAG, N, KD, AB, LDAB, WORK )
00199 *
00200          RAT = RMAX*( MIN( BIGNUM / MAX( ONE, ANORM ), ONE / EPS ) )
00201       END IF
00202 *
00203       RETURN
00204 *
00205 *     End of DTBT06
00206 *
00207       END
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