LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
ztrcon.f
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00001 *> \brief \b ZTRCON
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download ZTRCON + dependencies 
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00011 *> [TGZ]</a> 
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00013 *> [ZIP]</a> 
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00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE ZTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK,
00022 *                          RWORK, INFO )
00023 * 
00024 *       .. Scalar Arguments ..
00025 *       CHARACTER          DIAG, NORM, UPLO
00026 *       INTEGER            INFO, LDA, N
00027 *       DOUBLE PRECISION   RCOND
00028 *       ..
00029 *       .. Array Arguments ..
00030 *       DOUBLE PRECISION   RWORK( * )
00031 *       COMPLEX*16         A( LDA, * ), WORK( * )
00032 *       ..
00033 *  
00034 *
00035 *> \par Purpose:
00036 *  =============
00037 *>
00038 *> \verbatim
00039 *>
00040 *> ZTRCON estimates the reciprocal of the condition number of a
00041 *> triangular matrix A, in either the 1-norm or the infinity-norm.
00042 *>
00043 *> The norm of A is computed and an estimate is obtained for
00044 *> norm(inv(A)), then the reciprocal of the condition number is
00045 *> computed as
00046 *>    RCOND = 1 / ( norm(A) * norm(inv(A)) ).
00047 *> \endverbatim
00048 *
00049 *  Arguments:
00050 *  ==========
00051 *
00052 *> \param[in] NORM
00053 *> \verbatim
00054 *>          NORM is CHARACTER*1
00055 *>          Specifies whether the 1-norm condition number or the
00056 *>          infinity-norm condition number is required:
00057 *>          = '1' or 'O':  1-norm;
00058 *>          = 'I':         Infinity-norm.
00059 *> \endverbatim
00060 *>
00061 *> \param[in] UPLO
00062 *> \verbatim
00063 *>          UPLO is CHARACTER*1
00064 *>          = 'U':  A is upper triangular;
00065 *>          = 'L':  A is lower triangular.
00066 *> \endverbatim
00067 *>
00068 *> \param[in] DIAG
00069 *> \verbatim
00070 *>          DIAG is CHARACTER*1
00071 *>          = 'N':  A is non-unit triangular;
00072 *>          = 'U':  A is unit triangular.
00073 *> \endverbatim
00074 *>
00075 *> \param[in] N
00076 *> \verbatim
00077 *>          N is INTEGER
00078 *>          The order of the matrix A.  N >= 0.
00079 *> \endverbatim
00080 *>
00081 *> \param[in] A
00082 *> \verbatim
00083 *>          A is COMPLEX*16 array, dimension (LDA,N)
00084 *>          The triangular matrix A.  If UPLO = 'U', the leading N-by-N
00085 *>          upper triangular part of the array A contains the upper
00086 *>          triangular matrix, and the strictly lower triangular part of
00087 *>          A is not referenced.  If UPLO = 'L', the leading N-by-N lower
00088 *>          triangular part of the array A contains the lower triangular
00089 *>          matrix, and the strictly upper triangular part of A is not
00090 *>          referenced.  If DIAG = 'U', the diagonal elements of A are
00091 *>          also not referenced and are assumed to be 1.
00092 *> \endverbatim
00093 *>
00094 *> \param[in] LDA
00095 *> \verbatim
00096 *>          LDA is INTEGER
00097 *>          The leading dimension of the array A.  LDA >= max(1,N).
00098 *> \endverbatim
00099 *>
00100 *> \param[out] RCOND
00101 *> \verbatim
00102 *>          RCOND is DOUBLE PRECISION
00103 *>          The reciprocal of the condition number of the matrix A,
00104 *>          computed as RCOND = 1/(norm(A) * norm(inv(A))).
00105 *> \endverbatim
00106 *>
00107 *> \param[out] WORK
00108 *> \verbatim
00109 *>          WORK is COMPLEX*16 array, dimension (2*N)
00110 *> \endverbatim
00111 *>
00112 *> \param[out] RWORK
00113 *> \verbatim
00114 *>          RWORK is DOUBLE PRECISION array, dimension (N)
00115 *> \endverbatim
00116 *>
00117 *> \param[out] INFO
00118 *> \verbatim
00119 *>          INFO is INTEGER
00120 *>          = 0:  successful exit
00121 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00122 *> \endverbatim
00123 *
00124 *  Authors:
00125 *  ========
00126 *
00127 *> \author Univ. of Tennessee 
00128 *> \author Univ. of California Berkeley 
00129 *> \author Univ. of Colorado Denver 
00130 *> \author NAG Ltd. 
00131 *
00132 *> \date November 2011
00133 *
00134 *> \ingroup complex16OTHERcomputational
00135 *
00136 *  =====================================================================
00137       SUBROUTINE ZTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK,
00138      $                   RWORK, INFO )
00139 *
00140 *  -- LAPACK computational routine (version 3.4.0) --
00141 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00142 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00143 *     November 2011
00144 *
00145 *     .. Scalar Arguments ..
00146       CHARACTER          DIAG, NORM, UPLO
00147       INTEGER            INFO, LDA, N
00148       DOUBLE PRECISION   RCOND
00149 *     ..
00150 *     .. Array Arguments ..
00151       DOUBLE PRECISION   RWORK( * )
00152       COMPLEX*16         A( LDA, * ), WORK( * )
00153 *     ..
00154 *
00155 *  =====================================================================
00156 *
00157 *     .. Parameters ..
00158       DOUBLE PRECISION   ONE, ZERO
00159       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
00160 *     ..
00161 *     .. Local Scalars ..
00162       LOGICAL            NOUNIT, ONENRM, UPPER
00163       CHARACTER          NORMIN
00164       INTEGER            IX, KASE, KASE1
00165       DOUBLE PRECISION   AINVNM, ANORM, SCALE, SMLNUM, XNORM
00166       COMPLEX*16         ZDUM
00167 *     ..
00168 *     .. Local Arrays ..
00169       INTEGER            ISAVE( 3 )
00170 *     ..
00171 *     .. External Functions ..
00172       LOGICAL            LSAME
00173       INTEGER            IZAMAX
00174       DOUBLE PRECISION   DLAMCH, ZLANTR
00175       EXTERNAL           LSAME, IZAMAX, DLAMCH, ZLANTR
00176 *     ..
00177 *     .. External Subroutines ..
00178       EXTERNAL           XERBLA, ZDRSCL, ZLACN2, ZLATRS
00179 *     ..
00180 *     .. Intrinsic Functions ..
00181       INTRINSIC          ABS, DBLE, DIMAG, MAX
00182 *     ..
00183 *     .. Statement Functions ..
00184       DOUBLE PRECISION   CABS1
00185 *     ..
00186 *     .. Statement Function definitions ..
00187       CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
00188 *     ..
00189 *     .. Executable Statements ..
00190 *
00191 *     Test the input parameters.
00192 *
00193       INFO = 0
00194       UPPER = LSAME( UPLO, 'U' )
00195       ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
00196       NOUNIT = LSAME( DIAG, 'N' )
00197 *
00198       IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
00199          INFO = -1
00200       ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00201          INFO = -2
00202       ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
00203          INFO = -3
00204       ELSE IF( N.LT.0 ) THEN
00205          INFO = -4
00206       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00207          INFO = -6
00208       END IF
00209       IF( INFO.NE.0 ) THEN
00210          CALL XERBLA( 'ZTRCON', -INFO )
00211          RETURN
00212       END IF
00213 *
00214 *     Quick return if possible
00215 *
00216       IF( N.EQ.0 ) THEN
00217          RCOND = ONE
00218          RETURN
00219       END IF
00220 *
00221       RCOND = ZERO
00222       SMLNUM = DLAMCH( 'Safe minimum' )*DBLE( MAX( 1, N ) )
00223 *
00224 *     Compute the norm of the triangular matrix A.
00225 *
00226       ANORM = ZLANTR( NORM, UPLO, DIAG, N, N, A, LDA, RWORK )
00227 *
00228 *     Continue only if ANORM > 0.
00229 *
00230       IF( ANORM.GT.ZERO ) THEN
00231 *
00232 *        Estimate the norm of the inverse of A.
00233 *
00234          AINVNM = ZERO
00235          NORMIN = 'N'
00236          IF( ONENRM ) THEN
00237             KASE1 = 1
00238          ELSE
00239             KASE1 = 2
00240          END IF
00241          KASE = 0
00242    10    CONTINUE
00243          CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
00244          IF( KASE.NE.0 ) THEN
00245             IF( KASE.EQ.KASE1 ) THEN
00246 *
00247 *              Multiply by inv(A).
00248 *
00249                CALL ZLATRS( UPLO, 'No transpose', DIAG, NORMIN, N, A,
00250      $                      LDA, WORK, SCALE, RWORK, INFO )
00251             ELSE
00252 *
00253 *              Multiply by inv(A**H).
00254 *
00255                CALL ZLATRS( UPLO, 'Conjugate transpose', DIAG, NORMIN,
00256      $                      N, A, LDA, WORK, SCALE, RWORK, INFO )
00257             END IF
00258             NORMIN = 'Y'
00259 *
00260 *           Multiply by 1/SCALE if doing so will not cause overflow.
00261 *
00262             IF( SCALE.NE.ONE ) THEN
00263                IX = IZAMAX( N, WORK, 1 )
00264                XNORM = CABS1( WORK( IX ) )
00265                IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO )
00266      $            GO TO 20
00267                CALL ZDRSCL( N, SCALE, WORK, 1 )
00268             END IF
00269             GO TO 10
00270          END IF
00271 *
00272 *        Compute the estimate of the reciprocal condition number.
00273 *
00274          IF( AINVNM.NE.ZERO )
00275      $      RCOND = ( ONE / ANORM ) / AINVNM
00276       END IF
00277 *
00278    20 CONTINUE
00279       RETURN
00280 *
00281 *     End of ZTRCON
00282 *
00283       END
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