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00001 *> \brief \b ZLA_HERCOND_C
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
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00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       DOUBLE PRECISION FUNCTION ZLA_HERCOND_C( UPLO, N, A, LDA, AF, 
00022 *                                                LDAF, IPIV, C, CAPPLY,
00023 *                                                INFO, WORK, RWORK )
00024 * 
00025 *       .. Scalar Arguments ..
00026 *       CHARACTER          UPLO
00027 *       LOGICAL            CAPPLY
00028 *       INTEGER            N, LDA, LDAF, INFO
00029 *       ..
00030 *       .. Array Arguments ..
00031 *       INTEGER            IPIV( * )
00032 *       COMPLEX*16         A( LDA, * ), AF( LDAF, * ), WORK( * )
00033 *       DOUBLE PRECISION   C ( * ), RWORK( * )
00034 *       ..
00035 *  
00036 *
00037 *> \par Purpose:
00038 *  =============
00039 *>
00040 *> \verbatim
00041 *>
00042 *>    ZLA_HERCOND_C computes the infinity norm condition number of
00043 *>    op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.
00044 *> \endverbatim
00045 *
00046 *  Arguments:
00047 *  ==========
00048 *
00049 *> \param[in] UPLO
00050 *> \verbatim
00051 *>          UPLO is CHARACTER*1
00052 *>       = 'U':  Upper triangle of A is stored;
00053 *>       = 'L':  Lower triangle of A is stored.
00054 *> \endverbatim
00055 *>
00056 *> \param[in] N
00057 *> \verbatim
00058 *>          N is INTEGER
00059 *>     The number of linear equations, i.e., the order of the
00060 *>     matrix A.  N >= 0.
00061 *> \endverbatim
00062 *>
00063 *> \param[in] A
00064 *> \verbatim
00065 *>          A is COMPLEX*16 array, dimension (LDA,N)
00066 *>     On entry, the N-by-N matrix A
00067 *> \endverbatim
00068 *>
00069 *> \param[in] LDA
00070 *> \verbatim
00071 *>          LDA is INTEGER
00072 *>     The leading dimension of the array A.  LDA >= max(1,N).
00073 *> \endverbatim
00074 *>
00075 *> \param[in] AF
00076 *> \verbatim
00077 *>          AF is COMPLEX*16 array, dimension (LDAF,N)
00078 *>     The block diagonal matrix D and the multipliers used to
00079 *>     obtain the factor U or L as computed by ZHETRF.
00080 *> \endverbatim
00081 *>
00082 *> \param[in] LDAF
00083 *> \verbatim
00084 *>          LDAF is INTEGER
00085 *>     The leading dimension of the array AF.  LDAF >= max(1,N).
00086 *> \endverbatim
00087 *>
00088 *> \param[in] IPIV
00089 *> \verbatim
00090 *>          IPIV is INTEGER array, dimension (N)
00091 *>     Details of the interchanges and the block structure of D
00092 *>     as determined by CHETRF.
00093 *> \endverbatim
00094 *>
00095 *> \param[in] C
00096 *> \verbatim
00097 *>          C is DOUBLE PRECISION array, dimension (N)
00098 *>     The vector C in the formula op(A) * inv(diag(C)).
00099 *> \endverbatim
00100 *>
00101 *> \param[in] CAPPLY
00102 *> \verbatim
00103 *>          CAPPLY is LOGICAL
00104 *>     If .TRUE. then access the vector C in the formula above.
00105 *> \endverbatim
00106 *>
00107 *> \param[out] INFO
00108 *> \verbatim
00109 *>          INFO is INTEGER
00110 *>       = 0:  Successful exit.
00111 *>     i > 0:  The ith argument is invalid.
00112 *> \endverbatim
00113 *>
00114 *> \param[in] WORK
00115 *> \verbatim
00116 *>          WORK is COMPLEX*16 array, dimension (2*N).
00117 *>     Workspace.
00118 *> \endverbatim
00119 *>
00120 *> \param[in] RWORK
00121 *> \verbatim
00122 *>          RWORK is DOUBLE PRECISION array, dimension (N).
00123 *>     Workspace.
00124 *> \endverbatim
00125 *
00126 *  Authors:
00127 *  ========
00128 *
00129 *> \author Univ. of Tennessee 
00130 *> \author Univ. of California Berkeley 
00131 *> \author Univ. of Colorado Denver 
00132 *> \author NAG Ltd. 
00133 *
00134 *> \date November 2011
00135 *
00136 *> \ingroup complex16HEcomputational
00137 *
00138 *  =====================================================================
00139       DOUBLE PRECISION FUNCTION ZLA_HERCOND_C( UPLO, N, A, LDA, AF, 
00140      $                                         LDAF, IPIV, C, CAPPLY,
00141      $                                         INFO, WORK, RWORK )
00142 *
00143 *  -- LAPACK computational routine (version 3.4.0) --
00144 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00145 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00146 *     November 2011
00147 *
00148 *     .. Scalar Arguments ..
00149       CHARACTER          UPLO
00150       LOGICAL            CAPPLY
00151       INTEGER            N, LDA, LDAF, INFO
00152 *     ..
00153 *     .. Array Arguments ..
00154       INTEGER            IPIV( * )
00155       COMPLEX*16         A( LDA, * ), AF( LDAF, * ), WORK( * )
00156       DOUBLE PRECISION   C ( * ), RWORK( * )
00157 *     ..
00158 *
00159 *  =====================================================================
00160 *
00161 *     .. Local Scalars ..
00162       INTEGER            KASE, I, J
00163       DOUBLE PRECISION   AINVNM, ANORM, TMP
00164       LOGICAL            UP
00165       COMPLEX*16         ZDUM
00166 *     ..
00167 *     .. Local Arrays ..
00168       INTEGER            ISAVE( 3 )
00169 *     ..
00170 *     .. External Functions ..
00171       LOGICAL            LSAME
00172       EXTERNAL           LSAME
00173 *     ..
00174 *     .. External Subroutines ..
00175       EXTERNAL           ZLACN2, ZHETRS, XERBLA
00176 *     ..
00177 *     .. Intrinsic Functions ..
00178       INTRINSIC          ABS, MAX
00179 *     ..
00180 *     .. Statement Functions ..
00181       DOUBLE PRECISION   CABS1
00182 *     ..
00183 *     .. Statement Function Definitions ..
00184       CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
00185 *     ..
00186 *     .. Executable Statements ..
00187 *
00188       ZLA_HERCOND_C = 0.0D+0
00189 *
00190       INFO = 0
00191       IF( N.LT.0 ) THEN
00192          INFO = -2
00193       END IF
00194       IF( INFO.NE.0 ) THEN
00195          CALL XERBLA( 'ZLA_HERCOND_C', -INFO )
00196          RETURN
00197       END IF
00198       UP = .FALSE.
00199       IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
00200 *
00201 *     Compute norm of op(A)*op2(C).
00202 *
00203       ANORM = 0.0D+0
00204       IF ( UP ) THEN
00205          DO I = 1, N
00206             TMP = 0.0D+0
00207             IF ( CAPPLY ) THEN
00208                DO J = 1, I
00209                   TMP = TMP + CABS1( A( J, I ) ) / C( J )
00210                END DO
00211                DO J = I+1, N
00212                   TMP = TMP + CABS1( A( I, J ) ) / C( J )
00213                END DO
00214             ELSE
00215                DO J = 1, I
00216                   TMP = TMP + CABS1( A( J, I ) )
00217                END DO
00218                DO J = I+1, N
00219                   TMP = TMP + CABS1( A( I, J ) )
00220                END DO
00221             END IF
00222             RWORK( I ) = TMP
00223             ANORM = MAX( ANORM, TMP )
00224          END DO
00225       ELSE
00226          DO I = 1, N
00227             TMP = 0.0D+0
00228             IF ( CAPPLY ) THEN
00229                DO J = 1, I
00230                   TMP = TMP + CABS1( A( I, J ) ) / C( J )
00231                END DO
00232                DO J = I+1, N
00233                   TMP = TMP + CABS1( A( J, I ) ) / C( J )
00234                END DO
00235             ELSE
00236                DO J = 1, I
00237                   TMP = TMP + CABS1( A( I, J ) )
00238                END DO
00239                DO J = I+1, N
00240                   TMP = TMP + CABS1( A( J, I ) )
00241                END DO
00242             END IF
00243             RWORK( I ) = TMP
00244             ANORM = MAX( ANORM, TMP )
00245          END DO
00246       END IF
00247 *
00248 *     Quick return if possible.
00249 *
00250       IF( N.EQ.0 ) THEN
00251          ZLA_HERCOND_C = 1.0D+0
00252          RETURN
00253       ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
00254          RETURN
00255       END IF
00256 *
00257 *     Estimate the norm of inv(op(A)).
00258 *
00259       AINVNM = 0.0D+0
00260 *
00261       KASE = 0
00262    10 CONTINUE
00263       CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
00264       IF( KASE.NE.0 ) THEN
00265          IF( KASE.EQ.2 ) THEN
00266 *
00267 *           Multiply by R.
00268 *
00269             DO I = 1, N
00270                WORK( I ) = WORK( I ) * RWORK( I )
00271             END DO
00272 *
00273             IF ( UP ) THEN
00274                CALL ZHETRS( 'U', N, 1, AF, LDAF, IPIV,
00275      $            WORK, N, INFO )
00276             ELSE
00277                CALL ZHETRS( 'L', N, 1, AF, LDAF, IPIV,
00278      $            WORK, N, INFO )
00279             ENDIF
00280 *
00281 *           Multiply by inv(C).
00282 *
00283             IF ( CAPPLY ) THEN
00284                DO I = 1, N
00285                   WORK( I ) = WORK( I ) * C( I )
00286                END DO
00287             END IF
00288          ELSE
00289 *
00290 *           Multiply by inv(C**H).
00291 *
00292             IF ( CAPPLY ) THEN
00293                DO I = 1, N
00294                   WORK( I ) = WORK( I ) * C( I )
00295                END DO
00296             END IF
00297 *
00298             IF ( UP ) THEN
00299                CALL ZHETRS( 'U', N, 1, AF, LDAF, IPIV,
00300      $            WORK, N, INFO )
00301             ELSE
00302                CALL ZHETRS( 'L', N, 1, AF, LDAF, IPIV,
00303      $            WORK, N, INFO )
00304             END IF
00305 *
00306 *           Multiply by R.
00307 *
00308             DO I = 1, N
00309                WORK( I ) = WORK( I ) * RWORK( I )
00310             END DO
00311          END IF
00312          GO TO 10
00313       END IF
00314 *
00315 *     Compute the estimate of the reciprocal condition number.
00316 *
00317       IF( AINVNM .NE. 0.0D+0 )
00318      $   ZLA_HERCOND_C = 1.0D+0 / AINVNM
00319 *
00320       RETURN
00321 *
00322       END