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00001 *> \brief \b ZLA_PORCOND_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_PORCOND_C( UPLO, N, A, LDA, AF, 
00022 *                                                LDAF, C, CAPPLY, INFO,
00023 *                                                WORK, RWORK )
00024 * 
00025 *       .. Scalar Arguments ..
00026 *       CHARACTER          UPLO
00027 *       LOGICAL            CAPPLY
00028 *       INTEGER            N, LDA, LDAF, INFO
00029 *       ..
00030 *       .. Array Arguments ..
00031 *       COMPLEX*16         A( LDA, * ), AF( LDAF, * ), WORK( * )
00032 *       DOUBLE PRECISION   C( * ), RWORK( * )
00033 *       ..
00034 *  
00035 *
00036 *> \par Purpose:
00037 *  =============
00038 *>
00039 *> \verbatim
00040 *>
00041 *>    ZLA_PORCOND_C Computes the infinity norm condition number of
00042 *>    op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector
00043 *> \endverbatim
00044 *
00045 *  Arguments:
00046 *  ==========
00047 *
00048 *> \param[in] UPLO
00049 *> \verbatim
00050 *>          UPLO is CHARACTER*1
00051 *>       = 'U':  Upper triangle of A is stored;
00052 *>       = 'L':  Lower triangle of A is stored.
00053 *> \endverbatim
00054 *>
00055 *> \param[in] N
00056 *> \verbatim
00057 *>          N is INTEGER
00058 *>     The number of linear equations, i.e., the order of the
00059 *>     matrix A.  N >= 0.
00060 *> \endverbatim
00061 *>
00062 *> \param[in] A
00063 *> \verbatim
00064 *>          A is COMPLEX*16 array, dimension (LDA,N)
00065 *>     On entry, the N-by-N matrix A
00066 *> \endverbatim
00067 *>
00068 *> \param[in] LDA
00069 *> \verbatim
00070 *>          LDA is INTEGER
00071 *>     The leading dimension of the array A.  LDA >= max(1,N).
00072 *> \endverbatim
00073 *>
00074 *> \param[in] AF
00075 *> \verbatim
00076 *>          AF is COMPLEX*16 array, dimension (LDAF,N)
00077 *>     The triangular factor U or L from the Cholesky factorization
00078 *>     A = U**H*U or A = L*L**H, as computed by ZPOTRF.
00079 *> \endverbatim
00080 *>
00081 *> \param[in] LDAF
00082 *> \verbatim
00083 *>          LDAF is INTEGER
00084 *>     The leading dimension of the array AF.  LDAF >= max(1,N).
00085 *> \endverbatim
00086 *>
00087 *> \param[in] C
00088 *> \verbatim
00089 *>          C is DOUBLE PRECISION array, dimension (N)
00090 *>     The vector C in the formula op(A) * inv(diag(C)).
00091 *> \endverbatim
00092 *>
00093 *> \param[in] CAPPLY
00094 *> \verbatim
00095 *>          CAPPLY is LOGICAL
00096 *>     If .TRUE. then access the vector C in the formula above.
00097 *> \endverbatim
00098 *>
00099 *> \param[out] INFO
00100 *> \verbatim
00101 *>          INFO is INTEGER
00102 *>       = 0:  Successful exit.
00103 *>     i > 0:  The ith argument is invalid.
00104 *> \endverbatim
00105 *>
00106 *> \param[in] WORK
00107 *> \verbatim
00108 *>          WORK is COMPLEX*16 array, dimension (2*N).
00109 *>     Workspace.
00110 *> \endverbatim
00111 *>
00112 *> \param[in] RWORK
00113 *> \verbatim
00114 *>          RWORK is DOUBLE PRECISION array, dimension (N).
00115 *>     Workspace.
00116 *> \endverbatim
00117 *
00118 *  Authors:
00119 *  ========
00120 *
00121 *> \author Univ. of Tennessee 
00122 *> \author Univ. of California Berkeley 
00123 *> \author Univ. of Colorado Denver 
00124 *> \author NAG Ltd. 
00125 *
00126 *> \date November 2011
00127 *
00128 *> \ingroup complex16POcomputational
00129 *
00130 *  =====================================================================
00131       DOUBLE PRECISION FUNCTION ZLA_PORCOND_C( UPLO, N, A, LDA, AF, 
00132      $                                         LDAF, C, CAPPLY, INFO,
00133      $                                         WORK, RWORK )
00134 *
00135 *  -- LAPACK computational routine (version 3.4.0) --
00136 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00137 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00138 *     November 2011
00139 *
00140 *     .. Scalar Arguments ..
00141       CHARACTER          UPLO
00142       LOGICAL            CAPPLY
00143       INTEGER            N, LDA, LDAF, INFO
00144 *     ..
00145 *     .. Array Arguments ..
00146       COMPLEX*16         A( LDA, * ), AF( LDAF, * ), WORK( * )
00147       DOUBLE PRECISION   C( * ), RWORK( * )
00148 *     ..
00149 *
00150 *  =====================================================================
00151 *
00152 *     .. Local Scalars ..
00153       INTEGER            KASE
00154       DOUBLE PRECISION   AINVNM, ANORM, TMP
00155       INTEGER            I, J
00156       LOGICAL            UP
00157       COMPLEX*16         ZDUM
00158 *     ..
00159 *     .. Local Arrays ..
00160       INTEGER            ISAVE( 3 )
00161 *     ..
00162 *     .. External Functions ..
00163       LOGICAL            LSAME
00164       EXTERNAL           LSAME
00165 *     ..
00166 *     .. External Subroutines ..
00167       EXTERNAL           ZLACN2, ZPOTRS, XERBLA
00168 *     ..
00169 *     .. Intrinsic Functions ..
00170       INTRINSIC          ABS, MAX, REAL, DIMAG
00171 *     ..
00172 *     .. Statement Functions ..
00173       DOUBLE PRECISION CABS1
00174 *     ..
00175 *     .. Statement Function Definitions ..
00176       CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
00177 *     ..
00178 *     .. Executable Statements ..
00179 *
00180       ZLA_PORCOND_C = 0.0D+0
00181 *
00182       INFO = 0
00183       IF( N.LT.0 ) THEN
00184          INFO = -2
00185       END IF
00186       IF( INFO.NE.0 ) THEN
00187          CALL XERBLA( 'ZLA_PORCOND_C', -INFO )
00188          RETURN
00189       END IF
00190       UP = .FALSE.
00191       IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
00192 *
00193 *     Compute norm of op(A)*op2(C).
00194 *
00195       ANORM = 0.0D+0
00196       IF ( UP ) THEN
00197          DO I = 1, N
00198             TMP = 0.0D+0
00199             IF ( CAPPLY ) THEN
00200                DO J = 1, I
00201                   TMP = TMP + CABS1( A( J, I ) ) / C( J )
00202                END DO
00203                DO J = I+1, N
00204                   TMP = TMP + CABS1( A( I, J ) ) / C( J )
00205                END DO
00206             ELSE
00207                DO J = 1, I
00208                   TMP = TMP + CABS1( A( J, I ) )
00209                END DO
00210                DO J = I+1, N
00211                   TMP = TMP + CABS1( A( I, J ) )
00212                END DO
00213             END IF
00214             RWORK( I ) = TMP
00215             ANORM = MAX( ANORM, TMP )
00216          END DO
00217       ELSE
00218          DO I = 1, N
00219             TMP = 0.0D+0
00220             IF ( CAPPLY ) THEN
00221                DO J = 1, I
00222                   TMP = TMP + CABS1( A( I, J ) ) / C( J )
00223                END DO
00224                DO J = I+1, N
00225                   TMP = TMP + CABS1( A( J, I ) ) / C( J )
00226                END DO
00227             ELSE
00228                DO J = 1, I
00229                   TMP = TMP + CABS1( A( I, J ) )
00230                END DO
00231                DO J = I+1, N
00232                   TMP = TMP + CABS1( A( J, I ) )
00233                END DO
00234             END IF
00235             RWORK( I ) = TMP
00236             ANORM = MAX( ANORM, TMP )
00237          END DO
00238       END IF
00239 *
00240 *     Quick return if possible.
00241 *
00242       IF( N.EQ.0 ) THEN
00243          ZLA_PORCOND_C = 1.0D+0
00244          RETURN
00245       ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
00246          RETURN
00247       END IF
00248 *
00249 *     Estimate the norm of inv(op(A)).
00250 *
00251       AINVNM = 0.0D+0
00252 *
00253       KASE = 0
00254    10 CONTINUE
00255       CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
00256       IF( KASE.NE.0 ) THEN
00257          IF( KASE.EQ.2 ) THEN
00258 *
00259 *           Multiply by R.
00260 *
00261             DO I = 1, N
00262                WORK( I ) = WORK( I ) * RWORK( I )
00263             END DO
00264 *
00265             IF ( UP ) THEN
00266                CALL ZPOTRS( 'U', N, 1, AF, LDAF,
00267      $            WORK, N, INFO )
00268             ELSE
00269                CALL ZPOTRS( 'L', N, 1, AF, LDAF,
00270      $            WORK, N, INFO )
00271             ENDIF
00272 *
00273 *           Multiply by inv(C).
00274 *
00275             IF ( CAPPLY ) THEN
00276                DO I = 1, N
00277                   WORK( I ) = WORK( I ) * C( I )
00278                END DO
00279             END IF
00280          ELSE
00281 *
00282 *           Multiply by inv(C**H).
00283 *
00284             IF ( CAPPLY ) THEN
00285                DO I = 1, N
00286                   WORK( I ) = WORK( I ) * C( I )
00287                END DO
00288             END IF
00289 *
00290             IF ( UP ) THEN
00291                CALL ZPOTRS( 'U', N, 1, AF, LDAF,
00292      $            WORK, N, INFO )
00293             ELSE
00294                CALL ZPOTRS( 'L', N, 1, AF, LDAF,
00295      $            WORK, N, INFO )
00296             END IF
00297 *
00298 *           Multiply by R.
00299 *
00300             DO I = 1, N
00301                WORK( I ) = WORK( I ) * RWORK( I )
00302             END DO
00303          END IF
00304          GO TO 10
00305       END IF
00306 *
00307 *     Compute the estimate of the reciprocal condition number.
00308 *
00309       IF( AINVNM .NE. 0.0D+0 )
00310      $   ZLA_PORCOND_C = 1.0D+0 / AINVNM
00311 *
00312       RETURN
00313 *
00314       END