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00001 *> \brief \b ZLA_SYRCOND_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_SYRCOND_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_SYRCOND_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 ZSYTRF.
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 ZSYTRF.
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 complex16SYcomputational
00137 *
00138 *  =====================================================================
00139       DOUBLE PRECISION FUNCTION ZLA_SYRCOND_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
00163       DOUBLE PRECISION   AINVNM, ANORM, TMP
00164       INTEGER            I, J
00165       LOGICAL            UP
00166       COMPLEX*16         ZDUM
00167 *     ..
00168 *     .. Local Arrays ..
00169       INTEGER            ISAVE( 3 )
00170 *     ..
00171 *     .. External Functions ..
00172       LOGICAL            LSAME
00173       EXTERNAL           LSAME
00174 *     ..
00175 *     .. External Subroutines ..
00176       EXTERNAL           ZLACN2, ZSYTRS, XERBLA
00177 *     ..
00178 *     .. Intrinsic Functions ..
00179       INTRINSIC          ABS, MAX
00180 *     ..
00181 *     .. Statement Functions ..
00182       DOUBLE PRECISION CABS1
00183 *     ..
00184 *     .. Statement Function Definitions ..
00185       CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
00186 *     ..
00187 *     .. Executable Statements ..
00188 *
00189       ZLA_SYRCOND_C = 0.0D+0
00190 *
00191       INFO = 0
00192       IF( N.LT.0 ) THEN
00193          INFO = -2
00194       END IF
00195       IF( INFO.NE.0 ) THEN
00196          CALL XERBLA( 'ZLA_SYRCOND_C', -INFO )
00197          RETURN
00198       END IF
00199       UP = .FALSE.
00200       IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
00201 *
00202 *     Compute norm of op(A)*op2(C).
00203 *
00204       ANORM = 0.0D+0
00205       IF ( UP ) THEN
00206          DO I = 1, N
00207             TMP = 0.0D+0
00208             IF ( CAPPLY ) THEN
00209                DO J = 1, I
00210                   TMP = TMP + CABS1( A( J, I ) ) / C( J )
00211                END DO
00212                DO J = I+1, N
00213                   TMP = TMP + CABS1( A( I, J ) ) / C( J )
00214                END DO
00215             ELSE
00216                DO J = 1, I
00217                   TMP = TMP + CABS1( A( J, I ) )
00218                END DO
00219                DO J = I+1, N
00220                   TMP = TMP + CABS1( A( I, J ) )
00221                END DO
00222             END IF
00223             RWORK( I ) = TMP
00224             ANORM = MAX( ANORM, TMP )
00225          END DO
00226       ELSE
00227          DO I = 1, N
00228             TMP = 0.0D+0
00229             IF ( CAPPLY ) THEN
00230                DO J = 1, I
00231                   TMP = TMP + CABS1( A( I, J ) ) / C( J )
00232                END DO
00233                DO J = I+1, N
00234                   TMP = TMP + CABS1( A( J, I ) ) / C( J )
00235                END DO
00236             ELSE
00237                DO J = 1, I
00238                   TMP = TMP + CABS1( A( I, J ) )
00239                END DO
00240                DO J = I+1, N
00241                   TMP = TMP + CABS1( A( J, I ) )
00242                END DO
00243             END IF
00244             RWORK( I ) = TMP
00245             ANORM = MAX( ANORM, TMP )
00246          END DO
00247       END IF
00248 *
00249 *     Quick return if possible.
00250 *
00251       IF( N.EQ.0 ) THEN
00252          ZLA_SYRCOND_C = 1.0D+0
00253          RETURN
00254       ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
00255          RETURN
00256       END IF
00257 *
00258 *     Estimate the norm of inv(op(A)).
00259 *
00260       AINVNM = 0.0D+0
00261 *
00262       KASE = 0
00263    10 CONTINUE
00264       CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
00265       IF( KASE.NE.0 ) THEN
00266          IF( KASE.EQ.2 ) THEN
00267 *
00268 *           Multiply by R.
00269 *
00270             DO I = 1, N
00271                WORK( I ) = WORK( I ) * RWORK( I )
00272             END DO
00273 *
00274             IF ( UP ) THEN
00275                CALL ZSYTRS( 'U', N, 1, AF, LDAF, IPIV,
00276      $            WORK, N, INFO )
00277             ELSE
00278                CALL ZSYTRS( 'L', N, 1, AF, LDAF, IPIV,
00279      $            WORK, N, INFO )
00280             ENDIF
00281 *
00282 *           Multiply by inv(C).
00283 *
00284             IF ( CAPPLY ) THEN
00285                DO I = 1, N
00286                   WORK( I ) = WORK( I ) * C( I )
00287                END DO
00288             END IF
00289          ELSE
00290 *
00291 *           Multiply by inv(C**T).
00292 *
00293             IF ( CAPPLY ) THEN
00294                DO I = 1, N
00295                   WORK( I ) = WORK( I ) * C( I )
00296                END DO
00297             END IF
00298 *
00299             IF ( UP ) THEN
00300                CALL ZSYTRS( 'U', N, 1, AF, LDAF, IPIV,
00301      $            WORK, N, INFO )
00302             ELSE
00303                CALL ZSYTRS( 'L', N, 1, AF, LDAF, IPIV,
00304      $            WORK, N, INFO )
00305             END IF
00306 *
00307 *           Multiply by R.
00308 *
00309             DO I = 1, N
00310                WORK( I ) = WORK( I ) * RWORK( I )
00311             END DO
00312          END IF
00313          GO TO 10
00314       END IF
00315 *
00316 *     Compute the estimate of the reciprocal condition number.
00317 *
00318       IF( AINVNM .NE. 0.0D+0 )
00319      $   ZLA_SYRCOND_C = 1.0D+0 / AINVNM
00320 *
00321       RETURN
00322 *
00323       END