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00001 *> \brief \b CLA_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 *       REAL FUNCTION CLA_HERCOND_C( UPLO, N, A, LDA, AF, LDAF, IPIV, C,
00022 *                                    CAPPLY, INFO, WORK, RWORK )
00023 * 
00024 *       .. Scalar Arguments ..
00025 *       CHARACTER          UPLO
00026 *       LOGICAL            CAPPLY
00027 *       INTEGER            N, LDA, LDAF, INFO
00028 *       ..
00029 *       .. Array Arguments ..
00030 *       INTEGER            IPIV( * )
00031 *       COMPLEX            A( LDA, * ), AF( LDAF, * ), WORK( * )
00032 *       REAL               C ( * ), RWORK( * )
00033 *       ..
00034 *  
00035 *
00036 *> \par Purpose:
00037 *  =============
00038 *>
00039 *> \verbatim
00040 *>
00041 *>    CLA_HERCOND_C computes the infinity norm condition number of
00042 *>    op(A) * inv(diag(C)) where C is a REAL 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 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 array, dimension (LDAF,N)
00077 *>     The block diagonal matrix D and the multipliers used to
00078 *>     obtain the factor U or L as computed by CHETRF.
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] IPIV
00088 *> \verbatim
00089 *>          IPIV is INTEGER array, dimension (N)
00090 *>     Details of the interchanges and the block structure of D
00091 *>     as determined by CHETRF.
00092 *> \endverbatim
00093 *>
00094 *> \param[in] C
00095 *> \verbatim
00096 *>          C is REAL array, dimension (N)
00097 *>     The vector C in the formula op(A) * inv(diag(C)).
00098 *> \endverbatim
00099 *>
00100 *> \param[in] CAPPLY
00101 *> \verbatim
00102 *>          CAPPLY is LOGICAL
00103 *>     If .TRUE. then access the vector C in the formula above.
00104 *> \endverbatim
00105 *>
00106 *> \param[out] INFO
00107 *> \verbatim
00108 *>          INFO is INTEGER
00109 *>       = 0:  Successful exit.
00110 *>     i > 0:  The ith argument is invalid.
00111 *> \endverbatim
00112 *>
00113 *> \param[in] WORK
00114 *> \verbatim
00115 *>          WORK is COMPLEX array, dimension (2*N).
00116 *>     Workspace.
00117 *> \endverbatim
00118 *>
00119 *> \param[in] RWORK
00120 *> \verbatim
00121 *>          RWORK is REAL array, dimension (N).
00122 *>     Workspace.
00123 *> \endverbatim
00124 *
00125 *  Authors:
00126 *  ========
00127 *
00128 *> \author Univ. of Tennessee 
00129 *> \author Univ. of California Berkeley 
00130 *> \author Univ. of Colorado Denver 
00131 *> \author NAG Ltd. 
00132 *
00133 *> \date November 2011
00134 *
00135 *> \ingroup complexHEcomputational
00136 *
00137 *  =====================================================================
00138       REAL FUNCTION CLA_HERCOND_C( UPLO, N, A, LDA, AF, LDAF, IPIV, C,
00139      $                             CAPPLY, INFO, WORK, RWORK )
00140 *
00141 *  -- LAPACK computational routine (version 3.4.0) --
00142 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00143 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00144 *     November 2011
00145 *
00146 *     .. Scalar Arguments ..
00147       CHARACTER          UPLO
00148       LOGICAL            CAPPLY
00149       INTEGER            N, LDA, LDAF, INFO
00150 *     ..
00151 *     .. Array Arguments ..
00152       INTEGER            IPIV( * )
00153       COMPLEX            A( LDA, * ), AF( LDAF, * ), WORK( * )
00154       REAL               C ( * ), RWORK( * )
00155 *     ..
00156 *
00157 *  =====================================================================
00158 *
00159 *     .. Local Scalars ..
00160       INTEGER            KASE, I, J
00161       REAL               AINVNM, ANORM, TMP
00162       LOGICAL            UP
00163       COMPLEX            ZDUM
00164 *     ..
00165 *     .. Local Arrays ..
00166       INTEGER            ISAVE( 3 )
00167 *     ..
00168 *     .. External Functions ..
00169       LOGICAL            LSAME
00170       EXTERNAL           LSAME
00171 *     ..
00172 *     .. External Subroutines ..
00173       EXTERNAL           CLACN2, CHETRS, XERBLA
00174 *     ..
00175 *     .. Intrinsic Functions ..
00176       INTRINSIC          ABS, MAX
00177 *     ..
00178 *     .. Statement Functions ..
00179       REAL               CABS1
00180 *     ..
00181 *     .. Statement Function Definitions ..
00182       CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
00183 *     ..
00184 *     .. Executable Statements ..
00185 *
00186       CLA_HERCOND_C = 0.0E+0
00187 *
00188       INFO = 0
00189       IF( N.LT.0 ) THEN
00190          INFO = -2
00191       END IF
00192       IF( INFO.NE.0 ) THEN
00193          CALL XERBLA( 'CLA_HERCOND_C', -INFO )
00194          RETURN
00195       END IF
00196       UP = .FALSE.
00197       IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
00198 *
00199 *     Compute norm of op(A)*op2(C).
00200 *
00201       ANORM = 0.0E+0
00202       IF ( UP ) THEN
00203          DO I = 1, N
00204             TMP = 0.0E+0
00205             IF ( CAPPLY ) THEN
00206                DO J = 1, I
00207                   TMP = TMP + CABS1( A( J, I ) ) / C( J )
00208                END DO
00209                DO J = I+1, N
00210                   TMP = TMP + CABS1( A( I, J ) ) / C( J )
00211                END DO
00212             ELSE
00213                DO J = 1, I
00214                   TMP = TMP + CABS1( A( J, I ) )
00215                END DO
00216                DO J = I+1, N
00217                   TMP = TMP + CABS1( A( I, J ) )
00218                END DO
00219             END IF
00220             RWORK( I ) = TMP
00221             ANORM = MAX( ANORM, TMP )
00222          END DO
00223       ELSE
00224          DO I = 1, N
00225             TMP = 0.0E+0
00226             IF ( CAPPLY ) THEN
00227                DO J = 1, I
00228                   TMP = TMP + CABS1( A( I, J ) ) / C( J )
00229                END DO
00230                DO J = I+1, N
00231                   TMP = TMP + CABS1( A( J, I ) ) / C( J )
00232                END DO
00233             ELSE
00234                DO J = 1, I
00235                   TMP = TMP + CABS1( A( I, J ) )
00236                END DO
00237                DO J = I+1, N
00238                   TMP = TMP + CABS1( A( J, I ) )
00239                END DO
00240             END IF
00241             RWORK( I ) = TMP
00242             ANORM = MAX( ANORM, TMP )
00243          END DO
00244       END IF
00245 *
00246 *     Quick return if possible.
00247 *
00248       IF( N.EQ.0 ) THEN
00249          CLA_HERCOND_C = 1.0E+0
00250          RETURN
00251       ELSE IF( ANORM .EQ. 0.0E+0 ) THEN
00252          RETURN
00253       END IF
00254 *
00255 *     Estimate the norm of inv(op(A)).
00256 *
00257       AINVNM = 0.0E+0
00258 *
00259       KASE = 0
00260    10 CONTINUE
00261       CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
00262       IF( KASE.NE.0 ) THEN
00263          IF( KASE.EQ.2 ) THEN
00264 *
00265 *           Multiply by R.
00266 *
00267             DO I = 1, N
00268                WORK( I ) = WORK( I ) * RWORK( I )
00269             END DO
00270 *
00271             IF ( UP ) THEN
00272                CALL CHETRS( 'U', N, 1, AF, LDAF, IPIV,
00273      $            WORK, N, INFO )
00274             ELSE
00275                CALL CHETRS( 'L', N, 1, AF, LDAF, IPIV,
00276      $            WORK, N, INFO )
00277             ENDIF
00278 *
00279 *           Multiply by inv(C).
00280 *
00281             IF ( CAPPLY ) THEN
00282                DO I = 1, N
00283                   WORK( I ) = WORK( I ) * C( I )
00284                END DO
00285             END IF
00286          ELSE
00287 *
00288 *           Multiply by inv(C**H).
00289 *
00290             IF ( CAPPLY ) THEN
00291                DO I = 1, N
00292                   WORK( I ) = WORK( I ) * C( I )
00293                END DO
00294             END IF
00295 *
00296             IF ( UP ) THEN
00297                CALL CHETRS( 'U', N, 1, AF, LDAF, IPIV,
00298      $            WORK, N, INFO )
00299             ELSE
00300                CALL CHETRS( 'L', N, 1, AF, LDAF, IPIV,
00301      $            WORK, N, INFO )
00302             END IF
00303 *
00304 *           Multiply by R.
00305 *
00306             DO I = 1, N
00307                WORK( I ) = WORK( I ) * RWORK( I )
00308             END DO
00309          END IF
00310          GO TO 10
00311       END IF
00312 *
00313 *     Compute the estimate of the reciprocal condition number.
00314 *
00315       IF( AINVNM .NE. 0.0E+0 )
00316      $   CLA_HERCOND_C = 1.0E+0 / AINVNM
00317 *
00318       RETURN
00319 *
00320       END