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00001 *> \brief \b CLA_GERCOND_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_GERCOND_C( TRANS, N, A, LDA, AF, LDAF, IPIV, C,
00022 *                                    CAPPLY, INFO, WORK, RWORK )
00023 * 
00024 *       .. Scalar Aguments ..
00025 *       CHARACTER          TRANS
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 *> 
00042 *>    CLA_GERCOND_C computes the infinity norm condition number of
00043 *>    op(A) * inv(diag(C)) where C is a REAL vector.
00044 *> \endverbatim
00045 *
00046 *  Arguments:
00047 *  ==========
00048 *
00049 *> \param[in] TRANS
00050 *> \verbatim
00051 *>          TRANS is CHARACTER*1
00052 *>     Specifies the form of the system of equations:
00053 *>       = 'N':  A * X = B     (No transpose)
00054 *>       = 'T':  A**T * X = B  (Transpose)
00055 *>       = 'C':  A**H * X = B  (Conjugate Transpose = Transpose)
00056 *> \endverbatim
00057 *>
00058 *> \param[in] N
00059 *> \verbatim
00060 *>          N is INTEGER
00061 *>     The number of linear equations, i.e., the order of the
00062 *>     matrix A.  N >= 0.
00063 *> \endverbatim
00064 *>
00065 *> \param[in] A
00066 *> \verbatim
00067 *>          A is COMPLEX array, dimension (LDA,N)
00068 *>     On entry, the N-by-N matrix A
00069 *> \endverbatim
00070 *>
00071 *> \param[in] LDA
00072 *> \verbatim
00073 *>          LDA is INTEGER
00074 *>     The leading dimension of the array A.  LDA >= max(1,N).
00075 *> \endverbatim
00076 *>
00077 *> \param[in] AF
00078 *> \verbatim
00079 *>          AF is COMPLEX array, dimension (LDAF,N)
00080 *>     The factors L and U from the factorization
00081 *>     A = P*L*U as computed by CGETRF.
00082 *> \endverbatim
00083 *>
00084 *> \param[in] LDAF
00085 *> \verbatim
00086 *>          LDAF is INTEGER
00087 *>     The leading dimension of the array AF.  LDAF >= max(1,N).
00088 *> \endverbatim
00089 *>
00090 *> \param[in] IPIV
00091 *> \verbatim
00092 *>          IPIV is INTEGER array, dimension (N)
00093 *>     The pivot indices from the factorization A = P*L*U
00094 *>     as computed by CGETRF; row i of the matrix was interchanged
00095 *>     with row IPIV(i).
00096 *> \endverbatim
00097 *>
00098 *> \param[in] C
00099 *> \verbatim
00100 *>          C is REAL array, dimension (N)
00101 *>     The vector C in the formula op(A) * inv(diag(C)).
00102 *> \endverbatim
00103 *>
00104 *> \param[in] CAPPLY
00105 *> \verbatim
00106 *>          CAPPLY is LOGICAL
00107 *>     If .TRUE. then access the vector C in the formula above.
00108 *> \endverbatim
00109 *>
00110 *> \param[out] INFO
00111 *> \verbatim
00112 *>          INFO is INTEGER
00113 *>       = 0:  Successful exit.
00114 *>     i > 0:  The ith argument is invalid.
00115 *> \endverbatim
00116 *>
00117 *> \param[in] WORK
00118 *> \verbatim
00119 *>          WORK is COMPLEX array, dimension (2*N).
00120 *>     Workspace.
00121 *> \endverbatim
00122 *>
00123 *> \param[in] RWORK
00124 *> \verbatim
00125 *>          RWORK is REAL array, dimension (N).
00126 *>     Workspace.
00127 *> \endverbatim
00128 *
00129 *  Authors:
00130 *  ========
00131 *
00132 *> \author Univ. of Tennessee 
00133 *> \author Univ. of California Berkeley 
00134 *> \author Univ. of Colorado Denver 
00135 *> \author NAG Ltd. 
00136 *
00137 *> \date November 2011
00138 *
00139 *> \ingroup complexGEcomputational
00140 *
00141 *  =====================================================================
00142       REAL FUNCTION CLA_GERCOND_C( TRANS, N, A, LDA, AF, LDAF, IPIV, C,
00143      $                             CAPPLY, INFO, WORK, RWORK )
00144 *
00145 *  -- LAPACK computational routine (version 3.4.0) --
00146 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00147 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00148 *     November 2011
00149 *
00150 *     .. Scalar Aguments ..
00151       CHARACTER          TRANS
00152       LOGICAL            CAPPLY
00153       INTEGER            N, LDA, LDAF, INFO
00154 *     ..
00155 *     .. Array Arguments ..
00156       INTEGER            IPIV( * )
00157       COMPLEX            A( LDA, * ), AF( LDAF, * ), WORK( * )
00158       REAL               C( * ), RWORK( * )
00159 *     ..
00160 *
00161 *  =====================================================================
00162 *
00163 *     .. Local Scalars ..
00164       LOGICAL            NOTRANS
00165       INTEGER            KASE, I, J
00166       REAL               AINVNM, ANORM, TMP
00167       COMPLEX            ZDUM
00168 *     ..
00169 *     .. Local Arrays ..
00170       INTEGER            ISAVE( 3 )
00171 *     ..
00172 *     .. External Functions ..
00173       LOGICAL            LSAME
00174       EXTERNAL           LSAME
00175 *     ..
00176 *     .. External Subroutines ..
00177       EXTERNAL           CLACN2, CGETRS, XERBLA
00178 *     ..
00179 *     .. Intrinsic Functions ..
00180       INTRINSIC          ABS, MAX, REAL, AIMAG
00181 *     ..
00182 *     .. Statement Functions ..
00183       REAL               CABS1
00184 *     ..
00185 *     .. Statement Function Definitions ..
00186       CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
00187 *     ..
00188 *     .. Executable Statements ..
00189       CLA_GERCOND_C = 0.0E+0
00190 *
00191       INFO = 0
00192       NOTRANS = LSAME( TRANS, 'N' )
00193       IF ( .NOT. NOTRANS .AND. .NOT. LSAME( TRANS, 'T' ) .AND. .NOT.
00194      $     LSAME( TRANS, 'C' ) ) THEN
00195       ELSE IF( N.LT.0 ) THEN
00196          INFO = -2
00197       END IF
00198       IF( INFO.NE.0 ) THEN
00199          CALL XERBLA( 'CLA_GERCOND_C', -INFO )
00200          RETURN
00201       END IF
00202 *
00203 *     Compute norm of op(A)*op2(C).
00204 *
00205       ANORM = 0.0E+0
00206       IF ( NOTRANS ) THEN
00207          DO I = 1, N
00208             TMP = 0.0E+0
00209             IF ( CAPPLY ) THEN
00210                DO J = 1, N
00211                   TMP = TMP + CABS1( A( I, J ) ) / C( J )
00212                END DO
00213             ELSE
00214                DO J = 1, N
00215                   TMP = TMP + CABS1( A( I, J ) )
00216                END DO
00217             END IF
00218             RWORK( I ) = TMP
00219             ANORM = MAX( ANORM, TMP )
00220          END DO
00221       ELSE
00222          DO I = 1, N
00223             TMP = 0.0E+0
00224             IF ( CAPPLY ) THEN
00225                DO J = 1, N
00226                   TMP = TMP + CABS1( A( J, I ) ) / C( J )
00227                END DO
00228             ELSE
00229                DO J = 1, N
00230                   TMP = TMP + CABS1( A( J, I ) )
00231                END DO
00232             END IF
00233             RWORK( I ) = TMP
00234             ANORM = MAX( ANORM, TMP )
00235          END DO
00236       END IF
00237 *
00238 *     Quick return if possible.
00239 *
00240       IF( N.EQ.0 ) THEN
00241          CLA_GERCOND_C = 1.0E+0
00242          RETURN
00243       ELSE IF( ANORM .EQ. 0.0E+0 ) THEN
00244          RETURN
00245       END IF
00246 *
00247 *     Estimate the norm of inv(op(A)).
00248 *
00249       AINVNM = 0.0E+0
00250 *
00251       KASE = 0
00252    10 CONTINUE
00253       CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
00254       IF( KASE.NE.0 ) THEN
00255          IF( KASE.EQ.2 ) THEN
00256 *
00257 *           Multiply by R.
00258 *
00259             DO I = 1, N
00260                WORK( I ) = WORK( I ) * RWORK( I )
00261             END DO
00262 *
00263             IF (NOTRANS) THEN
00264                CALL CGETRS( 'No transpose', N, 1, AF, LDAF, IPIV,
00265      $            WORK, N, INFO )
00266             ELSE
00267                CALL CGETRS( 'Conjugate transpose', N, 1, AF, LDAF, IPIV,
00268      $            WORK, N, INFO )
00269             ENDIF
00270 *
00271 *           Multiply by inv(C).
00272 *
00273             IF ( CAPPLY ) THEN
00274                DO I = 1, N
00275                   WORK( I ) = WORK( I ) * C( I )
00276                END DO
00277             END IF
00278          ELSE
00279 *
00280 *           Multiply by inv(C**H).
00281 *
00282             IF ( CAPPLY ) THEN
00283                DO I = 1, N
00284                   WORK( I ) = WORK( I ) * C( I )
00285                END DO
00286             END IF
00287 *
00288             IF ( NOTRANS ) THEN
00289                CALL CGETRS( 'Conjugate transpose', N, 1, AF, LDAF, IPIV,
00290      $            WORK, N, INFO )
00291             ELSE
00292                CALL CGETRS( 'No transpose', N, 1, AF, LDAF, IPIV,
00293      $            WORK, N, INFO )
00294             END IF
00295 *
00296 *           Multiply by R.
00297 *
00298             DO I = 1, N
00299                WORK( I ) = WORK( I ) * RWORK( I )
00300             END DO
00301          END IF
00302          GO TO 10
00303       END IF
00304 *
00305 *     Compute the estimate of the reciprocal condition number.
00306 *
00307       IF( AINVNM .NE. 0.0E+0 )
00308      $   CLA_GERCOND_C = 1.0E+0 / AINVNM
00309 *
00310       RETURN
00311 *
00312       END