LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
zla_gercond_c.f
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00001 *> \brief \b ZLA_GERCOND_C
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download ZLA_GERCOND_C + dependencies 
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00011 *> [TGZ]</a> 
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00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_gercond_c.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       DOUBLE PRECISION FUNCTION ZLA_GERCOND_C( TRANS, N, A, LDA, AF, 
00022 *                                                LDAF, IPIV, C, CAPPLY,
00023 *                                                INFO, WORK, RWORK )
00024 * 
00025 *       .. Scalar Aguments ..
00026 *       CHARACTER          TRANS
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_GERCOND_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] 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*16 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*16 array, dimension (LDAF,N)
00080 *>     The factors L and U from the factorization
00081 *>     A = P*L*U as computed by ZGETRF.
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 ZGETRF; row i of the matrix was interchanged
00095 *>     with row IPIV(i).
00096 *> \endverbatim
00097 *>
00098 *> \param[in] C
00099 *> \verbatim
00100 *>          C is DOUBLE PRECISION 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*16 array, dimension (2*N).
00120 *>     Workspace.
00121 *> \endverbatim
00122 *>
00123 *> \param[in] RWORK
00124 *> \verbatim
00125 *>          RWORK is DOUBLE PRECISION 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 complex16GEcomputational
00140 *
00141 *  =====================================================================
00142       DOUBLE PRECISION FUNCTION ZLA_GERCOND_C( TRANS, N, A, LDA, AF, 
00143      $                                         LDAF, IPIV, C, CAPPLY,
00144      $                                         INFO, WORK, RWORK )
00145 *
00146 *  -- LAPACK computational routine (version 3.4.0) --
00147 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00148 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00149 *     November 2011
00150 *
00151 *     .. Scalar Aguments ..
00152       CHARACTER          TRANS
00153       LOGICAL            CAPPLY
00154       INTEGER            N, LDA, LDAF, INFO
00155 *     ..
00156 *     .. Array Arguments ..
00157       INTEGER            IPIV( * )
00158       COMPLEX*16         A( LDA, * ), AF( LDAF, * ), WORK( * )
00159       DOUBLE PRECISION   C( * ), RWORK( * )
00160 *     ..
00161 *
00162 *  =====================================================================
00163 *
00164 *     .. Local Scalars ..
00165       LOGICAL            NOTRANS
00166       INTEGER            KASE, I, J
00167       DOUBLE PRECISION   AINVNM, ANORM, TMP
00168       COMPLEX*16         ZDUM
00169 *     ..
00170 *     .. Local Arrays ..
00171       INTEGER            ISAVE( 3 )
00172 *     ..
00173 *     .. External Functions ..
00174       LOGICAL            LSAME
00175       EXTERNAL           LSAME
00176 *     ..
00177 *     .. External Subroutines ..
00178       EXTERNAL           ZLACN2, ZGETRS, XERBLA
00179 *     ..
00180 *     .. Intrinsic Functions ..
00181       INTRINSIC          ABS, MAX, REAL, DIMAG
00182 *     ..
00183 *     .. Statement Functions ..
00184       DOUBLE PRECISION   CABS1
00185 *     ..
00186 *     .. Statement Function Definitions ..
00187       CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
00188 *     ..
00189 *     .. Executable Statements ..
00190       ZLA_GERCOND_C = 0.0D+0
00191 *
00192       INFO = 0
00193       NOTRANS = LSAME( TRANS, 'N' )
00194       IF ( .NOT. NOTRANS .AND. .NOT. LSAME( TRANS, 'T' ) .AND. .NOT.
00195      $     LSAME( TRANS, 'C' ) ) THEN
00196          INFO = -1
00197       ELSE IF( N.LT.0 ) THEN
00198          INFO = -2
00199       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00200          INFO = -4
00201       ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
00202          INFO = -6
00203       END IF
00204       IF( INFO.NE.0 ) THEN
00205          CALL XERBLA( 'ZLA_GERCOND_C', -INFO )
00206          RETURN
00207       END IF
00208 *
00209 *     Compute norm of op(A)*op2(C).
00210 *
00211       ANORM = 0.0D+0
00212       IF ( NOTRANS ) THEN
00213          DO I = 1, N
00214             TMP = 0.0D+0
00215             IF ( CAPPLY ) THEN
00216                DO J = 1, N
00217                   TMP = TMP + CABS1( A( I, J ) ) / C( J )
00218                END DO
00219             ELSE
00220                DO J = 1, N
00221                   TMP = TMP + CABS1( A( I, J ) )
00222                END DO
00223             END IF
00224             RWORK( I ) = TMP
00225             ANORM = MAX( ANORM, TMP )
00226          END DO
00227       ELSE
00228          DO I = 1, N
00229             TMP = 0.0D+0
00230             IF ( CAPPLY ) THEN
00231                DO J = 1, N
00232                   TMP = TMP + CABS1( A( J, I ) ) / C( J )
00233                END DO
00234             ELSE
00235                DO J = 1, N
00236                   TMP = TMP + CABS1( A( J, I ) )
00237                END DO
00238             END IF
00239             RWORK( I ) = TMP
00240             ANORM = MAX( ANORM, TMP )
00241          END DO
00242       END IF
00243 *
00244 *     Quick return if possible.
00245 *
00246       IF( N.EQ.0 ) THEN
00247          ZLA_GERCOND_C = 1.0D+0
00248          RETURN
00249       ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
00250          RETURN
00251       END IF
00252 *
00253 *     Estimate the norm of inv(op(A)).
00254 *
00255       AINVNM = 0.0D+0
00256 *
00257       KASE = 0
00258    10 CONTINUE
00259       CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
00260       IF( KASE.NE.0 ) THEN
00261          IF( KASE.EQ.2 ) THEN
00262 *
00263 *           Multiply by R.
00264 *
00265             DO I = 1, N
00266                WORK( I ) = WORK( I ) * RWORK( I )
00267             END DO
00268 *
00269             IF (NOTRANS) THEN
00270                CALL ZGETRS( 'No transpose', N, 1, AF, LDAF, IPIV,
00271      $            WORK, N, INFO )
00272             ELSE
00273                CALL ZGETRS( 'Conjugate transpose', N, 1, AF, LDAF, IPIV,
00274      $            WORK, N, INFO )
00275             ENDIF
00276 *
00277 *           Multiply by inv(C).
00278 *
00279             IF ( CAPPLY ) THEN
00280                DO I = 1, N
00281                   WORK( I ) = WORK( I ) * C( I )
00282                END DO
00283             END IF
00284          ELSE
00285 *
00286 *           Multiply by inv(C**H).
00287 *
00288             IF ( CAPPLY ) THEN
00289                DO I = 1, N
00290                   WORK( I ) = WORK( I ) * C( I )
00291                END DO
00292             END IF
00293 *
00294             IF ( NOTRANS ) THEN
00295                CALL ZGETRS( 'Conjugate transpose', N, 1, AF, LDAF, IPIV,
00296      $            WORK, N, INFO )
00297             ELSE
00298                CALL ZGETRS( 'No transpose', N, 1, AF, LDAF, IPIV,
00299      $            WORK, N, INFO )
00300             END IF
00301 *
00302 *           Multiply by R.
00303 *
00304             DO I = 1, N
00305                WORK( I ) = WORK( I ) * RWORK( I )
00306             END DO
00307          END IF
00308          GO TO 10
00309       END IF
00310 *
00311 *     Compute the estimate of the reciprocal condition number.
00312 *
00313       IF( AINVNM .NE. 0.0D+0 )
00314      $   ZLA_GERCOND_C = 1.0D+0 / AINVNM
00315 *
00316       RETURN
00317 *
00318       END
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