LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
zla_syrcond_x.f
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00001 *> \brief \b ZLA_SYRCOND_X
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download ZLA_SYRCOND_X + 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_syrcond_x.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       DOUBLE PRECISION FUNCTION ZLA_SYRCOND_X( UPLO, N, A, LDA, AF,
00022 *                                                LDAF, IPIV, X, INFO,
00023 *                                                WORK, RWORK )
00024 * 
00025 *       .. Scalar Arguments ..
00026 *       CHARACTER          UPLO
00027 *       INTEGER            N, LDA, LDAF, INFO
00028 *       ..
00029 *       .. Array Arguments ..
00030 *       INTEGER            IPIV( * )
00031 *       COMPLEX*16         A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * )
00032 *       DOUBLE PRECISION   RWORK( * )
00033 *       ..
00034 *  
00035 *
00036 *> \par Purpose:
00037 *  =============
00038 *>
00039 *> \verbatim
00040 *>
00041 *>    ZLA_SYRCOND_X Computes the infinity norm condition number of
00042 *>    op(A) * diag(X) where X is a COMPLEX*16 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 block diagonal matrix D and the multipliers used to
00078 *>     obtain the factor U or L as computed by ZSYTRF.
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 ZSYTRF.
00092 *> \endverbatim
00093 *>
00094 *> \param[in] X
00095 *> \verbatim
00096 *>          X is COMPLEX*16 array, dimension (N)
00097 *>     The vector X in the formula op(A) * diag(X).
00098 *> \endverbatim
00099 *>
00100 *> \param[out] INFO
00101 *> \verbatim
00102 *>          INFO is INTEGER
00103 *>       = 0:  Successful exit.
00104 *>     i > 0:  The ith argument is invalid.
00105 *> \endverbatim
00106 *>
00107 *> \param[in] WORK
00108 *> \verbatim
00109 *>          WORK is COMPLEX*16 array, dimension (2*N).
00110 *>     Workspace.
00111 *> \endverbatim
00112 *>
00113 *> \param[in] RWORK
00114 *> \verbatim
00115 *>          RWORK is DOUBLE PRECISION array, dimension (N).
00116 *>     Workspace.
00117 *> \endverbatim
00118 *
00119 *  Authors:
00120 *  ========
00121 *
00122 *> \author Univ. of Tennessee 
00123 *> \author Univ. of California Berkeley 
00124 *> \author Univ. of Colorado Denver 
00125 *> \author NAG Ltd. 
00126 *
00127 *> \date November 2011
00128 *
00129 *> \ingroup complex16SYcomputational
00130 *
00131 *  =====================================================================
00132       DOUBLE PRECISION FUNCTION ZLA_SYRCOND_X( UPLO, N, A, LDA, AF,
00133      $                                         LDAF, IPIV, X, INFO,
00134      $                                         WORK, RWORK )
00135 *
00136 *  -- LAPACK computational routine (version 3.4.0) --
00137 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00138 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00139 *     November 2011
00140 *
00141 *     .. Scalar Arguments ..
00142       CHARACTER          UPLO
00143       INTEGER            N, LDA, LDAF, INFO
00144 *     ..
00145 *     .. Array Arguments ..
00146       INTEGER            IPIV( * )
00147       COMPLEX*16         A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * )
00148       DOUBLE PRECISION   RWORK( * )
00149 *     ..
00150 *
00151 *  =====================================================================
00152 *
00153 *     .. Local Scalars ..
00154       INTEGER            KASE
00155       DOUBLE PRECISION   AINVNM, ANORM, TMP
00156       INTEGER            I, J
00157       LOGICAL            UP, UPPER
00158       COMPLEX*16         ZDUM
00159 *     ..
00160 *     .. Local Arrays ..
00161       INTEGER            ISAVE( 3 )
00162 *     ..
00163 *     .. External Functions ..
00164       LOGICAL            LSAME
00165       EXTERNAL           LSAME
00166 *     ..
00167 *     .. External Subroutines ..
00168       EXTERNAL           ZLACN2, ZSYTRS, XERBLA
00169 *     ..
00170 *     .. Intrinsic Functions ..
00171       INTRINSIC          ABS, MAX
00172 *     ..
00173 *     .. Statement Functions ..
00174       DOUBLE PRECISION   CABS1
00175 *     ..
00176 *     .. Statement Function Definitions ..
00177       CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
00178 *     ..
00179 *     .. Executable Statements ..
00180 *
00181       ZLA_SYRCOND_X = 0.0D+0
00182 *
00183       INFO = 0
00184       UPPER = LSAME( UPLO, 'U' )
00185       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00186          INFO = -1
00187       ELSE IF( N.LT.0 ) THEN
00188          INFO = -2
00189       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00190          INFO = -4
00191       ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
00192          INFO = -6
00193       END IF
00194       IF( INFO.NE.0 ) THEN
00195          CALL XERBLA( 'ZLA_SYRCOND_X', -INFO )
00196          RETURN
00197       END IF
00198       UP = .FALSE.
00199       IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
00200 *
00201 *     Compute norm of op(A)*op2(C).
00202 *
00203       ANORM = 0.0D+0
00204       IF ( UP ) THEN
00205          DO I = 1, N
00206             TMP = 0.0D+0
00207             DO J = 1, I
00208                TMP = TMP + CABS1( A( J, I ) * X( J ) )
00209             END DO
00210             DO J = I+1, N
00211                TMP = TMP + CABS1( A( I, J ) * X( J ) )
00212             END DO
00213             RWORK( I ) = TMP
00214             ANORM = MAX( ANORM, TMP )
00215          END DO
00216       ELSE
00217          DO I = 1, N
00218             TMP = 0.0D+0
00219             DO J = 1, I
00220                TMP = TMP + CABS1( A( I, J ) * X( J ) )
00221             END DO
00222             DO J = I+1, N
00223                TMP = TMP + CABS1( A( J, I ) * X( J ) )
00224             END DO
00225             RWORK( I ) = TMP
00226             ANORM = MAX( ANORM, TMP )
00227          END DO
00228       END IF
00229 *
00230 *     Quick return if possible.
00231 *
00232       IF( N.EQ.0 ) THEN
00233          ZLA_SYRCOND_X = 1.0D+0
00234          RETURN
00235       ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
00236          RETURN
00237       END IF
00238 *
00239 *     Estimate the norm of inv(op(A)).
00240 *
00241       AINVNM = 0.0D+0
00242 *
00243       KASE = 0
00244    10 CONTINUE
00245       CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
00246       IF( KASE.NE.0 ) THEN
00247          IF( KASE.EQ.2 ) THEN
00248 *
00249 *           Multiply by R.
00250 *
00251             DO I = 1, N
00252                WORK( I ) = WORK( I ) * RWORK( I )
00253             END DO
00254 *
00255             IF ( UP ) THEN
00256                CALL ZSYTRS( 'U', N, 1, AF, LDAF, IPIV,
00257      $            WORK, N, INFO )
00258             ELSE
00259                CALL ZSYTRS( 'L', N, 1, AF, LDAF, IPIV,
00260      $            WORK, N, INFO )
00261             ENDIF
00262 *
00263 *           Multiply by inv(X).
00264 *
00265             DO I = 1, N
00266                WORK( I ) = WORK( I ) / X( I )
00267             END DO
00268          ELSE
00269 *
00270 *           Multiply by inv(X**T).
00271 *
00272             DO I = 1, N
00273                WORK( I ) = WORK( I ) / X( I )
00274             END DO
00275 *
00276             IF ( UP ) THEN
00277                CALL ZSYTRS( 'U', N, 1, AF, LDAF, IPIV,
00278      $            WORK, N, INFO )
00279             ELSE
00280                CALL ZSYTRS( 'L', N, 1, AF, LDAF, IPIV,
00281      $            WORK, N, INFO )
00282             END IF
00283 *
00284 *           Multiply by R.
00285 *
00286             DO I = 1, N
00287                WORK( I ) = WORK( I ) * RWORK( I )
00288             END DO
00289          END IF
00290          GO TO 10
00291       END IF
00292 *
00293 *     Compute the estimate of the reciprocal condition number.
00294 *
00295       IF( AINVNM .NE. 0.0D+0 )
00296      $   ZLA_SYRCOND_X = 1.0D+0 / AINVNM
00297 *
00298       RETURN
00299 *
00300       END
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