LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
zheevx.f
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00001 *> \brief <b> ZHEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices</b>
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download ZHEEVX + dependencies 
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00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zheevx.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zheevx.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE ZHEEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
00022 *                          ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK,
00023 *                          IWORK, IFAIL, INFO )
00024 * 
00025 *       .. Scalar Arguments ..
00026 *       CHARACTER          JOBZ, RANGE, UPLO
00027 *       INTEGER            IL, INFO, IU, LDA, LDZ, LWORK, M, N
00028 *       DOUBLE PRECISION   ABSTOL, VL, VU
00029 *       ..
00030 *       .. Array Arguments ..
00031 *       INTEGER            IFAIL( * ), IWORK( * )
00032 *       DOUBLE PRECISION   RWORK( * ), W( * )
00033 *       COMPLEX*16         A( LDA, * ), WORK( * ), Z( LDZ, * )
00034 *       ..
00035 *  
00036 *
00037 *> \par Purpose:
00038 *  =============
00039 *>
00040 *> \verbatim
00041 *>
00042 *> ZHEEVX computes selected eigenvalues and, optionally, eigenvectors
00043 *> of a complex Hermitian matrix A.  Eigenvalues and eigenvectors can
00044 *> be selected by specifying either a range of values or a range of
00045 *> indices for the desired eigenvalues.
00046 *> \endverbatim
00047 *
00048 *  Arguments:
00049 *  ==========
00050 *
00051 *> \param[in] JOBZ
00052 *> \verbatim
00053 *>          JOBZ is CHARACTER*1
00054 *>          = 'N':  Compute eigenvalues only;
00055 *>          = 'V':  Compute eigenvalues and eigenvectors.
00056 *> \endverbatim
00057 *>
00058 *> \param[in] RANGE
00059 *> \verbatim
00060 *>          RANGE is CHARACTER*1
00061 *>          = 'A': all eigenvalues will be found.
00062 *>          = 'V': all eigenvalues in the half-open interval (VL,VU]
00063 *>                 will be found.
00064 *>          = 'I': the IL-th through IU-th eigenvalues will be found.
00065 *> \endverbatim
00066 *>
00067 *> \param[in] UPLO
00068 *> \verbatim
00069 *>          UPLO is CHARACTER*1
00070 *>          = 'U':  Upper triangle of A is stored;
00071 *>          = 'L':  Lower triangle of A is stored.
00072 *> \endverbatim
00073 *>
00074 *> \param[in] N
00075 *> \verbatim
00076 *>          N is INTEGER
00077 *>          The order of the matrix A.  N >= 0.
00078 *> \endverbatim
00079 *>
00080 *> \param[in,out] A
00081 *> \verbatim
00082 *>          A is COMPLEX*16 array, dimension (LDA, N)
00083 *>          On entry, the Hermitian matrix A.  If UPLO = 'U', the
00084 *>          leading N-by-N upper triangular part of A contains the
00085 *>          upper triangular part of the matrix A.  If UPLO = 'L',
00086 *>          the leading N-by-N lower triangular part of A contains
00087 *>          the lower triangular part of the matrix A.
00088 *>          On exit, the lower triangle (if UPLO='L') or the upper
00089 *>          triangle (if UPLO='U') of A, including the diagonal, is
00090 *>          destroyed.
00091 *> \endverbatim
00092 *>
00093 *> \param[in] LDA
00094 *> \verbatim
00095 *>          LDA is INTEGER
00096 *>          The leading dimension of the array A.  LDA >= max(1,N).
00097 *> \endverbatim
00098 *>
00099 *> \param[in] VL
00100 *> \verbatim
00101 *>          VL is DOUBLE PRECISION
00102 *> \endverbatim
00103 *>
00104 *> \param[in] VU
00105 *> \verbatim
00106 *>          VU is DOUBLE PRECISION
00107 *>          If RANGE='V', the lower and upper bounds of the interval to
00108 *>          be searched for eigenvalues. VL < VU.
00109 *>          Not referenced if RANGE = 'A' or 'I'.
00110 *> \endverbatim
00111 *>
00112 *> \param[in] IL
00113 *> \verbatim
00114 *>          IL is INTEGER
00115 *> \endverbatim
00116 *>
00117 *> \param[in] IU
00118 *> \verbatim
00119 *>          IU is INTEGER
00120 *>          If RANGE='I', the indices (in ascending order) of the
00121 *>          smallest and largest eigenvalues to be returned.
00122 *>          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
00123 *>          Not referenced if RANGE = 'A' or 'V'.
00124 *> \endverbatim
00125 *>
00126 *> \param[in] ABSTOL
00127 *> \verbatim
00128 *>          ABSTOL is DOUBLE PRECISION
00129 *>          The absolute error tolerance for the eigenvalues.
00130 *>          An approximate eigenvalue is accepted as converged
00131 *>          when it is determined to lie in an interval [a,b]
00132 *>          of width less than or equal to
00133 *>
00134 *>                  ABSTOL + EPS *   max( |a|,|b| ) ,
00135 *>
00136 *>          where EPS is the machine precision.  If ABSTOL is less than
00137 *>          or equal to zero, then  EPS*|T|  will be used in its place,
00138 *>          where |T| is the 1-norm of the tridiagonal matrix obtained
00139 *>          by reducing A to tridiagonal form.
00140 *>
00141 *>          Eigenvalues will be computed most accurately when ABSTOL is
00142 *>          set to twice the underflow threshold 2*DLAMCH('S'), not zero.
00143 *>          If this routine returns with INFO>0, indicating that some
00144 *>          eigenvectors did not converge, try setting ABSTOL to
00145 *>          2*DLAMCH('S').
00146 *>
00147 *>          See "Computing Small Singular Values of Bidiagonal Matrices
00148 *>          with Guaranteed High Relative Accuracy," by Demmel and
00149 *>          Kahan, LAPACK Working Note #3.
00150 *> \endverbatim
00151 *>
00152 *> \param[out] M
00153 *> \verbatim
00154 *>          M is INTEGER
00155 *>          The total number of eigenvalues found.  0 <= M <= N.
00156 *>          If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
00157 *> \endverbatim
00158 *>
00159 *> \param[out] W
00160 *> \verbatim
00161 *>          W is DOUBLE PRECISION array, dimension (N)
00162 *>          On normal exit, the first M elements contain the selected
00163 *>          eigenvalues in ascending order.
00164 *> \endverbatim
00165 *>
00166 *> \param[out] Z
00167 *> \verbatim
00168 *>          Z is COMPLEX*16 array, dimension (LDZ, max(1,M))
00169 *>          If JOBZ = 'V', then if INFO = 0, the first M columns of Z
00170 *>          contain the orthonormal eigenvectors of the matrix A
00171 *>          corresponding to the selected eigenvalues, with the i-th
00172 *>          column of Z holding the eigenvector associated with W(i).
00173 *>          If an eigenvector fails to converge, then that column of Z
00174 *>          contains the latest approximation to the eigenvector, and the
00175 *>          index of the eigenvector is returned in IFAIL.
00176 *>          If JOBZ = 'N', then Z is not referenced.
00177 *>          Note: the user must ensure that at least max(1,M) columns are
00178 *>          supplied in the array Z; if RANGE = 'V', the exact value of M
00179 *>          is not known in advance and an upper bound must be used.
00180 *> \endverbatim
00181 *>
00182 *> \param[in] LDZ
00183 *> \verbatim
00184 *>          LDZ is INTEGER
00185 *>          The leading dimension of the array Z.  LDZ >= 1, and if
00186 *>          JOBZ = 'V', LDZ >= max(1,N).
00187 *> \endverbatim
00188 *>
00189 *> \param[out] WORK
00190 *> \verbatim
00191 *>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
00192 *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
00193 *> \endverbatim
00194 *>
00195 *> \param[in] LWORK
00196 *> \verbatim
00197 *>          LWORK is INTEGER
00198 *>          The length of the array WORK.  LWORK >= 1, when N <= 1;
00199 *>          otherwise 2*N.
00200 *>          For optimal efficiency, LWORK >= (NB+1)*N,
00201 *>          where NB is the max of the blocksize for ZHETRD and for
00202 *>          ZUNMTR as returned by ILAENV.
00203 *>
00204 *>          If LWORK = -1, then a workspace query is assumed; the routine
00205 *>          only calculates the optimal size of the WORK array, returns
00206 *>          this value as the first entry of the WORK array, and no error
00207 *>          message related to LWORK is issued by XERBLA.
00208 *> \endverbatim
00209 *>
00210 *> \param[out] RWORK
00211 *> \verbatim
00212 *>          RWORK is DOUBLE PRECISION array, dimension (7*N)
00213 *> \endverbatim
00214 *>
00215 *> \param[out] IWORK
00216 *> \verbatim
00217 *>          IWORK is INTEGER array, dimension (5*N)
00218 *> \endverbatim
00219 *>
00220 *> \param[out] IFAIL
00221 *> \verbatim
00222 *>          IFAIL is INTEGER array, dimension (N)
00223 *>          If JOBZ = 'V', then if INFO = 0, the first M elements of
00224 *>          IFAIL are zero.  If INFO > 0, then IFAIL contains the
00225 *>          indices of the eigenvectors that failed to converge.
00226 *>          If JOBZ = 'N', then IFAIL is not referenced.
00227 *> \endverbatim
00228 *>
00229 *> \param[out] INFO
00230 *> \verbatim
00231 *>          INFO is INTEGER
00232 *>          = 0:  successful exit
00233 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00234 *>          > 0:  if INFO = i, then i eigenvectors failed to converge.
00235 *>                Their indices are stored in array IFAIL.
00236 *> \endverbatim
00237 *
00238 *  Authors:
00239 *  ========
00240 *
00241 *> \author Univ. of Tennessee 
00242 *> \author Univ. of California Berkeley 
00243 *> \author Univ. of Colorado Denver 
00244 *> \author NAG Ltd. 
00245 *
00246 *> \date November 2011
00247 *
00248 *> \ingroup complex16HEeigen
00249 *
00250 *  =====================================================================
00251       SUBROUTINE ZHEEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
00252      $                   ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK,
00253      $                   IWORK, IFAIL, INFO )
00254 *
00255 *  -- LAPACK driver routine (version 3.4.0) --
00256 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00257 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00258 *     November 2011
00259 *
00260 *     .. Scalar Arguments ..
00261       CHARACTER          JOBZ, RANGE, UPLO
00262       INTEGER            IL, INFO, IU, LDA, LDZ, LWORK, M, N
00263       DOUBLE PRECISION   ABSTOL, VL, VU
00264 *     ..
00265 *     .. Array Arguments ..
00266       INTEGER            IFAIL( * ), IWORK( * )
00267       DOUBLE PRECISION   RWORK( * ), W( * )
00268       COMPLEX*16         A( LDA, * ), WORK( * ), Z( LDZ, * )
00269 *     ..
00270 *
00271 *  =====================================================================
00272 *
00273 *     .. Parameters ..
00274       DOUBLE PRECISION   ZERO, ONE
00275       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
00276       COMPLEX*16         CONE
00277       PARAMETER          ( CONE = ( 1.0D+0, 0.0D+0 ) )
00278 *     ..
00279 *     .. Local Scalars ..
00280       LOGICAL            ALLEIG, INDEIG, LOWER, LQUERY, TEST, VALEIG,
00281      $                   WANTZ
00282       CHARACTER          ORDER
00283       INTEGER            I, IINFO, IMAX, INDD, INDE, INDEE, INDIBL,
00284      $                   INDISP, INDIWK, INDRWK, INDTAU, INDWRK, ISCALE,
00285      $                   ITMP1, J, JJ, LLWORK, LWKMIN, LWKOPT, NB,
00286      $                   NSPLIT
00287       DOUBLE PRECISION   ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
00288      $                   SIGMA, SMLNUM, TMP1, VLL, VUU
00289 *     ..
00290 *     .. External Functions ..
00291       LOGICAL            LSAME
00292       INTEGER            ILAENV
00293       DOUBLE PRECISION   DLAMCH, ZLANHE
00294       EXTERNAL           LSAME, ILAENV, DLAMCH, ZLANHE
00295 *     ..
00296 *     .. External Subroutines ..
00297       EXTERNAL           DCOPY, DSCAL, DSTEBZ, DSTERF, XERBLA, ZDSCAL,
00298      $                   ZHETRD, ZLACPY, ZSTEIN, ZSTEQR, ZSWAP, ZUNGTR,
00299      $                   ZUNMTR
00300 *     ..
00301 *     .. Intrinsic Functions ..
00302       INTRINSIC          DBLE, MAX, MIN, SQRT
00303 *     ..
00304 *     .. Executable Statements ..
00305 *
00306 *     Test the input parameters.
00307 *
00308       LOWER = LSAME( UPLO, 'L' )
00309       WANTZ = LSAME( JOBZ, 'V' )
00310       ALLEIG = LSAME( RANGE, 'A' )
00311       VALEIG = LSAME( RANGE, 'V' )
00312       INDEIG = LSAME( RANGE, 'I' )
00313       LQUERY = ( LWORK.EQ.-1 )
00314 *
00315       INFO = 0
00316       IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
00317          INFO = -1
00318       ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
00319          INFO = -2
00320       ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
00321          INFO = -3
00322       ELSE IF( N.LT.0 ) THEN
00323          INFO = -4
00324       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00325          INFO = -6
00326       ELSE
00327          IF( VALEIG ) THEN
00328             IF( N.GT.0 .AND. VU.LE.VL )
00329      $         INFO = -8
00330          ELSE IF( INDEIG ) THEN
00331             IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
00332                INFO = -9
00333             ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
00334                INFO = -10
00335             END IF
00336          END IF
00337       END IF
00338       IF( INFO.EQ.0 ) THEN
00339          IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
00340             INFO = -15
00341          END IF
00342       END IF
00343 *
00344       IF( INFO.EQ.0 ) THEN
00345          IF( N.LE.1 ) THEN
00346             LWKMIN = 1
00347             WORK( 1 ) = LWKMIN
00348          ELSE
00349             LWKMIN = 2*N
00350             NB = ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 )
00351             NB = MAX( NB, ILAENV( 1, 'ZUNMTR', UPLO, N, -1, -1, -1 ) )
00352             LWKOPT = MAX( 1, ( NB + 1 )*N )
00353             WORK( 1 ) = LWKOPT
00354          END IF
00355 *
00356          IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY )
00357      $      INFO = -17
00358       END IF
00359 *
00360       IF( INFO.NE.0 ) THEN
00361          CALL XERBLA( 'ZHEEVX', -INFO )
00362          RETURN
00363       ELSE IF( LQUERY ) THEN
00364          RETURN
00365       END IF
00366 *
00367 *     Quick return if possible
00368 *
00369       M = 0
00370       IF( N.EQ.0 ) THEN
00371          RETURN
00372       END IF
00373 *
00374       IF( N.EQ.1 ) THEN
00375          IF( ALLEIG .OR. INDEIG ) THEN
00376             M = 1
00377             W( 1 ) = A( 1, 1 )
00378          ELSE IF( VALEIG ) THEN
00379             IF( VL.LT.DBLE( A( 1, 1 ) ) .AND. VU.GE.DBLE( A( 1, 1 ) ) )
00380      $           THEN
00381                M = 1
00382                W( 1 ) = A( 1, 1 )
00383             END IF
00384          END IF
00385          IF( WANTZ )
00386      $      Z( 1, 1 ) = CONE
00387          RETURN
00388       END IF
00389 *
00390 *     Get machine constants.
00391 *
00392       SAFMIN = DLAMCH( 'Safe minimum' )
00393       EPS = DLAMCH( 'Precision' )
00394       SMLNUM = SAFMIN / EPS
00395       BIGNUM = ONE / SMLNUM
00396       RMIN = SQRT( SMLNUM )
00397       RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) )
00398 *
00399 *     Scale matrix to allowable range, if necessary.
00400 *
00401       ISCALE = 0
00402       ABSTLL = ABSTOL
00403       IF( VALEIG ) THEN
00404          VLL = VL
00405          VUU = VU
00406       END IF
00407       ANRM = ZLANHE( 'M', UPLO, N, A, LDA, RWORK )
00408       IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
00409          ISCALE = 1
00410          SIGMA = RMIN / ANRM
00411       ELSE IF( ANRM.GT.RMAX ) THEN
00412          ISCALE = 1
00413          SIGMA = RMAX / ANRM
00414       END IF
00415       IF( ISCALE.EQ.1 ) THEN
00416          IF( LOWER ) THEN
00417             DO 10 J = 1, N
00418                CALL ZDSCAL( N-J+1, SIGMA, A( J, J ), 1 )
00419    10       CONTINUE
00420          ELSE
00421             DO 20 J = 1, N
00422                CALL ZDSCAL( J, SIGMA, A( 1, J ), 1 )
00423    20       CONTINUE
00424          END IF
00425          IF( ABSTOL.GT.0 )
00426      $      ABSTLL = ABSTOL*SIGMA
00427          IF( VALEIG ) THEN
00428             VLL = VL*SIGMA
00429             VUU = VU*SIGMA
00430          END IF
00431       END IF
00432 *
00433 *     Call ZHETRD to reduce Hermitian matrix to tridiagonal form.
00434 *
00435       INDD = 1
00436       INDE = INDD + N
00437       INDRWK = INDE + N
00438       INDTAU = 1
00439       INDWRK = INDTAU + N
00440       LLWORK = LWORK - INDWRK + 1
00441       CALL ZHETRD( UPLO, N, A, LDA, RWORK( INDD ), RWORK( INDE ),
00442      $             WORK( INDTAU ), WORK( INDWRK ), LLWORK, IINFO )
00443 *
00444 *     If all eigenvalues are desired and ABSTOL is less than or equal to
00445 *     zero, then call DSTERF or ZUNGTR and ZSTEQR.  If this fails for
00446 *     some eigenvalue, then try DSTEBZ.
00447 *
00448       TEST = .FALSE.
00449       IF( INDEIG ) THEN
00450          IF( IL.EQ.1 .AND. IU.EQ.N ) THEN
00451             TEST = .TRUE.
00452          END IF
00453       END IF
00454       IF( ( ALLEIG .OR. TEST ) .AND. ( ABSTOL.LE.ZERO ) ) THEN
00455          CALL DCOPY( N, RWORK( INDD ), 1, W, 1 )
00456          INDEE = INDRWK + 2*N
00457          IF( .NOT.WANTZ ) THEN
00458             CALL DCOPY( N-1, RWORK( INDE ), 1, RWORK( INDEE ), 1 )
00459             CALL DSTERF( N, W, RWORK( INDEE ), INFO )
00460          ELSE
00461             CALL ZLACPY( 'A', N, N, A, LDA, Z, LDZ )
00462             CALL ZUNGTR( UPLO, N, Z, LDZ, WORK( INDTAU ),
00463      $                   WORK( INDWRK ), LLWORK, IINFO )
00464             CALL DCOPY( N-1, RWORK( INDE ), 1, RWORK( INDEE ), 1 )
00465             CALL ZSTEQR( JOBZ, N, W, RWORK( INDEE ), Z, LDZ,
00466      $                   RWORK( INDRWK ), INFO )
00467             IF( INFO.EQ.0 ) THEN
00468                DO 30 I = 1, N
00469                   IFAIL( I ) = 0
00470    30          CONTINUE
00471             END IF
00472          END IF
00473          IF( INFO.EQ.0 ) THEN
00474             M = N
00475             GO TO 40
00476          END IF
00477          INFO = 0
00478       END IF
00479 *
00480 *     Otherwise, call DSTEBZ and, if eigenvectors are desired, ZSTEIN.
00481 *
00482       IF( WANTZ ) THEN
00483          ORDER = 'B'
00484       ELSE
00485          ORDER = 'E'
00486       END IF
00487       INDIBL = 1
00488       INDISP = INDIBL + N
00489       INDIWK = INDISP + N
00490       CALL DSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL,
00491      $             RWORK( INDD ), RWORK( INDE ), M, NSPLIT, W,
00492      $             IWORK( INDIBL ), IWORK( INDISP ), RWORK( INDRWK ),
00493      $             IWORK( INDIWK ), INFO )
00494 *
00495       IF( WANTZ ) THEN
00496          CALL ZSTEIN( N, RWORK( INDD ), RWORK( INDE ), M, W,
00497      $                IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ,
00498      $                RWORK( INDRWK ), IWORK( INDIWK ), IFAIL, INFO )
00499 *
00500 *        Apply unitary matrix used in reduction to tridiagonal
00501 *        form to eigenvectors returned by ZSTEIN.
00502 *
00503          CALL ZUNMTR( 'L', UPLO, 'N', N, M, A, LDA, WORK( INDTAU ), Z,
00504      $                LDZ, WORK( INDWRK ), LLWORK, IINFO )
00505       END IF
00506 *
00507 *     If matrix was scaled, then rescale eigenvalues appropriately.
00508 *
00509    40 CONTINUE
00510       IF( ISCALE.EQ.1 ) THEN
00511          IF( INFO.EQ.0 ) THEN
00512             IMAX = M
00513          ELSE
00514             IMAX = INFO - 1
00515          END IF
00516          CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
00517       END IF
00518 *
00519 *     If eigenvalues are not in order, then sort them, along with
00520 *     eigenvectors.
00521 *
00522       IF( WANTZ ) THEN
00523          DO 60 J = 1, M - 1
00524             I = 0
00525             TMP1 = W( J )
00526             DO 50 JJ = J + 1, M
00527                IF( W( JJ ).LT.TMP1 ) THEN
00528                   I = JJ
00529                   TMP1 = W( JJ )
00530                END IF
00531    50       CONTINUE
00532 *
00533             IF( I.NE.0 ) THEN
00534                ITMP1 = IWORK( INDIBL+I-1 )
00535                W( I ) = W( J )
00536                IWORK( INDIBL+I-1 ) = IWORK( INDIBL+J-1 )
00537                W( J ) = TMP1
00538                IWORK( INDIBL+J-1 ) = ITMP1
00539                CALL ZSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 )
00540                IF( INFO.NE.0 ) THEN
00541                   ITMP1 = IFAIL( I )
00542                   IFAIL( I ) = IFAIL( J )
00543                   IFAIL( J ) = ITMP1
00544                END IF
00545             END IF
00546    60    CONTINUE
00547       END IF
00548 *
00549 *     Set WORK(1) to optimal complex workspace size.
00550 *
00551       WORK( 1 ) = LWKOPT
00552 *
00553       RETURN
00554 *
00555 *     End of ZHEEVX
00556 *
00557       END
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