LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
zhbevx.f
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00001 *> \brief <b> ZHBEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER 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 ZHBEVX + dependencies 
00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhbevx.f"> 
00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhbevx.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhbevx.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE ZHBEVX( JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ, VL,
00022 *                          VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK,
00023 *                          IWORK, IFAIL, INFO )
00024 * 
00025 *       .. Scalar Arguments ..
00026 *       CHARACTER          JOBZ, RANGE, UPLO
00027 *       INTEGER            IL, INFO, IU, KD, LDAB, LDQ, LDZ, M, N
00028 *       DOUBLE PRECISION   ABSTOL, VL, VU
00029 *       ..
00030 *       .. Array Arguments ..
00031 *       INTEGER            IFAIL( * ), IWORK( * )
00032 *       DOUBLE PRECISION   RWORK( * ), W( * )
00033 *       COMPLEX*16         AB( LDAB, * ), Q( LDQ, * ), WORK( * ),
00034 *      $                   Z( LDZ, * )
00035 *       ..
00036 *  
00037 *
00038 *> \par Purpose:
00039 *  =============
00040 *>
00041 *> \verbatim
00042 *>
00043 *> ZHBEVX computes selected eigenvalues and, optionally, eigenvectors
00044 *> of a complex Hermitian band matrix A.  Eigenvalues and eigenvectors
00045 *> can be selected by specifying either a range of values or a range of
00046 *> indices for the desired eigenvalues.
00047 *> \endverbatim
00048 *
00049 *  Arguments:
00050 *  ==========
00051 *
00052 *> \param[in] JOBZ
00053 *> \verbatim
00054 *>          JOBZ is CHARACTER*1
00055 *>          = 'N':  Compute eigenvalues only;
00056 *>          = 'V':  Compute eigenvalues and eigenvectors.
00057 *> \endverbatim
00058 *>
00059 *> \param[in] RANGE
00060 *> \verbatim
00061 *>          RANGE is CHARACTER*1
00062 *>          = 'A': all eigenvalues will be found;
00063 *>          = 'V': all eigenvalues in the half-open interval (VL,VU]
00064 *>                 will be found;
00065 *>          = 'I': the IL-th through IU-th eigenvalues will be found.
00066 *> \endverbatim
00067 *>
00068 *> \param[in] UPLO
00069 *> \verbatim
00070 *>          UPLO is CHARACTER*1
00071 *>          = 'U':  Upper triangle of A is stored;
00072 *>          = 'L':  Lower triangle of A is stored.
00073 *> \endverbatim
00074 *>
00075 *> \param[in] N
00076 *> \verbatim
00077 *>          N is INTEGER
00078 *>          The order of the matrix A.  N >= 0.
00079 *> \endverbatim
00080 *>
00081 *> \param[in] KD
00082 *> \verbatim
00083 *>          KD is INTEGER
00084 *>          The number of superdiagonals of the matrix A if UPLO = 'U',
00085 *>          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
00086 *> \endverbatim
00087 *>
00088 *> \param[in,out] AB
00089 *> \verbatim
00090 *>          AB is COMPLEX*16 array, dimension (LDAB, N)
00091 *>          On entry, the upper or lower triangle of the Hermitian band
00092 *>          matrix A, stored in the first KD+1 rows of the array.  The
00093 *>          j-th column of A is stored in the j-th column of the array AB
00094 *>          as follows:
00095 *>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
00096 *>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
00097 *>
00098 *>          On exit, AB is overwritten by values generated during the
00099 *>          reduction to tridiagonal form.
00100 *> \endverbatim
00101 *>
00102 *> \param[in] LDAB
00103 *> \verbatim
00104 *>          LDAB is INTEGER
00105 *>          The leading dimension of the array AB.  LDAB >= KD + 1.
00106 *> \endverbatim
00107 *>
00108 *> \param[out] Q
00109 *> \verbatim
00110 *>          Q is COMPLEX*16 array, dimension (LDQ, N)
00111 *>          If JOBZ = 'V', the N-by-N unitary matrix used in the
00112 *>                          reduction to tridiagonal form.
00113 *>          If JOBZ = 'N', the array Q is not referenced.
00114 *> \endverbatim
00115 *>
00116 *> \param[in] LDQ
00117 *> \verbatim
00118 *>          LDQ is INTEGER
00119 *>          The leading dimension of the array Q.  If JOBZ = 'V', then
00120 *>          LDQ >= max(1,N).
00121 *> \endverbatim
00122 *>
00123 *> \param[in] VL
00124 *> \verbatim
00125 *>          VL is DOUBLE PRECISION
00126 *> \endverbatim
00127 *>
00128 *> \param[in] VU
00129 *> \verbatim
00130 *>          VU is DOUBLE PRECISION
00131 *>          If RANGE='V', the lower and upper bounds of the interval to
00132 *>          be searched for eigenvalues. VL < VU.
00133 *>          Not referenced if RANGE = 'A' or 'I'.
00134 *> \endverbatim
00135 *>
00136 *> \param[in] IL
00137 *> \verbatim
00138 *>          IL is INTEGER
00139 *> \endverbatim
00140 *>
00141 *> \param[in] IU
00142 *> \verbatim
00143 *>          IU is INTEGER
00144 *>          If RANGE='I', the indices (in ascending order) of the
00145 *>          smallest and largest eigenvalues to be returned.
00146 *>          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
00147 *>          Not referenced if RANGE = 'A' or 'V'.
00148 *> \endverbatim
00149 *>
00150 *> \param[in] ABSTOL
00151 *> \verbatim
00152 *>          ABSTOL is DOUBLE PRECISION
00153 *>          The absolute error tolerance for the eigenvalues.
00154 *>          An approximate eigenvalue is accepted as converged
00155 *>          when it is determined to lie in an interval [a,b]
00156 *>          of width less than or equal to
00157 *>
00158 *>                  ABSTOL + EPS *   max( |a|,|b| ) ,
00159 *>
00160 *>          where EPS is the machine precision.  If ABSTOL is less than
00161 *>          or equal to zero, then  EPS*|T|  will be used in its place,
00162 *>          where |T| is the 1-norm of the tridiagonal matrix obtained
00163 *>          by reducing AB to tridiagonal form.
00164 *>
00165 *>          Eigenvalues will be computed most accurately when ABSTOL is
00166 *>          set to twice the underflow threshold 2*DLAMCH('S'), not zero.
00167 *>          If this routine returns with INFO>0, indicating that some
00168 *>          eigenvectors did not converge, try setting ABSTOL to
00169 *>          2*DLAMCH('S').
00170 *>
00171 *>          See "Computing Small Singular Values of Bidiagonal Matrices
00172 *>          with Guaranteed High Relative Accuracy," by Demmel and
00173 *>          Kahan, LAPACK Working Note #3.
00174 *> \endverbatim
00175 *>
00176 *> \param[out] M
00177 *> \verbatim
00178 *>          M is INTEGER
00179 *>          The total number of eigenvalues found.  0 <= M <= N.
00180 *>          If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
00181 *> \endverbatim
00182 *>
00183 *> \param[out] W
00184 *> \verbatim
00185 *>          W is DOUBLE PRECISION array, dimension (N)
00186 *>          The first M elements contain the selected eigenvalues in
00187 *>          ascending order.
00188 *> \endverbatim
00189 *>
00190 *> \param[out] Z
00191 *> \verbatim
00192 *>          Z is COMPLEX*16 array, dimension (LDZ, max(1,M))
00193 *>          If JOBZ = 'V', then if INFO = 0, the first M columns of Z
00194 *>          contain the orthonormal eigenvectors of the matrix A
00195 *>          corresponding to the selected eigenvalues, with the i-th
00196 *>          column of Z holding the eigenvector associated with W(i).
00197 *>          If an eigenvector fails to converge, then that column of Z
00198 *>          contains the latest approximation to the eigenvector, and the
00199 *>          index of the eigenvector is returned in IFAIL.
00200 *>          If JOBZ = 'N', then Z is not referenced.
00201 *>          Note: the user must ensure that at least max(1,M) columns are
00202 *>          supplied in the array Z; if RANGE = 'V', the exact value of M
00203 *>          is not known in advance and an upper bound must be used.
00204 *> \endverbatim
00205 *>
00206 *> \param[in] LDZ
00207 *> \verbatim
00208 *>          LDZ is INTEGER
00209 *>          The leading dimension of the array Z.  LDZ >= 1, and if
00210 *>          JOBZ = 'V', LDZ >= max(1,N).
00211 *> \endverbatim
00212 *>
00213 *> \param[out] WORK
00214 *> \verbatim
00215 *>          WORK is COMPLEX*16 array, dimension (N)
00216 *> \endverbatim
00217 *>
00218 *> \param[out] RWORK
00219 *> \verbatim
00220 *>          RWORK is DOUBLE PRECISION array, dimension (7*N)
00221 *> \endverbatim
00222 *>
00223 *> \param[out] IWORK
00224 *> \verbatim
00225 *>          IWORK is INTEGER array, dimension (5*N)
00226 *> \endverbatim
00227 *>
00228 *> \param[out] IFAIL
00229 *> \verbatim
00230 *>          IFAIL is INTEGER array, dimension (N)
00231 *>          If JOBZ = 'V', then if INFO = 0, the first M elements of
00232 *>          IFAIL are zero.  If INFO > 0, then IFAIL contains the
00233 *>          indices of the eigenvectors that failed to converge.
00234 *>          If JOBZ = 'N', then IFAIL is not referenced.
00235 *> \endverbatim
00236 *>
00237 *> \param[out] INFO
00238 *> \verbatim
00239 *>          INFO is INTEGER
00240 *>          = 0:  successful exit
00241 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00242 *>          > 0:  if INFO = i, then i eigenvectors failed to converge.
00243 *>                Their indices are stored in array IFAIL.
00244 *> \endverbatim
00245 *
00246 *  Authors:
00247 *  ========
00248 *
00249 *> \author Univ. of Tennessee 
00250 *> \author Univ. of California Berkeley 
00251 *> \author Univ. of Colorado Denver 
00252 *> \author NAG Ltd. 
00253 *
00254 *> \date November 2011
00255 *
00256 *> \ingroup complex16OTHEReigen
00257 *
00258 *  =====================================================================
00259       SUBROUTINE ZHBEVX( JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ, VL,
00260      $                   VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK,
00261      $                   IWORK, IFAIL, INFO )
00262 *
00263 *  -- LAPACK driver routine (version 3.4.0) --
00264 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00265 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00266 *     November 2011
00267 *
00268 *     .. Scalar Arguments ..
00269       CHARACTER          JOBZ, RANGE, UPLO
00270       INTEGER            IL, INFO, IU, KD, LDAB, LDQ, LDZ, M, N
00271       DOUBLE PRECISION   ABSTOL, VL, VU
00272 *     ..
00273 *     .. Array Arguments ..
00274       INTEGER            IFAIL( * ), IWORK( * )
00275       DOUBLE PRECISION   RWORK( * ), W( * )
00276       COMPLEX*16         AB( LDAB, * ), Q( LDQ, * ), WORK( * ),
00277      $                   Z( LDZ, * )
00278 *     ..
00279 *
00280 *  =====================================================================
00281 *
00282 *     .. Parameters ..
00283       DOUBLE PRECISION   ZERO, ONE
00284       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
00285       COMPLEX*16         CZERO, CONE
00286       PARAMETER          ( CZERO = ( 0.0D0, 0.0D0 ),
00287      $                   CONE = ( 1.0D0, 0.0D0 ) )
00288 *     ..
00289 *     .. Local Scalars ..
00290       LOGICAL            ALLEIG, INDEIG, LOWER, TEST, VALEIG, WANTZ
00291       CHARACTER          ORDER
00292       INTEGER            I, IINFO, IMAX, INDD, INDE, INDEE, INDIBL,
00293      $                   INDISP, INDIWK, INDRWK, INDWRK, ISCALE, ITMP1,
00294      $                   J, JJ, NSPLIT
00295       DOUBLE PRECISION   ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
00296      $                   SIGMA, SMLNUM, TMP1, VLL, VUU
00297       COMPLEX*16         CTMP1
00298 *     ..
00299 *     .. External Functions ..
00300       LOGICAL            LSAME
00301       DOUBLE PRECISION   DLAMCH, ZLANHB
00302       EXTERNAL           LSAME, DLAMCH, ZLANHB
00303 *     ..
00304 *     .. External Subroutines ..
00305       EXTERNAL           DCOPY, DSCAL, DSTEBZ, DSTERF, XERBLA, ZCOPY,
00306      $                   ZGEMV, ZHBTRD, ZLACPY, ZLASCL, ZSTEIN, ZSTEQR,
00307      $                   ZSWAP
00308 *     ..
00309 *     .. Intrinsic Functions ..
00310       INTRINSIC          DBLE, MAX, MIN, SQRT
00311 *     ..
00312 *     .. Executable Statements ..
00313 *
00314 *     Test the input parameters.
00315 *
00316       WANTZ = LSAME( JOBZ, 'V' )
00317       ALLEIG = LSAME( RANGE, 'A' )
00318       VALEIG = LSAME( RANGE, 'V' )
00319       INDEIG = LSAME( RANGE, 'I' )
00320       LOWER = LSAME( UPLO, 'L' )
00321 *
00322       INFO = 0
00323       IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
00324          INFO = -1
00325       ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
00326          INFO = -2
00327       ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
00328          INFO = -3
00329       ELSE IF( N.LT.0 ) THEN
00330          INFO = -4
00331       ELSE IF( KD.LT.0 ) THEN
00332          INFO = -5
00333       ELSE IF( LDAB.LT.KD+1 ) THEN
00334          INFO = -7
00335       ELSE IF( WANTZ .AND. LDQ.LT.MAX( 1, N ) ) THEN
00336          INFO = -9
00337       ELSE
00338          IF( VALEIG ) THEN
00339             IF( N.GT.0 .AND. VU.LE.VL )
00340      $         INFO = -11
00341          ELSE IF( INDEIG ) THEN
00342             IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
00343                INFO = -12
00344             ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
00345                INFO = -13
00346             END IF
00347          END IF
00348       END IF
00349       IF( INFO.EQ.0 ) THEN
00350          IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) )
00351      $      INFO = -18
00352       END IF
00353 *
00354       IF( INFO.NE.0 ) THEN
00355          CALL XERBLA( 'ZHBEVX', -INFO )
00356          RETURN
00357       END IF
00358 *
00359 *     Quick return if possible
00360 *
00361       M = 0
00362       IF( N.EQ.0 )
00363      $   RETURN
00364 *
00365       IF( N.EQ.1 ) THEN
00366          M = 1
00367          IF( LOWER ) THEN
00368             CTMP1 = AB( 1, 1 )
00369          ELSE
00370             CTMP1 = AB( KD+1, 1 )
00371          END IF
00372          TMP1 = DBLE( CTMP1 )
00373          IF( VALEIG ) THEN
00374             IF( .NOT.( VL.LT.TMP1 .AND. VU.GE.TMP1 ) )
00375      $         M = 0
00376          END IF
00377          IF( M.EQ.1 ) THEN
00378             W( 1 ) = CTMP1
00379             IF( WANTZ )
00380      $         Z( 1, 1 ) = CONE
00381          END IF
00382          RETURN
00383       END IF
00384 *
00385 *     Get machine constants.
00386 *
00387       SAFMIN = DLAMCH( 'Safe minimum' )
00388       EPS = DLAMCH( 'Precision' )
00389       SMLNUM = SAFMIN / EPS
00390       BIGNUM = ONE / SMLNUM
00391       RMIN = SQRT( SMLNUM )
00392       RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) )
00393 *
00394 *     Scale matrix to allowable range, if necessary.
00395 *
00396       ISCALE = 0
00397       ABSTLL = ABSTOL
00398       IF( VALEIG ) THEN
00399          VLL = VL
00400          VUU = VU
00401       ELSE
00402          VLL = ZERO
00403          VUU = ZERO
00404       END IF
00405       ANRM = ZLANHB( 'M', UPLO, N, KD, AB, LDAB, RWORK )
00406       IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
00407          ISCALE = 1
00408          SIGMA = RMIN / ANRM
00409       ELSE IF( ANRM.GT.RMAX ) THEN
00410          ISCALE = 1
00411          SIGMA = RMAX / ANRM
00412       END IF
00413       IF( ISCALE.EQ.1 ) THEN
00414          IF( LOWER ) THEN
00415             CALL ZLASCL( 'B', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
00416          ELSE
00417             CALL ZLASCL( 'Q', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
00418          END IF
00419          IF( ABSTOL.GT.0 )
00420      $      ABSTLL = ABSTOL*SIGMA
00421          IF( VALEIG ) THEN
00422             VLL = VL*SIGMA
00423             VUU = VU*SIGMA
00424          END IF
00425       END IF
00426 *
00427 *     Call ZHBTRD to reduce Hermitian band matrix to tridiagonal form.
00428 *
00429       INDD = 1
00430       INDE = INDD + N
00431       INDRWK = INDE + N
00432       INDWRK = 1
00433       CALL ZHBTRD( JOBZ, UPLO, N, KD, AB, LDAB, RWORK( INDD ),
00434      $             RWORK( INDE ), Q, LDQ, WORK( INDWRK ), IINFO )
00435 *
00436 *     If all eigenvalues are desired and ABSTOL is less than or equal
00437 *     to zero, then call DSTERF or ZSTEQR.  If this fails for some
00438 *     eigenvalue, then try DSTEBZ.
00439 *
00440       TEST = .FALSE.
00441       IF (INDEIG) THEN
00442          IF (IL.EQ.1 .AND. IU.EQ.N) THEN
00443             TEST = .TRUE.
00444          END IF
00445       END IF
00446       IF ((ALLEIG .OR. TEST) .AND. (ABSTOL.LE.ZERO)) THEN
00447          CALL DCOPY( N, RWORK( INDD ), 1, W, 1 )
00448          INDEE = INDRWK + 2*N
00449          IF( .NOT.WANTZ ) THEN
00450             CALL DCOPY( N-1, RWORK( INDE ), 1, RWORK( INDEE ), 1 )
00451             CALL DSTERF( N, W, RWORK( INDEE ), INFO )
00452          ELSE
00453             CALL ZLACPY( 'A', N, N, Q, LDQ, Z, LDZ )
00454             CALL DCOPY( N-1, RWORK( INDE ), 1, RWORK( INDEE ), 1 )
00455             CALL ZSTEQR( JOBZ, N, W, RWORK( INDEE ), Z, LDZ,
00456      $                   RWORK( INDRWK ), INFO )
00457             IF( INFO.EQ.0 ) THEN
00458                DO 10 I = 1, N
00459                   IFAIL( I ) = 0
00460    10          CONTINUE
00461             END IF
00462          END IF
00463          IF( INFO.EQ.0 ) THEN
00464             M = N
00465             GO TO 30
00466          END IF
00467          INFO = 0
00468       END IF
00469 *
00470 *     Otherwise, call DSTEBZ and, if eigenvectors are desired, ZSTEIN.
00471 *
00472       IF( WANTZ ) THEN
00473          ORDER = 'B'
00474       ELSE
00475          ORDER = 'E'
00476       END IF
00477       INDIBL = 1
00478       INDISP = INDIBL + N
00479       INDIWK = INDISP + N
00480       CALL DSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL,
00481      $             RWORK( INDD ), RWORK( INDE ), M, NSPLIT, W,
00482      $             IWORK( INDIBL ), IWORK( INDISP ), RWORK( INDRWK ),
00483      $             IWORK( INDIWK ), INFO )
00484 *
00485       IF( WANTZ ) THEN
00486          CALL ZSTEIN( N, RWORK( INDD ), RWORK( INDE ), M, W,
00487      $                IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ,
00488      $                RWORK( INDRWK ), IWORK( INDIWK ), IFAIL, INFO )
00489 *
00490 *        Apply unitary matrix used in reduction to tridiagonal
00491 *        form to eigenvectors returned by ZSTEIN.
00492 *
00493          DO 20 J = 1, M
00494             CALL ZCOPY( N, Z( 1, J ), 1, WORK( 1 ), 1 )
00495             CALL ZGEMV( 'N', N, N, CONE, Q, LDQ, WORK, 1, CZERO,
00496      $                  Z( 1, J ), 1 )
00497    20    CONTINUE
00498       END IF
00499 *
00500 *     If matrix was scaled, then rescale eigenvalues appropriately.
00501 *
00502    30 CONTINUE
00503       IF( ISCALE.EQ.1 ) THEN
00504          IF( INFO.EQ.0 ) THEN
00505             IMAX = M
00506          ELSE
00507             IMAX = INFO - 1
00508          END IF
00509          CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
00510       END IF
00511 *
00512 *     If eigenvalues are not in order, then sort them, along with
00513 *     eigenvectors.
00514 *
00515       IF( WANTZ ) THEN
00516          DO 50 J = 1, M - 1
00517             I = 0
00518             TMP1 = W( J )
00519             DO 40 JJ = J + 1, M
00520                IF( W( JJ ).LT.TMP1 ) THEN
00521                   I = JJ
00522                   TMP1 = W( JJ )
00523                END IF
00524    40       CONTINUE
00525 *
00526             IF( I.NE.0 ) THEN
00527                ITMP1 = IWORK( INDIBL+I-1 )
00528                W( I ) = W( J )
00529                IWORK( INDIBL+I-1 ) = IWORK( INDIBL+J-1 )
00530                W( J ) = TMP1
00531                IWORK( INDIBL+J-1 ) = ITMP1
00532                CALL ZSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 )
00533                IF( INFO.NE.0 ) THEN
00534                   ITMP1 = IFAIL( I )
00535                   IFAIL( I ) = IFAIL( J )
00536                   IFAIL( J ) = ITMP1
00537                END IF
00538             END IF
00539    50    CONTINUE
00540       END IF
00541 *
00542       RETURN
00543 *
00544 *     End of ZHBEVX
00545 *
00546       END
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