Annotation of rpl/lapack/lapack/zgeev.f, revision 1.13

1.8       bertrand    1: *> \brief <b> ZGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices</b>
                      2: *
                      3: *  =========== DOCUMENTATION ===========
                      4: *
                      5: * Online html documentation available at 
                      6: *            http://www.netlib.org/lapack/explore-html/ 
                      7: *
                      8: *> \htmlonly
                      9: *> Download ZGEEV + dependencies 
                     10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgeev.f"> 
                     11: *> [TGZ]</a> 
                     12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgeev.f"> 
                     13: *> [ZIP]</a> 
                     14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgeev.f"> 
                     15: *> [TXT]</a>
                     16: *> \endhtmlonly 
                     17: *
                     18: *  Definition:
                     19: *  ===========
                     20: *
                     21: *       SUBROUTINE ZGEEV( JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR,
                     22: *                         WORK, LWORK, RWORK, INFO )
                     23: * 
                     24: *       .. Scalar Arguments ..
                     25: *       CHARACTER          JOBVL, JOBVR
                     26: *       INTEGER            INFO, LDA, LDVL, LDVR, LWORK, N
                     27: *       ..
                     28: *       .. Array Arguments ..
                     29: *       DOUBLE PRECISION   RWORK( * )
                     30: *       COMPLEX*16         A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ),
                     31: *      $                   W( * ), WORK( * )
                     32: *       ..
                     33: *  
                     34: *
                     35: *> \par Purpose:
                     36: *  =============
                     37: *>
                     38: *> \verbatim
                     39: *>
                     40: *> ZGEEV computes for an N-by-N complex nonsymmetric matrix A, the
                     41: *> eigenvalues and, optionally, the left and/or right eigenvectors.
                     42: *>
                     43: *> The right eigenvector v(j) of A satisfies
                     44: *>                  A * v(j) = lambda(j) * v(j)
                     45: *> where lambda(j) is its eigenvalue.
                     46: *> The left eigenvector u(j) of A satisfies
                     47: *>               u(j)**H * A = lambda(j) * u(j)**H
                     48: *> where u(j)**H denotes the conjugate transpose of u(j).
                     49: *>
                     50: *> The computed eigenvectors are normalized to have Euclidean norm
                     51: *> equal to 1 and largest component real.
                     52: *> \endverbatim
                     53: *
                     54: *  Arguments:
                     55: *  ==========
                     56: *
                     57: *> \param[in] JOBVL
                     58: *> \verbatim
                     59: *>          JOBVL is CHARACTER*1
                     60: *>          = 'N': left eigenvectors of A are not computed;
                     61: *>          = 'V': left eigenvectors of are computed.
                     62: *> \endverbatim
                     63: *>
                     64: *> \param[in] JOBVR
                     65: *> \verbatim
                     66: *>          JOBVR is CHARACTER*1
                     67: *>          = 'N': right eigenvectors of A are not computed;
                     68: *>          = 'V': right eigenvectors of A are computed.
                     69: *> \endverbatim
                     70: *>
                     71: *> \param[in] N
                     72: *> \verbatim
                     73: *>          N is INTEGER
                     74: *>          The order of the matrix A. N >= 0.
                     75: *> \endverbatim
                     76: *>
                     77: *> \param[in,out] A
                     78: *> \verbatim
                     79: *>          A is COMPLEX*16 array, dimension (LDA,N)
                     80: *>          On entry, the N-by-N matrix A.
                     81: *>          On exit, A has been overwritten.
                     82: *> \endverbatim
                     83: *>
                     84: *> \param[in] LDA
                     85: *> \verbatim
                     86: *>          LDA is INTEGER
                     87: *>          The leading dimension of the array A.  LDA >= max(1,N).
                     88: *> \endverbatim
                     89: *>
                     90: *> \param[out] W
                     91: *> \verbatim
                     92: *>          W is COMPLEX*16 array, dimension (N)
                     93: *>          W contains the computed eigenvalues.
                     94: *> \endverbatim
                     95: *>
                     96: *> \param[out] VL
                     97: *> \verbatim
                     98: *>          VL is COMPLEX*16 array, dimension (LDVL,N)
                     99: *>          If JOBVL = 'V', the left eigenvectors u(j) are stored one
                    100: *>          after another in the columns of VL, in the same order
                    101: *>          as their eigenvalues.
                    102: *>          If JOBVL = 'N', VL is not referenced.
                    103: *>          u(j) = VL(:,j), the j-th column of VL.
                    104: *> \endverbatim
                    105: *>
                    106: *> \param[in] LDVL
                    107: *> \verbatim
                    108: *>          LDVL is INTEGER
                    109: *>          The leading dimension of the array VL.  LDVL >= 1; if
                    110: *>          JOBVL = 'V', LDVL >= N.
                    111: *> \endverbatim
                    112: *>
                    113: *> \param[out] VR
                    114: *> \verbatim
                    115: *>          VR is COMPLEX*16 array, dimension (LDVR,N)
                    116: *>          If JOBVR = 'V', the right eigenvectors v(j) are stored one
                    117: *>          after another in the columns of VR, in the same order
                    118: *>          as their eigenvalues.
                    119: *>          If JOBVR = 'N', VR is not referenced.
                    120: *>          v(j) = VR(:,j), the j-th column of VR.
                    121: *> \endverbatim
                    122: *>
                    123: *> \param[in] LDVR
                    124: *> \verbatim
                    125: *>          LDVR is INTEGER
                    126: *>          The leading dimension of the array VR.  LDVR >= 1; if
                    127: *>          JOBVR = 'V', LDVR >= N.
                    128: *> \endverbatim
                    129: *>
                    130: *> \param[out] WORK
                    131: *> \verbatim
                    132: *>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
                    133: *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
                    134: *> \endverbatim
                    135: *>
                    136: *> \param[in] LWORK
                    137: *> \verbatim
                    138: *>          LWORK is INTEGER
                    139: *>          The dimension of the array WORK.  LWORK >= max(1,2*N).
                    140: *>          For good performance, LWORK must generally be larger.
                    141: *>
                    142: *>          If LWORK = -1, then a workspace query is assumed; the routine
                    143: *>          only calculates the optimal size of the WORK array, returns
                    144: *>          this value as the first entry of the WORK array, and no error
                    145: *>          message related to LWORK is issued by XERBLA.
                    146: *> \endverbatim
                    147: *>
                    148: *> \param[out] RWORK
                    149: *> \verbatim
                    150: *>          RWORK is DOUBLE PRECISION array, dimension (2*N)
                    151: *> \endverbatim
                    152: *>
                    153: *> \param[out] INFO
                    154: *> \verbatim
                    155: *>          INFO is INTEGER
                    156: *>          = 0:  successful exit
                    157: *>          < 0:  if INFO = -i, the i-th argument had an illegal value.
                    158: *>          > 0:  if INFO = i, the QR algorithm failed to compute all the
                    159: *>                eigenvalues, and no eigenvectors have been computed;
                    160: *>                elements and i+1:N of W contain eigenvalues which have
                    161: *>                converged.
                    162: *> \endverbatim
                    163: *
                    164: *  Authors:
                    165: *  ========
                    166: *
                    167: *> \author Univ. of Tennessee 
                    168: *> \author Univ. of California Berkeley 
                    169: *> \author Univ. of Colorado Denver 
                    170: *> \author NAG Ltd. 
                    171: *
1.13    ! bertrand  172: *> \date June 2016
        !           173: *
        !           174: *  @precisions fortran z -> c
1.8       bertrand  175: *
                    176: *> \ingroup complex16GEeigen
                    177: *
                    178: *  =====================================================================
1.1       bertrand  179:       SUBROUTINE ZGEEV( JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR,
                    180:      $                  WORK, LWORK, RWORK, INFO )
1.13    ! bertrand  181:       implicit none
1.1       bertrand  182: *
1.13    ! bertrand  183: *  -- LAPACK driver routine (version 3.6.1) --
1.1       bertrand  184: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                    185: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.13    ! bertrand  186: *     June 2016
1.1       bertrand  187: *
                    188: *     .. Scalar Arguments ..
                    189:       CHARACTER          JOBVL, JOBVR
                    190:       INTEGER            INFO, LDA, LDVL, LDVR, LWORK, N
                    191: *     ..
                    192: *     .. Array Arguments ..
                    193:       DOUBLE PRECISION   RWORK( * )
                    194:       COMPLEX*16         A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ),
                    195:      $                   W( * ), WORK( * )
                    196: *     ..
                    197: *
                    198: *  =====================================================================
                    199: *
                    200: *     .. Parameters ..
                    201:       DOUBLE PRECISION   ZERO, ONE
                    202:       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
                    203: *     ..
                    204: *     .. Local Scalars ..
                    205:       LOGICAL            LQUERY, SCALEA, WANTVL, WANTVR
                    206:       CHARACTER          SIDE
                    207:       INTEGER            HSWORK, I, IBAL, IERR, IHI, ILO, IRWORK, ITAU,
1.13    ! bertrand  208:      $                   IWRK, K, LWORK_TREVC, MAXWRK, MINWRK, NOUT
1.1       bertrand  209:       DOUBLE PRECISION   ANRM, BIGNUM, CSCALE, EPS, SCL, SMLNUM
                    210:       COMPLEX*16         TMP
                    211: *     ..
                    212: *     .. Local Arrays ..
                    213:       LOGICAL            SELECT( 1 )
                    214:       DOUBLE PRECISION   DUM( 1 )
                    215: *     ..
                    216: *     .. External Subroutines ..
                    217:       EXTERNAL           DLABAD, XERBLA, ZDSCAL, ZGEBAK, ZGEBAL, ZGEHRD,
1.13    ! bertrand  218:      $                   ZHSEQR, ZLACPY, ZLASCL, ZSCAL, ZTREVC3, ZUNGHR
1.1       bertrand  219: *     ..
                    220: *     .. External Functions ..
                    221:       LOGICAL            LSAME
                    222:       INTEGER            IDAMAX, ILAENV
                    223:       DOUBLE PRECISION   DLAMCH, DZNRM2, ZLANGE
                    224:       EXTERNAL           LSAME, IDAMAX, ILAENV, DLAMCH, DZNRM2, ZLANGE
                    225: *     ..
                    226: *     .. Intrinsic Functions ..
1.13    ! bertrand  227:       INTRINSIC          DBLE, DCMPLX, CONJG, AIMAG, MAX, SQRT
1.1       bertrand  228: *     ..
                    229: *     .. Executable Statements ..
                    230: *
                    231: *     Test the input arguments
                    232: *
                    233:       INFO = 0
                    234:       LQUERY = ( LWORK.EQ.-1 )
                    235:       WANTVL = LSAME( JOBVL, 'V' )
                    236:       WANTVR = LSAME( JOBVR, 'V' )
                    237:       IF( ( .NOT.WANTVL ) .AND. ( .NOT.LSAME( JOBVL, 'N' ) ) ) THEN
                    238:          INFO = -1
                    239:       ELSE IF( ( .NOT.WANTVR ) .AND. ( .NOT.LSAME( JOBVR, 'N' ) ) ) THEN
                    240:          INFO = -2
                    241:       ELSE IF( N.LT.0 ) THEN
                    242:          INFO = -3
                    243:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
                    244:          INFO = -5
                    245:       ELSE IF( LDVL.LT.1 .OR. ( WANTVL .AND. LDVL.LT.N ) ) THEN
                    246:          INFO = -8
                    247:       ELSE IF( LDVR.LT.1 .OR. ( WANTVR .AND. LDVR.LT.N ) ) THEN
                    248:          INFO = -10
                    249:       END IF
                    250: *
                    251: *     Compute workspace
                    252: *      (Note: Comments in the code beginning "Workspace:" describe the
                    253: *       minimal amount of workspace needed at that point in the code,
                    254: *       as well as the preferred amount for good performance.
                    255: *       CWorkspace refers to complex workspace, and RWorkspace to real
                    256: *       workspace. NB refers to the optimal block size for the
                    257: *       immediately following subroutine, as returned by ILAENV.
                    258: *       HSWORK refers to the workspace preferred by ZHSEQR, as
                    259: *       calculated below. HSWORK is computed assuming ILO=1 and IHI=N,
                    260: *       the worst case.)
                    261: *
                    262:       IF( INFO.EQ.0 ) THEN
                    263:          IF( N.EQ.0 ) THEN
                    264:             MINWRK = 1
                    265:             MAXWRK = 1
                    266:          ELSE
                    267:             MAXWRK = N + N*ILAENV( 1, 'ZGEHRD', ' ', N, 1, N, 0 )
                    268:             MINWRK = 2*N
                    269:             IF( WANTVL ) THEN
                    270:                MAXWRK = MAX( MAXWRK, N + ( N - 1 )*ILAENV( 1, 'ZUNGHR',
                    271:      $                       ' ', N, 1, N, -1 ) )
1.13    ! bertrand  272:                CALL ZTREVC3( 'L', 'B', SELECT, N, A, LDA,
        !           273:      $                       VL, LDVL, VR, LDVR,
        !           274:      $                       N, NOUT, WORK, -1, RWORK, -1, IERR )
        !           275:                LWORK_TREVC = INT( WORK(1) )
        !           276:                MAXWRK = MAX( MAXWRK, N + LWORK_TREVC )
1.1       bertrand  277:                CALL ZHSEQR( 'S', 'V', N, 1, N, A, LDA, W, VL, LDVL,
1.13    ! bertrand  278:      $                      WORK, -1, INFO )
1.1       bertrand  279:             ELSE IF( WANTVR ) THEN
                    280:                MAXWRK = MAX( MAXWRK, N + ( N - 1 )*ILAENV( 1, 'ZUNGHR',
                    281:      $                       ' ', N, 1, N, -1 ) )
1.13    ! bertrand  282:                CALL ZTREVC3( 'R', 'B', SELECT, N, A, LDA,
        !           283:      $                       VL, LDVL, VR, LDVR,
        !           284:      $                       N, NOUT, WORK, -1, RWORK, -1, IERR )
        !           285:                LWORK_TREVC = INT( WORK(1) )
        !           286:                MAXWRK = MAX( MAXWRK, N + LWORK_TREVC )
1.1       bertrand  287:                CALL ZHSEQR( 'S', 'V', N, 1, N, A, LDA, W, VR, LDVR,
1.13    ! bertrand  288:      $                      WORK, -1, INFO )
1.1       bertrand  289:             ELSE
                    290:                CALL ZHSEQR( 'E', 'N', N, 1, N, A, LDA, W, VR, LDVR,
1.13    ! bertrand  291:      $                      WORK, -1, INFO )
1.1       bertrand  292:             END IF
1.13    ! bertrand  293:             HSWORK = INT( WORK(1) )
1.1       bertrand  294:             MAXWRK = MAX( MAXWRK, HSWORK, MINWRK )
                    295:          END IF
                    296:          WORK( 1 ) = MAXWRK
                    297: *
                    298:          IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
                    299:             INFO = -12
                    300:          END IF
                    301:       END IF
                    302: *
                    303:       IF( INFO.NE.0 ) THEN
                    304:          CALL XERBLA( 'ZGEEV ', -INFO )
                    305:          RETURN
                    306:       ELSE IF( LQUERY ) THEN
                    307:          RETURN
                    308:       END IF
                    309: *
                    310: *     Quick return if possible
                    311: *
                    312:       IF( N.EQ.0 )
                    313:      $   RETURN
                    314: *
                    315: *     Get machine constants
                    316: *
                    317:       EPS = DLAMCH( 'P' )
                    318:       SMLNUM = DLAMCH( 'S' )
                    319:       BIGNUM = ONE / SMLNUM
                    320:       CALL DLABAD( SMLNUM, BIGNUM )
                    321:       SMLNUM = SQRT( SMLNUM ) / EPS
                    322:       BIGNUM = ONE / SMLNUM
                    323: *
                    324: *     Scale A if max element outside range [SMLNUM,BIGNUM]
                    325: *
                    326:       ANRM = ZLANGE( 'M', N, N, A, LDA, DUM )
                    327:       SCALEA = .FALSE.
                    328:       IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
                    329:          SCALEA = .TRUE.
                    330:          CSCALE = SMLNUM
                    331:       ELSE IF( ANRM.GT.BIGNUM ) THEN
                    332:          SCALEA = .TRUE.
                    333:          CSCALE = BIGNUM
                    334:       END IF
                    335:       IF( SCALEA )
                    336:      $   CALL ZLASCL( 'G', 0, 0, ANRM, CSCALE, N, N, A, LDA, IERR )
                    337: *
                    338: *     Balance the matrix
                    339: *     (CWorkspace: none)
                    340: *     (RWorkspace: need N)
                    341: *
                    342:       IBAL = 1
                    343:       CALL ZGEBAL( 'B', N, A, LDA, ILO, IHI, RWORK( IBAL ), IERR )
                    344: *
                    345: *     Reduce to upper Hessenberg form
                    346: *     (CWorkspace: need 2*N, prefer N+N*NB)
                    347: *     (RWorkspace: none)
                    348: *
                    349:       ITAU = 1
                    350:       IWRK = ITAU + N
                    351:       CALL ZGEHRD( N, ILO, IHI, A, LDA, WORK( ITAU ), WORK( IWRK ),
                    352:      $             LWORK-IWRK+1, IERR )
                    353: *
                    354:       IF( WANTVL ) THEN
                    355: *
                    356: *        Want left eigenvectors
                    357: *        Copy Householder vectors to VL
                    358: *
                    359:          SIDE = 'L'
                    360:          CALL ZLACPY( 'L', N, N, A, LDA, VL, LDVL )
                    361: *
                    362: *        Generate unitary matrix in VL
                    363: *        (CWorkspace: need 2*N-1, prefer N+(N-1)*NB)
                    364: *        (RWorkspace: none)
                    365: *
                    366:          CALL ZUNGHR( N, ILO, IHI, VL, LDVL, WORK( ITAU ), WORK( IWRK ),
                    367:      $                LWORK-IWRK+1, IERR )
                    368: *
                    369: *        Perform QR iteration, accumulating Schur vectors in VL
                    370: *        (CWorkspace: need 1, prefer HSWORK (see comments) )
                    371: *        (RWorkspace: none)
                    372: *
                    373:          IWRK = ITAU
                    374:          CALL ZHSEQR( 'S', 'V', N, ILO, IHI, A, LDA, W, VL, LDVL,
                    375:      $                WORK( IWRK ), LWORK-IWRK+1, INFO )
                    376: *
                    377:          IF( WANTVR ) THEN
                    378: *
                    379: *           Want left and right eigenvectors
                    380: *           Copy Schur vectors to VR
                    381: *
                    382:             SIDE = 'B'
                    383:             CALL ZLACPY( 'F', N, N, VL, LDVL, VR, LDVR )
                    384:          END IF
                    385: *
                    386:       ELSE IF( WANTVR ) THEN
                    387: *
                    388: *        Want right eigenvectors
                    389: *        Copy Householder vectors to VR
                    390: *
                    391:          SIDE = 'R'
                    392:          CALL ZLACPY( 'L', N, N, A, LDA, VR, LDVR )
                    393: *
                    394: *        Generate unitary matrix in VR
                    395: *        (CWorkspace: need 2*N-1, prefer N+(N-1)*NB)
                    396: *        (RWorkspace: none)
                    397: *
                    398:          CALL ZUNGHR( N, ILO, IHI, VR, LDVR, WORK( ITAU ), WORK( IWRK ),
                    399:      $                LWORK-IWRK+1, IERR )
                    400: *
                    401: *        Perform QR iteration, accumulating Schur vectors in VR
                    402: *        (CWorkspace: need 1, prefer HSWORK (see comments) )
                    403: *        (RWorkspace: none)
                    404: *
                    405:          IWRK = ITAU
                    406:          CALL ZHSEQR( 'S', 'V', N, ILO, IHI, A, LDA, W, VR, LDVR,
                    407:      $                WORK( IWRK ), LWORK-IWRK+1, INFO )
                    408: *
                    409:       ELSE
                    410: *
                    411: *        Compute eigenvalues only
                    412: *        (CWorkspace: need 1, prefer HSWORK (see comments) )
                    413: *        (RWorkspace: none)
                    414: *
                    415:          IWRK = ITAU
                    416:          CALL ZHSEQR( 'E', 'N', N, ILO, IHI, A, LDA, W, VR, LDVR,
                    417:      $                WORK( IWRK ), LWORK-IWRK+1, INFO )
                    418:       END IF
                    419: *
1.13    ! bertrand  420: *     If INFO .NE. 0 from ZHSEQR, then quit
1.1       bertrand  421: *
1.13    ! bertrand  422:       IF( INFO.NE.0 )
1.1       bertrand  423:      $   GO TO 50
                    424: *
                    425:       IF( WANTVL .OR. WANTVR ) THEN
                    426: *
                    427: *        Compute left and/or right eigenvectors
1.13    ! bertrand  428: *        (CWorkspace: need 2*N, prefer N + 2*N*NB)
1.1       bertrand  429: *        (RWorkspace: need 2*N)
                    430: *
                    431:          IRWORK = IBAL + N
1.13    ! bertrand  432:          CALL ZTREVC3( SIDE, 'B', SELECT, N, A, LDA, VL, LDVL, VR, LDVR,
        !           433:      $                 N, NOUT, WORK( IWRK ), LWORK-IWRK+1,
        !           434:      $                 RWORK( IRWORK ), N, IERR )
1.1       bertrand  435:       END IF
                    436: *
                    437:       IF( WANTVL ) THEN
                    438: *
                    439: *        Undo balancing of left eigenvectors
                    440: *        (CWorkspace: none)
                    441: *        (RWorkspace: need N)
                    442: *
                    443:          CALL ZGEBAK( 'B', 'L', N, ILO, IHI, RWORK( IBAL ), N, VL, LDVL,
                    444:      $                IERR )
                    445: *
                    446: *        Normalize left eigenvectors and make largest component real
                    447: *
                    448:          DO 20 I = 1, N
                    449:             SCL = ONE / DZNRM2( N, VL( 1, I ), 1 )
                    450:             CALL ZDSCAL( N, SCL, VL( 1, I ), 1 )
                    451:             DO 10 K = 1, N
                    452:                RWORK( IRWORK+K-1 ) = DBLE( VL( K, I ) )**2 +
1.13    ! bertrand  453:      $                               AIMAG( VL( K, I ) )**2
1.1       bertrand  454:    10       CONTINUE
                    455:             K = IDAMAX( N, RWORK( IRWORK ), 1 )
1.13    ! bertrand  456:             TMP = CONJG( VL( K, I ) ) / SQRT( RWORK( IRWORK+K-1 ) )
1.1       bertrand  457:             CALL ZSCAL( N, TMP, VL( 1, I ), 1 )
                    458:             VL( K, I ) = DCMPLX( DBLE( VL( K, I ) ), ZERO )
                    459:    20    CONTINUE
                    460:       END IF
                    461: *
                    462:       IF( WANTVR ) THEN
                    463: *
                    464: *        Undo balancing of right eigenvectors
                    465: *        (CWorkspace: none)
                    466: *        (RWorkspace: need N)
                    467: *
                    468:          CALL ZGEBAK( 'B', 'R', N, ILO, IHI, RWORK( IBAL ), N, VR, LDVR,
                    469:      $                IERR )
                    470: *
                    471: *        Normalize right eigenvectors and make largest component real
                    472: *
                    473:          DO 40 I = 1, N
                    474:             SCL = ONE / DZNRM2( N, VR( 1, I ), 1 )
                    475:             CALL ZDSCAL( N, SCL, VR( 1, I ), 1 )
                    476:             DO 30 K = 1, N
                    477:                RWORK( IRWORK+K-1 ) = DBLE( VR( K, I ) )**2 +
1.13    ! bertrand  478:      $                               AIMAG( VR( K, I ) )**2
1.1       bertrand  479:    30       CONTINUE
                    480:             K = IDAMAX( N, RWORK( IRWORK ), 1 )
1.13    ! bertrand  481:             TMP = CONJG( VR( K, I ) ) / SQRT( RWORK( IRWORK+K-1 ) )
1.1       bertrand  482:             CALL ZSCAL( N, TMP, VR( 1, I ), 1 )
                    483:             VR( K, I ) = DCMPLX( DBLE( VR( K, I ) ), ZERO )
                    484:    40    CONTINUE
                    485:       END IF
                    486: *
                    487: *     Undo scaling if necessary
                    488: *
                    489:    50 CONTINUE
                    490:       IF( SCALEA ) THEN
                    491:          CALL ZLASCL( 'G', 0, 0, CSCALE, ANRM, N-INFO, 1, W( INFO+1 ),
                    492:      $                MAX( N-INFO, 1 ), IERR )
                    493:          IF( INFO.GT.0 ) THEN
                    494:             CALL ZLASCL( 'G', 0, 0, CSCALE, ANRM, ILO-1, 1, W, N, IERR )
                    495:          END IF
                    496:       END IF
                    497: *
                    498:       WORK( 1 ) = MAXWRK
                    499:       RETURN
                    500: *
                    501: *     End of ZGEEV
                    502: *
                    503:       END

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