LAPACK: SRC/cgeevx.f Source File

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00001       SUBROUTINE CGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, W, VL,
00002      $                   LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM, RCONDE,
00003      $                   RCONDV, WORK, LWORK, RWORK, INFO )
00004 *
00005 *  -- LAPACK driver routine (version 3.2) --
00006 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00007 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00008 *     November 2006
00009 *
00010 *     .. Scalar Arguments ..
00011       CHARACTER          BALANC, JOBVL, JOBVR, SENSE
00012       INTEGER            IHI, ILO, INFO, LDA, LDVL, LDVR, LWORK, N
00013       REAL               ABNRM
00014 *     ..
00015 *     .. Array Arguments ..
00016       REAL               RCONDE( * ), RCONDV( * ), RWORK( * ),
00017      $                   SCALE( * )
00018       COMPLEX            A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ),
00019      $                   W( * ), WORK( * )
00020 *     ..
00021 *
00022 *  Purpose
00023 *  =======
00024 *
00025 *  CGEEVX computes for an N-by-N complex nonsymmetric matrix A, the
00026 *  eigenvalues and, optionally, the left and/or right eigenvectors.
00027 *
00028 *  Optionally also, it computes a balancing transformation to improve
00029 *  the conditioning of the eigenvalues and eigenvectors (ILO, IHI,
00030 *  SCALE, and ABNRM), reciprocal condition numbers for the eigenvalues
00031 *  (RCONDE), and reciprocal condition numbers for the right
00032 *  eigenvectors (RCONDV).
00033 *
00034 *  The right eigenvector v(j) of A satisfies
00035 *                   A * v(j) = lambda(j) * v(j)
00036 *  where lambda(j) is its eigenvalue.
00037 *  The left eigenvector u(j) of A satisfies
00038 *                u(j)**H * A = lambda(j) * u(j)**H
00039 *  where u(j)**H denotes the conjugate transpose of u(j).
00040 *
00041 *  The computed eigenvectors are normalized to have Euclidean norm
00042 *  equal to 1 and largest component real.
00043 *
00044 *  Balancing a matrix means permuting the rows and columns to make it
00045 *  more nearly upper triangular, and applying a diagonal similarity
00046 *  transformation D * A * D**(-1), where D is a diagonal matrix, to
00047 *  make its rows and columns closer in norm and the condition numbers
00048 *  of its eigenvalues and eigenvectors smaller.  The computed
00049 *  reciprocal condition numbers correspond to the balanced matrix.
00050 *  Permuting rows and columns will not change the condition numbers
00051 *  (in exact arithmetic) but diagonal scaling will.  For further
00052 *  explanation of balancing, see section 4.10.2 of the LAPACK
00053 *  Users' Guide.
00054 *
00055 *  Arguments
00056 *  =========
00057 *
00058 *  BALANC  (input) CHARACTER*1
00059 *          Indicates how the input matrix should be diagonally scaled
00060 *          and/or permuted to improve the conditioning of its
00061 *          eigenvalues.
00062 *          = 'N': Do not diagonally scale or permute;
00063 *          = 'P': Perform permutations to make the matrix more nearly
00064 *                 upper triangular. Do not diagonally scale;
00065 *          = 'S': Diagonally scale the matrix, ie. replace A by
00066 *                 D*A*D**(-1), where D is a diagonal matrix chosen
00067 *                 to make the rows and columns of A more equal in
00068 *                 norm. Do not permute;
00069 *          = 'B': Both diagonally scale and permute A.
00070 *
00071 *          Computed reciprocal condition numbers will be for the matrix
00072 *          after balancing and/or permuting. Permuting does not change
00073 *          condition numbers (in exact arithmetic), but balancing does.
00074 *
00075 *  JOBVL   (input) CHARACTER*1
00076 *          = 'N': left eigenvectors of A are not computed;
00077 *          = 'V': left eigenvectors of A are computed.
00078 *          If SENSE = 'E' or 'B', JOBVL must = 'V'.
00079 *
00080 *  JOBVR   (input) CHARACTER*1
00081 *          = 'N': right eigenvectors of A are not computed;
00082 *          = 'V': right eigenvectors of A are computed.
00083 *          If SENSE = 'E' or 'B', JOBVR must = 'V'.
00084 *
00085 *  SENSE   (input) CHARACTER*1
00086 *          Determines which reciprocal condition numbers are computed.
00087 *          = 'N': None are computed;
00088 *          = 'E': Computed for eigenvalues only;
00089 *          = 'V': Computed for right eigenvectors only;
00090 *          = 'B': Computed for eigenvalues and right eigenvectors.
00091 *
00092 *          If SENSE = 'E' or 'B', both left and right eigenvectors
00093 *          must also be computed (JOBVL = 'V' and JOBVR = 'V').
00094 *
00095 *  N       (input) INTEGER
00096 *          The order of the matrix A. N >= 0.
00097 *
00098 *  A       (input/output) COMPLEX array, dimension (LDA,N)
00099 *          On entry, the N-by-N matrix A.
00100 *          On exit, A has been overwritten.  If JOBVL = 'V' or
00101 *          JOBVR = 'V', A contains the Schur form of the balanced 
00102 *          version of the matrix A.
00103 *
00104 *  LDA     (input) INTEGER
00105 *          The leading dimension of the array A.  LDA >= max(1,N).
00106 *
00107 *  W       (output) COMPLEX array, dimension (N)
00108 *          W contains the computed eigenvalues.
00109 *
00110 *  VL      (output) COMPLEX array, dimension (LDVL,N)
00111 *          If JOBVL = 'V', the left eigenvectors u(j) are stored one
00112 *          after another in the columns of VL, in the same order
00113 *          as their eigenvalues.
00114 *          If JOBVL = 'N', VL is not referenced.
00115 *          u(j) = VL(:,j), the j-th column of VL.
00116 *
00117 *  LDVL    (input) INTEGER
00118 *          The leading dimension of the array VL.  LDVL >= 1; if
00119 *          JOBVL = 'V', LDVL >= N.
00120 *
00121 *  VR      (output) COMPLEX array, dimension (LDVR,N)
00122 *          If JOBVR = 'V', the right eigenvectors v(j) are stored one
00123 *          after another in the columns of VR, in the same order
00124 *          as their eigenvalues.
00125 *          If JOBVR = 'N', VR is not referenced.
00126 *          v(j) = VR(:,j), the j-th column of VR.
00127 *
00128 *  LDVR    (input) INTEGER
00129 *          The leading dimension of the array VR.  LDVR >= 1; if
00130 *          JOBVR = 'V', LDVR >= N.
00131 *
00132 *  ILO     (output) INTEGER
00133 *  IHI     (output) INTEGER
00134 *          ILO and IHI are integer values determined when A was
00135 *          balanced.  The balanced A(i,j) = 0 if I > J and
00136 *          J = 1,...,ILO-1 or I = IHI+1,...,N.
00137 *
00138 *  SCALE   (output) REAL array, dimension (N)
00139 *          Details of the permutations and scaling factors applied
00140 *          when balancing A.  If P(j) is the index of the row and column
00141 *          interchanged with row and column j, and D(j) is the scaling
00142 *          factor applied to row and column j, then
00143 *          SCALE(J) = P(J),    for J = 1,...,ILO-1
00144 *                   = D(J),    for J = ILO,...,IHI
00145 *                   = P(J)     for J = IHI+1,...,N.
00146 *          The order in which the interchanges are made is N to IHI+1,
00147 *          then 1 to ILO-1.
00148 *
00149 *  ABNRM   (output) REAL
00150 *          The one-norm of the balanced matrix (the maximum
00151 *          of the sum of absolute values of elements of any column).
00152 *
00153 *  RCONDE  (output) REAL array, dimension (N)
00154 *          RCONDE(j) is the reciprocal condition number of the j-th
00155 *          eigenvalue.
00156 *
00157 *  RCONDV  (output) REAL array, dimension (N)
00158 *          RCONDV(j) is the reciprocal condition number of the j-th
00159 *          right eigenvector.
00160 *
00161 *  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
00162 *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
00163 *
00164 *  LWORK   (input) INTEGER
00165 *          The dimension of the array WORK.  If SENSE = 'N' or 'E',
00166 *          LWORK >= max(1,2*N), and if SENSE = 'V' or 'B',
00167 *          LWORK >= N*N+2*N.
00168 *          For good performance, LWORK must generally be larger.
00169 *
00170 *          If LWORK = -1, then a workspace query is assumed; the routine
00171 *          only calculates the optimal size of the WORK array, returns
00172 *          this value as the first entry of the WORK array, and no error
00173 *          message related to LWORK is issued by XERBLA.
00174 *
00175 *  RWORK   (workspace) REAL array, dimension (2*N)
00176 *
00177 *  INFO    (output) INTEGER
00178 *          = 0:  successful exit
00179 *          < 0:  if INFO = -i, the i-th argument had an illegal value.
00180 *          > 0:  if INFO = i, the QR algorithm failed to compute all the
00181 *                eigenvalues, and no eigenvectors or condition numbers
00182 *                have been computed; elements 1:ILO-1 and i+1:N of W
00183 *                contain eigenvalues which have converged.
00184 *
00185 *  =====================================================================
00186 *
00187 *     .. Parameters ..
00188       REAL               ZERO, ONE
00189       PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
00190 *     ..
00191 *     .. Local Scalars ..
00192       LOGICAL            LQUERY, SCALEA, WANTVL, WANTVR, WNTSNB, WNTSNE,
00193      $                   WNTSNN, WNTSNV
00194       CHARACTER          JOB, SIDE
00195       INTEGER            HSWORK, I, ICOND, IERR, ITAU, IWRK, K, MAXWRK,
00196      $                   MINWRK, NOUT
00197       REAL               ANRM, BIGNUM, CSCALE, EPS, SCL, SMLNUM
00198       COMPLEX            TMP
00199 *     ..
00200 *     .. Local Arrays ..
00201       LOGICAL            SELECT( 1 )
00202       REAL               DUM( 1 )
00203 *     ..
00204 *     .. External Subroutines ..
00205       EXTERNAL           CGEBAK, CGEBAL, CGEHRD, CHSEQR, CLACPY, CLASCL,
00206      $                   CSCAL, CSSCAL, CTREVC, CTRSNA, CUNGHR, SLABAD,
00207      $                   SLASCL, XERBLA
00208 *     ..
00209 *     .. External Functions ..
00210       LOGICAL            LSAME
00211       INTEGER            ILAENV, ISAMAX
00212       REAL               CLANGE, SCNRM2, SLAMCH
00213       EXTERNAL           LSAME, ILAENV, ISAMAX, CLANGE, SCNRM2, SLAMCH
00214 *     ..
00215 *     .. Intrinsic Functions ..
00216       INTRINSIC          AIMAG, CMPLX, CONJG, MAX, REAL, SQRT
00217 *     ..
00218 *     .. Executable Statements ..
00219 *
00220 *     Test the input arguments
00221 *
00222       INFO = 0
00223       LQUERY = ( LWORK.EQ.-1 )
00224       WANTVL = LSAME( JOBVL, 'V' )
00225       WANTVR = LSAME( JOBVR, 'V' )
00226       WNTSNN = LSAME( SENSE, 'N' )
00227       WNTSNE = LSAME( SENSE, 'E' )
00228       WNTSNV = LSAME( SENSE, 'V' )
00229       WNTSNB = LSAME( SENSE, 'B' )
00230       IF( .NOT.( LSAME( BALANC, 'N' ) .OR. LSAME( BALANC, 'S' ) .OR.
00231      $    LSAME( BALANC, 'P' ) .OR. LSAME( BALANC, 'B' ) ) ) THEN
00232          INFO = -1
00233       ELSE IF( ( .NOT.WANTVL ) .AND. ( .NOT.LSAME( JOBVL, 'N' ) ) ) THEN
00234          INFO = -2
00235       ELSE IF( ( .NOT.WANTVR ) .AND. ( .NOT.LSAME( JOBVR, 'N' ) ) ) THEN
00236          INFO = -3
00237       ELSE IF( .NOT.( WNTSNN .OR. WNTSNE .OR. WNTSNB .OR. WNTSNV ) .OR.
00238      $         ( ( WNTSNE .OR. WNTSNB ) .AND. .NOT.( WANTVL .AND.
00239      $         WANTVR ) ) ) THEN
00240          INFO = -4
00241       ELSE IF( N.LT.0 ) THEN
00242          INFO = -5
00243       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00244          INFO = -7
00245       ELSE IF( LDVL.LT.1 .OR. ( WANTVL .AND. LDVL.LT.N ) ) THEN
00246          INFO = -10
00247       ELSE IF( LDVR.LT.1 .OR. ( WANTVR .AND. LDVR.LT.N ) ) THEN
00248          INFO = -12
00249       END IF
00250 *
00251 *     Compute workspace
00252 *      (Note: Comments in the code beginning "Workspace:" describe the
00253 *       minimal amount of workspace needed at that point in the code,
00254 *       as well as the preferred amount for good performance.
00255 *       CWorkspace refers to complex workspace, and RWorkspace to real
00256 *       workspace. NB refers to the optimal block size for the
00257 *       immediately following subroutine, as returned by ILAENV.
00258 *       HSWORK refers to the workspace preferred by CHSEQR, as
00259 *       calculated below. HSWORK is computed assuming ILO=1 and IHI=N,
00260 *       the worst case.)
00261 *
00262       IF( INFO.EQ.0 ) THEN
00263          IF( N.EQ.0 ) THEN
00264             MINWRK = 1
00265             MAXWRK = 1
00266          ELSE
00267             MAXWRK = N + N*ILAENV( 1, 'CGEHRD', ' ', N, 1, N, 0 )
00268 *
00269             IF( WANTVL ) THEN
00270                CALL CHSEQR( 'S', 'V', N, 1, N, A, LDA, W, VL, LDVL,
00271      $                WORK, -1, INFO )
00272             ELSE IF( WANTVR ) THEN
00273                CALL CHSEQR( 'S', 'V', N, 1, N, A, LDA, W, VR, LDVR,
00274      $                WORK, -1, INFO )
00275             ELSE
00276                IF( WNTSNN ) THEN
00277                   CALL CHSEQR( 'E', 'N', N, 1, N, A, LDA, W, VR, LDVR,
00278      $                WORK, -1, INFO )
00279                ELSE
00280                   CALL CHSEQR( 'S', 'N', N, 1, N, A, LDA, W, VR, LDVR,
00281      $                WORK, -1, INFO )
00282                END IF
00283             END IF
00284             HSWORK = WORK( 1 )
00285 *
00286             IF( ( .NOT.WANTVL ) .AND. ( .NOT.WANTVR ) ) THEN
00287                MINWRK = 2*N
00288                IF( .NOT.( WNTSNN .OR. WNTSNE ) )
00289      $            MINWRK = MAX( MINWRK, N*N + 2*N )
00290                MAXWRK = MAX( MAXWRK, HSWORK )
00291                IF( .NOT.( WNTSNN .OR. WNTSNE ) )
00292      $            MAXWRK = MAX( MAXWRK, N*N + 2*N )
00293             ELSE
00294                MINWRK = 2*N
00295                IF( .NOT.( WNTSNN .OR. WNTSNE ) )
00296      $            MINWRK = MAX( MINWRK, N*N + 2*N )
00297                MAXWRK = MAX( MAXWRK, HSWORK )
00298                MAXWRK = MAX( MAXWRK, N + ( N - 1 )*ILAENV( 1, 'CUNGHR',
00299      $                       ' ', N, 1, N, -1 ) )
00300                IF( .NOT.( WNTSNN .OR. WNTSNE ) )
00301      $            MAXWRK = MAX( MAXWRK, N*N + 2*N )
00302                MAXWRK = MAX( MAXWRK, 2*N )
00303             END IF
00304             MAXWRK = MAX( MAXWRK, MINWRK )
00305          END IF
00306          WORK( 1 ) = MAXWRK
00307 *
00308          IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
00309             INFO = -20
00310          END IF
00311       END IF
00312 *
00313       IF( INFO.NE.0 ) THEN
00314          CALL XERBLA( 'CGEEVX', -INFO )
00315          RETURN
00316       ELSE IF( LQUERY ) THEN
00317          RETURN
00318       END IF
00319 *
00320 *     Quick return if possible
00321 *
00322       IF( N.EQ.0 )
00323      $   RETURN
00324 *
00325 *     Get machine constants
00326 *
00327       EPS = SLAMCH( 'P' )
00328       SMLNUM = SLAMCH( 'S' )
00329       BIGNUM = ONE / SMLNUM
00330       CALL SLABAD( SMLNUM, BIGNUM )
00331       SMLNUM = SQRT( SMLNUM ) / EPS
00332       BIGNUM = ONE / SMLNUM
00333 *
00334 *     Scale A if max element outside range [SMLNUM,BIGNUM]
00335 *
00336       ICOND = 0
00337       ANRM = CLANGE( 'M', N, N, A, LDA, DUM )
00338       SCALEA = .FALSE.
00339       IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
00340          SCALEA = .TRUE.
00341          CSCALE = SMLNUM
00342       ELSE IF( ANRM.GT.BIGNUM ) THEN
00343          SCALEA = .TRUE.
00344          CSCALE = BIGNUM
00345       END IF
00346       IF( SCALEA )
00347      $   CALL CLASCL( 'G', 0, 0, ANRM, CSCALE, N, N, A, LDA, IERR )
00348 *
00349 *     Balance the matrix and compute ABNRM
00350 *
00351       CALL CGEBAL( BALANC, N, A, LDA, ILO, IHI, SCALE, IERR )
00352       ABNRM = CLANGE( '1', N, N, A, LDA, DUM )
00353       IF( SCALEA ) THEN
00354          DUM( 1 ) = ABNRM
00355          CALL SLASCL( 'G', 0, 0, CSCALE, ANRM, 1, 1, DUM, 1, IERR )
00356          ABNRM = DUM( 1 )
00357       END IF
00358 *
00359 *     Reduce to upper Hessenberg form
00360 *     (CWorkspace: need 2*N, prefer N+N*NB)
00361 *     (RWorkspace: none)
00362 *
00363       ITAU = 1
00364       IWRK = ITAU + N
00365       CALL CGEHRD( N, ILO, IHI, A, LDA, WORK( ITAU ), WORK( IWRK ),
00366      $             LWORK-IWRK+1, IERR )
00367 *
00368       IF( WANTVL ) THEN
00369 *
00370 *        Want left eigenvectors
00371 *        Copy Householder vectors to VL
00372 *
00373          SIDE = 'L'
00374          CALL CLACPY( 'L', N, N, A, LDA, VL, LDVL )
00375 *
00376 *        Generate unitary matrix in VL
00377 *        (CWorkspace: need 2*N-1, prefer N+(N-1)*NB)
00378 *        (RWorkspace: none)
00379 *
00380          CALL CUNGHR( N, ILO, IHI, VL, LDVL, WORK( ITAU ), WORK( IWRK ),
00381      $                LWORK-IWRK+1, IERR )
00382 *
00383 *        Perform QR iteration, accumulating Schur vectors in VL
00384 *        (CWorkspace: need 1, prefer HSWORK (see comments) )
00385 *        (RWorkspace: none)
00386 *
00387          IWRK = ITAU
00388          CALL CHSEQR( 'S', 'V', N, ILO, IHI, A, LDA, W, VL, LDVL,
00389      $                WORK( IWRK ), LWORK-IWRK+1, INFO )
00390 *
00391          IF( WANTVR ) THEN
00392 *
00393 *           Want left and right eigenvectors
00394 *           Copy Schur vectors to VR
00395 *
00396             SIDE = 'B'
00397             CALL CLACPY( 'F', N, N, VL, LDVL, VR, LDVR )
00398          END IF
00399 *
00400       ELSE IF( WANTVR ) THEN
00401 *
00402 *        Want right eigenvectors
00403 *        Copy Householder vectors to VR
00404 *
00405          SIDE = 'R'
00406          CALL CLACPY( 'L', N, N, A, LDA, VR, LDVR )
00407 *
00408 *        Generate unitary matrix in VR
00409 *        (CWorkspace: need 2*N-1, prefer N+(N-1)*NB)
00410 *        (RWorkspace: none)
00411 *
00412          CALL CUNGHR( N, ILO, IHI, VR, LDVR, WORK( ITAU ), WORK( IWRK ),
00413      $                LWORK-IWRK+1, IERR )
00414 *
00415 *        Perform QR iteration, accumulating Schur vectors in VR
00416 *        (CWorkspace: need 1, prefer HSWORK (see comments) )
00417 *        (RWorkspace: none)
00418 *
00419          IWRK = ITAU
00420          CALL CHSEQR( 'S', 'V', N, ILO, IHI, A, LDA, W, VR, LDVR,
00421      $                WORK( IWRK ), LWORK-IWRK+1, INFO )
00422 *
00423       ELSE
00424 *
00425 *        Compute eigenvalues only
00426 *        If condition numbers desired, compute Schur form
00427 *
00428          IF( WNTSNN ) THEN
00429             JOB = 'E'
00430          ELSE
00431             JOB = 'S'
00432          END IF
00433 *
00434 *        (CWorkspace: need 1, prefer HSWORK (see comments) )
00435 *        (RWorkspace: none)
00436 *
00437          IWRK = ITAU
00438          CALL CHSEQR( JOB, 'N', N, ILO, IHI, A, LDA, W, VR, LDVR,
00439      $                WORK( IWRK ), LWORK-IWRK+1, INFO )
00440       END IF
00441 *
00442 *     If INFO > 0 from CHSEQR, then quit
00443 *
00444       IF( INFO.GT.0 )
00445      $   GO TO 50
00446 *
00447       IF( WANTVL .OR. WANTVR ) THEN
00448 *
00449 *        Compute left and/or right eigenvectors
00450 *        (CWorkspace: need 2*N)
00451 *        (RWorkspace: need N)
00452 *
00453          CALL CTREVC( SIDE, 'B', SELECT, N, A, LDA, VL, LDVL, VR, LDVR,
00454      $                N, NOUT, WORK( IWRK ), RWORK, IERR )
00455       END IF
00456 *
00457 *     Compute condition numbers if desired
00458 *     (CWorkspace: need N*N+2*N unless SENSE = 'E')
00459 *     (RWorkspace: need 2*N unless SENSE = 'E')
00460 *
00461       IF( .NOT.WNTSNN ) THEN
00462          CALL CTRSNA( SENSE, 'A', SELECT, N, A, LDA, VL, LDVL, VR, LDVR,
00463      $                RCONDE, RCONDV, N, NOUT, WORK( IWRK ), N, RWORK,
00464      $                ICOND )
00465       END IF
00466 *
00467       IF( WANTVL ) THEN
00468 *
00469 *        Undo balancing of left eigenvectors
00470 *
00471          CALL CGEBAK( BALANC, 'L', N, ILO, IHI, SCALE, N, VL, LDVL,
00472      $                IERR )
00473 *
00474 *        Normalize left eigenvectors and make largest component real
00475 *
00476          DO 20 I = 1, N
00477             SCL = ONE / SCNRM2( N, VL( 1, I ), 1 )
00478             CALL CSSCAL( N, SCL, VL( 1, I ), 1 )
00479             DO 10 K = 1, N
00480                RWORK( K ) = REAL( VL( K, I ) )**2 +
00481      $                      AIMAG( VL( K, I ) )**2
00482    10       CONTINUE
00483             K = ISAMAX( N, RWORK, 1 )
00484             TMP = CONJG( VL( K, I ) ) / SQRT( RWORK( K ) )
00485             CALL CSCAL( N, TMP, VL( 1, I ), 1 )
00486             VL( K, I ) = CMPLX( REAL( VL( K, I ) ), ZERO )
00487    20    CONTINUE
00488       END IF
00489 *
00490       IF( WANTVR ) THEN
00491 *
00492 *        Undo balancing of right eigenvectors
00493 *
00494          CALL CGEBAK( BALANC, 'R', N, ILO, IHI, SCALE, N, VR, LDVR,
00495      $                IERR )
00496 *
00497 *        Normalize right eigenvectors and make largest component real
00498 *
00499          DO 40 I = 1, N
00500             SCL = ONE / SCNRM2( N, VR( 1, I ), 1 )
00501             CALL CSSCAL( N, SCL, VR( 1, I ), 1 )
00502             DO 30 K = 1, N
00503                RWORK( K ) = REAL( VR( K, I ) )**2 +
00504      $                      AIMAG( VR( K, I ) )**2
00505    30       CONTINUE
00506             K = ISAMAX( N, RWORK, 1 )
00507             TMP = CONJG( VR( K, I ) ) / SQRT( RWORK( K ) )
00508             CALL CSCAL( N, TMP, VR( 1, I ), 1 )
00509             VR( K, I ) = CMPLX( REAL( VR( K, I ) ), ZERO )
00510    40    CONTINUE
00511       END IF
00512 *
00513 *     Undo scaling if necessary
00514 *
00515    50 CONTINUE
00516       IF( SCALEA ) THEN
00517          CALL CLASCL( 'G', 0, 0, CSCALE, ANRM, N-INFO, 1, W( INFO+1 ),
00518      $                MAX( N-INFO, 1 ), IERR )
00519          IF( INFO.EQ.0 ) THEN
00520             IF( ( WNTSNV .OR. WNTSNB ) .AND. ICOND.EQ.0 )
00521      $         CALL SLASCL( 'G', 0, 0, CSCALE, ANRM, N, 1, RCONDV, N,
00522      $                      IERR )
00523          ELSE
00524             CALL CLASCL( 'G', 0, 0, CSCALE, ANRM, ILO-1, 1, W, N, IERR )
00525          END IF
00526       END IF
00527 *
00528       WORK( 1 ) = MAXWRK
00529       RETURN
00530 *
00531 *     End of CGEEVX
00532 *
00533       END