Annotation of rpl/lapack/lapack/zggevx.f, revision 1.8

1.8     ! bertrand    1: *> \brief <b> ZGGEVX 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 ZGGEVX + dependencies 
        !            10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zggevx.f"> 
        !            11: *> [TGZ]</a> 
        !            12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zggevx.f"> 
        !            13: *> [ZIP]</a> 
        !            14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zggevx.f"> 
        !            15: *> [TXT]</a>
        !            16: *> \endhtmlonly 
        !            17: *
        !            18: *  Definition:
        !            19: *  ===========
        !            20: *
        !            21: *       SUBROUTINE ZGGEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, B, LDB,
        !            22: *                          ALPHA, BETA, VL, LDVL, VR, LDVR, ILO, IHI,
        !            23: *                          LSCALE, RSCALE, ABNRM, BBNRM, RCONDE, RCONDV,
        !            24: *                          WORK, LWORK, RWORK, IWORK, BWORK, INFO )
        !            25: * 
        !            26: *       .. Scalar Arguments ..
        !            27: *       CHARACTER          BALANC, JOBVL, JOBVR, SENSE
        !            28: *       INTEGER            IHI, ILO, INFO, LDA, LDB, LDVL, LDVR, LWORK, N
        !            29: *       DOUBLE PRECISION   ABNRM, BBNRM
        !            30: *       ..
        !            31: *       .. Array Arguments ..
        !            32: *       LOGICAL            BWORK( * )
        !            33: *       INTEGER            IWORK( * )
        !            34: *       DOUBLE PRECISION   LSCALE( * ), RCONDE( * ), RCONDV( * ),
        !            35: *      $                   RSCALE( * ), RWORK( * )
        !            36: *       COMPLEX*16         A( LDA, * ), ALPHA( * ), B( LDB, * ),
        !            37: *      $                   BETA( * ), VL( LDVL, * ), VR( LDVR, * ),
        !            38: *      $                   WORK( * )
        !            39: *       ..
        !            40: *  
        !            41: *
        !            42: *> \par Purpose:
        !            43: *  =============
        !            44: *>
        !            45: *> \verbatim
        !            46: *>
        !            47: *> ZGGEVX computes for a pair of N-by-N complex nonsymmetric matrices
        !            48: *> (A,B) the generalized eigenvalues, and optionally, the left and/or
        !            49: *> right generalized eigenvectors.
        !            50: *>
        !            51: *> Optionally, it also computes a balancing transformation to improve
        !            52: *> the conditioning of the eigenvalues and eigenvectors (ILO, IHI,
        !            53: *> LSCALE, RSCALE, ABNRM, and BBNRM), reciprocal condition numbers for
        !            54: *> the eigenvalues (RCONDE), and reciprocal condition numbers for the
        !            55: *> right eigenvectors (RCONDV).
        !            56: *>
        !            57: *> A generalized eigenvalue for a pair of matrices (A,B) is a scalar
        !            58: *> lambda or a ratio alpha/beta = lambda, such that A - lambda*B is
        !            59: *> singular. It is usually represented as the pair (alpha,beta), as
        !            60: *> there is a reasonable interpretation for beta=0, and even for both
        !            61: *> being zero.
        !            62: *>
        !            63: *> The right eigenvector v(j) corresponding to the eigenvalue lambda(j)
        !            64: *> of (A,B) satisfies
        !            65: *>                  A * v(j) = lambda(j) * B * v(j) .
        !            66: *> The left eigenvector u(j) corresponding to the eigenvalue lambda(j)
        !            67: *> of (A,B) satisfies
        !            68: *>                  u(j)**H * A  = lambda(j) * u(j)**H * B.
        !            69: *> where u(j)**H is the conjugate-transpose of u(j).
        !            70: *>
        !            71: *> \endverbatim
        !            72: *
        !            73: *  Arguments:
        !            74: *  ==========
        !            75: *
        !            76: *> \param[in] BALANC
        !            77: *> \verbatim
        !            78: *>          BALANC is CHARACTER*1
        !            79: *>          Specifies the balance option to be performed:
        !            80: *>          = 'N':  do not diagonally scale or permute;
        !            81: *>          = 'P':  permute only;
        !            82: *>          = 'S':  scale only;
        !            83: *>          = 'B':  both permute and scale.
        !            84: *>          Computed reciprocal condition numbers will be for the
        !            85: *>          matrices after permuting and/or balancing. Permuting does
        !            86: *>          not change condition numbers (in exact arithmetic), but
        !            87: *>          balancing does.
        !            88: *> \endverbatim
        !            89: *>
        !            90: *> \param[in] JOBVL
        !            91: *> \verbatim
        !            92: *>          JOBVL is CHARACTER*1
        !            93: *>          = 'N':  do not compute the left generalized eigenvectors;
        !            94: *>          = 'V':  compute the left generalized eigenvectors.
        !            95: *> \endverbatim
        !            96: *>
        !            97: *> \param[in] JOBVR
        !            98: *> \verbatim
        !            99: *>          JOBVR is CHARACTER*1
        !           100: *>          = 'N':  do not compute the right generalized eigenvectors;
        !           101: *>          = 'V':  compute the right generalized eigenvectors.
        !           102: *> \endverbatim
        !           103: *>
        !           104: *> \param[in] SENSE
        !           105: *> \verbatim
        !           106: *>          SENSE is CHARACTER*1
        !           107: *>          Determines which reciprocal condition numbers are computed.
        !           108: *>          = 'N': none are computed;
        !           109: *>          = 'E': computed for eigenvalues only;
        !           110: *>          = 'V': computed for eigenvectors only;
        !           111: *>          = 'B': computed for eigenvalues and eigenvectors.
        !           112: *> \endverbatim
        !           113: *>
        !           114: *> \param[in] N
        !           115: *> \verbatim
        !           116: *>          N is INTEGER
        !           117: *>          The order of the matrices A, B, VL, and VR.  N >= 0.
        !           118: *> \endverbatim
        !           119: *>
        !           120: *> \param[in,out] A
        !           121: *> \verbatim
        !           122: *>          A is COMPLEX*16 array, dimension (LDA, N)
        !           123: *>          On entry, the matrix A in the pair (A,B).
        !           124: *>          On exit, A has been overwritten. If JOBVL='V' or JOBVR='V'
        !           125: *>          or both, then A contains the first part of the complex Schur
        !           126: *>          form of the "balanced" versions of the input A and B.
        !           127: *> \endverbatim
        !           128: *>
        !           129: *> \param[in] LDA
        !           130: *> \verbatim
        !           131: *>          LDA is INTEGER
        !           132: *>          The leading dimension of A.  LDA >= max(1,N).
        !           133: *> \endverbatim
        !           134: *>
        !           135: *> \param[in,out] B
        !           136: *> \verbatim
        !           137: *>          B is COMPLEX*16 array, dimension (LDB, N)
        !           138: *>          On entry, the matrix B in the pair (A,B).
        !           139: *>          On exit, B has been overwritten. If JOBVL='V' or JOBVR='V'
        !           140: *>          or both, then B contains the second part of the complex
        !           141: *>          Schur form of the "balanced" versions of the input A and B.
        !           142: *> \endverbatim
        !           143: *>
        !           144: *> \param[in] LDB
        !           145: *> \verbatim
        !           146: *>          LDB is INTEGER
        !           147: *>          The leading dimension of B.  LDB >= max(1,N).
        !           148: *> \endverbatim
        !           149: *>
        !           150: *> \param[out] ALPHA
        !           151: *> \verbatim
        !           152: *>          ALPHA is COMPLEX*16 array, dimension (N)
        !           153: *> \endverbatim
        !           154: *>
        !           155: *> \param[out] BETA
        !           156: *> \verbatim
        !           157: *>          BETA is COMPLEX*16 array, dimension (N)
        !           158: *>          On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the generalized
        !           159: *>          eigenvalues.
        !           160: *>
        !           161: *>          Note: the quotient ALPHA(j)/BETA(j) ) may easily over- or
        !           162: *>          underflow, and BETA(j) may even be zero.  Thus, the user
        !           163: *>          should avoid naively computing the ratio ALPHA/BETA.
        !           164: *>          However, ALPHA will be always less than and usually
        !           165: *>          comparable with norm(A) in magnitude, and BETA always less
        !           166: *>          than and usually comparable with norm(B).
        !           167: *> \endverbatim
        !           168: *>
        !           169: *> \param[out] VL
        !           170: *> \verbatim
        !           171: *>          VL is COMPLEX*16 array, dimension (LDVL,N)
        !           172: *>          If JOBVL = 'V', the left generalized eigenvectors u(j) are
        !           173: *>          stored one after another in the columns of VL, in the same
        !           174: *>          order as their eigenvalues.
        !           175: *>          Each eigenvector will be scaled so the largest component
        !           176: *>          will have abs(real part) + abs(imag. part) = 1.
        !           177: *>          Not referenced if JOBVL = 'N'.
        !           178: *> \endverbatim
        !           179: *>
        !           180: *> \param[in] LDVL
        !           181: *> \verbatim
        !           182: *>          LDVL is INTEGER
        !           183: *>          The leading dimension of the matrix VL. LDVL >= 1, and
        !           184: *>          if JOBVL = 'V', LDVL >= N.
        !           185: *> \endverbatim
        !           186: *>
        !           187: *> \param[out] VR
        !           188: *> \verbatim
        !           189: *>          VR is COMPLEX*16 array, dimension (LDVR,N)
        !           190: *>          If JOBVR = 'V', the right generalized eigenvectors v(j) are
        !           191: *>          stored one after another in the columns of VR, in the same
        !           192: *>          order as their eigenvalues.
        !           193: *>          Each eigenvector will be scaled so the largest component
        !           194: *>          will have abs(real part) + abs(imag. part) = 1.
        !           195: *>          Not referenced if JOBVR = 'N'.
        !           196: *> \endverbatim
        !           197: *>
        !           198: *> \param[in] LDVR
        !           199: *> \verbatim
        !           200: *>          LDVR is INTEGER
        !           201: *>          The leading dimension of the matrix VR. LDVR >= 1, and
        !           202: *>          if JOBVR = 'V', LDVR >= N.
        !           203: *> \endverbatim
        !           204: *>
        !           205: *> \param[out] ILO
        !           206: *> \verbatim
        !           207: *>          ILO is INTEGER
        !           208: *> \endverbatim
        !           209: *>
        !           210: *> \param[out] IHI
        !           211: *> \verbatim
        !           212: *>          IHI is INTEGER
        !           213: *>          ILO and IHI are integer values such that on exit
        !           214: *>          A(i,j) = 0 and B(i,j) = 0 if i > j and
        !           215: *>          j = 1,...,ILO-1 or i = IHI+1,...,N.
        !           216: *>          If BALANC = 'N' or 'S', ILO = 1 and IHI = N.
        !           217: *> \endverbatim
        !           218: *>
        !           219: *> \param[out] LSCALE
        !           220: *> \verbatim
        !           221: *>          LSCALE is DOUBLE PRECISION array, dimension (N)
        !           222: *>          Details of the permutations and scaling factors applied
        !           223: *>          to the left side of A and B.  If PL(j) is the index of the
        !           224: *>          row interchanged with row j, and DL(j) is the scaling
        !           225: *>          factor applied to row j, then
        !           226: *>            LSCALE(j) = PL(j)  for j = 1,...,ILO-1
        !           227: *>                      = DL(j)  for j = ILO,...,IHI
        !           228: *>                      = PL(j)  for j = IHI+1,...,N.
        !           229: *>          The order in which the interchanges are made is N to IHI+1,
        !           230: *>          then 1 to ILO-1.
        !           231: *> \endverbatim
        !           232: *>
        !           233: *> \param[out] RSCALE
        !           234: *> \verbatim
        !           235: *>          RSCALE is DOUBLE PRECISION array, dimension (N)
        !           236: *>          Details of the permutations and scaling factors applied
        !           237: *>          to the right side of A and B.  If PR(j) is the index of the
        !           238: *>          column interchanged with column j, and DR(j) is the scaling
        !           239: *>          factor applied to column j, then
        !           240: *>            RSCALE(j) = PR(j)  for j = 1,...,ILO-1
        !           241: *>                      = DR(j)  for j = ILO,...,IHI
        !           242: *>                      = PR(j)  for j = IHI+1,...,N
        !           243: *>          The order in which the interchanges are made is N to IHI+1,
        !           244: *>          then 1 to ILO-1.
        !           245: *> \endverbatim
        !           246: *>
        !           247: *> \param[out] ABNRM
        !           248: *> \verbatim
        !           249: *>          ABNRM is DOUBLE PRECISION
        !           250: *>          The one-norm of the balanced matrix A.
        !           251: *> \endverbatim
        !           252: *>
        !           253: *> \param[out] BBNRM
        !           254: *> \verbatim
        !           255: *>          BBNRM is DOUBLE PRECISION
        !           256: *>          The one-norm of the balanced matrix B.
        !           257: *> \endverbatim
        !           258: *>
        !           259: *> \param[out] RCONDE
        !           260: *> \verbatim
        !           261: *>          RCONDE is DOUBLE PRECISION array, dimension (N)
        !           262: *>          If SENSE = 'E' or 'B', the reciprocal condition numbers of
        !           263: *>          the eigenvalues, stored in consecutive elements of the array.
        !           264: *>          If SENSE = 'N' or 'V', RCONDE is not referenced.
        !           265: *> \endverbatim
        !           266: *>
        !           267: *> \param[out] RCONDV
        !           268: *> \verbatim
        !           269: *>          RCONDV is DOUBLE PRECISION array, dimension (N)
        !           270: *>          If JOB = 'V' or 'B', the estimated reciprocal condition
        !           271: *>          numbers of the eigenvectors, stored in consecutive elements
        !           272: *>          of the array. If the eigenvalues cannot be reordered to
        !           273: *>          compute RCONDV(j), RCONDV(j) is set to 0; this can only occur
        !           274: *>          when the true value would be very small anyway.
        !           275: *>          If SENSE = 'N' or 'E', RCONDV is not referenced.
        !           276: *> \endverbatim
        !           277: *>
        !           278: *> \param[out] WORK
        !           279: *> \verbatim
        !           280: *>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
        !           281: *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
        !           282: *> \endverbatim
        !           283: *>
        !           284: *> \param[in] LWORK
        !           285: *> \verbatim
        !           286: *>          LWORK is INTEGER
        !           287: *>          The dimension of the array WORK. LWORK >= max(1,2*N).
        !           288: *>          If SENSE = 'E', LWORK >= max(1,4*N).
        !           289: *>          If SENSE = 'V' or 'B', LWORK >= max(1,2*N*N+2*N).
        !           290: *>
        !           291: *>          If LWORK = -1, then a workspace query is assumed; the routine
        !           292: *>          only calculates the optimal size of the WORK array, returns
        !           293: *>          this value as the first entry of the WORK array, and no error
        !           294: *>          message related to LWORK is issued by XERBLA.
        !           295: *> \endverbatim
        !           296: *>
        !           297: *> \param[out] RWORK
        !           298: *> \verbatim
        !           299: *>          RWORK is REAL array, dimension (lrwork)
        !           300: *>          lrwork must be at least max(1,6*N) if BALANC = 'S' or 'B',
        !           301: *>          and at least max(1,2*N) otherwise.
        !           302: *>          Real workspace.
        !           303: *> \endverbatim
        !           304: *>
        !           305: *> \param[out] IWORK
        !           306: *> \verbatim
        !           307: *>          IWORK is INTEGER array, dimension (N+2)
        !           308: *>          If SENSE = 'E', IWORK is not referenced.
        !           309: *> \endverbatim
        !           310: *>
        !           311: *> \param[out] BWORK
        !           312: *> \verbatim
        !           313: *>          BWORK is LOGICAL array, dimension (N)
        !           314: *>          If SENSE = 'N', BWORK is not referenced.
        !           315: *> \endverbatim
        !           316: *>
        !           317: *> \param[out] INFO
        !           318: *> \verbatim
        !           319: *>          INFO is INTEGER
        !           320: *>          = 0:  successful exit
        !           321: *>          < 0:  if INFO = -i, the i-th argument had an illegal value.
        !           322: *>          = 1,...,N:
        !           323: *>                The QZ iteration failed.  No eigenvectors have been
        !           324: *>                calculated, but ALPHA(j) and BETA(j) should be correct
        !           325: *>                for j=INFO+1,...,N.
        !           326: *>          > N:  =N+1: other than QZ iteration failed in ZHGEQZ.
        !           327: *>                =N+2: error return from ZTGEVC.
        !           328: *> \endverbatim
        !           329: *
        !           330: *  Authors:
        !           331: *  ========
        !           332: *
        !           333: *> \author Univ. of Tennessee 
        !           334: *> \author Univ. of California Berkeley 
        !           335: *> \author Univ. of Colorado Denver 
        !           336: *> \author NAG Ltd. 
        !           337: *
        !           338: *> \date November 2011
        !           339: *
        !           340: *> \ingroup complex16GEeigen
        !           341: *
        !           342: *> \par Further Details:
        !           343: *  =====================
        !           344: *>
        !           345: *> \verbatim
        !           346: *>
        !           347: *>  Balancing a matrix pair (A,B) includes, first, permuting rows and
        !           348: *>  columns to isolate eigenvalues, second, applying diagonal similarity
        !           349: *>  transformation to the rows and columns to make the rows and columns
        !           350: *>  as close in norm as possible. The computed reciprocal condition
        !           351: *>  numbers correspond to the balanced matrix. Permuting rows and columns
        !           352: *>  will not change the condition numbers (in exact arithmetic) but
        !           353: *>  diagonal scaling will.  For further explanation of balancing, see
        !           354: *>  section 4.11.1.2 of LAPACK Users' Guide.
        !           355: *>
        !           356: *>  An approximate error bound on the chordal distance between the i-th
        !           357: *>  computed generalized eigenvalue w and the corresponding exact
        !           358: *>  eigenvalue lambda is
        !           359: *>
        !           360: *>       chord(w, lambda) <= EPS * norm(ABNRM, BBNRM) / RCONDE(I)
        !           361: *>
        !           362: *>  An approximate error bound for the angle between the i-th computed
        !           363: *>  eigenvector VL(i) or VR(i) is given by
        !           364: *>
        !           365: *>       EPS * norm(ABNRM, BBNRM) / DIF(i).
        !           366: *>
        !           367: *>  For further explanation of the reciprocal condition numbers RCONDE
        !           368: *>  and RCONDV, see section 4.11 of LAPACK User's Guide.
        !           369: *> \endverbatim
        !           370: *>
        !           371: *  =====================================================================
1.1       bertrand  372:       SUBROUTINE ZGGEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, B, LDB,
                    373:      $                   ALPHA, BETA, VL, LDVL, VR, LDVR, ILO, IHI,
                    374:      $                   LSCALE, RSCALE, ABNRM, BBNRM, RCONDE, RCONDV,
                    375:      $                   WORK, LWORK, RWORK, IWORK, BWORK, INFO )
                    376: *
1.8     ! bertrand  377: *  -- LAPACK driver routine (version 3.4.0) --
1.1       bertrand  378: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                    379: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8     ! bertrand  380: *     November 2011
1.1       bertrand  381: *
                    382: *     .. Scalar Arguments ..
                    383:       CHARACTER          BALANC, JOBVL, JOBVR, SENSE
                    384:       INTEGER            IHI, ILO, INFO, LDA, LDB, LDVL, LDVR, LWORK, N
                    385:       DOUBLE PRECISION   ABNRM, BBNRM
                    386: *     ..
                    387: *     .. Array Arguments ..
                    388:       LOGICAL            BWORK( * )
                    389:       INTEGER            IWORK( * )
                    390:       DOUBLE PRECISION   LSCALE( * ), RCONDE( * ), RCONDV( * ),
                    391:      $                   RSCALE( * ), RWORK( * )
                    392:       COMPLEX*16         A( LDA, * ), ALPHA( * ), B( LDB, * ),
                    393:      $                   BETA( * ), VL( LDVL, * ), VR( LDVR, * ),
                    394:      $                   WORK( * )
                    395: *     ..
                    396: *
1.8     ! bertrand  397: *  =====================================================================
1.1       bertrand  398: *
                    399: *     .. Parameters ..
                    400:       DOUBLE PRECISION   ZERO, ONE
                    401:       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
                    402:       COMPLEX*16         CZERO, CONE
                    403:       PARAMETER          ( CZERO = ( 0.0D+0, 0.0D+0 ),
                    404:      $                   CONE = ( 1.0D+0, 0.0D+0 ) )
                    405: *     ..
                    406: *     .. Local Scalars ..
                    407:       LOGICAL            ILASCL, ILBSCL, ILV, ILVL, ILVR, LQUERY, NOSCL,
                    408:      $                   WANTSB, WANTSE, WANTSN, WANTSV
                    409:       CHARACTER          CHTEMP
                    410:       INTEGER            I, ICOLS, IERR, IJOBVL, IJOBVR, IN, IROWS,
                    411:      $                   ITAU, IWRK, IWRK1, J, JC, JR, M, MAXWRK, MINWRK
                    412:       DOUBLE PRECISION   ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS,
                    413:      $                   SMLNUM, TEMP
                    414:       COMPLEX*16         X
                    415: *     ..
                    416: *     .. Local Arrays ..
                    417:       LOGICAL            LDUMMA( 1 )
                    418: *     ..
                    419: *     .. External Subroutines ..
                    420:       EXTERNAL           DLABAD, DLASCL, XERBLA, ZGEQRF, ZGGBAK, ZGGBAL,
                    421:      $                   ZGGHRD, ZHGEQZ, ZLACPY, ZLASCL, ZLASET, ZTGEVC,
                    422:      $                   ZTGSNA, ZUNGQR, ZUNMQR
                    423: *     ..
                    424: *     .. External Functions ..
                    425:       LOGICAL            LSAME
                    426:       INTEGER            ILAENV
                    427:       DOUBLE PRECISION   DLAMCH, ZLANGE
                    428:       EXTERNAL           LSAME, ILAENV, DLAMCH, ZLANGE
                    429: *     ..
                    430: *     .. Intrinsic Functions ..
                    431:       INTRINSIC          ABS, DBLE, DIMAG, MAX, SQRT
                    432: *     ..
                    433: *     .. Statement Functions ..
                    434:       DOUBLE PRECISION   ABS1
                    435: *     ..
                    436: *     .. Statement Function definitions ..
                    437:       ABS1( X ) = ABS( DBLE( X ) ) + ABS( DIMAG( X ) )
                    438: *     ..
                    439: *     .. Executable Statements ..
                    440: *
                    441: *     Decode the input arguments
                    442: *
                    443:       IF( LSAME( JOBVL, 'N' ) ) THEN
                    444:          IJOBVL = 1
                    445:          ILVL = .FALSE.
                    446:       ELSE IF( LSAME( JOBVL, 'V' ) ) THEN
                    447:          IJOBVL = 2
                    448:          ILVL = .TRUE.
                    449:       ELSE
                    450:          IJOBVL = -1
                    451:          ILVL = .FALSE.
                    452:       END IF
                    453: *
                    454:       IF( LSAME( JOBVR, 'N' ) ) THEN
                    455:          IJOBVR = 1
                    456:          ILVR = .FALSE.
                    457:       ELSE IF( LSAME( JOBVR, 'V' ) ) THEN
                    458:          IJOBVR = 2
                    459:          ILVR = .TRUE.
                    460:       ELSE
                    461:          IJOBVR = -1
                    462:          ILVR = .FALSE.
                    463:       END IF
                    464:       ILV = ILVL .OR. ILVR
                    465: *
                    466:       NOSCL  = LSAME( BALANC, 'N' ) .OR. LSAME( BALANC, 'P' )
                    467:       WANTSN = LSAME( SENSE, 'N' )
                    468:       WANTSE = LSAME( SENSE, 'E' )
                    469:       WANTSV = LSAME( SENSE, 'V' )
                    470:       WANTSB = LSAME( SENSE, 'B' )
                    471: *
                    472: *     Test the input arguments
                    473: *
                    474:       INFO = 0
                    475:       LQUERY = ( LWORK.EQ.-1 )
                    476:       IF( .NOT.( NOSCL .OR. LSAME( BALANC,'S' ) .OR.
                    477:      $    LSAME( BALANC, 'B' ) ) ) THEN
                    478:          INFO = -1
                    479:       ELSE IF( IJOBVL.LE.0 ) THEN
                    480:          INFO = -2
                    481:       ELSE IF( IJOBVR.LE.0 ) THEN
                    482:          INFO = -3
                    483:       ELSE IF( .NOT.( WANTSN .OR. WANTSE .OR. WANTSB .OR. WANTSV ) )
                    484:      $          THEN
                    485:          INFO = -4
                    486:       ELSE IF( N.LT.0 ) THEN
                    487:          INFO = -5
                    488:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
                    489:          INFO = -7
                    490:       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
                    491:          INFO = -9
                    492:       ELSE IF( LDVL.LT.1 .OR. ( ILVL .AND. LDVL.LT.N ) ) THEN
                    493:          INFO = -13
                    494:       ELSE IF( LDVR.LT.1 .OR. ( ILVR .AND. LDVR.LT.N ) ) THEN
                    495:          INFO = -15
                    496:       END IF
                    497: *
                    498: *     Compute workspace
                    499: *      (Note: Comments in the code beginning "Workspace:" describe the
                    500: *       minimal amount of workspace needed at that point in the code,
                    501: *       as well as the preferred amount for good performance.
                    502: *       NB refers to the optimal block size for the immediately
                    503: *       following subroutine, as returned by ILAENV. The workspace is
                    504: *       computed assuming ILO = 1 and IHI = N, the worst case.)
                    505: *
                    506:       IF( INFO.EQ.0 ) THEN
                    507:          IF( N.EQ.0 ) THEN
                    508:             MINWRK = 1
                    509:             MAXWRK = 1
                    510:          ELSE
                    511:             MINWRK = 2*N
                    512:             IF( WANTSE ) THEN
                    513:                MINWRK = 4*N
                    514:             ELSE IF( WANTSV .OR. WANTSB ) THEN
                    515:                MINWRK = 2*N*( N + 1)
                    516:             END IF
                    517:             MAXWRK = MINWRK
                    518:             MAXWRK = MAX( MAXWRK,
                    519:      $                    N + N*ILAENV( 1, 'ZGEQRF', ' ', N, 1, N, 0 ) )
                    520:             MAXWRK = MAX( MAXWRK,
                    521:      $                    N + N*ILAENV( 1, 'ZUNMQR', ' ', N, 1, N, 0 ) )
                    522:             IF( ILVL ) THEN
                    523:                MAXWRK = MAX( MAXWRK, N +
                    524:      $                       N*ILAENV( 1, 'ZUNGQR', ' ', N, 1, N, 0 ) )
                    525:             END IF 
                    526:          END IF
                    527:          WORK( 1 ) = MAXWRK
                    528: *
                    529:          IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
                    530:             INFO = -25
                    531:          END IF
                    532:       END IF
                    533: *
                    534:       IF( INFO.NE.0 ) THEN
                    535:          CALL XERBLA( 'ZGGEVX', -INFO )
                    536:          RETURN
                    537:       ELSE IF( LQUERY ) THEN
                    538:          RETURN
                    539:       END IF
                    540: *
                    541: *     Quick return if possible
                    542: *
                    543:       IF( N.EQ.0 )
                    544:      $   RETURN
                    545: *
                    546: *     Get machine constants
                    547: *
                    548:       EPS = DLAMCH( 'P' )
                    549:       SMLNUM = DLAMCH( 'S' )
                    550:       BIGNUM = ONE / SMLNUM
                    551:       CALL DLABAD( SMLNUM, BIGNUM )
                    552:       SMLNUM = SQRT( SMLNUM ) / EPS
                    553:       BIGNUM = ONE / SMLNUM
                    554: *
                    555: *     Scale A if max element outside range [SMLNUM,BIGNUM]
                    556: *
                    557:       ANRM = ZLANGE( 'M', N, N, A, LDA, RWORK )
                    558:       ILASCL = .FALSE.
                    559:       IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
                    560:          ANRMTO = SMLNUM
                    561:          ILASCL = .TRUE.
                    562:       ELSE IF( ANRM.GT.BIGNUM ) THEN
                    563:          ANRMTO = BIGNUM
                    564:          ILASCL = .TRUE.
                    565:       END IF
                    566:       IF( ILASCL )
                    567:      $   CALL ZLASCL( 'G', 0, 0, ANRM, ANRMTO, N, N, A, LDA, IERR )
                    568: *
                    569: *     Scale B if max element outside range [SMLNUM,BIGNUM]
                    570: *
                    571:       BNRM = ZLANGE( 'M', N, N, B, LDB, RWORK )
                    572:       ILBSCL = .FALSE.
                    573:       IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN
                    574:          BNRMTO = SMLNUM
                    575:          ILBSCL = .TRUE.
                    576:       ELSE IF( BNRM.GT.BIGNUM ) THEN
                    577:          BNRMTO = BIGNUM
                    578:          ILBSCL = .TRUE.
                    579:       END IF
                    580:       IF( ILBSCL )
                    581:      $   CALL ZLASCL( 'G', 0, 0, BNRM, BNRMTO, N, N, B, LDB, IERR )
                    582: *
                    583: *     Permute and/or balance the matrix pair (A,B)
                    584: *     (Real Workspace: need 6*N if BALANC = 'S' or 'B', 1 otherwise)
                    585: *
                    586:       CALL ZGGBAL( BALANC, N, A, LDA, B, LDB, ILO, IHI, LSCALE, RSCALE,
                    587:      $             RWORK, IERR )
                    588: *
                    589: *     Compute ABNRM and BBNRM
                    590: *
                    591:       ABNRM = ZLANGE( '1', N, N, A, LDA, RWORK( 1 ) )
                    592:       IF( ILASCL ) THEN
                    593:          RWORK( 1 ) = ABNRM
                    594:          CALL DLASCL( 'G', 0, 0, ANRMTO, ANRM, 1, 1, RWORK( 1 ), 1,
                    595:      $                IERR )
                    596:          ABNRM = RWORK( 1 )
                    597:       END IF
                    598: *
                    599:       BBNRM = ZLANGE( '1', N, N, B, LDB, RWORK( 1 ) )
                    600:       IF( ILBSCL ) THEN
                    601:          RWORK( 1 ) = BBNRM
                    602:          CALL DLASCL( 'G', 0, 0, BNRMTO, BNRM, 1, 1, RWORK( 1 ), 1,
                    603:      $                IERR )
                    604:          BBNRM = RWORK( 1 )
                    605:       END IF
                    606: *
                    607: *     Reduce B to triangular form (QR decomposition of B)
                    608: *     (Complex Workspace: need N, prefer N*NB )
                    609: *
                    610:       IROWS = IHI + 1 - ILO
                    611:       IF( ILV .OR. .NOT.WANTSN ) THEN
                    612:          ICOLS = N + 1 - ILO
                    613:       ELSE
                    614:          ICOLS = IROWS
                    615:       END IF
                    616:       ITAU = 1
                    617:       IWRK = ITAU + IROWS
                    618:       CALL ZGEQRF( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ),
                    619:      $             WORK( IWRK ), LWORK+1-IWRK, IERR )
                    620: *
                    621: *     Apply the unitary transformation to A
                    622: *     (Complex Workspace: need N, prefer N*NB)
                    623: *
                    624:       CALL ZUNMQR( 'L', 'C', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB,
                    625:      $             WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWRK ),
                    626:      $             LWORK+1-IWRK, IERR )
                    627: *
                    628: *     Initialize VL and/or VR
                    629: *     (Workspace: need N, prefer N*NB)
                    630: *
                    631:       IF( ILVL ) THEN
                    632:          CALL ZLASET( 'Full', N, N, CZERO, CONE, VL, LDVL )
                    633:          IF( IROWS.GT.1 ) THEN
                    634:             CALL ZLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB,
                    635:      $                   VL( ILO+1, ILO ), LDVL )
                    636:          END IF
                    637:          CALL ZUNGQR( IROWS, IROWS, IROWS, VL( ILO, ILO ), LDVL,
                    638:      $                WORK( ITAU ), WORK( IWRK ), LWORK+1-IWRK, IERR )
                    639:       END IF
                    640: *
                    641:       IF( ILVR )
                    642:      $   CALL ZLASET( 'Full', N, N, CZERO, CONE, VR, LDVR )
                    643: *
                    644: *     Reduce to generalized Hessenberg form
                    645: *     (Workspace: none needed)
                    646: *
                    647:       IF( ILV .OR. .NOT.WANTSN ) THEN
                    648: *
                    649: *        Eigenvectors requested -- work on whole matrix.
                    650: *
                    651:          CALL ZGGHRD( JOBVL, JOBVR, N, ILO, IHI, A, LDA, B, LDB, VL,
                    652:      $                LDVL, VR, LDVR, IERR )
                    653:       ELSE
                    654:          CALL ZGGHRD( 'N', 'N', IROWS, 1, IROWS, A( ILO, ILO ), LDA,
                    655:      $                B( ILO, ILO ), LDB, VL, LDVL, VR, LDVR, IERR )
                    656:       END IF
                    657: *
                    658: *     Perform QZ algorithm (Compute eigenvalues, and optionally, the
                    659: *     Schur forms and Schur vectors)
                    660: *     (Complex Workspace: need N)
                    661: *     (Real Workspace: need N)
                    662: *
                    663:       IWRK = ITAU
                    664:       IF( ILV .OR. .NOT.WANTSN ) THEN
                    665:          CHTEMP = 'S'
                    666:       ELSE
                    667:          CHTEMP = 'E'
                    668:       END IF
                    669: *
                    670:       CALL ZHGEQZ( CHTEMP, JOBVL, JOBVR, N, ILO, IHI, A, LDA, B, LDB,
                    671:      $             ALPHA, BETA, VL, LDVL, VR, LDVR, WORK( IWRK ),
                    672:      $             LWORK+1-IWRK, RWORK, IERR )
                    673:       IF( IERR.NE.0 ) THEN
                    674:          IF( IERR.GT.0 .AND. IERR.LE.N ) THEN
                    675:             INFO = IERR
                    676:          ELSE IF( IERR.GT.N .AND. IERR.LE.2*N ) THEN
                    677:             INFO = IERR - N
                    678:          ELSE
                    679:             INFO = N + 1
                    680:          END IF
                    681:          GO TO 90
                    682:       END IF
                    683: *
                    684: *     Compute Eigenvectors and estimate condition numbers if desired
                    685: *     ZTGEVC: (Complex Workspace: need 2*N )
                    686: *             (Real Workspace:    need 2*N )
                    687: *     ZTGSNA: (Complex Workspace: need 2*N*N if SENSE='V' or 'B')
                    688: *             (Integer Workspace: need N+2 )
                    689: *
                    690:       IF( ILV .OR. .NOT.WANTSN ) THEN
                    691:          IF( ILV ) THEN
                    692:             IF( ILVL ) THEN
                    693:                IF( ILVR ) THEN
                    694:                   CHTEMP = 'B'
                    695:                ELSE
                    696:                   CHTEMP = 'L'
                    697:                END IF
                    698:             ELSE
                    699:                CHTEMP = 'R'
                    700:             END IF
                    701: *
                    702:             CALL ZTGEVC( CHTEMP, 'B', LDUMMA, N, A, LDA, B, LDB, VL,
                    703:      $                   LDVL, VR, LDVR, N, IN, WORK( IWRK ), RWORK,
                    704:      $                   IERR )
                    705:             IF( IERR.NE.0 ) THEN
                    706:                INFO = N + 2
                    707:                GO TO 90
                    708:             END IF
                    709:          END IF
                    710: *
                    711:          IF( .NOT.WANTSN ) THEN
                    712: *
                    713: *           compute eigenvectors (DTGEVC) and estimate condition
                    714: *           numbers (DTGSNA). Note that the definition of the condition
                    715: *           number is not invariant under transformation (u,v) to
                    716: *           (Q*u, Z*v), where (u,v) are eigenvectors of the generalized
                    717: *           Schur form (S,T), Q and Z are orthogonal matrices. In order
                    718: *           to avoid using extra 2*N*N workspace, we have to
                    719: *           re-calculate eigenvectors and estimate the condition numbers
                    720: *           one at a time.
                    721: *
                    722:             DO 20 I = 1, N
                    723: *
                    724:                DO 10 J = 1, N
                    725:                   BWORK( J ) = .FALSE.
                    726:    10          CONTINUE
                    727:                BWORK( I ) = .TRUE.
                    728: *
                    729:                IWRK = N + 1
                    730:                IWRK1 = IWRK + N
                    731: *
                    732:                IF( WANTSE .OR. WANTSB ) THEN
                    733:                   CALL ZTGEVC( 'B', 'S', BWORK, N, A, LDA, B, LDB,
                    734:      $                         WORK( 1 ), N, WORK( IWRK ), N, 1, M,
                    735:      $                         WORK( IWRK1 ), RWORK, IERR )
                    736:                   IF( IERR.NE.0 ) THEN
                    737:                      INFO = N + 2
                    738:                      GO TO 90
                    739:                   END IF
                    740:                END IF
                    741: *
                    742:                CALL ZTGSNA( SENSE, 'S', BWORK, N, A, LDA, B, LDB,
                    743:      $                      WORK( 1 ), N, WORK( IWRK ), N, RCONDE( I ),
                    744:      $                      RCONDV( I ), 1, M, WORK( IWRK1 ),
                    745:      $                      LWORK-IWRK1+1, IWORK, IERR )
                    746: *
                    747:    20       CONTINUE
                    748:          END IF
                    749:       END IF
                    750: *
                    751: *     Undo balancing on VL and VR and normalization
                    752: *     (Workspace: none needed)
                    753: *
                    754:       IF( ILVL ) THEN
                    755:          CALL ZGGBAK( BALANC, 'L', N, ILO, IHI, LSCALE, RSCALE, N, VL,
                    756:      $                LDVL, IERR )
                    757: *
                    758:          DO 50 JC = 1, N
                    759:             TEMP = ZERO
                    760:             DO 30 JR = 1, N
                    761:                TEMP = MAX( TEMP, ABS1( VL( JR, JC ) ) )
                    762:    30       CONTINUE
                    763:             IF( TEMP.LT.SMLNUM )
                    764:      $         GO TO 50
                    765:             TEMP = ONE / TEMP
                    766:             DO 40 JR = 1, N
                    767:                VL( JR, JC ) = VL( JR, JC )*TEMP
                    768:    40       CONTINUE
                    769:    50    CONTINUE
                    770:       END IF
                    771: *
                    772:       IF( ILVR ) THEN
                    773:          CALL ZGGBAK( BALANC, 'R', N, ILO, IHI, LSCALE, RSCALE, N, VR,
                    774:      $                LDVR, IERR )
                    775:          DO 80 JC = 1, N
                    776:             TEMP = ZERO
                    777:             DO 60 JR = 1, N
                    778:                TEMP = MAX( TEMP, ABS1( VR( JR, JC ) ) )
                    779:    60       CONTINUE
                    780:             IF( TEMP.LT.SMLNUM )
                    781:      $         GO TO 80
                    782:             TEMP = ONE / TEMP
                    783:             DO 70 JR = 1, N
                    784:                VR( JR, JC ) = VR( JR, JC )*TEMP
                    785:    70       CONTINUE
                    786:    80    CONTINUE
                    787:       END IF
                    788: *
                    789: *     Undo scaling if necessary
                    790: *
                    791:       IF( ILASCL )
                    792:      $   CALL ZLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHA, N, IERR )
                    793: *
                    794:       IF( ILBSCL )
                    795:      $   CALL ZLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR )
                    796: *
                    797:    90 CONTINUE
                    798:       WORK( 1 ) = MAXWRK
                    799: *
                    800:       RETURN
                    801: *
                    802: *     End of ZGGEVX
                    803: *
                    804:       END

CVSweb interface <joel.bertrand@systella.fr>