cgegv.f(3)

NAME
cgegv.f -

SYNOPSIS

  Functions/Subroutines
subroutine CGEGV (JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO)
CGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

Function/Subroutine Documentation

  subroutine CGEGV (CHARACTERJOBVL, CHARACTERJOBVR, INTEGERN, COMPLEX, dimension( lda, * )A, INTEGERLDA, COMPLEX, dimension( ldb, * )B, INTEGERLDB, COMPLEX, dimension( * )ALPHA, COMPLEX, dimension( * )BETA, COMPLEX, dimension( ldvl, * )VL, INTEGERLDVL, COMPLEX, dimension( ldvr, * )VR, INTEGERLDVR, COMPLEX, dimension( * )WORK, INTEGERLWORK, REAL, dimension( * )RWORK, INTEGERINFO)

CGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

Purpose:

     This routine is deprecated and has been replaced by routine CGGEV.
     CGEGV computes the eigenvalues and, optionally, the left and/or right
     eigenvectors of a complex matrix pair (A,B).
     Given two square matrices A and B,
     the generalized nonsymmetric eigenvalue problem (GNEP) is to find the
     eigenvalues lambda and corresponding (non-zero) eigenvectors x such
     that
        A*x = lambda*B*x.
     An alternate form is to find the eigenvalues mu and corresponding
     eigenvectors y such that
        mu*A*y = B*y.
     These two forms are equivalent with mu = 1/lambda and x = y if
     neither lambda nor mu is zero.  In order to deal with the case that
     lambda or mu is zero or small, two values alpha and beta are returned
     for each eigenvalue, such that lambda = alpha/beta and
     mu = beta/alpha.

     The vectors x and y in the above equations are right eigenvectors of
     the matrix pair (A,B).  Vectors u and v satisfying
        u**H*A = lambda*u**H*B  or  mu*v**H*A = v**H*B
     are left eigenvectors of (A,B).
     Note: this routine performs "full balancing" on A and B

Parameters:
    JOBVL

              JOBVL is CHARACTER*1
              = 'N':  do not compute the left generalized eigenvectors;
              = 'V':  compute the left generalized eigenvectors (returned
                      in VL).

    JOBVR

              JOBVR is CHARACTER*1
              = 'N':  do not compute the right generalized eigenvectors;
              = 'V':  compute the right generalized eigenvectors (returned
                      in VR).

    N

              N is INTEGER
              The order of the matrices A, B, VL, and VR.  N >= 0.

    A

              A is COMPLEX array, dimension (LDA, N)
              On entry, the matrix A.
              If JOBVL = 'V' or JOBVR = 'V', then on exit A
              contains the Schur form of A from the generalized Schur
              factorization of the pair (A,B) after balancing.  If no
              eigenvectors were computed, then only the diagonal elements
              of the Schur form will be correct.  See CGGHRD and CHGEQZ
              for details.

    LDA

              LDA is INTEGER
              The leading dimension of A.  LDA >= max(1,N).

    B

              B is COMPLEX array, dimension (LDB, N)
              On entry, the matrix B.
              If JOBVL = 'V' or JOBVR = 'V', then on exit B contains the
              upper triangular matrix obtained from B in the generalized
              Schur factorization of the pair (A,B) after balancing.
              If no eigenvectors were computed, then only the diagonal
              elements of B will be correct.  See CGGHRD and CHGEQZ for
              details.

    LDB

              LDB is INTEGER
              The leading dimension of B.  LDB >= max(1,N).

    ALPHA

              ALPHA is COMPLEX array, dimension (N)
              The complex scalars alpha that define the eigenvalues of
              GNEP.

    BETA

              BETA is COMPLEX array, dimension (N)
              The complex scalars beta that define the eigenvalues of GNEP.

              Together, the quantities alpha = ALPHA(j) and beta = BETA(j)
              represent the j-th eigenvalue of the matrix pair (A,B), in
              one of the forms lambda = alpha/beta or mu = beta/alpha.
              Since either lambda or mu may overflow, they should not,
              in general, be computed.

    VL

              VL is COMPLEX array, dimension (LDVL,N)
              If JOBVL = 'V', the left eigenvectors u(j) are stored
              in the columns of VL, in the same order as their eigenvalues.
              Each eigenvector is scaled so that its largest component has
              abs(real part) + abs(imag. part) = 1, except for eigenvectors
              corresponding to an eigenvalue with alpha = beta = 0, which
              are set to zero.
              Not referenced if JOBVL = 'N'.

    LDVL

              LDVL is INTEGER
              The leading dimension of the matrix VL. LDVL >= 1, and
              if JOBVL = 'V', LDVL >= N.

    VR

              VR is COMPLEX array, dimension (LDVR,N)
              If JOBVR = 'V', the right eigenvectors x(j) are stored
              in the columns of VR, in the same order as their eigenvalues.
              Each eigenvector is scaled so that its largest component has
              abs(real part) + abs(imag. part) = 1, except for eigenvectors
              corresponding to an eigenvalue with alpha = beta = 0, which
              are set to zero.
              Not referenced if JOBVR = 'N'.

    LDVR

              LDVR is INTEGER
              The leading dimension of the matrix VR. LDVR >= 1, and
              if JOBVR = 'V', LDVR >= N.

    WORK

              WORK is COMPLEX array, dimension (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK.  LWORK >= max(1,2*N).
              For good performance, LWORK must generally be larger.
              To compute the optimal value of LWORK, call ILAENV to get
              blocksizes (for CGEQRF, CUNMQR, and CUNGQR.)  Then compute:
              NB  -- MAX of the blocksizes for CGEQRF, CUNMQR, and CUNGQR;
              The optimal LWORK is  MAX( 2*N, N*(NB+1) ).
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the WORK array, returns
              this value as the first entry of the WORK array, and no error
              message related to LWORK is issued by XERBLA.

    RWORK

              RWORK is REAL array, dimension (8*N)

    INFO

              INFO is INTEGER
              = 0:  successful exit
              < 0:  if INFO = -i, the i-th argument had an illegal value.
              =1,...,N:
                    The QZ iteration failed.  No eigenvectors have been
                    calculated, but ALPHA(j) and BETA(j) should be
                    correct for j=INFO+1,...,N.
              > N:  errors that usually indicate LAPACK problems:
                    =N+1: error return from CGGBAL
                    =N+2: error return from CGEQRF
                    =N+3: error return from CUNMQR
                    =N+4: error return from CUNGQR
                    =N+5: error return from CGGHRD
                    =N+6: error return from CHGEQZ (other than failed
                                                   iteration)
                    =N+7: error return from CTGEVC
                    =N+8: error return from CGGBAK (computing VL)
                    =N+9: error return from CGGBAK (computing VR)
                    =N+10: error return from CLASCL (various calls)

Author:
    Univ'. of Tennessee

    Univ'. of California Berkeley

    Univ'. of Colorado Denver

    NAG Ltd'.

Date:
    November 2011

Further Details:

      Balancing
      ---------
      This driver calls CGGBAL to both permute and scale rows and columns
      of A and B.  The permutations PL and PR are chosen so that PL*A*PR
      and PL*B*R will be upper triangular except for the diagonal blocks
      A(i:j,i:j) and B(i:j,i:j), with i and j as close together as
      possible.  The diagonal scaling matrices DL and DR are chosen so
      that the pair  DL*PL*A*PR*DR, DL*PL*B*PR*DR have elements close to
      one (except for the elements that start out zero.)
      After the eigenvalues and eigenvectors of the balanced matrices
      have been computed, CGGBAK transforms the eigenvectors back to what
      they would have been (in perfect arithmetic) if they had not been
      balanced.
      Contents of A and B on Exit
      -------- -- - --- - -- ----
      If any eigenvectors are computed (either JOBVL='V' or JOBVR='V' or
      both), then on exit the arrays A and B will contain the complex Schur
      form[*] of the "balanced" versions of A and B.  If no eigenvectors
      are computed, then only the diagonal blocks will be correct.
      [*] In other words, upper triangular form.

Definition at line 282 of file cgegv.f'.

Author

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