cgeev.f(3)

NAME
cgeev.f -

SYNOPSIS

  Functions/Subroutines

subroutine cgeev (JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO)
CGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

Function/Subroutine Documentation

  subroutine cgeev (characterJOBVL, characterJOBVR, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension( * )W, complex, dimension( ldvl, * )VL, integerLDVL, complex, dimension( ldvr, * )VR, integerLDVR, complex, dimension( * )WORK, integerLWORK, real, dimension( * )RWORK, integerINFO)

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

Purpose:

     CGEEV computes for an N-by-N complex nonsymmetric matrix A, the
     eigenvalues and, optionally, the left and/or right eigenvectors.

     The right eigenvector v(j) of A satisfies
                      A * v(j) = lambda(j) * v(j)
     where lambda(j) is its eigenvalue.
     The left eigenvector u(j) of A satisfies
                   u(j)**H * A = lambda(j) * u(j)**H
     where u(j)**H denotes the conjugate transpose of u(j).

     The computed eigenvectors are normalized to have Euclidean norm
     equal to 1 and largest component real.

Parameters:
    JOBVL

              JOBVL is CHARACTER*1
              = 'N': left eigenvectors of A are not computed;
              = 'V': left eigenvectors of are computed.

    JOBVR

              JOBVR is CHARACTER*1
              = 'N': right eigenvectors of A are not computed;
              = 'V': right eigenvectors of A are computed.

    N

              N is INTEGER
              The order of the matrix A. N >= 0.

    A

              A is COMPLEX array, dimension (LDA,N)
              On entry, the N-by-N matrix A.
              On exit, A has been overwritten.

    LDA

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

    W

              W is COMPLEX array, dimension (N)
              W contains the computed eigenvalues.

    VL

              VL is COMPLEX array, dimension (LDVL,N)
              If JOBVL = 'V', the left eigenvectors u(j) are stored one
              after another in the columns of VL, in the same order
              as their eigenvalues.
              If JOBVL = 'N', VL is not referenced.
              u(j) = VL(:,j), the j-th column of VL.

    LDVL

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

    VR

              VR is COMPLEX array, dimension (LDVR,N)
              If JOBVR = 'V', the right eigenvectors v(j) are stored one
              after another in the columns of VR, in the same order
              as their eigenvalues.
              If JOBVR = 'N', VR is not referenced.
              v(j) = VR(:,j), the j-th column of VR.

    LDVR

              LDVR is INTEGER
              The leading dimension of the array VR.  LDVR >= 1; 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.

              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 (2*N)

    INFO

              INFO is INTEGER
              = 0:  successful exit
              < 0:  if INFO = -i, the i-th argument had an illegal value.
              > 0:  if INFO = i, the QR algorithm failed to compute all the
                    eigenvalues, and no eigenvectors have been computed;
                    elements and i+1:N of W contain eigenvalues which have
                    converged.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2011

Definition at line 177 of file cgeev.f.

Author

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