Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  computes  for  an  N-by-N  real  nonsymmetric  matrix A, the eigenvalues and,
       optionally, the left and/or right eigenvectors

SYNOPSIS

       SUBROUTINE DGEEV( JOBVL, JOBVR, N, A, LDA, WR, WI, VL, LDVL, VR, LDVR, WORK, LWORK, INFO )

           CHARACTER     JOBVL, JOBVR

           INTEGER       INFO, LDA, LDVL, LDVR, LWORK, N

           DOUBLE        PRECISION A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ), WI( * ), WORK( * ),
                         WR( * )

PURPOSE

       DGEEV  computes for an N-by-N real 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)**T * A = lambda(j) * u(j)**T
        where u(j)**T denotes the transpose of u(j).
        The computed eigenvectors are normalized to have Euclidean norm
        equal to 1 and largest component real.

ARGUMENTS

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

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

        N       (input) INTEGER
                The order of the matrix A. N >= 0.

        A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
                On entry, the N-by-N matrix A.
                On exit, A has been overwritten.

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

        WR      (output) DOUBLE PRECISION array, dimension (N)
                WI      (output) DOUBLE PRECISION array, dimension (N)
                WR and WI contain the real and imaginary parts,
                respectively, of the computed eigenvalues.  Complex
                conjugate pairs of eigenvalues appear consecutively
                with the eigenvalue having the positive imaginary part
                first.

        VL      (output) DOUBLE PRECISION 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.
                If the j-th eigenvalue is real, then u(j) = VL(:,j),
                the j-th column of VL.
                If the j-th and (j+1)-st eigenvalues form a complex
                conjugate pair, then u(j) = VL(:,j) + i*VL(:,j+1) and
                u(j+1) = VL(:,j) - i*VL(:,j+1).

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

        VR      (output) DOUBLE PRECISION 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.
                If the j-th eigenvalue is real, then v(j) = VR(:,j),
                the j-th column of VR.
                If the j-th and (j+1)-st eigenvalues form a complex
                conjugate pair, then v(j) = VR(:,j) + i*VR(:,j+1) and
                v(j+1) = VR(:,j) - i*VR(:,j+1).

        LDVR    (input) INTEGER
                The leading dimension of the array VR.  LDVR >= 1; if
                JOBVR = 'V', LDVR >= N.

        WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
                On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

        LWORK   (input) INTEGER
                The dimension of the array WORK.  LWORK >= max(1,3*N), and
                if JOBVL = 'V' or JOBVR = 'V', LWORK >= 4*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.

        INFO    (output) 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 i+1:N of WR and WI contain eigenvalues which
                have converged.

 LAPACK driver routine (version 3.3.1)      April 2011                             DGEEV(3lapack)