NAME

       sgeev.f -

SYNOPSIS

   Functions/Subroutines
       subroutine sgeev (JOBVL, JOBVR, N, A, LDA, WR, WI, VL, LDVL, VR, LDVR, WORK, LWORK, INFO)
            SGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors
           for GE matrices

Function/Subroutine Documentation

   subroutine sgeev (characterJOBVL, characterJOBVR, integerN, real, dimension( lda, * )A,
       integerLDA, real, dimension( * )WR, real, dimension( * )WI, real, dimension( ldvl, * )VL,
       integerLDVL, real, dimension( ldvr, * )VR, integerLDVR, real, dimension( * )WORK,
       integerLWORK, integerINFO)
        SGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE
       matrices

       Purpose:

            SGEEV 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)**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 A 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 REAL 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).

           WR

                     WR is REAL array, dimension (N)

           WI

                     WI is REAL 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

                     VL is REAL 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

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

           VR

                     VR is REAL 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

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

           WORK

                     WORK is REAL 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(1,3*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

                     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 i+1:N of WR and WI contain eigenvalues which
                           have converged.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

       Definition at line 189 of file sgeev.f.

Author

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