ESMF_DGEEV Subroutine

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

\brief ESMF_DGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices \htmlonly Download ESMF_DGEEV + dependencies [TGZ] [ZIP] [TXT] \endhtmlonly \par Purpose:

\verbatim

ESMF_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)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. \endverbatim \param[in] JOBVL \verbatim JOBVL is CHARACTER*1 = ‘N’: left eigenvectors of A are not computed; = ‘V’: left eigenvectors of A are computed. \endverbatim

\param[in] JOBVR \verbatim JOBVR is CHARACTER*1 = ‘N’: right eigenvectors of A are not computed; = ‘V’: right eigenvectors of A are computed. \endverbatim

\param[in] N \verbatim N is INTEGER The order of the matrix A. N >= 0. \endverbatim

\param[in,out] A \verbatim A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the N-by-N matrix A. On exit, A has been overwritten. \endverbatim

\param[in] LDA \verbatim LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). \endverbatim

\param[out] WR \verbatim WR is DOUBLE PRECISION array, dimension (N) \endverbatim

\param[out] WI \verbatim WI is 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. \endverbatim

\param[out] VL \verbatim VL is 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) + iVL(:,j+1) and u(j+1) = VL(:,j) - iVL(:,j+1). \endverbatim

\param[in] LDVL \verbatim LDVL is INTEGER The leading dimension of the array VL. LDVL >= 1; if JOBVL = ‘V’, LDVL >= N. \endverbatim

\param[out] VR \verbatim VR is 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) + iVR(:,j+1) and v(j+1) = VR(:,j) - iVR(:,j+1). \endverbatim

\param[in] LDVR \verbatim LDVR is INTEGER The leading dimension of the array VR. LDVR >= 1; if JOBVR = ‘V’, LDVR >= N. \endverbatim

\param[out] WORK \verbatim WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. \endverbatim

\param[in] LWORK \verbatim LWORK is INTEGER The dimension of the array WORK. LWORK >= max(1,3N), and if JOBVL = ‘V’ or JOBVR = ‘V’, LWORK >= 4N. 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 ESMF_XERBLA.

\endverbatim

\param[out] INFO \verbatim 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. \endverbatim \author Univ. of Tennessee \author Univ. of California Berkeley \author Univ. of Colorado Denver \author NAG Ltd. \date June 2016 \ingroup doubleGEeigen

Arguments