dlib C++ Library - geev.h

    // Copyright (C) 2010  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #ifndef DLIB_LAPACk_GEEV_Hh_
    #define DLIB_LAPACk_GEEV_Hh_

    #include "fortran_id.h"
    #include "../matrix.h"

    namespace dlib
    {
        namespace lapack
        {
            namespace binding
            {
                extern "C"
                {
                    void DLIB_FORTRAN_ID(dgeev) (const char *jobvl, const char *jobvr, const integer *n, double * a,
                                                 const integer *lda, double *wr, double *wi, double *vl,
                                                 const integer *ldvl, double *vr, const integer *ldvr, double *work,
                                                 const integer *lwork, integer *info);

                    void DLIB_FORTRAN_ID(sgeev) (const char *jobvl, const char *jobvr, const integer *n, float * a,
                                                 const integer *lda, float *wr, float *wi, float *vl,
                                                 const integer *ldvl, float *vr, const integer *ldvr, float *work,
                                                 const integer *lwork, integer *info);

                }

                inline int geev (char jobvl, char jobvr, integer n, double *a,
                                 integer lda, double *wr, double *wi, double *vl,
                                 integer ldvl, double *vr, integer ldvr, double *work,
                                 integer lwork)
                {
                    integer info = 0;
                    DLIB_FORTRAN_ID(dgeev)(&jobvl, &jobvr, &n, a,
                                           &lda, wr, wi, vl,
                                           &ldvl, vr, &ldvr, work,
                                           &lwork, &info);
                    return info;
                }

                inline int geev (char jobvl, char jobvr, integer n, float *a,
                                 integer lda, float *wr, float *wi, float *vl,
                                 integer ldvl, float *vr, integer ldvr, float *work,
                                 integer lwork)
                {
                    integer info = 0;
                    DLIB_FORTRAN_ID(sgeev)(&jobvl, &jobvr, &n, a,
                                           &lda, wr, wi, vl,
                                           &ldvl, vr, &ldvr, work,
                                           &lwork, &info);
                    return info;
                }

            }

        // ------------------------------------------------------------------------------------

    /*  -- LAPACK driver routine (version 3.1) -- */
    /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
    /*     November 2006 */

    /*     .. Scalar Arguments .. */
    /*     .. */
    /*     .. Array Arguments .. */
    /*     .. */

    /*  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)**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. */

    /*  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. */

        // ------------------------------------------------------------------------------------

            template <
                typename T,
                long NR1, long NR2, long NR3, long NR4, long NR5,
                long NC1, long NC2, long NC3, long NC4, long NC5,
                typename MM,
                typename layout
                >
            int geev (
                const char jobvl,
                const char jobvr,
                matrix<T,NR1,NC1,MM,column_major_layout>& a,
                matrix<T,NR2,NC2,MM,layout>& wr,
                matrix<T,NR3,NC3,MM,layout>& wi,
                matrix<T,NR4,NC4,MM,column_major_layout>& vl,
                matrix<T,NR5,NC5,MM,column_major_layout>& vr
            )
            {
                matrix<T,0,1,MM,column_major_layout> work;

                const long n = a.nr();

                wr.set_size(n,1);
                wi.set_size(n,1);

                if (jobvl == 'V')
                    vl.set_size(n,n);
                else
                    vl.set_size(NR4?NR4:1, NC4?NC4:1);

                if (jobvr == 'V')
                    vr.set_size(n,n);
                else
                    vr.set_size(NR5?NR5:1, NC5?NC5:1);

                // figure out how big the workspace needs to be.
                T work_size = 1;
                int info = binding::geev(jobvl, jobvr, n, &a(0,0),
                                         a.nr(), &wr(0,0), &wi(0,0), &vl(0,0),
                                         vl.nr(), &vr(0,0), vr.nr(), &work_size,
                                         -1);

                if (info != 0)
                    return info;

                if (work.size() < work_size)
                    work.set_size(static_cast<long>(work_size), 1);

                // compute the actual decomposition
                info = binding::geev(jobvl, jobvr, n, &a(0,0),
                                     a.nr(), &wr(0,0), &wi(0,0), &vl(0,0),
                                     vl.nr(), &vr(0,0), vr.nr(), &work(0,0),
                                     work.size());

                return info;
            }

        // ------------------------------------------------------------------------------------

        }

    }

    // ----------------------------------------------------------------------------------------

    #endif // DLIB_LAPACk_GEEV_Hh_