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/* ----------------------------------------------------------------------- *
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/* ----------------------------------------------------------------------- *
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 * This file is part of GEL, http://www.imm.dtu.dk/GEL
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 * This file is part of GEL, http://www.imm.dtu.dk/GEL
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 * Copyright (C) the authors and DTU Informatics
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 * Copyright (C) the authors and DTU Informatics
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 * For license and list of authors, see ../../doc/intro.pdf
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 * For license and list of authors, see ../../doc/intro.pdf
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 * ----------------------------------------------------------------------- */
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 * ----------------------------------------------------------------------- */
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#include "eigensolution.h"
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#include "eigensolution.h"
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#include "Mat2x2f.h"
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#include "Mat2x2f.h"
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#include "Mat3x3f.h"
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#include "Mat3x3f.h"
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#include "Mat4x4f.h"
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#include "Mat4x4f.h"
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#include "Mat2x2d.h"
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#include "Mat2x2d.h"
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#include "Mat3x3d.h"
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#include "Mat3x3d.h"
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#include "Mat4x4d.h"
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#include "Mat4x4d.h"
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#include <iostream>
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#include <iostream>
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using namespace std;
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using namespace std;
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namespace
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namespace
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{
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{
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    const unsigned int KMAX = 1000000;
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    const unsigned int KMAX = 1000000;
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    const double EV_THRESH = 1e-6;
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    const double EV_THRESH = 1e-6;
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}
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}
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namespace CGLA
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namespace CGLA
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{
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{
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    template <class MT>
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    template <class MT>
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    int power_eigensolution(const MT& Ap, MT& Q, MT& L, unsigned int max_sol)
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    int power_eigensolution(const MT& Ap, MT& Q, MT& L, unsigned int max_sol)
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    {
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    {
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        L = MT(0);
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        L = MT(0);
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        typedef typename MT::VectorType VT;
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        typedef typename MT::VectorType VT;
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        MT A = Ap;
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        MT A = Ap;
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        unsigned int n = s_min(MT::get_v_dim(), max_sol);
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        unsigned int n = s_min(MT::get_v_dim(), max_sol);
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        gel_srand(0);
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        gel_srand(0);
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        for(unsigned int i=0;i<n;++i)
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        for(unsigned int i=0;i<n;++i)
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        {
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        {
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            // Seed the eigenvector estimate
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            // Seed the eigenvector estimate
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            VT q;
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            VT q;
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            for (int j=0; j<MT::get_v_dim(); ++j)
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            for (size_t j=0; j<MT::get_v_dim(); ++j)
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                q[j] = gel_rand()/static_cast<double>(GEL_RAND_MAX);
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                q[j] = gel_rand()/static_cast<double>(GEL_RAND_MAX);
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            q.normalize();
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            q.normalize();
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            double l=123,l_old;
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            double l=123,l_old;
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            // As long as we haven't reached the max iterations and the
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            // As long as we haven't reached the max iterations and the
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            // eigenvalue has not converged, do
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            // eigenvalue has not converged, do
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            unsigned int k=0;
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            unsigned int k=0;
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            do
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            do
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            {
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            {
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                const VT z = A * q;
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                const VT z = A * q;
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                double z_len = length(z);
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                double z_len = length(z);
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                if(z_len < EV_THRESH) return i;
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                if(z_len < EV_THRESH) return i;
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                l_old = l;
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                l_old = l;
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                l = dot(q, z)>0 ? z_len : -z_len;
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                l = dot(q, z)>0 ? z_len : -z_len;
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                q = z/z_len;
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                q = z/z_len;
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                if(++k==KMAX)
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                if(++k==KMAX)
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                    return i;
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                    return i;
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            }
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            }
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            while((fabs(l-l_old) > fabs(EV_THRESH * l)) || k<2);
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            while((fabs(l-l_old) > fabs(EV_THRESH * l)) || k<2);
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            // Update the solution by adding the eigenvector to Q and
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            // Update the solution by adding the eigenvector to Q and
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            // the eigenvalue to the diagonal of L.
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            // the eigenvalue to the diagonal of L.
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            Q[i] = q;
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            Q[i] = q;
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            L[i][i] = l;
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            L[i][i] = l;
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            // Update A by subtracting the subspace represented by the
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            // Update A by subtracting the subspace represented by the
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            // eigensolution just found. This is called the method of
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            // eigensolution just found. This is called the method of
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            // deflation.
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            // deflation.
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            MT B;
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            MT B;
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            outer_product(q,q,B);
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            outer_product(q,q,B);
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            A = A - l * B;
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            A = A - l * B;
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        }
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        }
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        return n;
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        return n;
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    }
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    }
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    /* There is no reason to put this template in a header file, since
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    /* There is no reason to put this template in a header file, since
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     we will only use it on matrices defined in CGLA. Instead, we
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     we will only use it on matrices defined in CGLA. Instead, we
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     explicitly instantiate the function for the square matrices
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     explicitly instantiate the function for the square matrices
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     of CGLA */
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     of CGLA */
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    template int power_eigensolution<Mat2x2f>(const Mat2x2f&,
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    template int power_eigensolution<Mat2x2f>(const Mat2x2f&,
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                                              Mat2x2f&,Mat2x2f&,unsigned int);
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                                              Mat2x2f&,Mat2x2f&,unsigned int);
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    template int power_eigensolution<Mat3x3f>(const Mat3x3f&,
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    template int power_eigensolution<Mat3x3f>(const Mat3x3f&,
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                                              Mat3x3f&,Mat3x3f&,unsigned int);
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                                              Mat3x3f&,Mat3x3f&,unsigned int);
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    template int power_eigensolution<Mat4x4f>(const Mat4x4f&,
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    template int power_eigensolution<Mat4x4f>(const Mat4x4f&,
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                                              Mat4x4f&,Mat4x4f&,unsigned int);
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                                              Mat4x4f&,Mat4x4f&,unsigned int);
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    template int power_eigensolution<Mat2x2d>(const Mat2x2d&,
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    template int power_eigensolution<Mat2x2d>(const Mat2x2d&,
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                                              Mat2x2d&,Mat2x2d&,unsigned int);
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                                              Mat2x2d&,Mat2x2d&,unsigned int);
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    template int power_eigensolution<Mat3x3d>(const Mat3x3d&,
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    template int power_eigensolution<Mat3x3d>(const Mat3x3d&,
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                                              Mat3x3d&,Mat3x3d&,unsigned int);
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                                              Mat3x3d&,Mat3x3d&,unsigned int);
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    template int power_eigensolution<Mat4x4d>(const Mat4x4d&,
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    template int power_eigensolution<Mat4x4d>(const Mat4x4d&,
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                                              Mat4x4d&,Mat4x4d&,unsigned int);
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                                              Mat4x4d&,Mat4x4d&,unsigned int);
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}
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}
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