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lyapunovfunction.cpp
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lyapunovfunction.cpp
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/* LyapXool – V3: Quadratic optimisations, is a program to compute Complete Lyapunov functions for dynamical systems described by non linear autonomous ordinary differential equations.
-> This is a free software; you can redistribute it and/or
-> modify it under the terms of the GNU General Public License
-> as published by the Free Software Foundation; either version 3
-> of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
-> but WITHOUT ANY WARRANTY; without even the implied warranty of
-> MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-> GNU General Public License for more details.
You should have received a copy of the GNU General Public License
-> along with this program. If not, see <http://www.gnu.org/licenses/>.
Author and main maintainer: Carlos Argáez
-> Bibliography attached to the corresponding publication.
*/
#include <math.h>
#include <iostream>
#include <iomanip>
#include <fstream>
#include <sstream>
#include <armadillo>
#include <fstream>
#include <list>
#include <gsl/gsl_math.h>
#include <gsl/gsl_eigen.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_qp.h>
#include <string>
#include "RBF.hpp"
#include "instructions.hpp"
#include "odesystem.hpp"
#include "wendland.hpp"
#include <numeric>
#include "generalities.hpp"
#include "lyapunovfunction.hpp"
#if defined(_OPENMP)
#include <omp.h>
#endif
using namespace arma;
using namespace std;
using namespace glovar;
arma::span const All=span::all;
LYAPUNOV::LYAPUNOV(int totaliterations, int ode_dimension, double cart_grid_density, int l, int k, double c, int points_directional, double critval, bool normal, bool printing, std::ofstream &outputf){
this->totaliterations=totaliterations;
this->ode_dimension=ode_dimension;
this->cart_grid_density=cart_grid_density;
this->l=l;
this->k=k;
this->c=c;
this->points_directional=points_directional;
this->critval=critval;
this->normal=normal;
this->printing=printing;
this->outputf=&outputf;
}
void LYAPUNOV::lyapequation(int currentiteration, RBFMETHOD &rbf)
{
wall_clock timer;
int maxbet=(int)rbf.collocationpoints.n_rows;
betaod.set_size(maxbet);
timer.tic();
switch (glovar::method_type){
case glovar::choose_the_method::minusone:
if(currentiteration==0)
{
rbf.choldecom();
rbf.Amat.clear();
try {
betaod=solve(trimatu(rbf.R), solve(trimatl(trimatu(rbf.R).t()), rbf.alphavector),solve_opts::fast);
} catch (const std::exception& balam){
*outputf << "Something has happened while solving the Lyapunov equation to get the beta vector." << endl;
*outputf << __FILE__ << endl;
*outputf << __LINE__ << endl;
}
}else{
try {
betaod=solve(trimatu(rbf.R), solve(trimatl(trimatu(rbf.R).t()), rbf.alphavector),solve_opts::fast);
} catch (const std::exception& balam){
*outputf << "Something has happened while solving the Lyapunov equation to get the beta vector." << endl;
*outputf << __FILE__ << endl;
*outputf << __LINE__ << endl;
}
}
break;
case glovar::choose_the_method::op:
quadraticoptimization(rbf);
rbf.Amat.clear();
break;
case glovar::choose_the_method::fpop:
quadratic_fixedpoint(rbf);
rbf.Amat.clear();
break;
default:
*outputf << "METHOD: THIS HAS NOT BEEN ASSIGNED" <<endl;
exit(9);
}
*outputf
<< "\n"
<< endl;
*outputf
<< left
<< setw(51)
<< "The whole procedure to solve the Lyapunov equation at iteration "
<< left
<< setw(2)
<< currentiteration
<< left
<< setw(5)
<< "lasted "
<< right
<< setw(15)
<< setprecision(9)
<< std::fixed
<< timer.toc()
<< left
<< setw(5)
<< "s"
<< left
<< setw(5)
<< printhour()
<< endl;
if(printing)
{
printall("betavector", currentiteration, betaod);
}
}
void LYAPUNOV::quadraticoptimization(RBFMETHOD &rbf)
{
wall_clock timer, timeramat;
timer.tic();
int totalmatrixlength=(int)rbf.collocationpoints.n_rows;
int totalwidthlength=(int)rbf.collocationpoints.n_cols;
rbf.Amat*=2.0;
Row <double> tentativeq(totalmatrixlength);
tentativeq.zeros();
for(int j=0; j<totalmatrixlength; ++j)
{
for(int i=0; i<totalmatrixlength; ++i)
{
tentativeq(i)+=rbf.Amat(i,j)*pow(rbf.alpha,totalwidthlength);
}
}
tentativeq=tentativeq/totalmatrixlength;
gsl_vector *a=gsl_vector_alloc(totalmatrixlength);
for(int j=0; j<totalmatrixlength; ++j)
{
gsl_vector_set(a,j, tentativeq(j));
}
gsl_matrix *C=gsl_matrix_alloc(totalmatrixlength,totalmatrixlength);
gsl_vector *b=gsl_vector_alloc(totalmatrixlength);
gsl_vector *x=gsl_vector_alloc(totalmatrixlength);
double f;
gsl_matrix_view G
= gsl_matrix_view_array(rbf.Amat.memptr(), totalmatrixlength, totalmatrixlength);
void *work = malloc (gsl_qp_work_size (x->size));
gsl_vector_set_zero(b);
for(int i=0; i<totalmatrixlength; ++i)
{
for(int j=0; j<totalmatrixlength; ++j)
{
gsl_matrix_set(C,i,j, -1.0*gsl_matrix_get(&G.matrix, i, j));
}
}
timeramat.tic();
try {
gsl_qp_solve (CblasNoTrans, CblasNoTrans, &G.matrix, a, C, b, NULL, NULL, x, &f, work);
} catch (const std::exception& balam){
*outputf << "Something has happened while solving the quadratic optimisation." << endl;
*outputf << __FILE__ << endl;
*outputf << __LINE__ << endl;
}
*outputf
<< left
<< setw(65)
<< "Procedure to quadratically optimising "
<< right
<< setw(15)
<< setprecision(9)
<< std::fixed
<< timeramat.toc()
<< left
<< setw(5)
<< "s"
<< left
<< setw(5)
<< printhour()
<< endl;
for(int j=0; j<totalmatrixlength; ++j)
{
betaod(j)=gsl_vector_get(x, j);
}
gsl_vector_free(a);
gsl_matrix_free(C);
gsl_vector_free(b);
gsl_vector_free(x);
free (work);
*outputf
<< left
<< setw(65)
<< "Procedure to construct the input and quadratically optimised it "
<< right
<< setw(0)
<< setprecision(9)
<< std::fixed
<< timer.toc()
<< left
<< setw(5)
<< "s"
<< left
<< setw(5)
<< printhour()
<< endl;
}
void LYAPUNOV::quadratic_fixedpoint(RBFMETHOD &rbf)
{
wall_clock timer, timeramat;
int totalmatrixlength=(int)rbf.collocationpoints.n_rows;
int firstlength=(int)rbf.fix_points.n_rows;
int secondlength=(int)(totalmatrixlength-firstlength);
rbf.Amat*=2.0;
gsl_matrix_view G
= gsl_matrix_view_array(rbf.Amat.memptr(), totalmatrixlength, totalmatrixlength);
gsl_vector *a=gsl_vector_alloc(totalmatrixlength);
gsl_matrix *C=gsl_matrix_alloc(secondlength,totalmatrixlength);
gsl_vector *b=gsl_vector_alloc(secondlength);
gsl_matrix *CE=gsl_matrix_alloc(firstlength,totalmatrixlength);
gsl_vector *be=gsl_vector_alloc(firstlength);
gsl_vector *x=gsl_vector_alloc(totalmatrixlength);
double f;
void *work = malloc(gsl_qp_work_size(x->size));
gsl_vector_set_zero(b);
gsl_vector_set_all(be, -1.0);
gsl_vector_set_zero(a);
for(int i=0; i<firstlength; ++i)
{
for(int j=0; j<totalmatrixlength; ++j)
{
gsl_matrix_set(CE,i,j, gsl_matrix_get(&G.matrix, i, j));
}
}
for(int i=0; i<secondlength; ++i)
{
for(int j=0; j<totalmatrixlength; ++j)
{
gsl_matrix_set(C,i,j, -1.0*gsl_matrix_get(&G.matrix, firstlength+i, j));
}
}
timeramat.tic();
try {
gsl_qp_solve(CblasNoTrans, CblasNoTrans, &G.matrix, a, C, b, CE, be, x, &f, work);
} catch (const std::exception& balam){
*outputf << "Something has happened while solving the quadratic optimisation." << endl;
*outputf << __FILE__ << endl;
*outputf << __LINE__ << endl;
}
*outputf
<< left
<< setw(65)
<< "Procedure to quadratically optimising "
<< right
<< setw(15)
<< setprecision(9)
<< std::fixed
<< timeramat.toc()
<< left
<< setw(5)
<< "s"
<< left
<< setw(5)
<< printhour()
<< endl;
for(int j=0; j<totalmatrixlength; ++j)
{
betaod(j)=gsl_vector_get(x, j);
}
gsl_vector_free(a);
gsl_matrix_free(CE);
gsl_vector_free(be);
gsl_matrix_free(C);
gsl_vector_free(b);
gsl_vector_free(x);
free (work);
*outputf
<< left
<< setw(65)
<< "Procedure to construct the input and quadratically optimised it "
<< right
<< setw(0)
<< setprecision(9)
<< std::fixed
<< timer.toc()
<< left
<< setw(5)
<< "s"
<< left
<< setw(5)
<< printhour()
<< endl;
}
void LYAPUNOV::lyapunovfunctions(int currentiteration, bool type_of_grid, mat &evalcoordinates, WENDLAND &wendland, RBFMETHOD &rbf)
{
#if defined(_OPENMP)
omp_set_dynamic(0);
omp_set_num_threads(glovar::OMP_NUM_THREADS);
#endif
int i=0, k=0;
wall_clock timer;
timer.tic();
if(normal)
{
*outputf << "Computing the Lyapunov function with the normalisation approach" << endl;
}else{
*outputf << "Computing the Lyapunov function without the normalisation approach" << endl;
}
int chunk;
int maxite=(int)evalcoordinates.n_rows;
int maxbet=(int)rbf.collocationpoints.n_rows;
int pointdim=(int)rbf.collocationpoints.n_cols;
double totalweight=(double)sizeof(double)*(2.0*maxite)/1073741824.0;
rbf.checkcapability(totalweight,"lyapunovfunctions");
chunk = int(floor(maxite/glovar::OMP_NUM_THREADS));
#pragma omp parallel num_threads(glovar::OMP_NUM_THREADS) shared(lyapfunc,orbder,chunk) private(i,k)
{
lyapfunc.set_size(maxite);
orbder.set_size(maxite);
lyapfunc.zeros();
orbder.zeros();
rowvec diffpoints(pointdim), diffpointski(pointdim), diffpointskineg(pointdim);
rowvec resulti(pointdim), resultk(pointdim), saving(pointdim), savingdomain(pointdim);
diffpoints.zeros();
diffpointski.zeros();
diffpointskineg.zeros();
resulti.zeros();
resultk.zeros();
saving.zeros();
savingdomain.zeros();
//double proctk=0.0;
double producting=0.0;
double twopointsdistance=0.0;
double wdlfvalue1=0.0;
double wdlfvalue2=0.0;
double checking=0.0;
#pragma omp barrier
#pragma omp for schedule (dynamic, chunk)// nowait
for(i=0; i<maxite; ++i)
{
savingdomain=evalcoordinates(i,All);
odesystem(normal,savingdomain,resulti);
for(k=0; k<maxbet; ++k)
{
saving=rbf.collocationpoints(k,All);
diffpoints=savingdomain-saving;
twopointsdistance=sqrt(dot(diffpoints,diffpoints));
checking=1.0-c*twopointsdistance;
if(checking>0.0)
{
odesystem(normal,saving,resultk);
wdlfvalue1=wendland.evawdlfn(twopointsdistance, wendland.wdlf1);
wdlfvalue2=wendland.evawdlfn(twopointsdistance, wendland.wdlf2);
diffpointski=saving-savingdomain;
//proctk=dot(diffpointski,resultk);
producting=betaod(k)*dot(diffpointski,resultk);
lyapfunc(i)+=producting*wdlfvalue1;
orbder(i)+=-wdlfvalue2*producting*dot(diffpointski,resulti)-betaod(k)*wdlfvalue1*dot(resulti,resultk);
}
}
}
}
if(printing)
{
if(type_of_grid)
{
printall("lyapfuncdir", currentiteration, lyapfunc);
printall("orbderdir", currentiteration, orbder);
}else{
printall("lyapfunccar", currentiteration, lyapfunc);
printall("orbdercar", currentiteration, orbder);
}
}
*outputf
<< left
<< setw(65)
<< "The whole procedure to compute the Lyapunov function lasted "
<< right
<< setw(15)
<< setprecision(9)
<< std::fixed
<< timer.toc()
<< left
<< setw(5)
<< "s"
<< left
<< setw(5)
<< printhour()
<< endl;
}
void LYAPUNOV::lyapunovfunctions(int currentiteration, mat &evalcoordinates, WENDLAND &wendland, RBFMETHOD &rbf)
{
#if defined(_OPENMP)
omp_set_dynamic(0);
omp_set_num_threads(glovar::OMP_NUM_THREADS);
#endif
int i=0, k=0;
wall_clock timer;
timer.tic();
if(normal)
{
*outputf << "Computing the Lyapunov function with the normalisation approach" << endl;
}else{
*outputf << "Computing the Lyapunov function without the normalisation approach" << endl;
}
int chunk;
int maxite=(int)evalcoordinates.n_rows;
int maxbet=(int)rbf.collocationpoints.n_rows;
int pointdim=(int)rbf.collocationpoints.n_cols;
double totalweight=(double)sizeof(double)*(2.0*maxite)/1073741824.0;
rbf.checkcapability(totalweight,"lyapunovfunctions");
chunk = int(floor(maxite/glovar::OMP_NUM_THREADS));
#pragma omp parallel num_threads(glovar::OMP_NUM_THREADS) shared(lyapfunc,orbder,chunk) private(i,k)
{
lyapfunc.set_size(maxite);
orbder.set_size(maxite);
lyapfunc.zeros();
orbder.zeros();
rowvec diffpoints(pointdim), diffpointski(pointdim), diffpointskineg(pointdim);
rowvec resulti(pointdim), resultk(pointdim), saving(pointdim), savingdomain(pointdim);
diffpoints.zeros();
diffpointski.zeros();
diffpointskineg.zeros();
resulti.zeros();
resultk.zeros();
saving.zeros();
savingdomain.zeros();
//double proctk=0.0;
double producting=0.0;
double twopointsdistance=0.0;
double wdlfvalue1=0.0;
double wdlfvalue2=0.0;
double checking=0.0;
#pragma omp barrier
#pragma omp for schedule (dynamic, chunk)// nowait
for(i=0; i<maxite; ++i)
{
savingdomain=evalcoordinates(i,All);
odesystem(normal,savingdomain,resulti);
for(k=0; k<maxbet; ++k)
{
saving=rbf.collocationpoints(k,All);
diffpoints=savingdomain-saving;
twopointsdistance=sqrt(dot(diffpoints,diffpoints));
checking=1.0-c*twopointsdistance;
if(checking>0.0)
{
odesystem(normal,saving,resultk);
wdlfvalue1=wendland.evawdlfn(twopointsdistance, wendland.wdlf1);
wdlfvalue2=wendland.evawdlfn(twopointsdistance, wendland.wdlf2);
diffpointski=saving-savingdomain;
//proctk=dot(diffpointski,resultk);
producting=betaod(k)*dot(diffpointski,resultk);
orbder(i)+=-wdlfvalue2*producting*dot(diffpointski,resulti)-betaod(k)*wdlfvalue1*dot(resulti,resultk);
}
}
}
}
if(printing)
{
printall("orbderdir", currentiteration, orbder);
}
*outputf
<< left
<< setw(65)
<< "The whole procedure to compute the Lyapunov function lasted "
<< right
<< setw(15)
<< setprecision(9)
<< std::fixed
<< timer.toc()
<< left
<< setw(5)
<< "s"
<< left
<< setw(5)
<< printhour()
<< endl;
}
void LYAPUNOV::firstderivative(int currentiteration, bool type_of_grid, mat &evalcoordinates, WENDLAND &wendland, RBFMETHOD &rbf)
{
#if defined(_OPENMP)
omp_set_dynamic(0);
omp_set_num_threads(glovar::OMP_NUM_THREADS);
#endif
wall_clock timer;
timer.tic();
int i=0,j=0,k=0;
int evaldim=(int)evalcoordinates.n_rows;
fdvector.set_size(evaldim,ode_dimension);
normed.set_size(evaldim);
fdvector.zeros();
double totalweight=(double)sizeof(double)*(ode_dimension*evaldim+evaldim)/1073741824.0;
rbf.checkcapability(totalweight,"lyapunovfunctions");
double checking=0.0;
double twopointsdistance=0.0;
double wdlfvalue1=0.0;
double wdlfvalue2=0.0;
double product=0.0;
int chunk = int(floor(evaldim/glovar::OMP_NUM_THREADS));
#pragma omp parallel num_threads(glovar::OMP_NUM_THREADS) shared(fdvector,chunk) private(i,j,k,twopointsdistance,product,wdlfvalue1,wdlfvalue2,checking)
{
rowvec saving(ode_dimension), savingdomain(ode_dimension), diffpoints(ode_dimension),resultk(ode_dimension);
int maxite=(int)betaod.n_rows;
#pragma omp barrier
#pragma omp for schedule (dynamic, chunk) nowait
for(j=0; j<evaldim; ++j)
{
saving=evalcoordinates(j,All);
for(i=0; i<ode_dimension; ++i)
{
for(k=0; k<maxite; ++k)
{
savingdomain=rbf.collocationpoints(k, All);
odesystem(normal,savingdomain,resultk);
diffpoints=saving-savingdomain;
twopointsdistance=sqrt(dot(diffpoints,diffpoints));
checking=1.0-c*twopointsdistance;
if(checking>0.0)
{
wdlfvalue1=wendland.evawdlfn(twopointsdistance, wendland.wdlf1);
wdlfvalue2=wendland.evawdlfn(twopointsdistance, wendland.wdlf2);
fdvector(j,i)+=betaod(k)*(-resultk(i)*wdlfvalue1
-diffpoints(i)
*dot(diffpoints,resultk)
*wdlfvalue2);
}
}
}
product=dot(fdvector(j,All),fdvector(j,All));
normed(j)=sqrt(product);
}
}
if(printing)
{
if(type_of_grid)
{
printall("lyapprimexdir", currentiteration, fdvector);
printall("normeddire", currentiteration, normed);
}else{
printall("lyapprimexcar", currentiteration, fdvector);
printall("normedcar", currentiteration, normed);
}
}
*outputf
<< left
<< setw(65)
<< "The whole procedure to compute the gradient lasted "
<< right
<< setw(15)
<< setprecision(9)
<< std::fixed
<< timer.toc()
<< left
<< setw(5)
<< "s"
<< left
<< setw(5)
<< printhour()
<< endl;
}
void LYAPUNOV::secondderivative(mat &evalcoordinates, WENDLAND &wendland, RBFMETHOD &rbf)
{
#if defined(_OPENMP)
omp_set_dynamic(0);
omp_set_num_threads(glovar::OMP_NUM_THREADS);
#endif
wall_clock timer;
timer.tic();
int i=0,j=0,k=0;
int evaldim=(int)evalcoordinates.n_rows;
double totalweight=(double)sizeof(double)*(ode_dimension*ode_dimension*evaldim)/1073741824.0;
rbf.checkcapability(totalweight,"lyapunovfunctions");
sdvector.set_size(ode_dimension,ode_dimension,evaldim);
sdvector.zeros();
int chunk = int(floor(evaldim/glovar::OMP_NUM_THREADS));
#pragma omp parallel num_threads(glovar::OMP_NUM_THREADS) shared(sdvector,chunk) private(i,j,k)
{
rowvec resultk(ode_dimension), saving(ode_dimension), savingdomain(ode_dimension), diffpoints(ode_dimension);
int maxite=(int)betaod.n_rows;
double twopointsdistance=0.0;
double wdlfvalue2=0.0;
double wdlfvalue3=0.0;
double kdelta=0;
double product=0.0;
mat deltak=eye(ode_dimension,ode_dimension);
#pragma omp barrier
#pragma omp for schedule (dynamic, chunk) nowait
for(int p=0; p<evaldim; ++p)
{
savingdomain=evalcoordinates(p,All);//equis
for(i=0; i<ode_dimension; ++i)
{
for(j=0; j<ode_dimension; ++j)
{
kdelta=0.0;
if(i==j)
{
kdelta=1.0;
}
for(k=0; k<maxite; ++k)
{
saving=rbf.collocationpoints(k, All);//equisk
odesystem(normal,saving,resultk);
diffpoints=savingdomain-saving;
twopointsdistance=sqrt(dot(diffpoints,diffpoints));
product=dot(diffpoints,resultk);
checking=1.0-c*twopointsdistance;
if(checking>0.0)
{
wdlfvalue2=wendland.evawdlfn(twopointsdistance,wendland.wdlf2);
wdlfvalue3=wendland.evawdlfn(twopointsdistance,wendland.wdlf3);
sdvector(i,j,p)+=betaod(k)*(
-diffpoints(j)*resultk(i)*wdlfvalue2
-kdelta*product*wdlfvalue2
-diffpoints(i)*resultk(j)*wdlfvalue2
-diffpoints(i)*diffpoints(j)*product*wdlfvalue3
);
}
}
}
}
}
}
*outputf
<< left
<< setw(65)
<< "The whole procedure to compute the Hessian lasted "
<< right
<< setw(15)
<< setprecision(9)
<< std::fixed
<< timer.toc()
<< left
<< setw(5)
<< "s"
<< left
<< setw(5)
<< printhour()
<< endl;
}
void LYAPUNOV::findingeigenamount(int currentiteration, bool type_of_grid, RBFMETHOD &rbf)
{
#if defined(_OPENMP)
omp_set_dynamic(0);
omp_set_num_threads(glovar::OMP_NUM_THREADS);
#endif
wall_clock timer;
timer.tic();
int maxlim=(int)sdvector.n_slices;
int dimlim=(int)rbf.collocationpoints.n_cols;
double totalweight=(double)sizeof(double)*(maxlim*dimlim+dimlim*dimlim*maxlim)/1073741824.0;
rbf.checkcapability(totalweight,"lyapunovfunctions");
mat x(dimlim,dimlim);
TOTALEIGEN.set_size(maxlim,dimlim);
TOTALEIGENV.set_size(dimlim,dimlim,maxlim);
int i=0;
vec eigval;
mat eigvec;
int chunk = int(floor(maxlim/glovar::OMP_NUM_THREADS));
#pragma omp parallel shared(TOTALEIGEN,chunk) private(i,x,eigval, eigvec)
{
#pragma omp barrier
#pragma omp for schedule (dynamic, chunk) nowait
for(i=0; i<maxlim; ++i)
{
x=sdvector(All,All,span(i));
eig_sym(eigval, eigvec, x,"std");
TOTALEIGEN(i,All)=eigval.t();
TOTALEIGENV(span(0,dimlim-1),span(0,dimlim-1),span(i))=eigvec;
}
}
if(printing)
{
if(type_of_grid)
{
printall("eigendir", currentiteration, TOTALEIGEN);
printall("eigenvecdir", currentiteration, TOTALEIGENV);
}else{
printall("eigencar", currentiteration, TOTALEIGEN);
printall("eigenveccar", currentiteration, TOTALEIGENV);
}
}
*outputf
<< left
<< setw(65)
<< "The whole procedure to compute the Eigenvalues lasted "
<< right
<< setw(15)
<< setprecision(9)
<< std::fixed
<< timer.toc()
<< left
<< setw(5)
<< "s"
<< left
<< setw(5)
<< printhour()
<< endl;
}
void LYAPUNOV::chainrecurrentset(int currentiteration, bool type_of_grid, bool with_orbder, mat &evalcoordinates)
{
list<int> counterzero;
int maxlength=(int)evalcoordinates.n_rows;
int maxwidth=(int)evalcoordinates.n_cols;
for(int j=0; j<maxlength; ++j)
{
if(with_orbder)
{
if(orbder(j)>critval)
{
counterzero.push_back(j);
}
}else{
if(-normed(j)>-critval)
{
counterzero.push_back(j);
}
}
}
int faillength=(int)counterzero.size();
crslyapun.set_size(faillength);
crsorbder.set_size(faillength);
failinggrid.set_size(faillength,maxwidth);
failinglyapunov.set_size(faillength);
failingorbder.set_size(faillength);
int m=0;
{
for(list<int>::iterator ii=counterzero.begin(); ii!=counterzero.end(); ++ii)
{
crslyapun(m)=lyapfunc(*ii);
crsorbder(m)=orbder(*ii);
failinglyapunov(m)=lyapfunc((*ii));
failingorbder(m)=orbder((*ii));
failinggrid(m,All)=evalcoordinates(*ii,All);
m++;
}
}
counterzero.clear();
if(printing)
{
if(type_of_grid)
{
printall("fdirecgrid", currentiteration, failinggrid);
printall("flfdirecgrid", currentiteration, failinglyapunov);
printall("flfpdirecgrid", currentiteration, failingorbder);
}else{
printall("fcartesian", currentiteration, failinggrid);
printall("flfcartesian", currentiteration, failinglyapunov);
printall("flfpcartesian", currentiteration, failingorbder);
}
}
}
void LYAPUNOV::getnewalpha(int currentiteration, RBFMETHOD &rbf)
{
double summing=0.0;
double normalizationfactor=0.0;
rbf.alphavector.resize(rbf.alphasize);
for(int iii=0; iii<rbf.alphasize; ++iii)
{
summing=0.0;
for(int j=0; j<2*points_directional;++j)
{
summing+=orbder((2*points_directional)*(iii)+j);
}
if(summing>0.0)
{
summing=0.0;
}
rbf.alphavector(iii)=summing/((double)(2*points_directional));
normalizationfactor+=rbf.alphavector(iii);
}
rbf.alphavector=abs(rbf.alphasize/normalizationfactor)*rbf.alphavector;
if(printing)
{
printall("alphavector", currentiteration, rbf.alphavector);
}
}
void LYAPUNOV::make_lyap_direcional(WENDLAND &wendland, RBFMETHOD &rbf)
{
int i;
wall_clock timer1;
for(i=0; i<totaliterations; i++)
{
iteration(i);
timer1.tic();
lyapequation(i, rbf);
lyapunovfunctions(i, true, rbf.directgrid, wendland, rbf);
getnewalpha(i, rbf);
chainrecurrentset(i, true, true, rbf.directgrid);
firstderivative(i, true, rbf.directgrid, wendland, rbf);
normed.clear();
secondderivative(rbf.directgrid, wendland, rbf);
findingeigenamount(i, true, rbf);
*outputf
<< left
<< setw(50)
<< "The whole procedure to go through iteration "
<< left
<< setw(2)
<< i
<< left
<< setw(5)
<< "lasted "
<< left
<< setw(5)
<< setprecision(9)
<< std::fixed
<< timer1.toc()
<< left
<< setw(5)
<< "s"
<< left
<< setw(5)
<< printhour()
<< endl;
switch (glovar::method_type){
case glovar::choose_the_method::minusone:
break;
case glovar::choose_the_method::op:
case glovar::choose_the_method::fpop:
i=2*totaliterations;
break;
default:
*outputf << "METHOD: THIS HAS NOT BEEN ASSIGNED" <<endl;
exit(9);
}
}
}
void LYAPUNOV::make_lyap_direc_and_cart(WENDLAND &wendland, RBFMETHOD &rbf)
{
int i;
wall_clock timer1;
rbf.makeevalblpn(true);
bool decide;
for(i=0; i<totaliterations; i++)
{
timer1.tic();
iteration(i);
*outputf << " " << endl;
lyapequation(i, rbf);
*outputf << " " << endl;
*outputf << " " << endl;
*outputf << "Directional grid:" << endl;
*outputf << " " << endl;
*outputf << " " << endl;
decide=true;
lyapunovfunctions(i,decide, rbf.directgrid, wendland, rbf);
chainrecurrentset(i, decide, true, rbf.directgrid);
firstderivative(i, decide, rbf.directgrid, wendland, rbf);
normed.clear();
secondderivative(rbf.directgrid, wendland, rbf);
findingeigenamount(i, decide, rbf);
getnewalpha(i, rbf);
failinggrid.clear();
failinglyapunov.clear();
failingorbder.clear();
direcnozero.clear();
negcollocation.clear();
crslyapun.clear();
crsorbder.clear();