Polinomio* Polinomio::operator*(Polinomio *p) {
Polinomio *mult = new Polinomio(this->getGrado()+p->getGrado());
mult->setCoeficiente(this->getGrado()+p->getGrado(),0);
for(int i=0; i<=this->getGrado(); i++) {
for(int j=0; j<=p->getGrado(); j++) {
mult->setCoeficiente(i+j,(*mult)[i+j] + ((*this)[i] * (*p)[j]) );
}
}
return mult;
}
void RadialInterpolatePoints( const AcGePoint3dArray& datas, AcGePoint3dArray& pts )
{
MQ<double> rbf; // RBF as kernel we can use : MQ, IMQ, GAU, TPS, POT
Polinomio<double> pol;
double c;
Matrix<double> A;
Vector<double> x, y, f, b, lambda;
Vector<double> x_new, y_new, f_new;
int n, m;
//define the number of nodes
n = 10;
//define the shape parameter for MQ kernel
c = 3.0;
//make the 2d data, see 2d-comun.hpp
make_data( datas, x, y, f );
n = x.GetSize();
//configure the associate polynomial
// pol.make( data_dimension, degree_pol)
pol.make( 2 , rbf.get_degree_pol() );
//get the number of elements in the polynomial base
m = pol.get_M();
//make aditional data for: Ax=b
b.Reallocate( n + m );
b = 0.0;
//fill the expanded vector b = [f 0]
for( int i = 0; i < n; i++ )
b( i ) = f( i );
//fill the Gramm matrix
fill_gram( rbf, pol, c, x, y, A );
//solve the linear system by LU factorization
lambda = gauss( A, b );
make_data( pts, x_new, y_new, f_new );
//interpolate the data
f_new = interpolate( rbf, pol, c, lambda, x, y, x_new, y_new );
write_back_data( f_new, pts );
}
bool operator==(const Polinomio& m, const Polinomio& s) {
//se ho due polinomi nulli
if ( (m.Nullo()) && (s.Nullo()) ){
return true;
}
//se solamente uno dei polinomi e' nullo
else if ( (m.Nullo()) || (s.Nullo()) ) {
return false;
}
else {
return m.first->coefficiente == s.first->coefficiente
&& m.first->esponente == s.first->esponente
&& Polinomio(m.first->next) == Polinomio(s.first->next);
//invocazione ricorsiva su (m,s)->next;
}
}
Polinomio operator/(const Polinomio& m, const Polinomio& s) {
Polinomio aux;
//se (almeno) uno dei polinomi e' il polinomio nullo, ritorno 0
if (m.Nullo() || s.Nullo()) {
return aux;
}
//else
if (m.first->esponente >= s.first->esponente) {
aux = Polinomio(m.first->coefficiente/s.first->coefficiente,
m.first->esponente - s.first->esponente);
if (aux.first->esponente!=0) {
aux.first->next = (Polinomio((m - (aux*s)).first->next) / s).first;
}
}
return aux;
}
int main(int argc,char *argv[]){
char workspace[]="workspace.txt";
Pol_Directory the_directory;
the_directory.load_data(workspace);
static char buf[TAMDBUF],varname[TAMDBUF],coefici[TAMDBUF];
int fd,r,s1,numerador,denominador;
string coeficients,ms,ms1,string_num,string_den,newpol,coeffs;
string string_op1,string_op2;
String_Tokenizer ST0;
vector<string> pcoef;
Rac *RacPt;
Polinomio *Pol;
while(getcmd(buf,sizeof(buf))>=0){
echo_(buf);
if(cmd_is_exit(buf)){
break;
}
if(r=hay_equal_in_buf(buf)){
if(first_and_last_are(buf,'[',']')){
get_var_name(buf,varname);
ms=string(varname);/* ms contiene un nombre de variable polinomio */
get_coefici(buf,coefici,r);
coeficients=string(coefici);
ST0=String_Tokenizer(coeficients,",");
while(ST0.has_more_tokens()){
pcoef.push_back(ST0.next_token());
}
RacPt=new Rac[pcoef.size()];
for(int i=0;i<pcoef.size();i++){
if((fd=pcoef[i].find("/"))!=std::string::npos){
string_num=pcoef[i].substr(0,fd);
string_den=pcoef[i].substr(fd+1);
numerador=atoi(&(string_num[0]));
denominador=atoi(&(string_den[0]));
}else{
string_num=pcoef[i];
numerador=atoi(&(string_num[0]));
denominador=1;
}
*(RacPt+i)=Rac(numerador,denominador);
}/* end for() */
Pol=new Polinomio(pcoef.size()-1,RacPt);
newpol=Pol->string_show();
the_directory.add_or_change_entry(ms,newpol);
pcoef.clear();
}else{
/* En buf hay un '=' y tambi\'en hay un '+', \'o un '-', \'o un '*' */
/* La variable del lado izquierdo del signo de = */
get_var_name(buf,varname);
ms=string(varname);
/*obtener cadena despu\'es del = */
ms1=get_string_after_equal(buf);//cout<<"="<<ms1<<endl;
/*identificar las variables operandos*/
if(is_there_a_char_in_buf(buf,'+')){
if((fd=ms1.find("+"))!=std::string::npos){
string_op1=ms1.substr(0,fd);
string_op2=ms1.substr(fd+1);
fd=string_op1.find_first_not_of(' ');
string_op1=string_op1.substr(fd);
if((fd=string_op1.find(' '))!=std::string::npos){
string_op1=string_op1.substr(0,fd);
}
fd=string_op2.find_first_not_of(' ');
string_op2=string_op2.substr(fd);
if((fd=string_op2.find(' '))!=std::string::npos){
string_op2=string_op2.substr(0,fd);
}
}
do_suma(the_directory,string_op1,string_op2,ms);
}
if(is_there_a_char_in_buf(buf,'-')){
if((fd=ms1.find("-"))!=std::string::npos){
string_op1=ms1.substr(0,fd);
string_op2=ms1.substr(fd+1);
fd=string_op1.find_first_not_of(' ');
string_op1=string_op1.substr(fd);
if((fd=string_op1.find(' '))!=std::string::npos){
string_op1=string_op1.substr(0,fd);
}
fd=string_op2.find_first_not_of(' ');
string_op2=string_op2.substr(fd);
if((fd=string_op2.find(' '))!=std::string::npos){
string_op2=string_op2.substr(0,fd);
}
}
do_resta(the_directory,string_op1,string_op2,ms);
}
if(is_there_a_char_in_buf(buf,'*')){
if((fd=ms1.find("*"))!=std::string::npos){
string_op1=ms1.substr(0,fd);
string_op2=ms1.substr(fd+1);
fd=string_op1.find_first_not_of(' ');
string_op1=string_op1.substr(fd);
if((fd=string_op1.find(' '))!=std::string::npos){
string_op1=string_op1.substr(0,fd);
}
fd=string_op2.find_first_not_of(' ');
string_op2=string_op2.substr(fd);
if((fd=string_op2.find(' '))!=std::string::npos){
string_op2=string_op2.substr(0,fd);
}
}
do_multiplicacion(the_directory,string_op1,string_op2,ms);
}
}
}/* if(r=hay_equal_in_buf(buf)) */
if(!(r=hay_equal_in_buf(buf))){
if(get_var_name1(buf,varname)){
ms=string(varname);
coeffs=the_directory.lookup_entry(ms);
cout<<ms<<" = "<<coeffs<<endl;
}else{
/*En caso de que un buf sin '=' contenga +,-, o * no se hace algo*/
/*Nothing to be done here*/
}
}
}//end while(getcmd(buf, sizeof(buf)) >= 0)
printf("Exiting now...\n");
do_save(the_directory);
system("PAUSE");
return 0;
}//end main()
//---------------------------------------------------------
int main(int argc, char **argv)
{
TPS<double> rbf;
Polinomio<double> pol;
Matrix<double> A,B;
Vector<double> x,y,f;
Vector<double> lambda,b;
Vector<double> xnew,ynew,fnew;
double c=0.01;
int n,ni,m;
//make the data in the square [0,1] x [0,1]
make_data(0,1,0,1, 21, 21, x, y, ni, n);
//stablish the exponent in: r^beta log(r)
rbf.set_beta(4);
//configure the associate polynomial
// pol.make( data_dimension, degree_pol)
pol.make(2 , rbf.get_degree_pol());
//show the rbf and pol info
cout<<rbf;
cout<<pol;
//show the number of nodes
cout<<endl;
cout<<"total nodes N = "<<n<<endl;
cout<<"interior nodes ni = "<<ni<<endl;
cout<<"boundary nodes nf = "<<n-ni<<endl;
cout<<endl;
//get the number of elements in the polynomial base
m = pol.get_M();
//resize the matrices to store the partial derivatives
A.Resize(n+m,n+m); A = 0.0;
B.Resize(n+m,n+m); B = 0.0;
//Recall that this problem has the general form
// (Uxx+Uyy) (Pxx+Pyy) = f interior nodes 0..ni
// U P_b = g boundary nodes ni..n
// P^transpose 0 = 0 momentun conditions in P
//
// P is the polynomial wit size n x m
// P_b is the polynomial working in the boundary nodes, size nf x m
// Pxx+Pyy has size ni x m
//make the matriz derivatives
fill_matrix( "dxx" , rbf , pol , c , x , y, 0 , ni , A);
fill_matrix( "dyy" , rbf , pol , c , x , y, 0 , ni , B);
A = A + B; // A <- Uxx + Uyy
//Add the submatriz for the boundary nodes: U , P_b boundary nodes ni..n
fill_matrix( "normal" , rbf , pol , c , x , y, ni, n , A);
//Add the submatriz P^transpose at the end: P^transpose
fill_matrix( "pol_trans" , rbf , pol , c , x , y, n , n+m, A);
//resize the vector to store the right_size of the PDE
b.Resize(n+m); b = 0.0;
//fill with f
for(int i=0;i<ni;i++)
b(i) = right_side(x(i), y(i));
//fill with the boundary condition
for(int i=ni;i<n;i++)
b(i) = boundary_condition(x(i),y(i));
//solve the linear system of equations
lambda = gauss(A,b);
//make the new data grid
int ni2,n2;
make_data(0,1,0,1, 41, 41, xnew, ynew, ni2, n2);
//interpolate on this new data grid (xnew,ynew)
fnew = interpolate(rbf,pol,c,lambda,x,y,xnew,ynew);
//determine the maximum error
double e=0.0;
for(int i=0;i<ni2;i++)
{
e = max(e, fabs(fnew(i) - sin(2*M_PI*xnew(i))*cos(2*M_PI*ynew(i))) );
}
//show the error
cout<<endl;
cout<<"The maximum error: e_max = "<<e<<endl<<endl;
//store the interpolated data
save_gnu_data("data",xnew,ynew,fnew);
return 0;
}
