static void right_side(node *root){
if(root == NULL){
return;
}
cout << root->data << " ";
right_side(root->right);
}
static void top_view(node * root)
{
if(root == NULL){
return;
}
left_side(root->left);
cout << root->data << " ";
right_side(root->right);
}
int is_identical(struct node_dll *head, struct node *root){
int n,n1, n2;
if (root == NULL || head == NULL)
return -1;
n = check_node(head, root->data);
if (n == 0)
return 0;
n1=left_side(root->left, head);
n2=right_side(root->right, head);
if (n1 == 1 && n2 == 1)
return 1;
else
return 0;
}
int left_side(node *curr, node_dll *head)
{
int n,n1, n2;
if (curr == NULL)
return -1;
else
{
n = check_node(head, curr->data);
if (n == 0)
return 0;
n1 = left_side(curr->left, head);
n2 = right_side(curr->right, head);
if (n1 == 1 && n2 == 1)
return 1;
else
return 0;
}
}
IntPoint to_the_right_of(window_t window){
return {right_side(window) + ui::small_item_spacing, top(window)};
}
//---------------------------------------------------------
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;
}
