void lagrange_interpolation(double x[], double y[], int nr, double where) {

cout<<"Intermediate steps: ";

double sum = 0;

for (int i=0; i<nr; i++) {

double product = y[i];

for (int j=0; j<nr; j++) {

if (i!=j) product *= ((where - x[j])/(x[i] - x[j]));

}

sum += product;

cout.precision(10);

cout<<sum<<", ";

}

cout<<"\b\b;\n";

cout.precision(10);

cout<<"Aproximation: "<<sum<<endl;

}

void aitken_interpolation(double x[], double y[], int nr, double where) {

// i -> columns, j -> rows

double **matrix = matrix_alloc(nr, nr);

// create the table

for (int j=0; j<nr; j++) matrix[0][j] = y[j];

for (int i=1; i<nr; i++) {

for (int j=i; j<nr; j++) {

matrix[i][j] = (matrix[i-1][i-1] * (x[j] - where) -

matrix[i-1][j] * (x[i-1] - where)) /

(x[j] - x[i-1]);

}

}

cout<<"Here's Aitken's table:\n";

matrix_print(matrix, nr, nr);

cout<<"Aproximation: "<<matrix[nr-1][nr-1]<<endl;

matrix_delete(matrix, nr, nr);

}

void neville_interpolation(double x[], double y[], int nr, double where) {

// i -> columns, j -> rows

double** matrix = matrix_alloc(nr, nr);

// create the table

for (int j=0; j<nr; j++) matrix[0][j] = y[j];

for (int i=1; i<nr; i++) {

for (int j=i; j<nr; j++) {

double denominator = x[j] - x[j-i];

double determinant = matrix[i-1][j-1] * (x[j] - where) -

matrix[i-1][j] * (x[j-i] - where);

matrix[i][j] = determinant/denominator;

}

}

cout<<"Here's Neville's table:\n";

matrix_print(matrix, nr, nr);

cout<<"Aproximation: "<<matrix[nr-1][nr-1]<<endl;

matrix_delete(matrix, nr, nr);

}