Bernstein Polynomial Interpolation - c++

Question

For my assignment I have to implement an algorithm for the Bernstein polynomial defined on the interval [0,1].
My experiment needs to include the following function: f(x) = |ax|, for sake of simplicity in my code I let a = 1. When implementing the algorithm I used this Matlab code from our book (first picture) and the way the professors defines in his notes (second picture):matlab code professors defines in his notes
My output has all the same numbers, I think the problem is I am not sure what value k needs to be from the formula. Anyway here is my code:
#include <iostream>
#include <math.h>
using namespace std;
int combinations(int n, int k);
int fact(int n);
// Bernstein polynomial single precision
float Bernstein(float x[], float f[], int k, int n);
// Bernstein polynomial double precision
//float Bernstein(double x[], double k, int n);
//-------------------------------------------------------------
int main() {
int n,k;
cout << "Enter the degree: " << endl;
cin >> n;
cout << "Enter the k parameter: " << endl;
cin >> k;
float x[n];
double x_0[n];
// stepsize for interval [0,1]
double h = (1.0 - 0)/10.0;
for(int i = 0; i < n; i++){
x[i] = 0 + i*h;
x_0[i] = 0 + i*h;
}
// Compute the f(x_i) = y_i values single precision
float f_0[n], f_1[n], f_2[n];
float alpha = 1.0;
for(int i = 0; i < n; i++){
f_0[i] = fabs(alpha*x[i]);
f_1[i] = fabs(alpha*x[i]) + x[i]/2 - pow(x[i],2);
f_2[i] = 1/(1 + alpha*pow(x[i],2));
}
// Compute the f(x_i) = y_i values double precision
double alpha1 = 1.0;
double f0[n], f1[n], f2[n];
for(int i = 0; i < n; i++){
f0[i] = fabs(alpha1*x_0[i]);
f1[i] = fabs(alpha1*x_0[i]) + x_0[i]/2 - pow(x_0[i],2);
f2[i] = 1/(1 + alpha1*pow(x_0[i],2));
}
for(int i = 0; i < n; i++){
cout << Bernstein(x,f_0,k,n) << endl;
}
return 0;
}
//----------------------------------------------------------
float Bernstein(float x[], float f[], int k, int n){
int C;
float B;
if(k == 0){
C = 1;
}else{
C = combinations(n,k);
}
int t = n - k;
for(int i = 0; i < n; i++){
B = C*pow(x[i],k)*pow((1 - x[i]),t)*f[i];
}
return B;
}
int combinations(int n, int k){
return fact(n) / (fact(k) * fact(n - k));
}
int fact(int n){
int result = 1;
for (int i =1; i <= n; i++){
result = result*i;
}
return result;
}
Question:
Why does my output have all the same numbers, and what could be the problem?

Answer 1

bernstein(f,n,t) with a function handle f returns the nth-order Bernstein polynomial symsum(nchoosek(n,k)*t^k*(1-t)^(n-k)*f(k/n),k,0,n), evaluated at the point t. This polynomial approximates the function f over the interval [0,1].
Example:
bernstein(g,n,t) with a symbolic expression or function g returns the nth-order Bernstein polynomial, evaluated at the point t. This syntax regards g as a univariate function of the variable determined by symvar(g,1).
If any argument is symbolic, bernstein converts all arguments except a function handle to symbolic, and converts a function handle's results to symbolic.

Answer 2

I execute the program and how you say the output have the sames results. Did you make some changes at this program after your post? I am interesting on it, because i have a homework at home about bernstein polynomial.