% provient de TPinterpolation.tex

%% exemple 1.1
disp('exemple 1.1');
[D,Dt]=diff_div_dist([1 2 6],[-3 1 2]);
disp(Dt);
format rat;
disp(Dt);
format;
[D,Dt]=diff_div_dist(sym([1 2 6]),sym([-3 1 2]));
disp(Dt);


%% exemple 1.2
pause;
disp('exemple 1.2');
A=2;
B=3;
a=6;
b=7;
n=3;
No=-cos(pi*(0:n)/n);
Nob=(a+b)/2+(b-a)/2*No;
f=@(x) log(A*x+B);
[D,Dt]=diff_div_dist(Nob,f(Nob));
disp(Dt);

format long;
disp(Dt);
format;
for p=1:7
    [D,Dt]=diff_div_dist(Nob,round(f(Nob)*10^p)/10^p);disp(round(Dt*10^p)/10^p);
end

No=-cos(sym(pi)*(0:n)/n);
Nob=(a+b)/2+(b-a)/2*No;
[D,Dt]=diff_div_dist(Nob,f(Nob));
disp(Dt);
disp(double(Dt));


%% exemple 1.3
pause;
disp('exemple 1.3');
X=[1 2 6];
Y=[-3 1 2];
disp(norm(test_diff_div_dist(X,X,Y)-Y));
disp(test_diff_div_dist(1.8,X,Y));
syms x; 
disp(expand(test_diff_div_dist(x,X,Y)));


%% exemple 1.4
pause;
disp('exemple 1.4');
A=2;
B=3;
a=6;
b=7;
n=3;
No=-cos(pi*(0:n)/n);
Nob=(a+b)/2+(b-a)/2*No;
f=@(x) log(A*x+B);
x=linspace(a,b,1000);
y=test_diff_div_dist(x,Nob,f(Nob));
plot(x,y,x,f(x),Nob,f(Nob),'o');
figure;
plot(x,abs(y-f(x)));

z=linspace(a,b,1e6);
disp(max(abs(test_diff_div_dist(z,Nob,f(Nob))-f(z))));