% LAGRANZ

function L = lagr(x);
n = length(X);
l = 0;

for i=1:n
    p = 1;
    for j=1:n
        if i~=j
            p = p * ((x - X(j)) / (X(i) - X(j)));
        end
    end
    l = l + p * Y(i);
end

---

% Lagranz vrednosti polinoma

function L = lagr(a, b, n)
L = zeros(1,n);

for i=1:n
    p = 1;
    for j=1:n
        if i~=j
            p = conv(p, [1, -X(j)]) / (X(i) - X(j)));
        end
    end
    L = L + p * Y(i);
end
L = polyval(L, x);

---
% da li je tablica ekvidistantna
ekv = all(abs(diff(X)-h) <= eps);
---

njutn I / II - k i p razlike
function nj = njutn(x)
n = length(X)
k_razlike = zeros(n, n-1)

for i=1 : n-1
    k_razlike(i, 1) = Y(i+1) - Y(i) ... / X(i+1) - X(i)
end

for j = 2 : n-1
    for i = 1 : n-j
        k_razlike(i, j) = k_razlike(i+1, j-1) - k_razlike(i, j-1) ... / X(i+j) - X(i)
    end
end

y = Y(1|end)
h = X(2) - X(1)
q = (x - X(1|end)) / h
Q = q

for i = 1:n-1
    y = y + q * k_razlike(1|n-j, j) / factorial(j)
    q = q * (Q+j);
end

% Njutnov interpolacioni polinom sa podeljenim razlikama
y = Y(1);
p = 1;
for i = 1 : n-1
    p = p * (x - X(i));
    y = y + p * p_razlike(1, i);
end

--
inverz i ondlagranz normanlo

[X1, I] = sort(Y);
Y = X(I);

--
trapez
L = (h/2) * (Y(1) + Y(n) + 2 * sum(Y(2:n-1)));
simps
L = (h/3) * (Y(1) + Y(n) + 2 * sum(Y(3:2:n-1)) + 4 * sum(Y(2:2:n-1)));
runge - trap
runge = abs(I2 - I1) / 3;
runge - sims
runge = abs(I2 - I1) / 15;
che
C{i+1} = 2 * [C{i},0] - [0,0,C{i-1}];
lezandrov
L{i+1} = ((2 * i-1) * [L{i}, 0] - (i-1) * [0,0,L{i-1}])/i;













function x = polov(tol)

tablica;
n = length(X);
a = X(1);
b = X(n);

if (funk(a) * funk(b) > 0)
    error('greska');
end

if (funk(a) == 0)
    x = a;
elseif (funk(b) == 0)
    x = b;
end

if (funk(a) ~= 0 && funk(b) ~= 0)
    while (abs(a-b) > tol)
        x = (a+b) / 2;
        if funk(x) == 0
            break;
        else
            if funk(a) * funk(x) < 0
                b = x;
            else
                a = x;
            end
        end
    end
    x = (a+b) / 2;
end