w1 = [-5,5];
w2 = [-3,1];
w3 = [1,2];
w4 = [2,-1];
w5 = [-2,4];
w6 = [4,-1];
X = zeros(6,6);
X(1,1) = ((w1(1) - 0) * (w1(1) - w2(1)) * (w1(1) - w3(1)) * (w1(1) -
w4(1)) * (w1(1) - w5(1)) * (w1(1) - w6(1)));
X(2,2) = ((w2(1) - 0) * (w2(1) - w1(1)) * (w2(1) - w3(1)) * (w2(1) -
w4(1)) * (w2(1) - w5(1)) * (w2(1) - w6(1)));
X(3,3) = ((w3(1) - 0) * (w3(1) - w1(1)) * (w3(1) - w2(1)) * (w3(1) -
w4(1)) * (w3(1) - w5(1)) * (w3(1) - w6(1)));
X(4,4) = ((w4(1) - 0) * (w4(1) - w1(1)) * (w4(1) - w2(1)) * (w4(1) -
w3(1)) * (w4(1) - w5(1)) * (w4(1) - w6(1)));
X(5,5) = ((w5(1) - 0) * (w5(1) - w1(1)) * (w5(1) - w2(1)) * (w5(1) -
w3(1)) * (w5(1) - w4(1)) * (w5(1) - w6(1)));
X(6,6) = ((w6(1) - 0) * (w6(1) - w1(1)) * (w6(1) - w2(1)) * (w6(1) -
w3(1)) * (w6(1) - w4(1)) * (w6(1) - w5(1)));
Y = zeros(6,1);
Y(1,1) = w1(2);
Y(2,1) = w2(2);
Y(3,1) = w3(2);
Y(4,1) = w4(2);
Y(5,1) = w5(2);
Y(6,1) = w6(2);
display(X);
display(Y);
A = inv(X) * Y;
display(A);
fprintf(' W(x)=%f*x^6 + %f*x^5 + %f*x^4 + %f*x^3 + %f*x^2 + %f*x\n',
A(6,1), A(5,1), A(4,1),A(3,1), A(2,1), A(1,1));
x=[-5:1:5];
y=zeros(1,11);
for i=1:11
y(i)=A(1,1)+A(2,1)*x(i)+A(3,1)*x(i)^2+A(4,1)*x(i)^3+A(5,1)*x(i)^4+A(6,1)*x(i)^5;
end
plot(x, y);
grid on;
hold on;
vector_x=[w1(1,1), w2(1,1), w3(1,1), w4(1,1), w5(1,1), w6(1,1)];
vector_y=zeros(1, 6);
for i=1:3
 vector_y(1,1)=vector_y(1,1)+A(i,1)*w1(1,1)^(i-1);
 vector_y(1,2)=vector_y(1,2)+A(i,1)*w2(1,1)^(i-1);
 vector_y(1,3)=vector_y(1,3)+A(i,1)*w3(1,1)^(i-1);
 vector_y(1,4)=vector_y(1,4)+A(i,1)*w4(1,1)^(i-1);
 vector_y(1,5)=vector_y(1,5)+A(i,1)*w5(1,1)^(i-1);
 vector_y(1,6)=vector_y(1,6)+A(i,1)*w6(1,1)^(i-1);
end
plot(vector_x,vector_y,'rx');
plot(w1(1,1),w1(1,2),'--gs');
plot(w2(1,1),w2(1,2),'--gs');
plot(w3(1,1),w3(1,2),'--gs');
plot(w4(1,1),w4(1,2),'--gs');
plot(w5(1,1),w5(1,2),'--gs');
plot(w6(1,1),w6(1,2),'--gs');
title('Interpolacja Lagrange – Z2b');
ylabel('Os y');
xlabel('Os x');