1 %Zadanie 2b
2 w1 = [-5,5];
3 w2 = [-3,1];
4 w3 = [1,2];
5 w4 = [2,-1];
6 w5 = [-2,4];
7 w6 = [4,-1];
8 X = zeros(6,6);
9 X(1,1) = ((w1(1) - 0) * (w1(1) - w2(1)) * (w1(1) - w3(1)) * (w1(1) - w4(1)) * (w1(1) -
w5(1)) * (w1(1) -
10 w6(1)));
11 X(2,2) = ((w2(1) - 0) * (w2(1) - w1(1)) * (w2(1) - w3(1)) * (w2(1) - w4(1)) * (w2(1) -
w5(1)) * (w2(1) -
12 w6(1)));
13 X(3,3) = ((w3(1) - 0) * (w3(1) - w1(1)) * (w3(1) - w2(1)) * (w3(1) - w4(1)) * (w3(1) -
w5(1)) * (w3(1) -
14 w6(1)));
15 X(4,4) = ((w4(1) - 0) * (w4(1) - w1(1)) * (w4(1) - w2(1)) * (w4(1) - w3(1)) * (w4(1) -
w5(1)) * (w4(1) -
16 w6(1)));
17 X(5,5) = ((w5(1) - 0) * (w5(1) - w1(1)) * (w5(1) - w2(1)) * (w5(1) - w3(1)) * (w5(1) -
w4(1)) * (w5(1) -
18 w6(1)));
19 X(6,6) = ((w6(1) - 0) * (w6(1) - w1(1)) * (w6(1) - w2(1)) * (w6(1) - w3(1)) * (w6(1) -
w4(1)) * (w6(1) -
20 w5(1)));
21 Y = zeros(6,1);
22 Y(1,1) = w1(2);
23 Y(2,1) = w2(2);
24 Y(3,1) = w3(2);
25 Y(4,1) = w4(2);
26 Y(5,1) = w5(2);
27 Y(6,1) = w6(2);
28 display(X);
29 display(Y);
30 A = inv(X) * Y;
31 display(A);
32 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),
33 A(2,1), A(1,1));
34 x=[-5:1:5];
35 y=zeros(1,11);
36 for i=1:11
37 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;
38 end
39 plot(x, y);
40 grid on;
41 hold on;
42 vector_x=[w1(1,1), w2(1,1), w3(1,1), w4(1,1), w5(1,1), w6(1,1)];
43 vector_y=zeros(1, 6);
44 for i=1:3
45 vector_y(1,1)=vector_y(1,1)+A(i,1)*w1(1,1)^(i-1);
46 vector_y(1,2)=vector_y(1,2)+A(i,1)*w2(1,1)^(i-1);
47 vector_y(1,3)=vector_y(1,3)+A(i,1)*w3(1,1)^(i-1);
48 vector_y(1,4)=vector_y(1,4)+A(i,1)*w4(1,1)^(i-1);
49 vector_y(1,5)=vector_y(1,5)+A(i,1)*w5(1,1)^(i-1);
50 vector_y(1,6)=vector_y(1,6)+A(i,1)*w6(1,1)^(i-1);
51 end
52 plot(vector_x,vector_y,'rx');
53 plot(w1(1,1),w1(1,2),'--gs');
54 plot(w2(1,1),w2(1,2),'--gs');
55 plot(w3(1,1),w3(1,2),'--gs');
56 plot(w4(1,1),w4(1,2),'--gs');
57 plot(w5(1,1),w5(1,2),'--gs');
58 plot(w6(1,1),w6(1,2),'--gs');
59 title('Interpolacja Lagrange - zadanie 2b');
60 ylabel('Os y');
61 xlabel('Os x');