x = linspace(-5, 5, 11)
x=x';
y = [-5.8643; -6.7445; -5.2378; -3.2868; -2.2393;...
    -0.5084; -1.2237; -0.7893; -4.8761; -11.0466; -20.0868]

%Ax=b

[A1, b1] = matrixer(x, y, 1);
[A2, b2] = matrixer(x, y, 2);
[A3, b3] = matrixer(x, y, 3);
[A4, b4] = matrixer(x, y, 4);
[A5, b5] = matrixer(x, y, 5);
[A6, b6] = matrixer(x, y, 6);
[A7, b7] = matrixer(x, y, 7);
[A8, b8] = matrixer(x, y, 8);
[A9, b9] = matrixer(x, y, 9);
[A10, b10] = matrixer(x, y, 10);


% without QR factorization
coefficients1=flipud(inv(A1'*A1)*(A1'*b1));
coefficients2=flipud(inv(A2'*A2)*(A2'*b2));
coefficients3=flipud(inv(A3'*A3)*(A3'*b3));
coefficients4=flipud(inv(A4'*A4)*(A4'*b4));
coefficients5=flipud(inv(A5'*A5)*(A5'*b5));
coefficients6=flipud(inv(A6'*A6)*(A6'*b6));
coefficients7=flipud(inv(A7'*A7)*(A7'*b7));
coefficients8=flipud(inv(A8'*A8)*(A8'*b8));
coefficients9=flipud(inv(A9'*A9)*(A9'*b9));
coefficients10=flipud(inv(A10'*A10)*(A10'*b10));


xs = linspace(-5, 5);
ys1 = polyval(coefficients1, xs);
ys2 = polyval(coefficients2, xs);
ys3 = polyval(coefficients3, xs);
ys4 = polyval(coefficients4, xs);
ys5 = polyval(coefficients5, xs);
ys6 = polyval(coefficients6, xs);
ys7 = polyval(coefficients7, xs);
ys8 = polyval(coefficients8, xs);
ys9 = polyval(coefficients9, xs);
ys10 = polyval(coefficients10, xs);

figure
plot(x,y,'o')
hold on
grid on
plot(xs,ys1)
plot(xs,ys2)
plot(xs,ys3)
plot(xs,ys4)
plot(xs,ys5)
legend('exact points', 'n=1', 'n=2', 'n=3', 'n=4', 'n=5');
legend('Location','best')
title('Interpolating without QR factorization (1-5)')
ylim([-15,2])
hold off

figure
plot (x,y,'o')
hold on
grid on
plot(xs,ys6)
plot(xs,ys7)
plot(xs,ys8)
plot(xs,ys9)
plot(xs,ys10)
legend('exact points', 'n=6', 'n=7', 'n=8', 'n=9', 'n=10');
legend('Location','best')
title('Interpolating without QR factorization (6-10)')
ylim([-15,2])
hold off

% calculating errors
residuum1 = b1 - A1*coefficients1;
residuum2 = b2 - A2*coefficients2;
residuum3 = b3 - A3*coefficients3;
residuum4 = b4 - A4*coefficients4;
residuum5 = b5 - A5*coefficients5;
residuum6 = b6 - A6*coefficients6;
residuum7 = b7 - A7*coefficients7;
residuum8 = b8 - A8*coefficients8;
residuum9 = b9 - A9*coefficients9;
residuum10 = b10 - A10*coefficients10;



error1 = norm(residuum1);
error2 = norm(residuum2);
error3 = norm(residuum3);
error4 = norm(residuum4);
error5 = norm(residuum5);
error6 = norm(residuum6);
error7 = norm(residuum7);
error8 = norm(residuum8);
error9 = norm(residuum9);
error10 = norm(residuum10);

order2 =[6, 7, 8, 9, 10];
order1 = [1, 2, 3, 4, 5];
errors1 = [error1, error2, error3, error4, error5];
errors2 = [error6, error7, error8, error9, error10]

figure
plot(order1,errors1, '--o')
legend('Errors depending on order of polynomial')
title('Errors without QR factorization (1-5)')

figure
plot(order2,errors2, '--o')
legend('Errors depending on order of polynomial')
title('Errors without QR factorization (6-10)')

beep;