In a 'for loop' not getting difference of two consecutive iteration

format long
l=1/2;
u=1/3;
I=[1,0,0;0,1,0;0,0,1];
A=[4,3,3;2,4,1;3,1,2];
B=det(A)*inv(A);
G_1=[1/3,0,0;0,1/2,0;0,0,1];
G_2=[1/4,0,0;0,1/5,0;0,0,1/6];
T=[1,0,0;0,1,0;0,0,1];
F = [1/2,0,0;0,1/2,0;0,0,1/2];
i=1;
x(1) =1;
y(1) =1;
z(1) =1;
X_i=[x(i);y(i);z(i)];
for i   = 1:100
    a_i = 1/i^(1/2);
    t   = 1/5;
    Z_i = X_i-t*[(I-inv(I+l*G_1))*X_i + B*((I-inv(I+u*G_2)))*A*X_i];
    i   = i+1;
    X_i = a_i*F*X_i+(1-a_i)*T*Z_i
    E(i) = norm(X_i);
    L(i) = ((x(i+1) - x(i))^3 + (y(i+1) - y(i))^3 + (z(i+1) - z(i))^3)^(1/3);  % main problem is here
end
n=[2:1:100];
plot(n,E(n))

[Geoff Hayes]

feeroz - where in the above code are you trying to get the difference between two consecutive iterations? How should this difference be calculated?

[feeroz babu]

I am runing this code in GNU Octave, version 4.2.2. See we get X_i = [x(i); y(i); z(i)] in each iteration. So I want L(i). When I run this code, I got

error: x(3): out of bound 1

Answer 1

[Geoff Hayes]

feeroz - you never update your x, y, and z after their initialization, so perhaps you are intending to use X_i instead. Try the following which may be what you want

X_i = zeros(3,101);
X_i(:,1) = [1; 1; 1];
for i   = 1:100
    a_i = 1/i^(1/2);
    t   = 1/5;
    Z_i = X_i(:,i)-t*[(I-inv(I+l*G_1))*X_i(:,i) + B*((I-inv(I+u*G_2)))*A*X_i(:,i)];
    X_i(:,i+1) = a_i*F*X_i(:,i)+(1-a_i)*T*Z_i;
    E(i) = norm(X_i(:,i+1));
    L(i) = ((X_i(1,i+1) - X_i(1,i))^3 + (X_i(2,i+1) - X_i(2,i))^3 + (X_i(3,i+1) - X_i(3,i))^3)^(1/3);  % main problem is here
end

In the above, we pre-size the X_i array which we updated on each iteration of the loop. We then use that instead of the x, y and z when updating L(i). Note that you could pre-size E and L too.

[feeroz babu]

Thanks