Iterating using while loop over a vector

Dear all,

I want to iterate using while loop over a vector of size (10x1) to reach the convergence. how can I make this, such as the below figure

Can any one help me please ?

note P, ro, and z all of them are vetor with size 10x1

the actual values of ro,P, and z as follows:

ro=[1,0,0,0,0,0,0,0,0,0];

P=[1,1,1,1,1,1,1,1,1,1];

z=ro=[1,0,0,0,0,0,0,0,0,0];

Answer 1

[Torsten]

And how do we obtain ro_j and z_j from P_(j-1) in step 4 ?

And how to calculate P_j ?

j = 0;
error = 1;
rho=[1,0,0,0,0,0,0,0,0,0];
P=[1,1,1,1,1,1,1,1,1,1];
z=rho;
while error > 1e-4
    j = j + 1;
    [rho;z] = some function of P;  % calculate ro_j and z_j as functions of P_(j-1)
    P = ?   % calculate new P_j (most probably as solution of an optimization problem)
    error = ?  % calculate error
end

[Steven Lord]

I recommend using a different variable name. eps already has a meaning in MATLAB.

[Torsten]

Thank you, Steven.

[bassant tolba]

Thanks Torston for your comment.

so I have the value of G1 and G2

and ro,z,p are vector with size 10x1

G1=ro*p;

G2=z*p;

so to compelete your code, is the following code correct ?

j = 0;

eps = 1;

ro=[1,0,0,0,0,0,0,0,0,0];

P=[1,1,1,1,1,1,1,1,1,1];

z=ro;

while eps > 1e-4

j = j + 1;

[ro] = G1/p(j-1); % calculate ro_j

[z] = G2/p(j-1); z_j as functions of P_(j-1)

then calculate p(j) using the values of [ro] and [z]?, but should I make for loop over indexes, such as 10 indexes ??

end

[Torsten]

j is an iteration index, not a component of the vector p. p^(j-1) is meant as the complete vector p in the (j-1)-th iteration through the while-loop. So

ro = G1/p(j-1)

is incorrect.

I think this misunderstanding is the reason why you always try to optimize over one component of the vector p.

I don't know how ro is calculated from p, but the complete vector p at the (j-1)-th iteration (which is written as p^(j-1) in your graphics from the algorithm) has to be used for this operation.

[bassant tolba]

so how can I interpret this term p^(j-1) in the code please? how can I differentiate between p(j) and p(j-1)

[Torsten]

so how can I interpret this term p^(j-1) in the code please?

As a vector of length 10 that stems from the (j-1)th iteration within the while-loop.

how can I differentiate between p(j) and p(j-1)

Work with two vectors - call the first pjm1 and the second pj.

At the end of the while loop, set pjm1 = pj which means that you take the result of iteration j as the new input of iteration j+1.