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SelfConiugGradient.m
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SelfConiugGradient.m
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% Conjugate gradient method
% x - solution (at step k)
% k - step (number of iterations performed)
% resvec - vector that contains the residual at each iteration
function [x,k,resvec] = SelfConiugGradient(A,b,tau,maxn,x)
% System size
n = size(A,1);
% Initialize the vector x0
x0 = 100*ones(n,1);
% Initialize the residue
r = b - A*x;
% Initial direction
p = r;
% Iterations counter
k = 0;
% Starting the algorithm cycle with control condition. You can choose between:
% - residual control: norm (r) > tau * norm (b)
% - Cauchy condition: norm (x-x0) > tau * norm (x)
% I set however a maximum number of iterations
% Preallocation of resources for the residual vector
resvec=zeros(maxn,1);
while(norm(x-x0) > tau*norm(x)) && (k<maxn)
x0 = x;
k = k+1;
% Storing the residue
resvec(k) = norm(r);
% Optimize by calculating the matrix-vector product only once
s = A*p;
delta = p'*s;
% Step calculation
alpha = (p'*r)/delta;
% New solution
x = x0+alpha*p;
% Residual update
r = r-alpha*s;
beta = s'*r/delta;
p = r-beta*p;
end