Implement the pattern search method using one of the fixed direction sets Dn (e.g. the "coordinate direction set" or the "simplex set"). Use the sufficient decrease function ρ(t) = 0. Set some suitable hyperparameter values for γtol, θ and φ at the beginning of your function.

function [ alpha ] = Armijo_LS(f, df, p, x, alpha, rho, c)
% f: vector->scalar function -- the objective
% df: gradient function
% p: search direction; must satisfy that A) it is a descent direction at starting point x and B) norm(p)=1
% x: starting point
% alpha: initial (maximal) step length
% rho: step lenght multiplier
% c: descent condition multiplier
% This method performs a single linesearch on f in the descent direction p and returns the chosen step length;
%terminates when the Armijo condition is first satisfied w.r.t. input parameters alpha, rho and c.

f0 = f(x);
g0 = df(x);
x0 = x;
x = x0 + alpha * p;
fk = f(x);

% repeat until the Armijo condition is satisfied
while fk > f0 + c * alpha * (g0'*p)
alpha = rho * alpha;
x = x0 + alpha * p;
fk = f(x);
end
end

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