% Given environment

clear;
% Setup the function under test
syms x y;
fexpr = x^5 * exp(-x^2 - y^2);
title_fun = "$f(x,y) = x^5 \cdot e^{-x^2 - y^2}$";

% Calculate the gradient and Hessian
grad_fexpr = gradient(fexpr, [x, y]); % Gradient of f
hessian_fexpr = hessian(fexpr, [x, y]);   % Hessian of f

% Convert symbolic expressions to MATLAB functions
fun         = matlabFunction(fexpr, 'Vars', [x, y]);        % Function
grad_fun    = matlabFunction(grad_fexpr, 'Vars', [x, y]); % Gradient
hessian_fun = matlabFunction(hessian_fexpr, 'Vars', [x, y]);  % Hessian

% Minimum reference
Freference = @(x) x(1).^5 .* exp(-x(1).^2 - x(2).^2);
[Xmin, Fmin] = fminsearch(Freference, [-1, -1]);

% Amijo globals
global amijo_beta; % Step reduction factor in [0.1, 0.5] (typical range: [0.1, 0.8])
global amijo_sigma; % Sufficient decrease constant in [1e-5, 0.1] (typical range: [0.01, 0.3])

%fixed step size globals
global  gamma_fixed_step

global image_width, 
global image_height;

image_width = 960;
image_height = 640;