A version of Work 3 without some small parts

2024-12-02 23:52:26 +02:00
parent d5c8ed5e68
commit ed9807b1ca
21 changed files with 136 additions and 54 deletions
@@ -1,33 +0,0 @@
-% Given environment
-
-clear;
-% Setup the function under test
-syms x [2 1] real;
-fexpr = (1/3)*x(1)^2 +3*x(2)^2;
-title_fun = "$f(x) = frac{1}{3}{x_1}^2 + 3{x_2}^2$";
-
-% Calculate the gradient and Hessian
-grad_fexpr = gradient(fexpr, x); % Gradient of f
-hessian_fexpr = hessian(fexpr, x);   % Hessian of f
-
-% Convert symbolic expressions to MATLAB functions
-fun         = matlabFunction(fexpr, 'Vars', {x});        % Function
-grad_fun    = matlabFunction(grad_fexpr, 'Vars', {x}); % Gradient
-hessian_fun = matlabFunction(hessian_fexpr, 'Vars', {x});  % 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;
@@ -3,7 +3,7 @@ GivenEnv

 % Define parameters
 max_iter = 1000; % Maximum iterations
-tol = 1e-4; % Tolerance
+tol = 0.001; % Tolerance

 % Point x0 = (1, 1)
 % =========================================================================
@@ -15,15 +15,26 @@ gf = grad_fun(x0);
 hf = hessian_fun(x0);
 fprintf('Initial point (%d, %d), f = %f, grad = [%f;%f], hessian = [%f %f ; %f %f]=> Method applicable\n', x0, f, gf, hf);

-for g=[0.1, 0.3, 0.5, 3, 5]
+
+k = zeros(100, 1);
+j = 1;
+n = linspace(0.1, 1.5, 100);
+for g = n
+    gamma_fixed_step = g;
+    [~, ~, k(j)] = method_SteepDesc(fun, grad_fun, x0, tol, max_iter, 'fixed');
+    j = j + 1;
+end
+plotItersOverGamma(n, k, "Iteration for different $\gamma$ values", "figures/StDes_Iter_o_gamma_" + point + ".png");
+
+for g=[0.1, 0.3, 3, 5]
    gamma_fixed_step = g;

    [x_fixed, f_fixed, kk] = method_SteepDesc(fun, grad_fun, x0, tol, max_iter, 'fixed');
    fprintf('Fixed step g=%f:     Initial point (%f, %f), steps:%d, Final (x1,x2)=(%f, %f), f(x1,x2)=%f\n', g, x0, kk, x_fixed(:, end), f_fixed(end));
    if g <= 1
-        plotPointsOverContour(x_fixed, fun, XSetLimmits(1, :), XSetLimmits(2, :), 100, point_str + ": Steepest descent $\gamma$ = " + gamma_fixed_step, "");
+        plotPointsOverContour(x_fixed, fun, XSetLimmits(1, :), XSetLimmits(2, :), 100, point_str + ": Steepest descent $\gamma$ = " + gamma_fixed_step, "figures/StDes_gamma_" + g + ".png");
    else
-        plotPointsOverContour(x_fixed, fun, [-500, 500], [-500, 500], 100, point_str + ": Steepest descent $\gamma$ = " + gamma_fixed_step, "");
+        plotPointsOverContour(x_fixed, fun, [-500, 500], [-500, 500], 100, point_str + ": Steepest descent $\gamma$ = " + gamma_fixed_step, "figures/StDes_gamma_" + g + ".png");
    end
 end

@@ -23,7 +23,7 @@ fprintf('Initial point (%d, %d), f = %f, grad = [%f;%f], hessian = [%f %f ; %f %
 gamma_fixed_step = gamma;
 [x_fixed, f_fixed, kk] = method_SteepDesc_Proj(fun, grad_fun, x0, sk_step, XSetLimmits, tol, max_iter, 'fixed');
 fprintf('Fixed step g=%f:     Initial point (%f, %f), steps:%d, Final (x1,x2)=(%f, %f), f(x1,x2)=%f\n', gamma_fixed_step, x0, kk, x_fixed(:, end), f_fixed(end));
-plotPointsOverContour(x_fixed, fun, XSetLimmits(1, :), XSetLimmits(2, :), 100, point_str + ": Steepest descent $\gamma$ = " + gamma_fixed_step, "");
+plotPointsOverContour(x_fixed, fun, XSetLimmits(1, :), XSetLimmits(2, :), 100, point_str + ": Steepest descent proj $s_k$ = " + sk_step + ", $\gamma$ = " + gamma_fixed_step, "figures/StDesProj_sk_" + sk_step + "_gamma_" + gamma + ".png");

 %[x_minimized, f_minimized, kk] = method_SteepDesc_Proj(fun, grad_fun, x0, sk_step, XSetLimmits, tol, max_iter, 'minimized');
 %fprintf('Minimized f:         Initial point (%f, %f), steps:%d, Final (x1,x2)=(%f, %f), f(x1,x2)=%f\n', x0, kk, x_fixed(:, end), f_fixed(end));
@@ -8,7 +8,7 @@ max_iter = 1000; % Maximum iterations
 % =========================================================================
 x0 = [-5, 10]';
 gamma = 0.1;
-sk_step = 55;
+sk_step = 15;
 tol = 0.01; % Tolerance


@@ -23,5 +23,5 @@ fprintf('Initial point (%d, %d), f = %f, grad = [%f;%f], hessian = [%f %f ; %f %
 gamma_fixed_step = gamma;
 [x_fixed, f_fixed, kk] = method_SteepDesc_Proj(fun, grad_fun, x0, sk_step, XSetLimmits, tol, max_iter, 'fixed');
 fprintf('Fixed step g=%f:     Initial point (%f, %f), steps:%d, Final (x1,x2)=(%f, %f), f(x1,x2)=%f\n', gamma_fixed_step, x0, kk, x_fixed(:, end), f_fixed(end));
-plotPointsOverContour(x_fixed, fun, XSetLimmits(1, :), XSetLimmits(2, :), 100, point_str + ": Steepest descent $\gamma$ = " + gamma_fixed_step, "");
+plotPointsOverContour(x_fixed, fun, XSetLimmits(1, :), XSetLimmits(2, :), 100, point_str + ": Steepest descent proj $s_k$ = " + sk_step + ", $\gamma$ = " + gamma_fixed_step, "figures/StDesProj_sk_" + sk_step + "_gamma_" + gamma + ".png");

@@ -23,5 +23,5 @@ fprintf('Initial point (%d, %d), f = %f, grad = [%f;%f], hessian = [%f %f ; %f %
 gamma_fixed_step = gamma;
 [x_fixed, f_fixed, kk] = method_SteepDesc_Proj(fun, grad_fun, x0, sk_step, XSetLimmits, tol, max_iter, 'fixed');
 fprintf('Fixed step g=%f:     Initial point (%f, %f), steps:%d, Final (x1,x2)=(%f, %f), f(x1,x2)=%f\n', gamma_fixed_step, x0, kk, x_fixed(:, end), f_fixed(end));
-plotPointsOverContour(x_fixed, fun, XSetLimmits(1, :), XSetLimmits(2, :), 100, point_str + ": Steepest descent $\gamma$ = " + gamma_fixed_step, "");
+plotPointsOverContour(x_fixed, fun, XSetLimmits(1, :), XSetLimmits(2, :), 100, point_str + ": Steepest descent proj $s_k$ = " + sk_step + ", $\gamma$ = " + gamma_fixed_step, "figures/StDesProj_sk_" + sk_step + "_gamma_" + gamma + ".png");