midterm: done 1, 2.3-2.5 (minus report commentary)

Claudio_Maggioni_midterm/main.m

@@ -0,0 +1,48 @@
+clear
+clc
+close all
+syms xsym ysym
+
+%% 2.4 
+f1 = (ysym - 4 * xsym^2)^2 + (1 - xsym)^2;
+[x1, xs1, ~] = trust_region(f1, 2, 1, 0.2, [0;0], 1e-8, 1000);
+
+%% 2.4c - Energy function plot
+surf_iterates(f1, xs1, -0.25:0.01:1.25, -0.5:0.01:4.25);
+figure;
+
+%% 2.5 - Rosenbrock's function
+f2 = (1 - xsym)^2 + 100 * (ysym - xsym^2)^2;
+[x2, xs2, gnorms2] = trust_region(f2, 2, 1, 0.2, [0;0], 1e-8, 1000);
+
+%% 2.5b - Energy function plot
+surf_iterates(f2, xs2, -0.25:0.01:1.25, -0.25:0.01:1.25);
+
+%% 2.5c - Log gradient norms
+figure;
+semilogy(0:size(gnorms2, 2)-1, gnorms2, '.-k');
+
+%% Helper functions
+function surf_iterates(f, xs, xrange, yrange)
+    fl = matlabFunction(f);
+    Z = zeros(size(yrange,2), size(xrange,2));
+
+    for x = 1:size(xrange, 2)
+        for y = 1:size(yrange, 2)
+            Z(y,x) = fl(xrange(x), yrange(y));
+        end
+    end
+
+    surf(xrange, yrange', Z, 'EdgeColor', 'none', 'FaceAlpha', 0.4);
+
+    yrange = zeros(1, size(xs, 2));
+    for i=1:size(xs, 2)
+        yrange(1, i) = fl(xs(1, i), xs(2, i));
+    end
+
+    hold on
+    plot3(xs(1, :), xs(2, :), yrange, '.r-');
+    plot3(xs(1, 1), xs(2, 1), yrange(1), '.w-');
+    plot3(xs(1, size(xs,2)), xs(2, size(xs,2)), yrange(size(xs,2)), '.k-');
+    hold off
+end

Claudio_Maggioni_midterm/trust_region.m

@@ -1,19 +1,5 @@
-
-syms x y
-f1 = (y - 4 * x^2)^2 + (1 - x)^2;
-[x, xs, gnorms] = trust_reg(f1, 2, 1, 0.2, [0;0], 1e-8, 1000);
-
-% Convert lambda to accept vector parameters
-function vl = vecLambda(fl) 
-    vl = @(x) fl(x(1), x(2));
-end
-
-% Compute quadratic form
-function y = qf(B, g, p, fk)
-    y = fk + 1/2 * p' * B * p + dot(g, p);
-end
-
-function [xk, xs, gnorms] = trust_reg(f, delta_hat, delta0, eta, x0, tol, max_n)
+function [xk, xs, gnorms] = trust_region(f, delta_hat, delta0, eta, ...
+    x0, tol, max_n)
     xs = zeros(2, max_n);
     gnorms = zeros(max_n);
     
@@ -69,3 +55,13 @@ function [xk, xs, gnorms] = trust_reg(f, delta_hat, delta0, eta, x0, tol, max_n)
         xs(:, i) = xk;
     end
 end
+
+% Convert lambda to accept vector parameters
+function vl = vecLambda(fl) 
+    vl = @(x) fl(x(1), x(2));
+end
+
+% Compute quadratic form
+function y = qf(B, g, p, fk)
+    y = fk + 1/2 * p' * B * p + dot(g, p);
+end