51 lines
1.4 KiB
Matlab
51 lines
1.4 KiB
Matlab
clear
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clc
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close all
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syms xsym ysym
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%% 2.4
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f1 = (ysym - 4 * xsym^2)^2 + (1 - xsym)^2;
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[x1, xs1, ~] = trust_region(f1, 2, 1, 0.2, [0;0], 1e-8, 1000);
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%% 2.4c - Energy function plot
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surf_iterates(f1, xs1, -0.25:0.01:1.25, -0.5:0.01:4.25);
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exportgraphics(gca,'2-4-energy.png', 'Resolution', 200);
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figure;
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%% 2.5 - Rosenbrock's function
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f2 = (1 - xsym)^2 + 100 * (ysym - xsym^2)^2;
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[x2, xs2, gnorms2] = trust_region(f2, 2, 1, 0.2, [0;0], 1e-8, 1000);
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%% 2.5b - Energy function plot
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surf_iterates(f2, xs2, -0.25:0.01:1.25, -0.25:0.01:1.25);
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exportgraphics(gca,'2-5-energy.png', 'Resolution', 200);
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%% 2.5c - Log gradient norms
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figure;
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semilogy(0:size(gnorms2, 2)-1, gnorms2, '.-k');
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exportgraphics(gca,'2-5-gnorms.png', 'Resolution', 200);
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%% Helper functions
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function surf_iterates(f, xs, xrange, yrange)
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fl = matlabFunction(f);
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Z = zeros(size(yrange,2), size(xrange,2));
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for x = 1:size(xrange, 2)
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for y = 1:size(yrange, 2)
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Z(y,x) = fl(xrange(x), yrange(y));
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end
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end
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surf(xrange, yrange', Z, 'EdgeColor', 'none', 'FaceAlpha', 0.4);
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yrange = zeros(1, size(xs, 2));
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for i=1:size(xs, 2)
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yrange(1, i) = fl(xs(1, i), xs(2, i));
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end
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hold on
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plot3(xs(1, :), xs(2, :), yrange, '.r-');
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plot3(xs(1, 1), xs(2, 1), yrange(1), '.w-');
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plot3(xs(1, size(xs,2)), xs(2, size(xs,2)), yrange(size(xs,2)), '.k-');
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hold off
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end |