MATLAB for ex3 done
This commit is contained in:
Claudio Maggioni (maggicl)
parent
85bb62cced
commit
9ce1520076
7 changed files with 11290 additions and 14201 deletions
5240
hw1/contour.tex
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5240
hw1/contour.tex
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File diff suppressed because one or more lines are too long
161
hw1/ex3.asv
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161
hw1/ex3.asv
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%% Homework 1 - Optimization Methods
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% Author: Claudio Maggioni
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%
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% Sources:
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% - https://www.youtube.com/watch?v=91RZYO1cv_o
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clear
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clc
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close all
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format short
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%% Exercise 3.1
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% f(x1, x2) = x1^2 + u * x2^2;
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% 1/2 * [x1 x2] [2 0] [x1] + [0][x1]
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% [0 2u] [x2] + [0][x2]
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% A = [1 0; 0 u]; b = [0; 0]
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%% Exercise 3.2
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xaxis = -10:1:10;
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yaxis = xaxis;
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Zn = zeros(size(xaxis, 2), size(yaxis, 2));
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Zs = {Zn,Zn,Zn,Zn,Zn,Zn,Zn,Zn,Zn,Zn};
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for u = 1:10
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A = [1 0; 0 u];
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for i = 1:size(xaxis, 2)
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for j = 1:size(yaxis, 2)
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vec = [xaxis(i); yaxis(j)];
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Zs{u}(i, j) = vec' * A * vec;
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end
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end
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end
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for u = 1:10
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subplot(2, 5, u);
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h = surf(xaxis, yaxis, Zs{u});
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set(h,'LineStyle','none');
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title(sprintf("u=%d", u));
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end
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sgtitle("Surf plots");
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% comment these lines on submission
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addpath /home/claudio/git/matlab2tikz/src
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matlab2tikz('showInfo', false, './surf.tex')
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figure
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yi = zeros(30, 25);
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ni = zeros(30, 25);
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its = zeros(30, 1);
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for u = 1:10
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subplot(2, 5, u);
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contour(xaxis, yaxis, Zs{u}, 10);
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title(sprintf("u=%d", u));
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%% Exercise 3.3
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A = [2 0; 0 2*u];
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b = [0; 0];
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xs = [[0; 10] [10; 0] [10; 10]];
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syms sx sy
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f = 1/2 * [sx sy] * A * [sx; sy];
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g = gradient(f, [sx; sy]);
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hold on
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j = 1;
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for x0 = xs
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ri = u * 3 - 3 + j;
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x = x0;
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i = 1;
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xi = zeros(2, 25);
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xi(:, 1) = x0;
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yi(ri, 1) = subs(f, [sx sy], x0');
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while true
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p = -1 * double(subs(g, [sx sy], x'));
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ni(ri, i) = log10(norm(p, 2));
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if norm(p, 2) == 0 || ni(ri, i) <= -8
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break
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end
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alpha = dot(b - A * x, p) / dot(A * p, p);
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x = x + alpha * p;
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i = i + 1;
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xi(:, i) = x;
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yi(ri, i) = subs(f, [sx sy], x');
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end
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xi = xi(:, 1:i);
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plot(xi(1, :), xi(2, :), '-');
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fprintf("u=%2d x0=[%2d,%2d] it=%2d x=[%d,%d]\n", u, ...
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x0(1), x0(2), i, x(1), x(2));
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its(ri) = i;
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j = j + 1;
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end
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hold off
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end
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sgtitle("Contour plots and iteration steps");
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% comment these lines on submission
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addpath /home/claudio/git/matlab2tikz/src
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matlab2tikz('showInfo', false, './contour.tex')
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figure
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for u = 1:10
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subplot(2, 5, u);
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title(sprintf("u=%d", u));
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hold on
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for j = 1:3
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ri = u * 3 - 3 + j;
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vec = yi(ri, :);
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vec = vec(1:its(ri));
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plot(1:its(ri), vec);
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end
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hold off
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end
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sgtitle("Iterations over values of objective function");
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% comment these lines on submission
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addpath /home/claudio/git/matlab2tikz/src
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matlab2tikz('showInfo', false, './yseries.tex')
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figure
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for u = 1:10
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title(sprintf("u=%d", u));
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subplot(2, 5, u);
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hold on
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for j = 1:3
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ri = u * 3 - 3 + j;
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vec = ni(ri, :);
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vec = vec(1:its(ri));
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plot(1:its(ri), vec);
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end
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hold off
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end
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% comment these lines on submission
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addpath /home/claudio/git/matlab2tikz/src
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matlab2tikz('showInfo', false, './norms.tex')
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172
hw1/ex3.m
172
hw1/ex3.m
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@ -1,5 +1,13 @@
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%% Homework 1 - Optimization Methods
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% Author: Claudio Maggioni
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%
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% Sources:
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% https://www.youtube.com/watch?v=91RZYO1cv_o
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% - https://www.youtube.com/watch?v=91RZYO1cv_o
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clear
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clc
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close all
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format short
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%% Exercise 3.1
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@ -11,38 +19,144 @@
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% A = [1 0; 0 u]; b = [0; 0]
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%% Exercise 3.2
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xaxis = -10:1:10;
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yaxis = xaxis;
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Zn = zeros(size(xaxis, 2), size(yaxis, 2));
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Zs = {Zn,Zn,Zn,Zn,Zn,Zn,Zn,Zn,Zn,Zn};
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for u = 1:10
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A = [1 0; 0 u];
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xs = -10:1:10;
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ys = xs;
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Z = zeros(size(xs, 2), size(ys, 2));
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for i = 1:size(xs, 2)
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for j = 1:size(ys, 2)
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vec = [xs(i); ys(j)];
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Z(i, j) = vec' * A * vec;
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for i = 1:size(xaxis, 2)
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for j = 1:size(yaxis, 2)
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vec = [xaxis(i); yaxis(j)];
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Zs{u}(i, j) = vec' * A * vec;
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end
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end
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if u <= 5
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fig = u;
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con = 5 + u;
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else
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fig = 10 + u - 5;
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con = 15 + u - 5;
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end
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subplot(4, 5, fig);
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h = surf(xs, ys, Z);
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set(h,'LineStyle','none');
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title(sprintf("Surf for u=%d", u));
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subplot(4, 5, con);
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contour(xs, ys, Z, 20);
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title(sprintf("Contour for u=%d", u));
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end
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matlab2tikz('showInfo', false, './ex32.tex')
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for u = 1:10
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subplot(2, 5, u);
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h = surf(xaxis, yaxis, Zs{u});
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set(h,'LineStyle','none');
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title(sprintf("u=%d", u));
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end
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sgtitle("Surf plots");
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% comment these lines on submission
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addpath /home/claudio/git/matlab2tikz/src
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matlab2tikz('showInfo', false, './surf.tex')
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figure
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yi = zeros(30, 25);
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ni = zeros(30, 25);
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its = zeros(30, 1);
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for u = 1:10
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subplot(2, 5, u);
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contour(xaxis, yaxis, Zs{u}, 10);
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title(sprintf("u=%d", u));
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%% Exercise 3.3
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A = [2 0; 0 2*u];
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b = [0; 0];
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xs = [[0; 10] [10; 0] [10; 10]];
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syms sx sy
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f = 1/2 * [sx sy] * A * [sx; sy];
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g = gradient(f, [sx; sy]);
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hold on
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j = 1;
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for x0 = xs
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ri = u * 3 - 3 + j;
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x = x0;
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i = 1;
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xi = zeros(2, 25);
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xi(:, 1) = x0;
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yi(ri, 1) = subs(f, [sx sy], x0');
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while true
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p = -1 * double(subs(g, [sx sy], x'));
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ni(ri, i) = log10(norm(p, 2));
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if norm(p, 2) == 0 || ni(ri, i) <= -8
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break
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end
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alpha = dot(b - A * x, p) / dot(A * p, p);
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x = x + alpha * p;
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i = i + 1;
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xi(:, i) = x;
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yi(ri, i) = subs(f, [sx sy], x');
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end
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xi = xi(:, 1:i);
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plot(xi(1, :), xi(2, :), '-');
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fprintf("u=%2d x0=[%2d,%2d] it=%2d x=[%d,%d]\n", u, ...
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x0(1), x0(2), i, x(1), x(2));
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its(ri) = i;
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j = j + 1;
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end
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hold off
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end
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sgtitle("Contour plots and iteration steps");
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% comment these lines on submission
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addpath /home/claudio/git/matlab2tikz/src
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matlab2tikz('showInfo', false, './contour.tex')
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figure
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for u = 1:10
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subplot(2, 5, u);
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title(sprintf("u=%d", u));
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hold on
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for j = 1:3
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ri = u * 3 - 3 + j;
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vec = yi(ri, :);
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vec = vec(1:its(ri));
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plot(1:its(ri), vec);
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end
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hold off
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end
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sgtitle("Iterations over values of objective function");
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% comment these lines on submission
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addpath /home/claudio/git/matlab2tikz/src
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matlab2tikz('showInfo', false, './yseries.tex')
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figure
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for u = 1:10
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subplot(2, 5, u);
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hold on
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for j = 1:3
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ri = u * 3 - 3 + j;
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vec = ni(ri, :);
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vec = vec(1:its(ri));
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plot(1:its(ri), vec);
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end
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hold off
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title(sprintf("u=%d", u));
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end
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sgtitle("Iterations over log10 of gradient norms");
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% comment these lines on submission
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addpath /home/claudio/git/matlab2tikz/src
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matlab2tikz('showInfo', false, './norms.tex')
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14172
hw1/ex32.tex
14172
hw1/ex32.tex
File diff suppressed because one or more lines are too long
506
hw1/norms.tex
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506
hw1/norms.tex
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@ -0,0 +1,506 @@
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% This file was created by matlab2tikz.
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%
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\definecolor{mycolor1}{rgb}{0.00000,0.44700,0.74100}%
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\definecolor{mycolor2}{rgb}{0.85000,0.32500,0.09800}%
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\definecolor{mycolor3}{rgb}{0.92900,0.69400,0.12500}%
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%
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\begin{tikzpicture}
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\begin{axis}[%
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width=0.737in,
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height=1.524in,
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at={(0.774in,2.609in)},
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scale only axis,
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unbounded coords=jump,
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xmin=-0,
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xmax=2,
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ymin=1.3,
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ymax=1.45154499349597,
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axis background/.style={fill=white},
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title style={font=\bfseries},
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title={u=1},
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axis x line*=bottom,
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axis y line*=left
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]
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\addplot [color=mycolor1, forget plot]
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table[row sep=crcr]{%
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1 1.30102999566398\\
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2 -inf\\
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};
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\addplot [color=mycolor2, forget plot]
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table[row sep=crcr]{%
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1 1.30102999566398\\
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2 -inf\\
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};
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\addplot [color=mycolor3, forget plot]
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table[row sep=crcr]{%
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1 1.45154499349597\\
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2 -inf\\
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};
|
||||
\end{axis}
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|
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\begin{axis}[%
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width=0.737in,
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height=1.524in,
|
||||
at={(1.744in,2.609in)},
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scale only axis,
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unbounded coords=jump,
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xmin=0,
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xmax=20,
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ymin=-10,
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ymax=2,
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axis background/.style={fill=white},
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title style={font=\bfseries},
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title={u=2},
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axis x line*=bottom,
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axis y line*=left
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]
|
||||
\addplot [color=mycolor1, forget plot]
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||||
table[row sep=crcr]{%
|
||||
1 1.60205999132796\\
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2 -inf\\
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||||
};
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||||
\addplot [color=mycolor2, forget plot]
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||||
table[row sep=crcr]{%
|
||||
1 1.30102999566398\\
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||||
2 -inf\\
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||||
};
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||||
\addplot [color=mycolor3, forget plot]
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||||
table[row sep=crcr]{%
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||||
1 1.65051499783199\\
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||||
2 0.997302484056647\\
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||||
3 0.520181229336984\\
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4 -0.133031284438359\\
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5 -0.610152539158022\\
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11 -4.00115384464304\\
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12 -4.65436635841838\\
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||||
13 -5.13148761313805\\
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||||
14 -5.78470012691339\\
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15 -6.26182138163305\\
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16 -6.91503389540839\\
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17 -7.39215515012806\\
|
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18 -8.0453676639034\\
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};
|
||||
\end{axis}
|
||||
|
||||
\begin{axis}[%
|
||||
width=0.737in,
|
||||
height=1.524in,
|
||||
at={(2.714in,2.609in)},
|
||||
scale only axis,
|
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unbounded coords=jump,
|
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xmin=0,
|
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xmax=22,
|
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ymin=-10,
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ymax=2,
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axis background/.style={fill=white},
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title style={font=\bfseries},
|
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title={u=3},
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axis x line*=bottom,
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axis y line*=left
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]
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||||
\addplot [color=mycolor1, forget plot]
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table[row sep=crcr]{%
|
||||
1 1.77815125038364\\
|
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2 -inf\\
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||||
};
|
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\addplot [color=mycolor2, forget plot]
|
||||
table[row sep=crcr]{%
|
||||
1 1.30102999566398\\
|
||||
2 -inf\\
|
||||
};
|
||||
\addplot [color=mycolor3, forget plot]
|
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table[row sep=crcr]{%
|
||||
1 1.80102999566398\\
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||||
2 1.13202321470541\\
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||||
3 0.830993219041424\\
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||||
4 0.161986438082849\\
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||||
5 -0.139043557581132\\
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||||
6 -0.808050338539708\\
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||||
7 -1.10908033420369\\
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||||
8 -1.77808711516227\\
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||||
9 -2.07911711082625\\
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||||
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|
||||
11 -3.0491538874488\\
|
||||
12 -3.71816066840738\\
|
||||
13 -4.01919066407136\\
|
||||
14 -4.68819744502994\\
|
||||
15 -4.98922744069392\\
|
||||
16 -5.65823422165249\\
|
||||
17 -5.95926421731647\\
|
||||
18 -6.62827099827505\\
|
||||
19 -6.92930099393903\\
|
||||
20 -7.5983077748976\\
|
||||
21 -7.89933777056158\\
|
||||
22 -8.56834455152016\\
|
||||
};
|
||||
\end{axis}
|
||||
|
||||
\begin{axis}[%
|
||||
width=0.737in,
|
||||
height=1.524in,
|
||||
at={(3.684in,2.609in)},
|
||||
scale only axis,
|
||||
unbounded coords=jump,
|
||||
xmin=0,
|
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4744
hw1/surf.tex
Normal file
4744
hw1/surf.tex
Normal file
File diff suppressed because one or more lines are too long
496
hw1/yseries.tex
Normal file
496
hw1/yseries.tex
Normal file
|
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@ -0,0 +1,496 @@
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3 4.59183673469388\\
|
||||
4 0.49198250728863\\
|
||||
5 0.0527124114952103\\
|
||||
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|
||||
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|
||||
8 6.48339609316086e-05\\
|
||||
9 6.94649581410093e-06\\
|
||||
10 7.44267408653673e-07\\
|
||||
11 7.97429366414647e-08\\
|
||||
12 8.54388606872834e-09\\
|
||||
13 9.15416364506611e-10\\
|
||||
14 9.80803247685657e-11\\
|
||||
15 1.05086062252035e-11\\
|
||||
16 1.12592209555752e-12\\
|
||||
17 1.20634510238306e-13\\
|
||||
18 1.29251260969615e-14\\
|
||||
19 1.38483493896016e-15\\
|
||||
20 1.48375172031446e-16\\
|
||||
21 1.58973398605121e-17\\
|
||||
22 1.7032864136263e-18\\
|
||||
};
|
||||
\end{axis}
|
||||
|
||||
\begin{axis}[%
|
||||
width=0.737in,
|
||||
height=1.524in,
|
||||
at={(3.684in,2.609in)},
|
||||
scale only axis,
|
||||
xmin=0,
|
||||
xmax=22,
|
||||
ymin=0,
|
||||
ymax=500,
|
||||
axis background/.style={fill=white},
|
||||
title style={font=\bfseries},
|
||||
title={u=4},
|
||||
axis x line*=bottom,
|
||||
axis y line*=left
|
||||
]
|
||||
\addplot [color=mycolor1, forget plot]
|
||||
table[row sep=crcr]{%
|
||||
1 400\\
|
||||
2 0\\
|
||||
};
|
||||
\addplot [color=mycolor2, forget plot]
|
||||
table[row sep=crcr]{%
|
||||
1 100\\
|
||||
2 0\\
|
||||
};
|
||||
\addplot [color=mycolor3, forget plot]
|
||||
table[row sep=crcr]{%
|
||||
1 500\\
|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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|
||||
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||||
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||||
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|
||||
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||||
22 4.28323536732096e-18\\
|
||||
};
|
||||
\end{axis}
|
||||
|
||||
\begin{axis}[%
|
||||
width=0.737in,
|
||||
height=1.524in,
|
||||
at={(4.654in,2.609in)},
|
||||
scale only axis,
|
||||
xmin=0,
|
||||
xmax=22,
|
||||
ymin=0,
|
||||
ymax=600,
|
||||
axis background/.style={fill=white},
|
||||
title style={font=\bfseries},
|
||||
title={u=5},
|
||||
axis x line*=bottom,
|
||||
axis y line*=left
|
||||
]
|
||||
\addplot [color=mycolor1, forget plot]
|
||||
table[row sep=crcr]{%
|
||||
1 500\\
|
||||
2 0\\
|
||||
};
|
||||
\addplot [color=mycolor2, forget plot]
|
||||
table[row sep=crcr]{%
|
||||
1 100\\
|
||||
2 0\\
|
||||
};
|
||||
\addplot [color=mycolor3, forget plot]
|
||||
table[row sep=crcr]{%
|
||||
1 600\\
|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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||||
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|
||||
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|
||||
22 1.96826364869535e-18\\
|
||||
};
|
||||
\end{axis}
|
||||
|
||||
\begin{axis}[%
|
||||
width=0.737in,
|
||||
height=1.524in,
|
||||
at={(0.774in,0.491in)},
|
||||
scale only axis,
|
||||
xmin=0,
|
||||
xmax=22,
|
||||
ymin=0,
|
||||
ymax=800,
|
||||
axis background/.style={fill=white},
|
||||
title style={font=\bfseries},
|
||||
title={u=6},
|
||||
axis x line*=bottom,
|
||||
axis y line*=left
|
||||
]
|
||||
\addplot [color=mycolor1, forget plot]
|
||||
table[row sep=crcr]{%
|
||||
1 600\\
|
||||
2 0\\
|
||||
};
|
||||
\addplot [color=mycolor2, forget plot]
|
||||
table[row sep=crcr]{%
|
||||
1 100\\
|
||||
2 0\\
|
||||
};
|
||||
\addplot [color=mycolor3, forget plot]
|
||||
table[row sep=crcr]{%
|
||||
1 700\\
|
||||
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|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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||||
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|
||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
20 5.51104882519728e-17\\
|
||||
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|
||||
22 5.37404413817065e-19\\
|
||||
};
|
||||
\end{axis}
|
||||
|
||||
\begin{axis}[%
|
||||
width=0.737in,
|
||||
height=1.524in,
|
||||
at={(1.744in,0.491in)},
|
||||
scale only axis,
|
||||
xmin=0,
|
||||
xmax=20,
|
||||
ymin=0,
|
||||
ymax=800,
|
||||
axis background/.style={fill=white},
|
||||
title style={font=\bfseries},
|
||||
title={u=7},
|
||||
axis x line*=bottom,
|
||||
axis y line*=left
|
||||
]
|
||||
\addplot [color=mycolor1, forget plot]
|
||||
table[row sep=crcr]{%
|
||||
1 700\\
|
||||
2 0\\
|
||||
};
|
||||
\addplot [color=mycolor2, forget plot]
|
||||
table[row sep=crcr]{%
|
||||
1 100\\
|
||||
2 0\\
|
||||
};
|
||||
\addplot [color=mycolor3, forget plot]
|
||||
table[row sep=crcr]{%
|
||||
1 800\\
|
||||
2 73.2558139534884\\
|
||||
3 6.70801784748513\\
|
||||
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|
||||
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||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
20 1.50099795356954e-17\\
|
||||
};
|
||||
\end{axis}
|
||||
|
||||
\begin{axis}[%
|
||||
width=0.737in,
|
||||
height=1.524in,
|
||||
at={(2.714in,0.491in)},
|
||||
scale only axis,
|
||||
xmin=0,
|
||||
xmax=20,
|
||||
ymin=0,
|
||||
ymax=1000,
|
||||
axis background/.style={fill=white},
|
||||
title style={font=\bfseries},
|
||||
title={u=8},
|
||||
axis x line*=bottom,
|
||||
axis y line*=left
|
||||
]
|
||||
\addplot [color=mycolor1, forget plot]
|
||||
table[row sep=crcr]{%
|
||||
1 800\\
|
||||
2 0\\
|
||||
};
|
||||
\addplot [color=mycolor2, forget plot]
|
||||
table[row sep=crcr]{%
|
||||
1 100\\
|
||||
2 0\\
|
||||
};
|
||||
\addplot [color=mycolor3, forget plot]
|
||||
table[row sep=crcr]{%
|
||||
1 900\\
|
||||
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|
||||
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|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
18 5.57170073107532e-16\\
|
||||
19 4.73057545285173e-17\\
|
||||
20 4.01642966757197e-18\\
|
||||
};
|
||||
\end{axis}
|
||||
|
||||
\begin{axis}[%
|
||||
width=0.737in,
|
||||
height=1.524in,
|
||||
at={(3.684in,0.491in)},
|
||||
scale only axis,
|
||||
xmin=0,
|
||||
xmax=20,
|
||||
ymin=0,
|
||||
ymax=1000,
|
||||
axis background/.style={fill=white},
|
||||
title style={font=\bfseries},
|
||||
title={u=9},
|
||||
axis x line*=bottom,
|
||||
axis y line*=left
|
||||
]
|
||||
\addplot [color=mycolor1, forget plot]
|
||||
table[row sep=crcr]{%
|
||||
1 900\\
|
||||
2 0\\
|
||||
};
|
||||
\addplot [color=mycolor2, forget plot]
|
||||
table[row sep=crcr]{%
|
||||
1 100\\
|
||||
2 0\\
|
||||
};
|
||||
\addplot [color=mycolor3, forget plot]
|
||||
table[row sep=crcr]{%
|
||||
1 1000\\
|
||||
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|
||||
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||||
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||||
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||||
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||||
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|
||||
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||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
19 1.40537822233565e-17\\
|
||||
20 1.10890117269225e-18\\
|
||||
};
|
||||
\end{axis}
|
||||
|
||||
\begin{axis}[%
|
||||
width=0.737in,
|
||||
height=1.524in,
|
||||
at={(4.654in,0.491in)},
|
||||
scale only axis,
|
||||
xmin=0,
|
||||
xmax=20,
|
||||
ymin=0,
|
||||
ymax=1200,
|
||||
axis background/.style={fill=white},
|
||||
title style={font=\bfseries},
|
||||
title={u=10},
|
||||
axis x line*=bottom,
|
||||
axis y line*=left
|
||||
]
|
||||
\addplot [color=mycolor1, forget plot]
|
||||
table[row sep=crcr]{%
|
||||
1 1000\\
|
||||
2 0\\
|
||||
};
|
||||
\addplot [color=mycolor2, forget plot]
|
||||
table[row sep=crcr]{%
|
||||
1 100\\
|
||||
2 0\\
|
||||
};
|
||||
\addplot [color=mycolor3, forget plot]
|
||||
table[row sep=crcr]{%
|
||||
1 1100\\
|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
20 3.22032388911561e-19\\
|
||||
};
|
||||
\end{axis}
|
||||
\end{tikzpicture}%
|
||||
Reference in a new issue