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MATLAB for ex3 done

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Claudio Maggioni (maggicl) 2021-03-22 15:31:56 +01:00
parent 85bb62cced
commit 9ce1520076
7 changed files with 11290 additions and 14201 deletions
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5240
hw1/contour.tex Normal file
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hw1/ex3.asv Normal file
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%% Homework 1 - Optimization Methods
% Author: Claudio Maggioni
%
% Sources:
% - https://www.youtube.com/watch?v=91RZYO1cv_o
clear
clc
close all
format short
%% Exercise 3.1
% f(x1, x2) = x1^2 + u * x2^2;
% 1/2 * [x1 x2] [2 0] [x1] + [0][x1]
% [0 2u] [x2] + [0][x2]
% A = [1 0; 0 u]; b = [0; 0]
%% Exercise 3.2
xaxis = -10:1:10;
yaxis = xaxis;
Zn = zeros(size(xaxis, 2), size(yaxis, 2));
Zs = {Zn,Zn,Zn,Zn,Zn,Zn,Zn,Zn,Zn,Zn};
for u = 1:10
A = [1 0; 0 u];
for i = 1:size(xaxis, 2)
for j = 1:size(yaxis, 2)
vec = [xaxis(i); yaxis(j)];
Zs{u}(i, j) = vec' * A * vec;
end
end
end
for u = 1:10
subplot(2, 5, u);
h = surf(xaxis, yaxis, Zs{u});
set(h,'LineStyle','none');
title(sprintf("u=%d", u));
end
sgtitle("Surf plots");
% comment these lines on submission
addpath /home/claudio/git/matlab2tikz/src
matlab2tikz('showInfo', false, './surf.tex')
figure
yi = zeros(30, 25);
ni = zeros(30, 25);
its = zeros(30, 1);
for u = 1:10
subplot(2, 5, u);
contour(xaxis, yaxis, Zs{u}, 10);
title(sprintf("u=%d", u));
%% Exercise 3.3
A = [2 0; 0 2*u];
b = [0; 0];
xs = [[0; 10] [10; 0] [10; 10]];
syms sx sy
f = 1/2 * [sx sy] * A * [sx; sy];
g = gradient(f, [sx; sy]);
hold on
j = 1;
for x0 = xs
ri = u * 3 - 3 + j;
x = x0;
i = 1;
xi = zeros(2, 25);
xi(:, 1) = x0;
yi(ri, 1) = subs(f, [sx sy], x0');
while true
p = -1 * double(subs(g, [sx sy], x'));
ni(ri, i) = log10(norm(p, 2));
if norm(p, 2) == 0 || ni(ri, i) <= -8
break
end
alpha = dot(b - A * x, p) / dot(A * p, p);
x = x + alpha * p;
i = i + 1;
xi(:, i) = x;
yi(ri, i) = subs(f, [sx sy], x');
end
xi = xi(:, 1:i);
plot(xi(1, :), xi(2, :), '-');
fprintf("u=%2d x0=[%2d,%2d] it=%2d x=[%d,%d]\n", u, ...
x0(1), x0(2), i, x(1), x(2));
its(ri) = i;
j = j + 1;
end
hold off
end
sgtitle("Contour plots and iteration steps");
% comment these lines on submission
addpath /home/claudio/git/matlab2tikz/src
matlab2tikz('showInfo', false, './contour.tex')
figure
for u = 1:10
subplot(2, 5, u);
title(sprintf("u=%d", u));
hold on
for j = 1:3
ri = u * 3 - 3 + j;
vec = yi(ri, :);
vec = vec(1:its(ri));
plot(1:its(ri), vec);
end
hold off
end
sgtitle("Iterations over values of objective function");
% comment these lines on submission
addpath /home/claudio/git/matlab2tikz/src
matlab2tikz('showInfo', false, './yseries.tex')
figure
for u = 1:10
title(sprintf("u=%d", u));
subplot(2, 5, u);
hold on
for j = 1:3
ri = u * 3 - 3 + j;
vec = ni(ri, :);
vec = vec(1:its(ri));
plot(1:its(ri), vec);
end
hold off
end
% comment these lines on submission
addpath /home/claudio/git/matlab2tikz/src
matlab2tikz('showInfo', false, './norms.tex')

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hw1/ex3.m
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%% Homework 1 - Optimization Methods
% Author: Claudio Maggioni
%
% Sources: % Sources:
% https://www.youtube.com/watch?v=91RZYO1cv_o % - https://www.youtube.com/watch?v=91RZYO1cv_o
clear
clc
close all
format short
%% Exercise 3.1 %% Exercise 3.1
@ -11,38 +19,144 @@
% A = [1 0; 0 u]; b = [0; 0] % A = [1 0; 0 u]; b = [0; 0]
%% Exercise 3.2 %% Exercise 3.2
xaxis = -10:1:10;
yaxis = xaxis;
Zn = zeros(size(xaxis, 2), size(yaxis, 2));
Zs = {Zn,Zn,Zn,Zn,Zn,Zn,Zn,Zn,Zn,Zn};
for u = 1:10 for u = 1:10
A = [1 0; 0 u]; A = [1 0; 0 u];
xs = -10:1:10; for i = 1:size(xaxis, 2)
ys = xs; for j = 1:size(yaxis, 2)
vec = [xaxis(i); yaxis(j)];
Z = zeros(size(xs, 2), size(ys, 2)); Zs{u}(i, j) = vec' * A * vec;
for i = 1:size(xs, 2)
for j = 1:size(ys, 2)
vec = [xs(i); ys(j)];
Z(i, j) = vec' * A * vec;
end end
end end
if u <= 5
fig = u;
con = 5 + u;
else
fig = 10 + u - 5;
con = 15 + u - 5;
end
subplot(4, 5, fig);
h = surf(xs, ys, Z);
set(h,'LineStyle','none');
title(sprintf("Surf for u=%d", u));
subplot(4, 5, con);
contour(xs, ys, Z, 20);
title(sprintf("Contour for u=%d", u));
end end
matlab2tikz('showInfo', false, './ex32.tex')
for u = 1:10
subplot(2, 5, u);
h = surf(xaxis, yaxis, Zs{u});
set(h,'LineStyle','none');
title(sprintf("u=%d", u));
end
sgtitle("Surf plots");
% comment these lines on submission
addpath /home/claudio/git/matlab2tikz/src
matlab2tikz('showInfo', false, './surf.tex')
figure
yi = zeros(30, 25);
ni = zeros(30, 25);
its = zeros(30, 1);
for u = 1:10
subplot(2, 5, u);
contour(xaxis, yaxis, Zs{u}, 10);
title(sprintf("u=%d", u));
%% Exercise 3.3
A = [2 0; 0 2*u];
b = [0; 0];
xs = [[0; 10] [10; 0] [10; 10]];
syms sx sy
f = 1/2 * [sx sy] * A * [sx; sy];
g = gradient(f, [sx; sy]);
hold on
j = 1;
for x0 = xs
ri = u * 3 - 3 + j;
x = x0;
i = 1;
xi = zeros(2, 25);
xi(:, 1) = x0;
yi(ri, 1) = subs(f, [sx sy], x0');
while true
p = -1 * double(subs(g, [sx sy], x'));
ni(ri, i) = log10(norm(p, 2));
if norm(p, 2) == 0 || ni(ri, i) <= -8
break
end
alpha = dot(b - A * x, p) / dot(A * p, p);
x = x + alpha * p;
i = i + 1;
xi(:, i) = x;
yi(ri, i) = subs(f, [sx sy], x');
end
xi = xi(:, 1:i);
plot(xi(1, :), xi(2, :), '-');
fprintf("u=%2d x0=[%2d,%2d] it=%2d x=[%d,%d]\n", u, ...
x0(1), x0(2), i, x(1), x(2));
its(ri) = i;
j = j + 1;
end
hold off
end
sgtitle("Contour plots and iteration steps");
% comment these lines on submission
addpath /home/claudio/git/matlab2tikz/src
matlab2tikz('showInfo', false, './contour.tex')
figure
for u = 1:10
subplot(2, 5, u);
title(sprintf("u=%d", u));
hold on
for j = 1:3
ri = u * 3 - 3 + j;
vec = yi(ri, :);
vec = vec(1:its(ri));
plot(1:its(ri), vec);
end
hold off
end
sgtitle("Iterations over values of objective function");
% comment these lines on submission
addpath /home/claudio/git/matlab2tikz/src
matlab2tikz('showInfo', false, './yseries.tex')
figure
for u = 1:10
subplot(2, 5, u);
hold on
for j = 1:3
ri = u * 3 - 3 + j;
vec = ni(ri, :);
vec = vec(1:its(ri));
plot(1:its(ri), vec);
end
hold off
title(sprintf("u=%d", u));
end
sgtitle("Iterations over log10 of gradient norms");
% comment these lines on submission
addpath /home/claudio/git/matlab2tikz/src
matlab2tikz('showInfo', false, './norms.tex')

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hw1/ex32.tex
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hw1/norms.tex Normal file
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% This file was created by matlab2tikz.
%
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% This file was created by matlab2tikz.
%
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