hw1: matlab done, report almost done
This commit is contained in:
Claudio Maggioni (maggicl)
parent
9ce1520076
commit
59094974b1
8 changed files with 79 additions and 214 deletions
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@ -17,7 +17,7 @@ xmax=10,
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ymin=-10,
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ymax=10,
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axis background/.style={fill=white},
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title style={font=\bfseries},
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title style={yshift=1ex, font=\tiny\bfseries},
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title={u=1}
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]
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\addplot[contour prepared, contour prepared format=matlab, contour/labels=false] table[row sep=crcr] {%
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@ -533,7 +533,7 @@ xmax=10,
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ymin=-10,
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ymax=10,
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axis background/.style={fill=white},
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title style={font=\bfseries},
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title style={yshift=1ex, font=\tiny\bfseries},
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title={u=2}
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]
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\addplot[contour prepared, contour prepared format=matlab, contour/labels=false] table[row sep=crcr] {%
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@ -1065,7 +1065,7 @@ xmax=10,
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ymin=-10,
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ymax=10,
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axis background/.style={fill=white},
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title style={font=\bfseries},
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title style={yshift=1ex, font=\tiny\bfseries},
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title={u=3}
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]
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\addplot[contour prepared, contour prepared format=matlab, contour/labels=false] table[row sep=crcr] {%
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@ -1595,7 +1595,7 @@ xmax=10,
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ymin=-10,
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ymax=10,
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axis background/.style={fill=white},
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title style={font=\bfseries},
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title style={yshift=1ex, font=\tiny\bfseries},
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title={u=4}
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]
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\addplot[contour prepared, contour prepared format=matlab, contour/labels=false] table[row sep=crcr] {%
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@ -2113,7 +2113,7 @@ xmax=10,
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ymin=-10,
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ymax=10,
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axis background/.style={fill=white},
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title style={font=\bfseries},
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title style={yshift=1ex, font=\tiny\bfseries},
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title={u=5}
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]
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\addplot[contour prepared, contour prepared format=matlab, contour/labels=false] table[row sep=crcr] {%
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@ -2645,7 +2645,7 @@ xmax=10,
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ymin=-10,
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ymax=10,
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axis background/.style={fill=white},
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title style={font=\bfseries},
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title style={yshift=1ex, font=\tiny\bfseries},
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title={u=6}
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]
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\addplot[contour prepared, contour prepared format=matlab, contour/labels=false] table[row sep=crcr] {%
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@ -3161,7 +3161,7 @@ xmax=10,
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ymin=-10,
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ymax=10,
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axis background/.style={fill=white},
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title style={font=\bfseries},
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title style={yshift=1ex, font=\tiny\bfseries},
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title={u=7}
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]
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\addplot[contour prepared, contour prepared format=matlab, contour/labels=false] table[row sep=crcr] {%
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@ -3679,7 +3679,7 @@ xmax=10,
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ymin=-10,
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ymax=10,
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axis background/.style={fill=white},
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title style={font=\bfseries},
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title style={yshift=1ex, font=\tiny\bfseries},
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title={u=8}
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]
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\addplot[contour prepared, contour prepared format=matlab, contour/labels=false] table[row sep=crcr] {%
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@ -4205,7 +4205,7 @@ xmax=10,
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ymin=-10,
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ymax=10,
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axis background/.style={fill=white},
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title style={font=\bfseries},
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title style={yshift=1ex, font=\tiny\bfseries},
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title={u=9}
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]
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\addplot[contour prepared, contour prepared format=matlab, contour/labels=false] table[row sep=crcr] {%
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@ -4723,7 +4723,7 @@ xmax=10,
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ymin=-10,
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ymax=10,
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axis background/.style={fill=white},
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title style={font=\bfseries},
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title style={yshift=1ex, font=\tiny\bfseries},
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title={u=10}
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]
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\addplot[contour prepared, contour prepared format=matlab, contour/labels=false] table[row sep=crcr] {%
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161
hw1/ex3.asv
161
hw1/ex3.asv
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@ -1,161 +0,0 @@
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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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19
hw1/ex3.m
19
hw1/ex3.m
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@ -9,6 +9,9 @@ clc
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close all
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format short
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colw = 3;
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colh = 4;
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%% Exercise 3.1
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% f(x1, x2) = x1^2 + u * x2^2;
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@ -36,10 +39,10 @@ for u = 1:10
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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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subplot(colh, colw, 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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title(sprintf("\nu=%d", u));
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end
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sgtitle("Surf plots");
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@ -54,9 +57,9 @@ 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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subplot(colh, colw, u);
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contour(xaxis, yaxis, Zs{u}, 10);
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title(sprintf("u=%d", u));
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title(sprintf("\nu=%d", u));
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%% Exercise 3.3
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@ -121,8 +124,8 @@ 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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subplot(colh, colw, u);
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title(sprintf("\nu=%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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@ -142,7 +145,7 @@ 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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subplot(colh, colw, 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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@ -152,7 +155,7 @@ for u = 1:10
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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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title(sprintf("\nu=%d", u));
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end
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sgtitle("Iterations over log10 of gradient norms");
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BIN
hw1/main.pdf
BIN
hw1/main.pdf
Binary file not shown.
33
hw1/main.tex
33
hw1/main.tex
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@ -1,11 +1,28 @@
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\documentclass{scrartcl}
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\usepackage[utf8]{inputenc}
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\usepackage{graphicx}
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\usepackage{subcaption}
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\usepackage{amsmath}
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\usepackage{pgfplots}
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\pgfplotsset{compat=1.17}
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\usepackage{mathrsfs}
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\usepackage{hyperref}
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\usetikzlibrary{arrows}
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\pgfplotsset{compat=newest}
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\usetikzlibrary{plotmarks}
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\usetikzlibrary{arrows.meta}
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\usepgfplotslibrary{patchplots}
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\usepackage{grffile}
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\usepackage{amsmath}
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\usepackage{subcaption}
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\usepgfplotslibrary{external}
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\tikzexternalize
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\usepackage[margin=2.5cm]{geometry}
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% To compile:
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% sed -i 's#title style={font=\\bfseries#title style={yshift=1ex, font=\\tiny\\bfseries#' *.tex
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% luatex -enable-write18 -shellescape main.tex
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\pgfplotsset{every x tick label/.append style={font=\tiny, yshift=0.5ex}}
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\pgfplotsset{every title/.append style={font=\tiny, align=center}}
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\pgfplotsset{every y tick label/.append style={font=\tiny, xshift=0.5ex}}
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\pgfplotsset{every z tick label/.append style={font=\tiny, xshift=0.5ex}}
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\setlength{\parindent}{0cm}
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\setlength{\parskip}{0.5\baselineskip}
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@ -88,7 +105,13 @@ where:
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The graphs generated by MATLAB are shown below:
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\resizebox{\textwidth}{!}{\input{ex32.tex}}
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\resizebox{\textwidth}{!}{\input{surf.tex}}
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\resizebox{\textwidth}{!}{\input{contour.tex}}
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\resizebox{\textwidth}{!}{\input{yseries.tex}}
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\resizebox{\textwidth}{!}{\input{norms.tex}}
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Isolines get stretched along the y axis as $\mu$ increases. For a large $\mu$, points well far away from the axes could be a
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problem since picking search directions and steps using a naive gradient based method iterations will zig-zag to the minimizer reaching it slowly.
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@ -17,7 +17,7 @@ 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 style={yshift=1ex, font=\tiny\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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@ -50,7 +50,7 @@ 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 style={yshift=1ex, font=\tiny\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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@ -99,7 +99,7 @@ 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 style={yshift=1ex, font=\tiny\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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@ -152,7 +152,7 @@ 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 style={yshift=1ex, font=\tiny\bfseries},
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title={u=4},
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axis x line*=bottom,
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axis y line*=left
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@ -205,7 +205,7 @@ xmax=22,
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ymin=-10,
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ymax=2.00851666964939,
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axis background/.style={fill=white},
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title style={font=\bfseries},
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title style={yshift=1ex, font=\tiny\bfseries},
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title={u=5},
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axis x line*=bottom,
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axis y line*=left
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@ -258,7 +258,7 @@ xmax=22,
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ymin=-10,
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ymax=2.08513085769748,
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axis background/.style={fill=white},
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title style={font=\bfseries},
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title style={yshift=1ex, font=\tiny\bfseries},
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title={u=6},
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axis x line*=bottom,
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axis y line*=left
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@ -311,7 +311,7 @@ xmax=20,
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ymin=-10,
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ymax=2.15051499783199,
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axis background/.style={fill=white},
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title style={font=\bfseries},
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title style={yshift=1ex, font=\tiny\bfseries},
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title={u=7},
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axis x line*=bottom,
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axis y line*=left
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@ -362,7 +362,7 @@ xmax=20,
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ymin=-10,
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ymax=2.20748667398541,
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axis background/.style={fill=white},
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title style={font=\bfseries},
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title style={yshift=1ex, font=\tiny\bfseries},
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title={u=8},
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axis x line*=bottom,
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axis y line*=left
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@ -413,7 +413,7 @@ xmax=20,
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ymin=-10,
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ymax=2.25793692185584,
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axis background/.style={fill=white},
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title style={font=\bfseries},
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title style={yshift=1ex, font=\tiny\bfseries},
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title={u=9},
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axis x line*=bottom,
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axis y line*=left
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@ -464,7 +464,7 @@ xmax=20,
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ymin=-10,
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ymax=5,
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axis background/.style={fill=white},
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title style={font=\bfseries},
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title style={yshift=1ex, font=\tiny\bfseries},
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title={u=10},
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axis x line*=bottom,
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axis y line*=left
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20
hw1/surf.tex
20
hw1/surf.tex
|
|
@ -16,7 +16,7 @@ zmin=0,
|
|||
zmax=200,
|
||||
view={-37.5}{30},
|
||||
axis background/.style={fill=white},
|
||||
title style={font=\bfseries},
|
||||
title style={yshift=1ex, font=\tiny\bfseries},
|
||||
title={u=1},
|
||||
axis x line*=bottom,
|
||||
axis y line*=left,
|
||||
|
|
@ -490,7 +490,7 @@ zmin=0,
|
|||
zmax=300,
|
||||
view={-37.5}{30},
|
||||
axis background/.style={fill=white},
|
||||
title style={font=\bfseries},
|
||||
title style={yshift=1ex, font=\tiny\bfseries},
|
||||
title={u=2},
|
||||
axis x line*=bottom,
|
||||
axis y line*=left,
|
||||
|
|
@ -964,7 +964,7 @@ zmin=0,
|
|||
zmax=400,
|
||||
view={-37.5}{30},
|
||||
axis background/.style={fill=white},
|
||||
title style={font=\bfseries},
|
||||
title style={yshift=1ex, font=\tiny\bfseries},
|
||||
title={u=3},
|
||||
axis x line*=bottom,
|
||||
axis y line*=left,
|
||||
|
|
@ -1438,7 +1438,7 @@ zmin=0,
|
|||
zmax=600,
|
||||
view={-37.5}{30},
|
||||
axis background/.style={fill=white},
|
||||
title style={font=\bfseries},
|
||||
title style={yshift=1ex, font=\tiny\bfseries},
|
||||
title={u=4},
|
||||
axis x line*=bottom,
|
||||
axis y line*=left,
|
||||
|
|
@ -1912,7 +1912,7 @@ zmin=0,
|
|||
zmax=600,
|
||||
view={-37.5}{30},
|
||||
axis background/.style={fill=white},
|
||||
title style={font=\bfseries},
|
||||
title style={yshift=1ex, font=\tiny\bfseries},
|
||||
title={u=5},
|
||||
axis x line*=bottom,
|
||||
axis y line*=left,
|
||||
|
|
@ -2386,7 +2386,7 @@ zmin=0,
|
|||
zmax=700,
|
||||
view={-37.5}{30},
|
||||
axis background/.style={fill=white},
|
||||
title style={font=\bfseries},
|
||||
title style={yshift=1ex, font=\tiny\bfseries},
|
||||
title={u=6},
|
||||
axis x line*=bottom,
|
||||
axis y line*=left,
|
||||
|
|
@ -2860,7 +2860,7 @@ zmin=0,
|
|||
zmax=1000,
|
||||
view={-37.5}{30},
|
||||
axis background/.style={fill=white},
|
||||
title style={font=\bfseries},
|
||||
title style={yshift=1ex, font=\tiny\bfseries},
|
||||
title={u=7},
|
||||
axis x line*=bottom,
|
||||
axis y line*=left,
|
||||
|
|
@ -3334,7 +3334,7 @@ zmin=0,
|
|||
zmax=1000,
|
||||
view={-37.5}{30},
|
||||
axis background/.style={fill=white},
|
||||
title style={font=\bfseries},
|
||||
title style={yshift=1ex, font=\tiny\bfseries},
|
||||
title={u=8},
|
||||
axis x line*=bottom,
|
||||
axis y line*=left,
|
||||
|
|
@ -3808,7 +3808,7 @@ zmin=0,
|
|||
zmax=1000,
|
||||
view={-37.5}{30},
|
||||
axis background/.style={fill=white},
|
||||
title style={font=\bfseries},
|
||||
title style={yshift=1ex, font=\tiny\bfseries},
|
||||
title={u=9},
|
||||
axis x line*=bottom,
|
||||
axis y line*=left,
|
||||
|
|
@ -4282,7 +4282,7 @@ zmin=0,
|
|||
zmax=1100,
|
||||
view={-37.5}{30},
|
||||
axis background/.style={fill=white},
|
||||
title style={font=\bfseries},
|
||||
title style={yshift=1ex, font=\tiny\bfseries},
|
||||
title={u=10},
|
||||
axis x line*=bottom,
|
||||
axis y line*=left,
|
||||
|
|
|
|||
|
|
@ -16,7 +16,7 @@ xmax=2,
|
|||
ymin=0,
|
||||
ymax=200,
|
||||
axis background/.style={fill=white},
|
||||
title style={font=\bfseries},
|
||||
title style={yshift=1ex, font=\tiny\bfseries},
|
||||
title={u=1},
|
||||
axis x line*=bottom,
|
||||
axis y line*=left
|
||||
|
|
@ -48,7 +48,7 @@ xmax=20,
|
|||
ymin=0,
|
||||
ymax=300,
|
||||
axis background/.style={fill=white},
|
||||
title style={font=\bfseries},
|
||||
title style={yshift=1ex, font=\tiny\bfseries},
|
||||
title={u=2},
|
||||
axis x line*=bottom,
|
||||
axis y line*=left
|
||||
|
|
@ -96,7 +96,7 @@ xmax=22,
|
|||
ymin=0,
|
||||
ymax=400,
|
||||
axis background/.style={fill=white},
|
||||
title style={font=\bfseries},
|
||||
title style={yshift=1ex, font=\tiny\bfseries},
|
||||
title={u=3},
|
||||
axis x line*=bottom,
|
||||
axis y line*=left
|
||||
|
|
@ -148,7 +148,7 @@ xmax=22,
|
|||
ymin=0,
|
||||
ymax=500,
|
||||
axis background/.style={fill=white},
|
||||
title style={font=\bfseries},
|
||||
title style={yshift=1ex, font=\tiny\bfseries},
|
||||
title={u=4},
|
||||
axis x line*=bottom,
|
||||
axis y line*=left
|
||||
|
|
@ -200,7 +200,7 @@ xmax=22,
|
|||
ymin=0,
|
||||
ymax=600,
|
||||
axis background/.style={fill=white},
|
||||
title style={font=\bfseries},
|
||||
title style={yshift=1ex, font=\tiny\bfseries},
|
||||
title={u=5},
|
||||
axis x line*=bottom,
|
||||
axis y line*=left
|
||||
|
|
@ -252,7 +252,7 @@ xmax=22,
|
|||
ymin=0,
|
||||
ymax=800,
|
||||
axis background/.style={fill=white},
|
||||
title style={font=\bfseries},
|
||||
title style={yshift=1ex, font=\tiny\bfseries},
|
||||
title={u=6},
|
||||
axis x line*=bottom,
|
||||
axis y line*=left
|
||||
|
|
@ -304,7 +304,7 @@ xmax=20,
|
|||
ymin=0,
|
||||
ymax=800,
|
||||
axis background/.style={fill=white},
|
||||
title style={font=\bfseries},
|
||||
title style={yshift=1ex, font=\tiny\bfseries},
|
||||
title={u=7},
|
||||
axis x line*=bottom,
|
||||
axis y line*=left
|
||||
|
|
@ -354,7 +354,7 @@ xmax=20,
|
|||
ymin=0,
|
||||
ymax=1000,
|
||||
axis background/.style={fill=white},
|
||||
title style={font=\bfseries},
|
||||
title style={yshift=1ex, font=\tiny\bfseries},
|
||||
title={u=8},
|
||||
axis x line*=bottom,
|
||||
axis y line*=left
|
||||
|
|
@ -404,7 +404,7 @@ xmax=20,
|
|||
ymin=0,
|
||||
ymax=1000,
|
||||
axis background/.style={fill=white},
|
||||
title style={font=\bfseries},
|
||||
title style={yshift=1ex, font=\tiny\bfseries},
|
||||
title={u=9},
|
||||
axis x line*=bottom,
|
||||
axis y line*=left
|
||||
|
|
@ -454,7 +454,7 @@ xmax=20,
|
|||
ymin=0,
|
||||
ymax=1200,
|
||||
axis background/.style={fill=white},
|
||||
title style={font=\bfseries},
|
||||
title style={yshift=1ex, font=\tiny\bfseries},
|
||||
title={u=10},
|
||||
axis x line*=bottom,
|
||||
axis y line*=left
|
||||
|
|
|
|||
Reference in a new issue