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hw1: matlab done, report almost done

This commit is contained in:
Claudio Maggioni (maggicl) 2021-03-22 16:22:10 +01:00
parent 9ce1520076
commit 59094974b1
8 changed files with 79 additions and 214 deletions
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20
hw1/contour.tex
View File

@ -17,7 +17,7 @@ xmax=10,
ymin=-10,
ymax=10,
axis background/.style={fill=white},
title style={font=\bfseries},
title style={yshift=1ex, font=\tiny\bfseries},
title={u=1}
]
\addplot[contour prepared, contour prepared format=matlab, contour/labels=false] table[row sep=crcr] {%
@ -533,7 +533,7 @@ xmax=10,
ymin=-10,
ymax=10,
axis background/.style={fill=white},
title style={font=\bfseries},
title style={yshift=1ex, font=\tiny\bfseries},
title={u=2}
]
\addplot[contour prepared, contour prepared format=matlab, contour/labels=false] table[row sep=crcr] {%
@ -1065,7 +1065,7 @@ xmax=10,
ymin=-10,
ymax=10,
axis background/.style={fill=white},
title style={font=\bfseries},
title style={yshift=1ex, font=\tiny\bfseries},
title={u=3}
]
\addplot[contour prepared, contour prepared format=matlab, contour/labels=false] table[row sep=crcr] {%
@ -1595,7 +1595,7 @@ xmax=10,
ymin=-10,
ymax=10,
axis background/.style={fill=white},
title style={font=\bfseries},
title style={yshift=1ex, font=\tiny\bfseries},
title={u=4}
]
\addplot[contour prepared, contour prepared format=matlab, contour/labels=false] table[row sep=crcr] {%
@ -2113,7 +2113,7 @@ xmax=10,
ymin=-10,
ymax=10,
axis background/.style={fill=white},
title style={font=\bfseries},
title style={yshift=1ex, font=\tiny\bfseries},
title={u=5}
]
\addplot[contour prepared, contour prepared format=matlab, contour/labels=false] table[row sep=crcr] {%
@ -2645,7 +2645,7 @@ xmax=10,
ymin=-10,
ymax=10,
axis background/.style={fill=white},
title style={font=\bfseries},
title style={yshift=1ex, font=\tiny\bfseries},
title={u=6}
]
\addplot[contour prepared, contour prepared format=matlab, contour/labels=false] table[row sep=crcr] {%
@ -3161,7 +3161,7 @@ xmax=10,
ymin=-10,
ymax=10,
axis background/.style={fill=white},
title style={font=\bfseries},
title style={yshift=1ex, font=\tiny\bfseries},
title={u=7}
]
\addplot[contour prepared, contour prepared format=matlab, contour/labels=false] table[row sep=crcr] {%
@ -3679,7 +3679,7 @@ xmax=10,
ymin=-10,
ymax=10,
axis background/.style={fill=white},
title style={font=\bfseries},
title style={yshift=1ex, font=\tiny\bfseries},
title={u=8}
]
\addplot[contour prepared, contour prepared format=matlab, contour/labels=false] table[row sep=crcr] {%
@ -4205,7 +4205,7 @@ xmax=10,
ymin=-10,
ymax=10,
axis background/.style={fill=white},
title style={font=\bfseries},
title style={yshift=1ex, font=\tiny\bfseries},
title={u=9}
]
\addplot[contour prepared, contour prepared format=matlab, contour/labels=false] table[row sep=crcr] {%
@ -4723,7 +4723,7 @@ xmax=10,
ymin=-10,
ymax=10,
axis background/.style={fill=white},
title style={font=\bfseries},
title style={yshift=1ex, font=\tiny\bfseries},
title={u=10}
]
\addplot[contour prepared, contour prepared format=matlab, contour/labels=false] table[row sep=crcr] {%

161
hw1/ex3.asv
View File

@ -1,161 +0,0 @@
%% 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')

19
hw1/ex3.m
View File

@ -9,6 +9,9 @@ clc
close all
format short
colw = 3;
colh = 4;
%% Exercise 3.1
% f(x1, x2) = x1^2 + u * x2^2;
@ -36,10 +39,10 @@ for u = 1:10
end
for u = 1:10
subplot(2, 5, u);
subplot(colh, colw, u);
h = surf(xaxis, yaxis, Zs{u});
set(h,'LineStyle','none');
title(sprintf("u=%d", u));
title(sprintf("\nu=%d", u));
end
sgtitle("Surf plots");
@ -54,9 +57,9 @@ ni = zeros(30, 25);
its = zeros(30, 1);
for u = 1:10
subplot(2, 5, u);
subplot(colh, colw, u);
contour(xaxis, yaxis, Zs{u}, 10);
title(sprintf("u=%d", u));
title(sprintf("\nu=%d", u));
%% Exercise 3.3
@ -121,8 +124,8 @@ matlab2tikz('showInfo', false, './contour.tex')
figure
for u = 1:10
subplot(2, 5, u);
title(sprintf("u=%d", u));
subplot(colh, colw, u);
title(sprintf("\nu=%d", u));
hold on
for j = 1:3
ri = u * 3 - 3 + j;
@ -142,7 +145,7 @@ matlab2tikz('showInfo', false, './yseries.tex')
figure
for u = 1:10
subplot(2, 5, u);
subplot(colh, colw, u);
hold on
for j = 1:3
ri = u * 3 - 3 + j;
@ -152,7 +155,7 @@ for u = 1:10
plot(1:its(ri), vec);
end
hold off
title(sprintf("u=%d", u));
title(sprintf("\nu=%d", u));
end
sgtitle("Iterations over log10 of gradient norms");

BIN
hw1/main.pdf
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Binary file not shown.

33
hw1/main.tex
View File

@ -1,11 +1,28 @@
\documentclass{scrartcl}
\usepackage[utf8]{inputenc}
\usepackage{graphicx}
\usepackage{subcaption}
\usepackage{amsmath}
\usepackage{pgfplots}
\pgfplotsset{compat=1.17}
\usepackage{mathrsfs}
\usepackage{hyperref}
\usetikzlibrary{arrows}
\pgfplotsset{compat=newest}
\usetikzlibrary{plotmarks}
\usetikzlibrary{arrows.meta}
\usepgfplotslibrary{patchplots}
\usepackage{grffile}
\usepackage{amsmath}
\usepackage{subcaption}
\usepgfplotslibrary{external}
\tikzexternalize
\usepackage[margin=2.5cm]{geometry}
% To compile:
% sed -i 's#title style={font=\\bfseries#title style={yshift=1ex, font=\\tiny\\bfseries#' *.tex
% luatex -enable-write18 -shellescape main.tex
\pgfplotsset{every x tick label/.append style={font=\tiny, yshift=0.5ex}}
\pgfplotsset{every title/.append style={font=\tiny, align=center}}
\pgfplotsset{every y tick label/.append style={font=\tiny, xshift=0.5ex}}
\pgfplotsset{every z tick label/.append style={font=\tiny, xshift=0.5ex}}
\setlength{\parindent}{0cm}
\setlength{\parskip}{0.5\baselineskip}
@ -88,7 +105,13 @@ where:
The graphs generated by MATLAB are shown below:
\resizebox{\textwidth}{!}{\input{ex32.tex}}
\resizebox{\textwidth}{!}{\input{surf.tex}}
\resizebox{\textwidth}{!}{\input{contour.tex}}
\resizebox{\textwidth}{!}{\input{yseries.tex}}
\resizebox{\textwidth}{!}{\input{norms.tex}}
Isolines get stretched along the y axis as $\mu$ increases. For a large $\mu$, points well far away from the axes could be a
problem since picking search directions and steps using a naive gradient based method iterations will zig-zag to the minimizer reaching it slowly.

20
hw1/norms.tex
View File

@ -17,7 +17,7 @@ xmax=2,
ymin=1.3,
ymax=1.45154499349597,
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
@ -50,7 +50,7 @@ xmax=20,
ymin=-10,
ymax=2,
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
@ -99,7 +99,7 @@ xmax=22,
ymin=-10,
ymax=2,
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
@ -152,7 +152,7 @@ xmax=22,
ymin=-10,
ymax=2,
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
@ -205,7 +205,7 @@ xmax=22,
ymin=-10,
ymax=2.00851666964939,
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
@ -258,7 +258,7 @@ xmax=22,
ymin=-10,
ymax=2.08513085769748,
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
@ -311,7 +311,7 @@ xmax=20,
ymin=-10,
ymax=2.15051499783199,
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
@ -362,7 +362,7 @@ xmax=20,
ymin=-10,
ymax=2.20748667398541,
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
@ -413,7 +413,7 @@ xmax=20,
ymin=-10,
ymax=2.25793692185584,
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
@ -464,7 +464,7 @@ xmax=20,
ymin=-10,
ymax=5,
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

20
hw1/surf.tex
View File

@ -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,

20
hw1/yseries.tex
View File

@ -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