hw1: matlab done, report almost done

hw1/contour.tex

@@ -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] {%

hw1/ex3.asv

@@ -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')
-

hw1/ex3.m

@@ -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);
+    subplot(colh, colw, u);
-    title(sprintf("u=%d", 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");
 

hw1/main.tex

@@ -1,11 +1,28 @@
 \documentclass{scrartcl}
 \usepackage[utf8]{inputenc}
+\usepackage{graphicx}
+\usepackage{subcaption}
 \usepackage{amsmath}
 \usepackage{pgfplots}
-\pgfplotsset{compat=1.17}
+\pgfplotsset{compat=newest}
-\usepackage{mathrsfs}
+\usetikzlibrary{plotmarks}
-\usepackage{hyperref}
+\usetikzlibrary{arrows.meta}
-\usetikzlibrary{arrows}
+\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.

hw1/norms.tex

@@ -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

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,

hw1/yseries.tex

@@ -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