Updated maximum likelihood chapter.
Common latex header file.
This commit is contained in:
@@ -3,7 +3,7 @@
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for i = 1:140 % loop over different length
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for k = 1:10 % try several times
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a = randn( i, 1 ); % generate some data
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m = mymedian( a ) % compute median
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m = mymedian( a ); % compute median
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if length( a(a>m) ) ~= length( a(a<m) ) % check
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disp( 'error!' )
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end
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@@ -1,24 +1,27 @@
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% dependence of histogram on number of rolls:
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nrolls = [ 20, 100, 1000 ];
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nrolls = [20, 100, 1000];
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for i = [1:length(nrolls)]
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d = rollthedie( nrolls(i) );
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d = rollthedie(nrolls(i));
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% plain hist:
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%hist( d )
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%hist(d)
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% check bin counts of plain hist:
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% h = hist( d )
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% h = hist(d)
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% force 6 bins:
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%hist( d, 6 )
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%hist(d, 6)
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% set the right bin centers:
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%bins = 1:6;
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%hist( d, bins )
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bins = 1:6;
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%hist(d, bins)
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% normalize histogram and compare to expectation:
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plot([0 7], [1/6 1/6], '-r', 'linewidth', 10)
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[h, b] = hist(d, bins);
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h = h/sum(h) % normalization
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hold on
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plot( [0 7], [1/6 1/6], '-r', 'linewidth', 10 )
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hist( d, bins, 1.0, 'facecolor', 'b' )
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bar(b, h, 'facecolor', 'b')
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hold off
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pause
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title(sprintf('N=%d', length(d)))
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pause( 2.0 )
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end
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@@ -7,9 +7,9 @@ bins2 = -4:db2:4; % small bins
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[h2,b2] = hist(x,bins2);
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subplot( 1, 2, 1 );
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bar(b1,hn1)
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bar(b1,h1)
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hold on
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bar(b2,hn2, 'facecolor', 'r' )
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bar(b2,h2, 'facecolor', 'r' )
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xlabel('x')
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ylabel('Frequency')
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hold off
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@@ -1,30 +1,27 @@
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% plot Gaussian pdf:
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dx=0.1;
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dx=0.01;
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x = [-4.0:dx:4.0];
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p = exp(-0.5*x.^2)/sqrt(2.0*pi);
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plot(x, p, 'linewidth', 4)
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hold on
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plot(x, p, 'linewidth', 10)
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% show area of integral:
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x1=1.0;
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x2=2.0;
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area(x((x>=x1)&(x<=x2)), p((x>=x1)&(x<=x2)), 'FaceColor', 'r' )
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hold off
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% compute integral between x1 and x2:
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x1=1.0;
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x2=2.0;
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P = sum(p((x>=x1)&(x<x2)))*dx;
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disp( [ 'The integral between ', num2str(x1, 1), ' and ', num2str(x2, 1), ' is ', num2str(P, 3) ] );
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fprintf( 'The integral between %.2g and %.2g is %.3g\n', x1, x2, P );
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% draw random numbers:
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%r = randn( 10000, 1 );
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%hist(r,x,1.0/dx)
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r = randn( 10000, 1 );
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% check P:
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Pr = sum((r>=x1)&(r<x2))/length(r);
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disp( [ 'The probability of getting a number between ', num2str(x1, 1), ' and ', num2str(x2, 1), ' is ', num2str(Pr, 3) ] );
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fprintf( 'The probability of getting a number between %.2g and %.2g is %.3g\n', x1, x2, Pr );
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% infinite integral:
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P = sum(p)*dx;
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disp( [ 'The integral between -infinity and +infinity is ', num2str(P, 3) ] );
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disp( [ 'I.e. the probability to get any number is ', num2str(P, 3) ] );
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fprintf( 'The integral between -infinity and +infinity is %.3g\n', P );
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fprintf( 'I.e. the probability to get any number is %.3g\n', P );
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@@ -8,7 +8,7 @@ x1=0.0
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x2=1.0
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plt.xkcd()
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fig = plt.figure( figsize=(6,4) )
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fig = plt.figure( figsize=(6,3.8) )
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ax = fig.add_subplot( 1, 1, 1 )
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ax.spines['right'].set_visible(False)
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ax.spines['top'].set_visible(False)
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@@ -1,217 +1,8 @@
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\documentclass[12pt]{report}
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%%%%% title %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\title{\tr{Introduction to Scientific Computing}{Einf\"uhrung in die wissenschaftliche Datenverarbeitung}}
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\author{Jan Benda\\Abteilung Neuroethologie\\[2ex]\includegraphics[width=0.3\textwidth]{UT_WBMW_Rot_RGB}}
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\date{WS 15/16}
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\input{../../header}
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%%%% language %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% \newcommand{\tr}[2]{#1} % en
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% \usepackage[english]{babel}
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\newcommand{\tr}[2]{#2} % de
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\usepackage[german]{babel}
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%%%%% packages %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage{pslatex} % nice font for pdf file
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\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref}
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%%%% layout %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage[left=25mm,right=25mm,top=20mm,bottom=30mm]{geometry}
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\setcounter{tocdepth}{1}
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%%%%% section style %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage[sf,bf,it,big,clearempty]{titlesec}
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\setcounter{secnumdepth}{1}
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%%%%% units %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage[mediumspace,mediumqspace,Gray]{SIunits} % \ohm, \micro
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%%%%% figures %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage{graphicx}
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\usepackage{xcolor}
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\pagecolor{white}
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\newcommand{\ruler}{\par\noindent\setlength{\unitlength}{1mm}\begin{picture}(0,6)%
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\put(0,4){\line(1,0){170}}%
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\multiput(0,2)(10,0){18}{\line(0,1){4}}%
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\multiput(0,3)(1,0){170}{\line(0,1){2}}%
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\put(0,0){\makebox(0,0){{\tiny 0}}}%
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\put(10,0){\makebox(0,0){{\tiny 1}}}%
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\put(20,0){\makebox(0,0){{\tiny 2}}}%
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\put(30,0){\makebox(0,0){{\tiny 3}}}%
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\put(40,0){\makebox(0,0){{\tiny 4}}}%
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\put(50,0){\makebox(0,0){{\tiny 5}}}%
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\put(60,0){\makebox(0,0){{\tiny 6}}}%
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\put(70,0){\makebox(0,0){{\tiny 7}}}%
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\put(80,0){\makebox(0,0){{\tiny 8}}}%
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\put(90,0){\makebox(0,0){{\tiny 9}}}%
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\put(100,0){\makebox(0,0){{\tiny 10}}}%
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\put(110,0){\makebox(0,0){{\tiny 11}}}%
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\put(120,0){\makebox(0,0){{\tiny 12}}}%
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\put(130,0){\makebox(0,0){{\tiny 13}}}%
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\put(140,0){\makebox(0,0){{\tiny 14}}}%
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\put(150,0){\makebox(0,0){{\tiny 15}}}%
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\put(160,0){\makebox(0,0){{\tiny 16}}}%
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\put(170,0){\makebox(0,0){{\tiny 17}}}%
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\end{picture}\par}
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% figures:
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\setlength{\fboxsep}{0pt}
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\newcommand{\texpicture}[1]{{\sffamily\footnotesize\input{#1.tex}}}
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%\newcommand{\texpicture}[1]{\fbox{\sffamily\footnotesize\input{#1.tex}}}
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%\newcommand{\texpicture}[1]{\setlength{\fboxsep}{2mm}\fbox{#1}}
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%\newcommand{\texpicture}[1]{}
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\newcommand{\figlabel}[1]{\textsf{\textbf{\large \uppercase{#1}}}}
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% maximum number of floats:
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\setcounter{topnumber}{2}
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\setcounter{bottomnumber}{0}
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\setcounter{totalnumber}{2}
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% float placement fractions:
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\renewcommand{\textfraction}{0.2}
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\renewcommand{\topfraction}{0.8}
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\renewcommand{\bottomfraction}{0.0}
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\renewcommand{\floatpagefraction}{0.5}
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% spacing for floats:
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\setlength{\floatsep}{12pt plus 2pt minus 2pt}
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\setlength{\textfloatsep}{20pt plus 4pt minus 2pt}
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\setlength{\intextsep}{12pt plus 2pt minus 2pt}
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% spacing for a floating page:
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\makeatletter
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\setlength{\@fptop}{0pt}
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\setlength{\@fpsep}{8pt plus 2.0fil}
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\setlength{\@fpbot}{0pt plus 1.0fil}
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\makeatother
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% rules for floats:
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\newcommand{\topfigrule}{\vspace*{10pt}{\hrule height0.4pt}\vspace*{-10.4pt}}
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\newcommand{\bottomfigrule}{\vspace*{-10.4pt}{\hrule height0.4pt}\vspace*{10pt}}
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% captions:
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\usepackage[format=plain,singlelinecheck=off,labelfont=bf,font={small,sf}]{caption}
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% put caption on separate float:
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\newcommand{\breakfloat}{\end{figure}\begin{figure}[t]}
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% references to panels of a figure within the caption:
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\newcommand{\figitem}[1]{\textsf{\bfseries\uppercase{#1}}}
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% references to figures:
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\newcommand{\panel}[1]{\textsf{\uppercase{#1}}}
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\newcommand{\fref}[1]{\textup{\ref{#1}}}
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\newcommand{\subfref}[2]{\textup{\ref{#1}}\,\panel{#2}}
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% references to figures in normal text:
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\newcommand{\fig}{Fig.}
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\newcommand{\Fig}{Figure}
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\newcommand{\figs}{Figs.}
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\newcommand{\Figs}{Figures}
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\newcommand{\figref}[1]{\fig~\fref{#1}}
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\newcommand{\Figref}[1]{\Fig~\fref{#1}}
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\newcommand{\figsref}[1]{\figs~\fref{#1}}
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\newcommand{\Figsref}[1]{\Figs~\fref{#1}}
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\newcommand{\subfigref}[2]{\fig~\subfref{#1}{#2}}
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\newcommand{\Subfigref}[2]{\Fig~\subfref{#1}{#2}}
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\newcommand{\subfigsref}[2]{\figs~\subfref{#1}{#2}}
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\newcommand{\Subfigsref}[2]{\Figs~\subfref{#1}{#2}}
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% references to figures within bracketed text:
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\newcommand{\figb}{Fig.}
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\newcommand{\figsb}{Figs.}
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\newcommand{\figrefb}[1]{\figb~\fref{#1}}
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\newcommand{\figsrefb}[1]{\figsb~\fref{#1}}
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\newcommand{\subfigrefb}[2]{\figb~\subfref{#1}{#2}}
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\newcommand{\subfigsrefb}[2]{\figsb~\subfref{#1}{#2}}
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% references to tables:
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\newcommand{\tref}[1]{\textup{\ref{#1}}}
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% references to tables in normal text:
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\newcommand{\tab}{Tab.}
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\newcommand{\Tab}{Table}
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\newcommand{\tabs}{Tabs.}
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\newcommand{\Tabs}{Tables}
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\newcommand{\tabref}[1]{\tab~\tref{#1}}
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\newcommand{\Tabref}[1]{\Tab~\tref{#1}}
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\newcommand{\tabsref}[1]{\tabs~\tref{#1}}
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\newcommand{\Tabsref}[1]{\Tabs~\tref{#1}}
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% references to tables within bracketed text:
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\newcommand{\tabb}{Tab.}
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\newcommand{\tabsb}{Tab.}
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\newcommand{\tabrefb}[1]{\tabb~\tref{#1}}
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\newcommand{\tabsrefb}[1]{\tabsb~\tref{#1}}
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%%%%% equation references %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\newcommand{\eqref}[1]{(\ref{#1})}
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\newcommand{\eqn}{\tr{Eq}{Gl}.}
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\newcommand{\Eqn}{\tr{Eq}{Gl}.}
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\newcommand{\eqns}{\tr{Eqs}{Gln}.}
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\newcommand{\Eqns}{\tr{Eqs}{Gln}.}
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\newcommand{\eqnref}[1]{\eqn~\eqref{#1}}
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\newcommand{\Eqnref}[1]{\Eqn~\eqref{#1}}
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\newcommand{\eqnsref}[1]{\eqns~\eqref{#1}}
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\newcommand{\Eqnsref}[1]{\Eqns~\eqref{#1}}
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%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage{listings}
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\lstset{
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inputpath=../code,
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basicstyle=\ttfamily\footnotesize,
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numbers=left,
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showstringspaces=false,
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language=Matlab,
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commentstyle=\itshape\color{red!60!black},
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keywordstyle=\color{blue!50!black},
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stringstyle=\color{green!50!black},
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backgroundcolor=\color{blue!10},
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breaklines=true,
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breakautoindent=true,
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columns=flexible,
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frame=single,
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caption={\protect\filename@parse{\lstname}\protect\filename@base},
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captionpos=t,
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xleftmargin=1em,
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xrightmargin=1em,
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aboveskip=10pt
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}
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%%%%% math stuff: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage{amsmath}
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\usepackage{bm}
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\usepackage{dsfont}
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\newcommand{\naZ}{\mathds{N}}
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\newcommand{\gaZ}{\mathds{Z}}
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\newcommand{\raZ}{\mathds{Q}}
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\newcommand{\reZ}{\mathds{R}}
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\newcommand{\reZp}{\mathds{R^+}}
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\newcommand{\reZpN}{\mathds{R^+_0}}
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\newcommand{\koZ}{\mathds{C}}
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%%%%% structure: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage{ifthen}
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\newcommand{\code}[1]{\texttt{#1}}
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\newcommand{\source}[1]{
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\begin{flushright}
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\color{gray}\scriptsize \url{#1}
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\end{flushright}
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}
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\newenvironment{definition}[1][]{\medskip\noindent\textbf{Definition}\ifthenelse{\equal{#1}{}}{}{ #1}:\newline}%
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{\medskip}
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\newcounter{maxexercise}
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\setcounter{maxexercise}{9} % show listings up to exercise maxexercise
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\newcounter{theexercise}
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\setcounter{theexercise}{1}
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\newenvironment{exercise}[1][]{\medskip\noindent\textbf{\tr{Exercise}{\"Ubung}
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\arabic{theexercise}:}\newline \newcommand{\exercisesource}{#1}}%
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{\ifthenelse{\equal{\exercisesource}{}}{}{\ifthenelse{\value{theexercise}>\value{maxexercise}}{}{\medskip\lstinputlisting{\exercisesource}}}\medskip\stepcounter{theexercise}}
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\lstset{inputpath=../code}
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\graphicspath{{figures/}}
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@@ -53,7 +53,7 @@
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{Schreibe eine Funktion, die den Median eines Vektors zur\"uckgibt.}
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\end{exercise}
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\code{matlab} stellt die Funktion \code{median()} zur Berechnung des Medians bereit.
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\matlab{} stellt die Funktion \code{median()} zur Berechnung des Medians bereit.
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\begin{exercise}[checkmymedian.m]
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\tr{Write a script that tests whether your median function really
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@@ -70,24 +70,24 @@
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\caption{\label{quartilefig} Median und Quartile einer Normalverteilung.}
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\end{figure}
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\begin{definition}[\tr{quartile}{Quartile}]
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Die Quartile Q1, Q2 und Q3 unterteilen die Daten in vier gleich
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gro{\ss}e Gruppen, die jeweils ein Viertel der Daten enthalten.
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Das mittlere Quartil entspricht dem Median.
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\end{definition}
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% \begin{definition}[\tr{quartile}{Quartile}]
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% Die Quartile Q1, Q2 und Q3 unterteilen die Daten in vier gleich
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% gro{\ss}e Gruppen, die jeweils ein Viertel der Daten enthalten.
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% Das mittlere Quartil entspricht dem Median.
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% \end{definition}
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\begin{exercise}[quartiles.m]
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\tr{Write a function that computes the first, second, and third quartile of a vector.}
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{Schreibe eine Funktion, die das erste, zweite und dritte Quartil als Vektor zur\"uckgibt.}
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\end{exercise}
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% \begin{exercise}[quartiles.m]
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% \tr{Write a function that computes the first, second, and third quartile of a vector.}
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% {Schreibe eine Funktion, die das erste, zweite und dritte Quartil als Vektor zur\"uckgibt.}
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% \end{exercise}
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\section{\tr{Histogram}{Histogramm}}
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Histogramme z\"ahlen die H\"aufigkeit $n_i$ des Auftretens von
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$N=\sum_{i=1}^M n_i$ Messwerten in $M$ Messbereichsklassen $i$ (Bins).
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Die Klassen unterteilen den Wertebereich meist in angrenzende und
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gleich gro{\ss}e Intervalle. Histogramme sch\"atzen die
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Wahrscheinlichkeitsverteilung der Messwerte ab.
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gleich gro{\ss}e Intervalle. Histogramme k\"onnen verwendet werden, um die
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Wahrscheinlichkeitsverteilung der Messwerte abzusch\"atzen.
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\begin{exercise}[rollthedie.m]
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\tr{Write a function that simulates rolling a die $n$ times.}
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@@ -99,7 +99,7 @@ Wahrscheinlichkeitsverteilung der Messwerte ab.
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the plain hist(x) function, force 6 bins via hist( x, 6 ), and set
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meaningfull bins positions.} {Plotte Histogramme von 20, 100, und
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1000-mal w\"urfeln. Benutze \code{hist(x)}, erzwinge sechs Bins
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mit \code{hist(x,6)}, und setze selbst sinnvolle Bins. Normiere
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mit \code{hist(x,6)}, oder setze selbst sinnvolle Bins. Normiere
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anschliessend das Histogram auf geeignete Weise.}
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\end{exercise}
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@@ -216,7 +216,7 @@ Korrelationskoeffizient
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(x-\langle x \rangle)(y-\langle y \rangle) \rangle}{\sqrt{\langle
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(x-\langle x \rangle)^2} \rangle \sqrt{\langle (y-\langle y
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\rangle)^2} \rangle} \] quantifiziert einfache lineare
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Zusammenh\"ange. Perfekt korrelierte Variablen ergeben einen
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Zusammenh\"ange \matlabfun{corr}. Perfekt korrelierte Variablen ergeben einen
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Korrelationskoeffizienten von $+1$, antikorrelierte Daten einen
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Korrelationskoeffizienten von $-1$ und nicht korrelierte Daten einen
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Korrelationskoeffizienten nahe 0 (\figrefb{correlationfig}).
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Reference in New Issue
Block a user