diff --git a/Lectures_my/NumMet/2016/Lecture13/Makefile b/Lectures_my/NumMet/2016/Lecture13/Makefile new file mode 100644 index 0000000..e4cf8e8 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture13/Makefile @@ -0,0 +1,9 @@ +all: mchrzasz.pdf + +mchrzasz.pdf: mchrzasz.tex + xelatex mchrzasz.tex +# bibtex mchrzasz + xelatex mchrzasz.tex +# xelatex mchrzasz.tex +clean: + rm *.aux *.bbl *.blg *.log *.out *.pdf *.sh *.xml *.snm *.toc *.nav diff --git a/Lectures_my/NumMet/2016/Lecture13/beamercolorthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture13/beamercolorthemeFlip.sty new file mode 100755 index 0000000..d6b9c50 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture13/beamercolorthemeFlip.sty @@ -0,0 +1,179 @@ +% Color style file for the BEAMER FLIP THEME +% Copyright 2012 by Flip Tanedo +% This file may be distributed and/or modified +% 1. under the LaTeX Project Public License and/or +% 2. under the GNU Public License. + + + +\mode +\newif\ifbeamer@Flip@dark +\beamer@Flip@darkfalse +\DeclareOptionBeamer{dark}{\beamer@Flip@darktrue} +\ProcessOptionsBeamer + + +% These are a few colors that I like. + +\definecolor{crimsonred}{RGB}{153,0,0} % Neurtal red, good for dark or light bg +\definecolor{darkcharcoal}{RGB}{25,25,25} % Darker gray +\definecolor{charcoal}{RGB}{51,51,51} % Darker gray +\definecolor{ash}{RGB}{100,100,100} % medium gray +\definecolor{paleblue}{RGB}{0,102,102} % More of an `ocean' color +\definecolor{turtlegreen}{RGB}{51,153,0} % A more neutral green +\definecolor{paleale}{RGB}{204,204,102} % Only for dark BG +\definecolor{lager}{RGB}{140,110,10} % Use instead of pale ale for white BG +\definecolor{regal}{RGB}{90,0,120} % A more neutral purple +\definecolor{jeans}{RGB}{20,30,150} % A more neutral blue + + +% Define some "invariant colors" so that a color that doen't work with a +% light/dark background will automatically be substituted with one that does. +% These will be rewritten in beamercolorthemeFlipDark + +\ifbeamer@Flip@dark + \definecolor{FlipSand}{RGB}{204,204,102} % paleale, Only for dark BG + \definecolor{FlipGreen}{RGB}{0,255,0} % Neon-like green, only for dark BG +\else + \definecolor{FlipSand}{RGB}{140,110,10} % lager, Only for light BG + \definecolor{FlipGreen}{RGB}{51,153,0} % turtlegreen, works for both +\fi + +%% Future revision: It would be nice to define these in terms of the palette. + + +\ifbeamer@Flip@dark + \setbeamercolor{normal text}{fg=white, bg=black} + \setbeamercolor{structure}{fg=gray, bg=black} % fg controls bullets + \setbeamercolor*{footerlike}{fg=white,bg=black} % Controls the footerline +\else + % Default to black on white + \setbeamercolor*{footerlike}{fg=white,bg=charcoal} % for charcoal footer + \setbeamercolor{structure}{fg=charcoal, bg=white} % fg controls bullets + % \setbeamercolor{normal text}{fg=white, bg=black} +\fi + + + + + +% These defined colors can be used in \textcolor{colorname}{text in that color}. + +% Colors for Keynote background: DARK +\definecolor{keynotebottom}{rgb}{0.32,0.3,0.38} +\definecolor{keynotemiddle}{rgb}{0.08,0.08,0.16} +\definecolor{keynotetop}{rgb}{0,0,0} +%%% Example of usage: +%% \setbeamertemplate{background canvas}[vertical shading] +%% [bottom=keynotebottom, middle=keynotemiddle, top=keynotetop] + + + + +% ALERT AND COMMENT COLORS (just copies of the above colors) +% (I don't know how ot do this more elegantly) +\ifbeamer@Flip@dark + \definecolor{ALERT}{RGB}{153,0,0} % crimsonred + \definecolor{Alert}{RGB}{51,153,0} % turtlegreen + \definecolor{alert}{RGB}{204,204,102} % paleale + \definecolor{charcoal}{RGB}{51,51,51} % charcoal + \definecolor{comment}{RGB}{80,80,80} % light charcoal + \definecolor{Comment}{RGB}{100,100,100} % ash + \definecolor{COMMENT}{RGB}{80,20,120} % regal +\else +% \definecolor{ALERT}{RGB}{153,0,0} % crimsonred + \definecolor{ALERT}{RGB}{28,134,238} % DodgerBlue2 +% \definecolor{Alert}{RGB}{51,153,0} % turtlegreen + \definecolor{Alert}{RGB}{255,127,36} % chocolate1 +% \definecolor{alert}{RGB}{140,110,10} % lager + \definecolor{alert}{RGB}{0,205,102} % SpringGreen3 + \definecolor{charcoal}{RGB}{80,80,80} % light charcoal + \definecolor{comment}{RGB}{51,51,51} % charcoal + \definecolor{Comment}{RGB}{100,100,100} % ash + \definecolor{COMMENT}{RGB}{80,20,120} % regal +\fi + + +% \definecolor{crimsonred}{RGB}{153,0,0} % Neurtal red, good for dark or light bg +% \definecolor{charcoal}{RGB}{51,51,51} % Darker gray +% \definecolor{ash}{RGB}{100,100,100} % medium gray +% \definecolor{paleblue}{RGB}{0,102,102} % More of an `ocean' color +% \definecolor{turtlegreen}{RGB}{51,153,0} % A more neutral green +% \definecolor{paleale}{RGB}{204,204,102} % Only for dark BG +% \definecolor{lager}{RGB}{140,110,10} % Use instead of pale ale for white BG +% \definecolor{regal}{RGB}{90,0,120} % A more neutral purple +% \definecolor{jeans}{RGB}{20,30,150} % A more neutral blue + + +% A few useful colors +\setbeamercolor{alerted text}{fg=alert} + +%% I would like ot use these colors, but there seems to be a bug in Beamer +%% where the footnote color infects the normal text color +%% See: http://tex.stackexchange.com/questions/8264/beamer-changing-the-footnote-color-also-changes-the-normal-text-color/8268#8268 + +% \setbeamercolor{footnote}{parent=normal text, fg=FlipSand} +% \setbeamercolor{footnote mark}{parent=normal text, fg=FlipSand} + +% Blocks +\setbeamercolor{block title}{fg=gray!30!white,bg=charcoal} +\setbeamercolor{block body}{parent=normal text,bg=gray, fg=white} + +\setbeamercolor{block title example}{fg=turtlegreen!30!white,bg=turtlegreen!40!black} +\setbeamercolor{block body example}{parent=normal text,bg=turtlegreen, fg=white} +% +\setbeamercolor{block title alerted}{fg=crimsonred!30!white,bg=crimsonred!40!black} +\setbeamercolor{block body alerted}{parent=normal text,bg=crimsonred, fg=white} + + + +% These "setbeamercolor" commands are more standardized. + + +%% From the Beamer User Guide: +% Outer themes base the color of navigational elements and, possibly, also of other elements, on the +% four palette colors. The “primary” palette should be used for the most important navigational elements, +% which are usually the ones that change most often and hence require the most attention by the audience. +% The “secondary” and “tertiary” are less important, the “quaternary” one is least important. +% By default, the palette colors do not have a background and the foreground ranges from structure.fg to black. +% For the sidebar, there is an extra set of palette colors, see palette sidebar primary. + +\setbeamercolor*{palette primary}{fg=crimsonred,bg=charcoal} +\setbeamercolor*{palette secondary}{fg=paleale,bg=lager} +\setbeamercolor*{palette tertiary}{fg=turtlegreen,bg=jeans} +\setbeamercolor*{palette quaternary}{fg=paleblue,bg=regal} + +% \setbeamercolor*{palette primary}{fg=crimsonred,bg=white} +% \setbeamercolor*{palette secondary}{fg=charcoal,bg=white} +% \setbeamercolor*{palette tertiary}{fg=paleblue,bg=white} +% \setbeamercolor*{palette quaternary}{fg=turtlegreen,bg=white} + + + +%% These are some structures that I define for use in the outer theme. + +\setbeamercolor*{crimsontown}{fg=paleblue,bg=crimsonred} +\setbeamercolor*{bluetown}{fg=white,bg=DodgerBlue2} +%\setbeamercolor*{titlelike}{fg=crimsonred} +\setbeamercolor*{titlelike}{fg=DodgerBlue2} +\setbeamercolor*{topbarlike}{fg=white, bg=charcoal} + + + + + +%% Some old definitions that I might want to get back to +% +% \setbeamercolor*{frametitle}{bg=white,fg=charcoal} +% \setbeamercolor*{part title}{bg=white,fg=charcoal} +% \setbeamercolor*{item}{fg=charcoal, bg=white} +% +% \setbeamercolor*{separation line}{} +% \setbeamercolor*{fine separation line}{} + + + + + +\mode + diff --git a/Lectures_my/NumMet/2016/Lecture13/beamerinnerthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture13/beamerinnerthemeFlip.sty new file mode 100755 index 0000000..8dc12a0 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture13/beamerinnerthemeFlip.sty @@ -0,0 +1,95 @@ +% Inner style file for the BEAMER FLIP THEME +% Copyright 2010 by Flip Tanedo +% This file may be distributed and/or modified +% 1. under the LaTeX Project Public License and/or +% 2. under the GNU Public License. +% +% Based on: beamerinnerthemeFlip by Marco Barisione + +\mode + +% % Use alternative title page style. +% \DeclareOptionBeamer{alternativetitlepage}[true]{\def\beamer@Flip@alternativetitlepage{#1}} + +% Logo to use in the alternative title page. +% \def\beamer@Flip@titlepagelogo{} +% \DeclareOptionBeamer{titlepagelogo}{\def\beamer@Flip@titlepagelogo{#1}} + +% Bullet shape. +\DeclareOptionBeamer{bullet}{\def\beamer@Flip@bullet{#1}} +\DeclareOptionBeamer{shadow}[true]{\def\beamer@themerounded@shadow{#1}} +\ExecuteOptionsBeamer{shadow=false} + + +% \ExecuteOptionsBeamer{alternativetitlepage=false,bullet=square} +\ProcessOptionsBeamer + + + +% Margins. +\newlength{\beamer@Flip@normalmargin} +\setlength{\beamer@Flip@normalmargin}{.06\paperwidth} +\setbeamersize{text margin left=\beamer@Flip@normalmargin} +\setbeamersize{text margin right=\beamer@Flip@normalmargin} +\setlength\leftmargini{.6\beamer@Flip@normalmargin} +\setlength\leftmarginii{.6\beamer@Flip@normalmargin} +\setlength\leftmarginiii{.6\beamer@Flip@normalmargin} + +% Normal title page. +\defbeamertemplate*{title page normal}{Flip theme}[1][] +{ + \vbox{} + \vfill + \begin{centering} + \begin{beamercolorbox}[wd=\paperwidth,sep=8pt,center,#1]{title page header} + \usebeamerfont{title}\inserttitle\par% + \ifx\insertsubtitle\@empty% + \else% + \vskip0.25em% + {\usebeamerfont{subtitle}\usebeamercolor[fg]{subtitle}\insertsubtitle\par}% + \fi% + \end{beamercolorbox}% + %\vskip0.5em\par + \begin{beamercolorbox}[sep=8pt,center,#1]{author} + \usebeamerfont{author}\insertauthor + \end{beamercolorbox} + \begin{beamercolorbox}[sep=8pt,center,#1]{institute} + \usebeamerfont{institute}\insertinstitute + \end{beamercolorbox} + \begin{beamercolorbox}[sep=8pt,center,#1]{date} + \usebeamerfont{date}\insertdate + \end{beamercolorbox}\vskip0.5em + {\usebeamercolor[fg]{titlegraphic}\inserttitlegraphic\par} + \end{centering} + \vfill +} + + +% Items. +\defbeamertemplate{itemize item}{squarealt}% +{\tiny\raise.5ex\hbox{\donotcoloroutermaths$\blacksquare$}} +\defbeamertemplate{itemize subitem}{squarealt}% +{\tiny\raise.4ex\hbox{\donotcoloroutermaths$\square$}} +\defbeamertemplate{itemize subsubitem}{squarealt}% +{\tiny\raise.3ex\hbox{\donotcoloroutermaths$\blacksquare$}} +% +\defbeamertemplate{itemize item}{circlealt}% +{\small\raise.2ex\hbox{\donotcoloroutermaths$\bullet$}} +\defbeamertemplate{itemize subitem}{circlealt}% +{\small\raise.1ex\hbox{\donotcoloroutermaths$\circ$}} +\defbeamertemplate{itemize subsubitem}{circlealt}% +{\scriptsize\raise.1ex\hbox{\donotcoloroutermaths$\bullet$}} +\setbeamertemplate{items}[circlealt] +% +\def\circletext{circle} +\ifx\beamer@Flip@bullet\circletext + \setbeamertemplate{items}[circlealt] +\else + \setbeamertemplate{items}[squarealt] +\fi + +\setbeamertemplate{blocks}[rounded][shadow=\beamer@themerounded@shadow] + + +\mode + diff --git a/Lectures_my/NumMet/2016/Lecture13/beamerouterthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture13/beamerouterthemeFlip.sty new file mode 100755 index 0000000..d12f6d6 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture13/beamerouterthemeFlip.sty @@ -0,0 +1,189 @@ +% Outer style file for the BEAMER FLIP THEME 212 +% Copyright 2012 by Flip Tanedo +% This file may be distributed and/or modified +% 1. under the LaTeX Project Public License and/or +% 2. under the GNU Public License. +% +% Based on: beamerouterthemesplit by Till Tantau + + +\mode + +% Watermark +\DeclareOptionBeamer{watermark}{\def\beamer@Flip@watermark{#1}} +\ExecuteOptionsBeamer{watermark=} % Default value is empty + + +\newif\ifbeamer@Flip@bigpagenumber +\beamer@Flip@bigpagenumberfalse +\DeclareOptionBeamer{bigpagenumber}{\beamer@Flip@bigpagenumbertrue} + + +\def\beamer@Flip@truetext{true} % Kludge for true/false so I can use ifx + +\DeclareOptionBeamer{topline}[true]{\def\beamer@Flip@topline{#1}} +\ExecuteOptionsBeamer{topline=false} % Default + + + +% \ExecuteOptionsBeamer{topline=} % Default value is empty + + +\ProcessOptionsBeamer + + +\usepackage{tikz} % For fancy decorations + + +% I should fix these up to be more robust against color changes +\setbeamercolor{section in head/foot}{parent=footerlike} +\setbeamercolor{subsection in head/foot}{parent=footerlike} +\setbeamercolor{author in head/foot}{parent=footerlike} +\setbeamercolor{title in head/foot}{parent=footerlike} + + +% \setbeamercolor{author in head/foot}{parent=section in head/foot} +% \setbeamercolor{title in head/foot}{parent=subsection in head/foot} + +%\setbeamercolor{topbar}{parent=crimsontown} +\setbeamercolor{topbar}{parent=bluetown} + + + + +\usesectionheadtemplate + {\hfill\insertsectionhead} + {\hfill\color{fg!50!bg}\insertsectionhead} + + +%%%%%%%%%%%%%%%%%% +% The footer bar % +%%%%%%%%%%%%%%%%%% + +\defbeamertemplate*{footline}{Flip theme} +{% + \leavevmode% +% OBSERVATION: the "%" symbols inside hbox are all very important here. +% The \hbox enviroment will insert spaces whenever there's whitespace +% Adding a % at the END of each line ensures that any hard returns aren't +% interpreted as white space. This allows the color boxes to be flush against +% one another. If a faint white line appears one could probably do something like +% hspace{-1px} and add an additional pixel-or-two wide beamercolorbox. + +\hbox{% +\begin{beamercolorbox}[wd=.4\paperwidth,ht=2.5ex,dp=1.125ex,leftskip=.3cm, rightskip=.3cm plus1fil]{author in head/foot}% + \usebeamerfont{author in head/foot}\insertshortauthor \end{beamercolorbox}% +% +\begin{beamercolorbox}[wd=.6\paperwidth,ht=2.5ex,dp=1.125ex,leftskip=.3cm,rightskip=.3cm plus1fil]{title in head/foot}% + \usebeamerfont{title in head/foot}{\textit \insertshorttitle}% + \hskip2ex plus1fill% + % \insertpagenumber\,/\,\insertpresentationendpage %% Want FRAME, not SLIDE number + \insertframenumber/\inserttotalframenumber + \end{beamercolorbox}% +}% + +% This is a complete kludge for the faint white line which appears +% between the beamer color boxes above. (It doesnt appear in presentation mode +% but sometimes looks funny when the pdfs are viewed in a window) +\begin{tikzpicture}[overlay] + \usebeamercolor[bg]{author in head/foot} + \draw[thick] (0,3.625ex) -- (\paperwidth,3.625ex); + \draw (.4\paperwidth,0) -- (.4\paperwidth,3.625ex); + \draw[thick] (0,0) -- (\paperwidth,0); +\end{tikzpicture} + + + +\ifbeamer@Flip@bigpagenumber + \begin{tikzpicture}[overlay] + \usebeamercolor[bg]{author in head/foot} + \draw[fill] (\paperwidth-5ex,3.625ex) circle (6ex); + \usebeamercolor[fg]{author in head/foot} + \draw[fill] (\paperwidth-5ex,3.625ex) circle (5ex); + \usebeamercolor[bg]{author in head/foot} + \node at (\paperwidth-5ex,4ex) {\small$^\text{\insertframenumber}/_\text{\inserttotalframenumber}$}; + \end{tikzpicture} +\fi +} + + + +\defbeamertemplate*{frametitle}{Flip theme}[1][left] +{ +% \ifbeamercolorempty[bg]{frametitle}{}{\nointerlineskip}% +\@tempdima=\textwidth% +\advance\@tempdima by\beamer@leftmargin% +\advance\@tempdima by\beamer@rightmargin% + +\vbox{}\vskip-3.5ex% +% +\begin{beamercolorbox}[sep=0.3cm,#1,wd=\the\@tempdima]{titlelike} + \usebeamerfont{frametitle}% + \vbox{}\vskip-1ex% + \if@tempswa\else\csname beamer@fte#1\endcsname\fi% + % \strut{\bf\insertframetitle}\strut\par% %% Include the \bf + \strut{\insertframetitle}\strut\par% + {% + \ifx\insertframesubtitle\@empty% + \else + {\usebeamerfont{framesubtitle} + \usebeamercolor[fg]{framesubtitle} + \insertframesubtitle\strut\par}% + \fi + }% + % + \vskip-1ex% + \if@tempswa\else\vskip-.3cm\fi% set inside beamercolorbox... evil here... +\end{beamercolorbox}% +%% + +% \def\beamer@fteright{\vskip0.35cm\advance\leftskip by 1.7cm\advance\rightskip by1.7cm} +} + + + + +% Sidebar right is important: anything placed here will be +% visible *behind* the main text. This is where to put any +% interesting watermarks. +% +% +\defbeamertemplate*{sidebar right}{Flip theme} +{ +% \llap{\includegraphics[width=50px]{footdecoration}} +% \llap{\includegraphics[width=\paperwidth,height=\paperheight]{upperleft_watermark_transp}} +% +% THIS WOULD BE A NICE WAY TO PUT THE PARTICLE BUBBLE CHAMBER BG +% ... make a png of the background with TRANSPARENT BG +% ... then put the image here (use \hfill to get it on the left) +% Now one can FURTHER apply a slight gradient in the BG +% +% +% % Top Line +\ifx\beamer@Flip@topline\beamer@Flip@truetext + \begin{tikzpicture}[overlay] + \usebeamercolor[fg]{titlelike} % alternately, topbarlike would be a good beamercolor +% \usebeamercolor[fg]{topbarlike} % alternately, topbarlike would be a good beamercolor + \draw[fill] (-\paperwidth,0) rectangle (0,-3pt); + \end{tikzpicture} +\fi +% +% + \vskip.2\beamer@leftmargin% + %\llap{\insertlogo\hskip.5\beamer@leftmargin}% + \llap{\insertlogo\hskip.08\beamer@leftmargin}% + \vfill% + \if \beamer@Flip@watermark\@empty + % This is kind of a kludge since if I put anything in here, I automatically get errors + % Somehow LaTeX wants to read the \else part! + \else% + \llap{\includegraphics[width=\paperwidth,height=\paperheight]{\beamer@Flip@watermark}} + \fi +} + + + +\mode +\endinput + + diff --git a/Lectures_my/NumMet/2016/Lecture13/beamerouterthemedecolines.sty b/Lectures_my/NumMet/2016/Lecture13/beamerouterthemedecolines.sty new file mode 100755 index 0000000..669e493 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture13/beamerouterthemedecolines.sty @@ -0,0 +1,168 @@ +% Copyright 2007 by Marco Barisione +% +% This file may be distributed and/or modified +% +% 1. under the LaTeX Project Public License and/or +% 2. under the GNU Public License. + +\mode + +% String used between the current page and the total page count. +\def\beamer@decolines@pageofpages{/} +\DeclareOptionBeamer{pageofpages}{\def\beamer@decolines@pageofpages{#1}} + +% Show a line below the frame title. +\DeclareOptionBeamer{titleline}[true]{\def\beamer@decolines@titleline{#1}} + +% Image used for the watermark. +\def\beamer@decolines@watermarkorig{} +\DeclareOptionBeamer{watermark}{\def\beamer@decolines@watermarkorig{#1}} + +% Height of the watermark. +\def\beamer@decolines@watermarkheight{100px} +\DeclareOptionBeamer{watermarkheight}{\def\beamer@decolines@watermarkheight{#1}} + +% The original image height is watermarkheightmult * watermarkheight. +\def\beamer@decolines@watermarkheightmult{1} +\DeclareOptionBeamer{watermarkheightmult}{\def\beamer@decolines@watermarkheightmult{#1}} + +\ExecuteOptionsBeamer{titleline=false} +\ProcessOptionsBeamer + +% Enable/disable the watermark. +\def\watermarkon{% + \def\beamer@decolines@watermark{\beamer@decolines@watermarkorig}% +} +\def\watermarkoff{\def\beamer@decolines@watermark{}} + +% Initially enable the watermark. +\watermarkon + +% Colors. +\setbeamercolor*{lineup}{parent=palette primary} +\setbeamercolor*{linemid}{parent=palette secondary} +\setbeamercolor*{linebottom}{parent=palette tertiary} +\setbeamercolor*{page header}{parent=titlelike} + +% Lengths +\newlength{\headerheight} +\setlength{\headerheight}{.045\paperheight} +\newlength{\beamer@decolines@lineup} +\setlength{\beamer@decolines@lineup}{.025\paperheight} +\newlength{\beamer@decolines@linemid} +\setlength{\beamer@decolines@linemid}{.015\paperheight} +\newlength{\beamer@decolines@linebottom} +\setlength{\beamer@decolines@linebottom}{.01\paperheight} + +% The height of the watermark part below the 3 bottom lines. +\newlength{\beamer@decolines@watermarkheightbottom} +\addtolength{\beamer@decolines@watermarkheightbottom}{\beamer@decolines@lineup} +\addtolength{\beamer@decolines@watermarkheightbottom}{\beamer@decolines@linemid} +\addtolength{\beamer@decolines@watermarkheightbottom}{\beamer@decolines@linebottom} + +% The height of the watermark part over the 3 bottom lines before shrinking. +\newlength{\beamer@decolines@watermarkheightupperorig} +\setlength{\beamer@decolines@watermarkheightupperorig}{\beamer@decolines@watermarkheight} +\addtolength{\beamer@decolines@watermarkheightupperorig}{-\beamer@decolines@watermarkheightbottom} +\multiply\beamer@decolines@watermarkheightupperorig by \beamer@decolines@watermarkheightmult + +% % Footer. +% \defbeamertemplate*{footline}{decolines theme} +% { +% \leavevmode% +% % Page number. +% \hbox{% +% \begin{beamercolorbox}[wd=.2\paperwidth,ht=0ex,dp=0ex,center]{}% +% \usebeamerfont{palette primary}\insertframenumber{} \beamer@decolines@pageofpages{} \inserttotalframenumber% +% \end{beamercolorbox}% +% \begin{beamercolorbox}[wd=.8\paperwidth,ht=0ex,dp=0ex]{}% +% \end{beamercolorbox}% +% } % +% % First line. +% \hbox{% +% \begin{beamercolorbox}[wd=.2\paperwidth,ht=\beamer@decolines@lineup,dp=0pt]{}% +% \end{beamercolorbox}% +% \begin{beamercolorbox}[wd=.8\paperwidth,ht=\beamer@decolines@lineup,dp=0pt]{lineup}% +% \end{beamercolorbox}% +% } % +% % Second line. +% \hbox{% +% \begin{beamercolorbox}[wd=\paperwidth,ht=\beamer@decolines@linemid,dp=0pt]{linemid}% +% \end{beamercolorbox}% +% } % +% % Third line. +% \hbox{% +% \begin{beamercolorbox}[wd=.1\paperwidth,ht=\beamer@decolines@linebottom,dp=0pt]{}% +% \end{beamercolorbox}% +% \begin{beamercolorbox}[wd=.9\paperwidth,ht=\beamer@decolines@linebottom,dp=0pt]{linebottom}% +% \end{beamercolorbox}% +% }% +% % This seems to fix some alignment problems with the watermark. It has to be +% % always applied if you do not want to see the footer moving up and down when +% % moving from a page with watermark to a page without or vice versa. +% \vskip-.5px% +% % Watermark. +% \if\beamer@decolines@watermark\@empty\else% +% \vskip-\beamer@decolines@watermarkheightbottom% +% \llap{\includegraphics[height=\beamer@decolines@watermarkheightbottom,clip=true,% +% trim=0pt 0pt 0pt \beamer@decolines@watermarkheightupperorig]{\beamer@decolines@watermark}\hskip-\paperwidth}% +% \fi% +% } + +\defbeamertemplate*{headline}{decolines theme} +{ + \leavevmode% + \hbox{% + \begin{beamercolorbox}[wd=\paperwidth,ht=\headerheight,dp=0pt]{page header}% + \end{beamercolorbox}% + } % + \vskip0pt% +} + +\defbeamertemplate*{frametitle}{decolines theme}[1][left] +{ + \ifbeamercolorempty[bg]{frametitle}{}{\nointerlineskip}% + \@tempdima=\textwidth% + \advance\@tempdima by\beamer@leftmargin% + \advance\@tempdima by\beamer@rightmargin% + \vbox{}\vskip-.5\beamer@leftmargin% + \begin{beamercolorbox}[sep=\beamer@leftmargin,#1,wd=\the\@tempdima]{} + \usebeamerfont{frametitle}\usebeamercolor[bg]{framesubtitle}% + \vbox{}\vskip0ex% + \if@tempswa\else\csname beamer@fte#1\endcsname\fi% + \strut\insertframetitle\strut\par% + {% + \ifx\insertframesubtitle\@empty% + \else% + {\usebeamerfont{framesubtitle}\usebeamercolor[bg]{framesubtitle}\insertframesubtitle\strut\par}% + \fi + }% + \vskip-1ex% + \if@tempswa\else\vskip-\beamer@leftmargin\fi + \end{beamercolorbox}% + \def\beamer@decolines@truetext{true}% + \ifx\beamer@decolines@titleline\beamer@decolines@truetext% + \vskip-.5\beamer@leftmargin% + \begin{beamercolorbox}[wd=\textwidth,ht=.1ex,dp=0ex]{linemid}% + \end{beamercolorbox}% + \fi +} + +% Frame title continuations, default +\defbeamertemplate*{frametitle continuation}{decolines theme}{(\insertcontinuationcount)} + + + +\defbeamertemplate*{sidebar right}{decolines theme} +{ + \vskip.1\beamer@leftmargin% + \llap{\insertlogo\hskip.5\beamer@leftmargin}% + \vfill% + \if\beamer@decolines@watermark\@empty\else% + \llap{\includegraphics[height=\beamer@decolines@watermarkheight]{\beamer@decolines@watermark}}% + \vskip-\beamer@decolines@watermarkheightbottom% + \fi +} + +\mode + diff --git a/Lectures_my/NumMet/2016/Lecture13/beamerthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture13/beamerthemeFlip.sty new file mode 100755 index 0000000..a615ff5 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture13/beamerthemeFlip.sty @@ -0,0 +1,59 @@ +% Main style file for the BEAMER FLIP THEME 2012 +% Copyright 2012 by Flip Tanedo +% This file may be distributed and/or modified +% 1. under the LaTeX Project Public License and/or +% 2. under the GNU Public License. +% +% Comments: This is still a work in progress. +% A good way to present: http://www.cs.hmc.edu/~oneill/freesoftware/pdftokeynote.html + +% \usepackage{beamerthemesplit} +\mode + + +%% These are the options that are fed in through the driver file +%% Some of them get passed on to the other theme files +\DeclareOptionBeamer{bullet}{\PassOptionsToPackage{bullet=#1}{beamerinnerthemeFlip}} +\DeclareOptionBeamer{bigpagenumber}{\PassOptionsToPackage{bigpagenumber}{beamerouterthemeFlip}} +\DeclareOptionBeamer{topline}[true]{\PassOptionsToPackage{topline=#1}{beamerouterthemeFlip}} +\DeclareOptionBeamer{shadow}[false]{\PassOptionsToPackage{shadow=#1}{beamerinnerthemeFlip}} + +\DeclareOptionBeamer{watermark}{\PassOptionsToPackage{watermark=#1}{beamerouterthemeFlip}} + +\ProcessOptionsBeamer + +\useinnertheme{Flip} % Calls beamerinnerthemeFlip.sty +\useoutertheme{Flip} % Calls beamerouterthemeFlip.sty +\usecolortheme{Flip} % Calls beamercolorthemeFlip.sty + + + +%%%%%%%%%%%%%%%%%%%%%%%% +% Background Gradient % +%%%%%%%%%%%%%%%%%%%%%%%% + + +%% Usually I would leave this on +%% However, there seems to be problems with XeLaTeX +%% http://tex.stackexchange.com/questions/29497/xelatex-preventing-beamer-from-using-different-backgrounds +\setbeamertemplate{background canvas}[vertical shading][bottom=blue!.1, middle=white, top=white] + +%% HOWEVER: it seems to make it impossible to change this later on in the document + + +%% For a dark background: +% \setbeamertemplate{background canvas}[vertical shading][bottom=keynotebottom, middle=keynotemiddle, top=keynotetop] + + +%% An alternate way: \beamertemplateshadingbackground{blue!.1}{red!2} +%% In general: you want the gradient to be subtle! + + +%%%%%%%%%%%%%%%%%%%%%%% +% Navigation symbols % +%%%%%%%%%%%%%%%%%%%%%%% + +\setbeamertemplate{navigation symbols}{} % Turns off PDF navigation symbols + +\mode +\endinput \ No newline at end of file diff --git a/Lectures_my/NumMet/2016/Lecture13/images/BG_lower.png b/Lectures_my/NumMet/2016/Lecture13/images/BG_lower.png new file mode 100755 index 0000000..073034a --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture13/images/BG_lower.png Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture13/images/abc.png b/Lectures_my/NumMet/2016/Lecture13/images/abc.png new file mode 100644 index 0000000..baa9fe3 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture13/images/abc.png Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture13/images/abc1.png b/Lectures_my/NumMet/2016/Lecture13/images/abc1.png new file mode 100644 index 0000000..04d8d86 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture13/images/abc1.png Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture13/images/bernet.png b/Lectures_my/NumMet/2016/Lecture13/images/bernet.png new file mode 100644 index 0000000..f811a19 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture13/images/bernet.png Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture13/images/bubble.gif b/Lectures_my/NumMet/2016/Lecture13/images/bubble.gif new file mode 100644 index 0000000..ecff282 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture13/images/bubble.gif Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture13/images/bubble.jpg b/Lectures_my/NumMet/2016/Lecture13/images/bubble.jpg new file mode 100644 index 0000000..ceb584d --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture13/images/bubble.jpg Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture13/images/bubble2.jpg b/Lectures_my/NumMet/2016/Lecture13/images/bubble2.jpg new file mode 100644 index 0000000..0fd03bb --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture13/images/bubble2.jpg Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture13/images/gold.png b/Lectures_my/NumMet/2016/Lecture13/images/gold.png new file mode 100644 index 0000000..adbc540 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture13/images/gold.png Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture13/images/uzh-transp.pdf b/Lectures_my/NumMet/2016/Lecture13/images/uzh-transp.pdf new file mode 100644 index 0000000..977da67 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture13/images/uzh-transp.pdf Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture13/mchrzasz-blx.bib b/Lectures_my/NumMet/2016/Lecture13/mchrzasz-blx.bib new file mode 100644 index 0000000..9e405b3 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture13/mchrzasz-blx.bib @@ -0,0 +1,11 @@ +@Comment{$ biblatex control file $} +@Comment{$ biblatex version 2.3 $} +Do not modify this file! + +This is an auxiliary file used by the 'biblatex' package. +This file may safely be deleted. It will be recreated as +required. + +@Control{biblatex-control, + options = {2.3:0:0:1:0:0:1:1:0:0:0:0:1:1:3:1:79:+}, +} diff --git a/Lectures_my/NumMet/2016/Lecture13/mchrzasz.tex b/Lectures_my/NumMet/2016/Lecture13/mchrzasz.tex new file mode 100644 index 0000000..4c85aa7 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture13/mchrzasz.tex @@ -0,0 +1,508 @@ +\documentclass[11 pt,xcolor={dvipsnames,svgnames,x11names,table}]{beamer} + +\usepackage[english]{babel} +\usepackage{polski} + + +\usetheme[ + bullet=circle, % Other option: square + bigpagenumber, % circled page number on lower right + topline=true, % colored bar at the top of the frame + shadow=false, % Shading for beamer blocks + watermark=BG_lower, % png file for the watermark + ]{Flip} + +%\logo{\kern+1.em\includegraphics[height=1cm]{SHiP-3_LightCharcoal}} + + +\usepackage[lf]{berenis} +\usepackage[LY1]{fontenc} +\usepackage[utf8]{inputenc} +\usepackage{cases} +\usepackage{mathtools} +\usepackage{emerald} +\usefonttheme{professionalfonts} +\usepackage[no-math]{fontspec} +\defaultfontfeatures{Mapping=tex-text} % This seems to be important for mapping glyphs properly + +\setmainfont{Gillius ADF} % Beamer ignores "main font" in favor of sans font +\setsansfont{Gillius ADF} % This is the font that beamer will use by default +% \setmainfont{Gill Sans Light} % Prettier, but harder to read + +\setbeamerfont{title}{family=\fontspec{Gillius ADF}} + +\input t1augie.fd + +%\newcommand{\handwriting}{\fontspec{augie}} % From Emerald City, free font +%\newcommand{\handwriting}{\usefont{T1}{fau}{m}{n}} % From Emerald City, free font +% \newcommand{\handwriting}{} % If you prefer no special handwriting font or don't have augie + +%% Gill Sans doesn't look very nice when boldfaced +%% This is a hack to use Helvetica instead +%% Usage: \textbf{\forbold some stuff} +%\newcommand{\forbold}{\fontspec{Arial}} + +\usepackage{graphicx} +\usepackage[export]{adjustbox} + +\usepackage{amsmath} +\usepackage{amsfonts} +\usepackage{amssymb} +\usepackage{bm} +\usepackage{colortbl} +\usepackage{mathrsfs} % For Weinberg-esque letters +\usepackage{cancel} % For "SUSY-breaking" symbol +\usepackage{slashed} % for slashed characters in math mode +\usepackage{bbm} % for \mathbbm{1} (unit matrix) +\usepackage{amsthm} % For theorem environment +\usepackage{multirow} % For multi row cells in table +\usepackage{arydshln} % For dashed lines in arrays and tables +\usepackage{siunitx} +\usepackage{xhfill} +\usepackage{grffile} +\usepackage{textpos} +\usepackage{subfigure} +\usepackage{tikz} +\usepackage{hyperref} +%\usepackage{hepparticles} +\usepackage[italic]{hepparticles} + +\usepackage{hepnicenames} + +% Drawing a line +\tikzstyle{lw} = [line width=20pt] +\newcommand{\topline}{% + \tikz[remember picture,overlay] {% + \draw[crimsonred] ([yshift=-23.5pt]current page.north west) + -- ([yshift=-23.5pt,xshift=\paperwidth]current page.north west);}} + + + +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +\usepackage{tikzfeynman} % For Feynman diagrams +\usetikzlibrary{arrows,shapes} +\usetikzlibrary{trees} +\usetikzlibrary{matrix,arrows} % For commutative diagram +% http://www.felixl.de/commu.pdf +\usetikzlibrary{positioning} % For "above of=" commands +\usetikzlibrary{calc,through} % For coordinates +\usetikzlibrary{decorations.pathreplacing} % For curly braces +% http://www.math.ucla.edu/~getreuer/tikz.html +\usepackage{pgffor} % For repeating patterns + +\usetikzlibrary{decorations.pathmorphing} % For Feynman Diagrams +\usetikzlibrary{decorations.markings} +\tikzset{ + % >=stealth', %% Uncomment for more conventional arrows + vector/.style={decorate, decoration={snake}, draw}, + provector/.style={decorate, decoration={snake,amplitude=2.5pt}, draw}, + antivector/.style={decorate, decoration={snake,amplitude=-2.5pt}, draw}, + fermion/.style={draw=gray, postaction={decorate}, + decoration={markings,mark=at position .55 with {\arrow[draw=gray]{>}}}}, + fermionbar/.style={draw=gray, postaction={decorate}, + decoration={markings,mark=at position .55 with {\arrow[draw=gray]{<}}}}, + fermionnoarrow/.style={draw=gray}, + gluon/.style={decorate, draw=black, + decoration={coil,amplitude=4pt, segment length=5pt}}, + scalar/.style={dashed,draw=black, postaction={decorate}, + decoration={markings,mark=at position .55 with {\arrow[draw=black]{>}}}}, + scalarbar/.style={dashed,draw=black, postaction={decorate}, + decoration={markings,mark=at position .55 with {\arrow[draw=black]{<}}}}, + scalarnoarrow/.style={dashed,draw=black}, + electron/.style={draw=black, postaction={decorate}, + decoration={markings,mark=at position .55 with {\arrow[draw=black]{>}}}}, + bigvector/.style={decorate, decoration={snake,amplitude=4pt}, draw}, +} + +% TIKZ - for block diagrams, +% from http://www.texample.net/tikz/examples/control-system-principles/ +% \usetikzlibrary{shapes,arrows} +\tikzstyle{block} = [draw, rectangle, +minimum height=3em, minimum width=6em] + + + + +\usetikzlibrary{backgrounds} +\usetikzlibrary{mindmap,trees} % For mind map +\newcommand{\degree}{\ensuremath{^\circ}} +\newcommand{\E}{\mathrm{E}} +\newcommand{\Var}{\mathrm{Var}} +\newcommand{\Cov}{\mathrm{Cov}} +\newcommand\Ts{\rule{0pt}{2.6ex}} % Top strut +\newcommand\Bs{\rule[-1.2ex]{0pt}{0pt}} % Bottom strut + +\graphicspath{{images/}} % Put all images in this directory. Avoids clutter. + +% SOME COMMANDS THAT I FIND HANDY +% \renewcommand{\tilde}{\widetilde} % dinky tildes look silly, dosn't work with fontspec +\newcommand{\comment}[1]{\textcolor{comment}{\footnotesize{#1}\normalsize}} % comment mild +\newcommand{\Comment}[1]{\textcolor{Comment}{\footnotesize{#1}\normalsize}} % comment bold +\newcommand{\COMMENT}[1]{\textcolor{COMMENT}{\footnotesize{#1}\normalsize}} % comment crazy bold +\newcommand{\Alert}[1]{\textcolor{Alert}{#1}} % louder alert +\newcommand{\ALERT}[1]{\textcolor{ALERT}{#1}} % loudest alert +%% "\alert" is already a beamer pre-defined +\newcommand*{\Scale}[2][4]{\scalebox{#1}{$#2$}}% + +\def\Put(#1,#2)#3{\leavevmode\makebox(0,0){\put(#1,#2){#3}}} + +\usepackage{gmp} +\usepackage[final]{feynmp-auto} + +\usepackage[backend=bibtex,style=numeric-comp,firstinits=true]{biblatex} +\bibliography{bib} +\setbeamertemplate{bibliography item}[text] + +\makeatletter\let\frametextheight\beamer@frametextheight\makeatother + +% suppress frame numbering for backup slides +% you always need the appendix for this! +\newcommand{\backupbegin}{ + \newcounter{framenumberappendix} + \setcounter{framenumberappendix}{\value{framenumber}} +} +\newcommand{\backupend}{ + \addtocounter{framenumberappendix}{-\value{framenumber}} + \addtocounter{framenumber}{\value{framenumberappendix}} +} + + +\definecolor{links}{HTML}{2A1B81} +%\hypersetup{colorlinks,linkcolor=,urlcolor=links} + +% For shapo's formulas: +\def\lsi{\raise0.3ex\hbox{$<$\kern-0.75em\raise-1.1ex\hbox{$\sim$}}} +\def\gsi{\raise0.3ex\hbox{$>$\kern-0.75em\raise-1.1ex\hbox{$\sim$}}} +\newcommand{\lsim}{\mathop{\lsi}} +\newcommand{\gsim}{\mathop{\gsi}} +\newcommand{\wt}{\widetilde} +%\newcommand{\ol}{\overline} +\newcommand{\Tr}{\rm{Tr}} +\newcommand{\tr}{\rm{tr}} +\newcommand{\eqn}[1]{&\hspace{-0.7em}#1\hspace{-0.7em}&} +\newcommand{\vev}[1]{\rm{$\langle #1 \rangle$}} +\newcommand{\abs}[1]{\rm{$\left| #1 \right|$}} +\newcommand{\eV}{\rm{eV}} +\newcommand{\keV}{\rm{keV}} +\newcommand{\GeV}{\rm{GeV}} +\newcommand{\im}{\rm{Im}} +\newcommand{\disp}{\displaystyle} +\def\be{\begin{equation}} +\def\ee{\end{equation}} +\def\ba{\begin{eqnarray}} +\def\ea{\end{eqnarray}} +\def\d{\partial} +\def\l{\left(} +\def\r{\right)} +\def\la{\langle} +\def\ra{\rangle} +\def\e{{\rm e}} +\def\Br{{\rm Br}} +\def\fixme{{\color{red} FIXME!}} +\def\mc{{\color{Magenta}{MC}}\xspace} +\def\pdf{{\rm p.d.f.}} +\def\ARROW{{\color{JungleGreen}{$\Rrightarrow$}}\xspace} +\def\ARROWR{{\color{WildStrawberry}{$\Rrightarrow$}}\xspace} + +\author{ {\fontspec{Trebuchet MS}Marcin Chrz\k{a}szcz, Danny van Dyk} (UZH)} +\institute{UZH} +\title[Function minimalization II]{Function minimalization II} +\date{21 September 2016} + + +\begin{document} +\tikzstyle{every picture}+=[remember picture] + +{ +\setbeamertemplate{sidebar right}{\llap{\includegraphics[width=\paperwidth,height=\paperheight]{bubble2}}} +\begin{frame}[c]%{\phantom{title page}} +\begin{center} +\begin{center} + \begin{columns} + \begin{column}{0.9\textwidth} + \flushright\fontspec{Trebuchet MS}\bfseries \Huge {Function minimalization II} + \end{column} + \begin{column}{0.2\textwidth} + %\includegraphics[width=\textwidth]{SHiP-2} + \end{column} + \end{columns} +\end{center} + \quad + \vspace{3em} +\begin{columns} +\begin{column}{0.6\textwidth} +\flushright \vspace{-1.8em} {\fontspec{Trebuchet MS} \large Marcin Chrząszcz, Danny van Dyk\\\vspace{-0.1em}\small \href{mailto:mchrzasz@cern.ch}{mchrzasz@cern.ch}, \href{mailto:dany.van.dyk@gmail.com}{danny.van.dyk@gmail.com}} + +\end{column} +\begin{column}{0.4\textwidth} +\includegraphics[height=1.3cm]{uzh-transp} +\end{column} +\end{columns} + +\vspace{1em} +% \footnotesize\textcolor{gray}{With N. Serra, B. Storaci\\Thanks to the theory support from M. Shaposhnikov, D. Gorbunov}\normalsize\\ +\vspace{0.5em} + \textcolor{normal text.fg!50!Comment}{Numerical Methods, \\ 10 October, 2016} +\end{center} +\end{frame} +} + + +\begin{frame}\frametitle{Function minimalization} + +\ARROW Function mininalization if THE MOST important numerical technique. \\ +\ARROW We will discuss finding LOCAL minimum of functions in this lecture.\\ +\ARROW The numerical problem is to find the minimum one needs to evaluate the function many many times\\ +\pause +\ARROW Side note: If you want to find maximum do: $f(x) = - g(x)$.\\ +\ARROW How to find a minimum: +\begin{align*} +f(x_0+\delta) \simeq f(x_0) + f^{\prime}(x_0)\delta + \frac{1}{2} f^{\prime \prime}(x_0) \delta^2 +\end{align*} +\ARROW The first derivative $=0$. \\ +\ARROW If $\vert (f(x_0+\delta) - f(x_0) \vert \leq \epsilon$ where $\epsilon$ is the accuracy we are interested in.\\ +\ARROW From the above we see that: +\begin{align*} +\vert \delta \vert \sim \sqrt{\epsilon} +\end{align*} +\begin{exampleblock}{} +The minimum we are can calculate only with the $\sqrt{\epsilon}$ +\end{exampleblock} + +\end{frame} + + +\begin{frame}\frametitle{''RAW'' Minimum estimation} + +\ARROW We say that 3 points $(a,b,c)$ are bounding the minimum of $f(x)$ if: +\begin{align} +af(b),~f(c)>f(b) +\label{eq:eq1} +\end{align} +\ARROW How to find the points? The fist two we choose randomly.\\ +\ARROW Two points will show the fall of the function. We go in that direction by the same step as the distance between the first two points. If the above condition is not fulfilled we repeat the step.\\ +\begin{center} +\only<1>{ +\includegraphics[width=0.6\textwidth]{images/abc.png} +} +\only<2>{ +\includegraphics[width=0.6\textwidth]{images/abc1.png} +} +\end{center} + +\end{frame} + + +\begin{frame}\frametitle{''RAW'' Minimum estimation} + +\ARROW If we have 3 points that fulfil \ref{eq:eq1} we choose d such that: +\begin{align*} +a f(b)$\\ \hline\hline +If $d < b$ then $c=b$, $b=d$ & If $d < b$ then $a=d$\\ \hline +If $d > b$ then $a=b$, $b=d$ & If $d > b$ then $c=d$\\ \hline +\end{tabular} +\end{center} +\ARROW At each step we get new 3 points that fulfil the~\ref{eq:eq1} so we can iterate the whole procedure. Each step will have smaller distance of the points. \\ +\ARROW We and the iteration when the $\vert c -a \vert < \tau\left( \vert b \vert + \vert d \vert \right)$, where $\tau$ is our toleration. +\ARROW Now the only question is how to choose the d? + +\end{frame} + +\begin{frame}\frametitle{''RAW'' Minimum estimation} + +\ARROW If we have 3 points that fulfil \ref{eq:eq1} we choose d such that: +\begin{align*} +a f(b)$\\ \hline\hline +If $d < b$ then $c=b$, $b=d$ & If $d < b$ then $a=d$\\ \hline +If $d > b$ then $a=b$, $b=d$ & If $d > b$ then $c=d$\\ \hline +\label{tab1} +\end{tabular} +\end{center} +\ARROW At each step we get new 3 points that fulfil the~\ref{eq:eq1} so we can iterate the whole procedure. Each step will have smaller distance of the points. \\ +\ARROW We and the iteration when the $\vert c -a \vert < \tau\left( \vert b \vert + \vert d \vert \right)$, where $\tau$ is our toleration. +\ARROW Now the only question is how to choose the d? + +\end{frame} + +\begin{frame}\frametitle{Golden rule} + +\ARROW We seek for the $d$ point in the bigger $\left[a,b\right]$, $\left[b,c\right]$.\\ +\ARROW In order to minimalize the risk that the minimum will be in the smaller of the set we apply the golder rule: +\begin{align*} +\frac{\vert b-a \vert}{\vert c- a \vert}= \frac{\vert c - b \vert }{\vert b -a \vert} +\end{align*} +\ARROW Of course the initial 3 points will now have this feature, but we can obtain it fastly in the iterative procedure: +\begin{itemize} +\item If $\vert b -a \vert > \vert c -b \vert$, then $d = a + w \vert b -a \vert$ +\item If $\vert b -a \vert < \vert c -b \vert$, then $d = b + w \vert b -a \vert$ +\end{itemize} +where $w = \frac{3 -\sqrt{5}}{2}\simeq 0.381966...$ +\end{frame} + + + +\begin{frame}\frametitle{Golden rule} +\begin{center} +\includegraphics[width=0.75\textwidth]{images/gold.png} +\end{center} + +\end{frame} + +\begin{frame}\frametitle{Golden rule} + +\ARROW We seek for the $d$ point in the bigger $\left[a,b\right]$, $\left[b,c\right]$.\\ +\ARROW In order to minimalize the risk that the minimum will be in the smaller of the set we apply the golder rule: +\begin{align*} +\frac{\vert b-a \vert}{\vert c- a \vert}= \frac{\vert c - b \vert }{\vert b -a \vert} +\end{align*} +\ARROW Of course the initial 3 points will now have this feature, but we can obtain it fastly in the iterative procedure: +\begin{itemize} +\item If $\vert b -a \vert > \vert c -b \vert$, then $d = a + w \vert b -a \vert$ +\item If $\vert b -a \vert < \vert c -b \vert$, then $d = b + w \vert b -a \vert$ +\end{itemize} +where $w = \frac{3 -\sqrt{5}}{2}\simeq 0.381966...$ +\end{frame} + + + +\begin{frame}\frametitle{Golden rule - example} + +\begin{center} +\includegraphics[width=0.75\textwidth]{images/gold.png} +\end{center} + +\end{frame} + +\begin{frame}\frametitle{Brenet rule} + +\ARROW The better method then the golden rule is the parabolic interpolation.\\ +\ARROW Via 3 points we draw a parabola and as a new point we choose it's minimum: +\begin{align} +d = \frac{1}{2} \frac{a^2 (f_c - f_b) + b^2 (f_a + f_c ) + c^2 (f_b - f_a) }{a (f_c - f_b) + b (f_a + f_c ) + c (f_b - f_a)} +\label{eq:2} +\end{align} +\ARROW The justification of this method is the fact that arround the minimum the parabola is usually very good approximation.\\ +\ARROW We start from 3 points that fulfil~\ref{eq:eq1}. The $d$ we choose accordingly to~\ref{eq:2}.\\ +\ARROW We accept the new $d$ if: +\begin{itemize} +\item $d$ is in: $a 0$, $T>0$ are parameters. We do $M$ steps: +\begin{enumerate} +\item We calculate the $\hat{x} = x_k + \sigma \epsilon_k$, where$\epsilon_k$ is N dim random number for Gauss distribution. +\item We calculate $\hat{f}=f(\hat{x}$ +\item If $\hat{f} f_{\min}$ +\begin{itemize} +\item We choose $z$ from $\mathcal{U}(0,1)$. +\item If +\begin{align*} +z < \exp (- \frac{\hat{f}-f_k}{T} ) +\end{align*} +is true we accept new position. If not not we don't +\end{itemize} +\item We start over :) +\end{enumerate} + +\end{frame} + +\begin{frame}\frametitle{Why Monte Carlo - the algorithm} + +\ARROW There is no natural way to stop it.\\ +\ARROW We will do as many steps as we assumed.\\ +\ARROW Do couple of time the walk with different starting point.\\ +\ARROW The $\epsilon_k$ might not be a Gauss but some other distribution.\\ +\ARROW There are many this algorithms there: genetic algorithms, MCMC.\\ +\ARROW Current state of the art: "Metropolis-Hastings" algorithm.\\ +\ARROW Sign up for MC course if you want to learn those :) + +\end{frame} + + + + +\backupbegin + +\begin{frame}\frametitle{Backup} + + +\end{frame} + + + + + + + +\backupend +\end{document} diff --git a/Lectures_my/NumMet/2016/Lecture13/tikzfeynman.sty b/Lectures_my/NumMet/2016/Lecture13/tikzfeynman.sty new file mode 100755 index 0000000..521fc65 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture13/tikzfeynman.sty @@ -0,0 +1,43 @@ +% Tikz Feynman Diagrams +% by Flip Tanedo +% 4 January 2011, work in progress + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%% TIKZ - for drawing Feynman diagrams %%%% +%%% ... use with pdflatex %%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\usepackage{tikz} +\usetikzlibrary{arrows,shapes} +\usetikzlibrary{trees} +\usetikzlibrary{matrix,arrows} % For commutative diagram + % http://www.felixl.de/commu.pdf +\usetikzlibrary{positioning} % For "above of=" commands +\usetikzlibrary{calc,through} % For coordinates +\usetikzlibrary{decorations.pathreplacing} % For curly braces +\usepackage[tikz]{bclogo} % For cute logo boxes +\usepackage{pgffor} % For repeating patterns + +\usetikzlibrary{decorations.pathmorphing} % For Feynman Diagrams +\usetikzlibrary{decorations.markings} +\tikzset{ + % >=stealth', %% Different kind of arrows + vector/.style={decorate, decoration={snake}, draw}, + fermion/.style={postaction={decorate}, + decoration={markings,mark=at position .55 with {\arrow{>}}}}, + fermionbar/.style={draw, postaction={decorate}, + decoration={markings,mark=at position .55 with {\arrow{<}}}}, + fermionnoarrow/.style={}, + gluon/.style={decorate, + decoration={coil,amplitude=4pt, segment length=5pt}}, + scalar/.style={dashed, postaction={decorate}, + decoration={markings,mark=at position .55 with {\arrow{>}}}}, + scalarbar/.style={dashed, postaction={decorate}, + decoration={markings,mark=at position .55 with {\arrow{<}}}}, + scalarnoarrow/.style={dashed,draw}, +% +%% Special vectors (when you need to fine-tune wiggles) + provector/.style={decorate, decoration={snake,amplitude=2.5pt}, draw}, + antivector/.style={decorate, decoration={snake,amplitude=-2.5pt}, draw}, +} +