diff --git a/Lectures_my/EMPP/2016/Lecture3/mchrzasz.synctex.gz b/Lectures_my/EMPP/2016/Lecture3/mchrzasz.synctex.gz deleted file mode 100644 index a8c9780..0000000 --- a/Lectures_my/EMPP/2016/Lecture3/mchrzasz.synctex.gz +++ /dev/null Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture1/Examples/ex1/Makefile b/Lectures_my/NumMet/2016/Lecture1/Examples/ex1/Makefile new file mode 100644 index 0000000..c7813b2 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture1/Examples/ex1/Makefile @@ -0,0 +1,70 @@ +#---------------------------------------------------------------------- +# Przyklad linkowania bibliotek systemu ROOT z wlasnym programem +#---------------------------------------------------------------------- +.SUFFIXES: .o .c .cxx .cpp .C .f .l .s .sh .h .a .cc +#====================================================================== +# Biblioteki ROOTa dla linkera +# 1) Jawnie: +## Sciezka to systemu ROOT - nalezy ja ustawic odpowiednio +RPATH = /home/mchrzasz/ROOT/root/ +RLIB= -L$(RPATH)lib -lCore -lHist -lGraf -lGraf3d -lGpad -lTree -lRooFitCore -lRooFit -lRooStats \ + -lRint -lPostscript -lMatrix -lPhysics -lm -ldl -lpthread -rdynamic -Wl,--no-as-needed $(ROOTGLIBS) +#2) Niejawnie, przy uzyciu root-config +#RLIB= `root-config --libs` +#====================================================================== +# Nazwa biezacego katalogu +DIRNAME = ./ +#====================================================================== +# Nazwa rdzeniowa modulu programu +NAME1 = ex1 +# Pliki objectowe (po kompilacji) +OBJT1 = $(NAME1).o +# Pliki wykonawcze (po linkowaniu) +EXEC1 = $(NAME1).x +# Nazwa i opcje kompilatora +CXX = g++ +# 1) Jawnie +#CXXFLAGS = -O -Wall -pthread -I$(RPATH)include +# 2) Przy uzyciu root-config +CXXFLAGS = -O2 -Wall `root-config --cflags` +# Nazwa i opcje linkera +LD = $(CXX) +LDFLAGS = `root-config --ldflags` + + +CXXFLAGS += $(shell $(ROOTSYS)/bin/root-config --cflags) +#EXTRALIBS += $(shell $(ROOTSYS)/bin/root-config --libs) +LDFLAGS += $(shell $(ROOTSYS)/bin/root-config --libs) +RLIB += $(shell $(ROOTSYS)/bin/root-config --libs) + +#============================================================================== +# Kompilacja dla modulow z plikami naglowkowymi +%.o: %.cxx %.h + $(CXX) $(CXXFLAGS) -c $< +# Kompilacja dla modulow bez plikow naglowkowych +%.o: %.cxx + $(CXX) $(CXXFLAGS) -c $< +#============================================================================== +.PHONY: all run clean tar +all: ${EXEC1} +#============================================================================== +# Linkowanie +${EXEC1}: ${OBJT1} + $(LD) -o $@ $(LDFLAGS) $^ $(RLIB) + +#============================================================================== +# Uruchamianie +run: ${EXEC1} + ./${EXEC1} +#============================================================================== +clean: + (rm -f *.o *.a *~ *.exe *.x core lmap *.dvi *.aux *.log a.out) +#============================================================================== +tar: clean + (cd ../; tar -cvzf $(DIRNAME).tar.gz $(DIRNAME) ) +#============================================================================== +# Wszelkie akcje jakie należy podjąć aby program zaprezentował swoje działanie: +test: run + @echo 'Test run finished' +#============================================================================== + diff --git a/Lectures_my/NumMet/2016/Lecture1/Examples/ex1/Makefile~ b/Lectures_my/NumMet/2016/Lecture1/Examples/ex1/Makefile~ new file mode 100644 index 0000000..ec55feb --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture1/Examples/ex1/Makefile~ @@ -0,0 +1,70 @@ +#---------------------------------------------------------------------- +# Przyklad linkowania bibliotek systemu ROOT z wlasnym programem +#---------------------------------------------------------------------- +.SUFFIXES: .o .c .cxx .cpp .C .f .l .s .sh .h .a .cc +#====================================================================== +# Biblioteki ROOTa dla linkera +# 1) Jawnie: +## Sciezka to systemu ROOT - nalezy ja ustawic odpowiednio +RPATH = /home/mchrzasz/ROOT/root/ +RLIB= -L$(RPATH)lib -lCore -lHist -lGraf -lGraf3d -lGpad -lTree -lRooFitCore -lRooFit -lRooStats \ + -lRint -lPostscript -lMatrix -lPhysics -lm -ldl -lpthread -rdynamic -Wl,--no-as-needed $(ROOTGLIBS) +#2) Niejawnie, przy uzyciu root-config +#RLIB= `root-config --libs` +#====================================================================== +# Nazwa biezacego katalogu +DIRNAME = ./ +#====================================================================== +# Nazwa rdzeniowa modulu programu +NAME1 = Add_variables +# Pliki objectowe (po kompilacji) +OBJT1 = $(NAME1).o +# Pliki wykonawcze (po linkowaniu) +EXEC1 = $(NAME1).x +# Nazwa i opcje kompilatora +CXX = g++ +# 1) Jawnie +#CXXFLAGS = -O -Wall -pthread -I$(RPATH)include +# 2) Przy uzyciu root-config +CXXFLAGS = -O2 -Wall `root-config --cflags` +# Nazwa i opcje linkera +LD = $(CXX) +LDFLAGS = `root-config --ldflags` + + +CXXFLAGS += $(shell $(ROOTSYS)/bin/root-config --cflags) +#EXTRALIBS += $(shell $(ROOTSYS)/bin/root-config --libs) +LDFLAGS += $(shell $(ROOTSYS)/bin/root-config --libs) +RLIB += $(shell $(ROOTSYS)/bin/root-config --libs) + +#============================================================================== +# Kompilacja dla modulow z plikami naglowkowymi +%.o: %.cxx %.h + $(CXX) $(CXXFLAGS) -c $< +# Kompilacja dla modulow bez plikow naglowkowych +%.o: %.cxx + $(CXX) $(CXXFLAGS) -c $< +#============================================================================== +.PHONY: all run clean tar +all: ${EXEC1} +#============================================================================== +# Linkowanie +${EXEC1}: ${OBJT1} + $(LD) -o $@ $(LDFLAGS) $^ $(RLIB) + +#============================================================================== +# Uruchamianie +run: ${EXEC1} + ./${EXEC1} +#============================================================================== +clean: + (rm -f *.o *.a *~ *.exe *.x core lmap *.dvi *.aux *.log a.out) +#============================================================================== +tar: clean + (cd ../; tar -cvzf $(DIRNAME).tar.gz $(DIRNAME) ) +#============================================================================== +# Wszelkie akcje jakie należy podjąć aby program zaprezentował swoje działanie: +test: run + @echo 'Test run finished' +#============================================================================== + diff --git a/Lectures_my/NumMet/2016/Lecture1/Examples/ex1/ex1.cc b/Lectures_my/NumMet/2016/Lecture1/Examples/ex1/ex1.cc new file mode 100644 index 0000000..82364cd --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture1/Examples/ex1/ex1.cc @@ -0,0 +1,99 @@ +#include "RooRealVar.h" +#include "RooDataSet.h" +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include "math.h" +#include "RooCBShape.h" +#include "RooRealVar.h" +#include "RooAbsReal.h" +#include "RooExponential.h" +#include "RooDataSet.h" +#include "RooPlot.h" +#include "TFile.h" +#include +#include +#include "RooGenericPdf.h" +#include "RooPolynomial.h" +#include "RooAddPdf.h" +#include "RooExtendPdf.h" +#include +#include "RooGaussian.h" +#include +#include "RooStats/SPlot.h" +#include "RooDataHist.h" +#include "RooAbsReal.h" +#include "RooMinuit.h" +#include "TLorentzVector.h" + +// use this order for safety on library loading +using namespace RooFit ; +using namespace RooStats ; +using namespace std; + + +const double PI=3.14159265358979323846264338327950288419716939937510; +const long double PIdd=3.14159265358979323846264338327950288419716939937510; + + + + +double calc(int a) +{ + return (1./a)*(pow(10.,a)*(1.+a*PI*pow(10,-a))-pow(10,a)); +} + +double calc2d(int a) +{ + long double const1=1.; + long double const10=10.; + return (const1/a)*(pow(const10, a)*(const1+a*PIdd*pow(const10,-a))-pow(const10,a)); +} + + +int main(int argc, char *argv[]) +{ + if(argc != 2) + { + + cout<<"Wrong number of arguments"< +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include "math.h" +#include "RooCBShape.h" +#include "RooRealVar.h" +#include "RooAbsReal.h" +#include "RooExponential.h" +#include "RooDataSet.h" +#include "RooPlot.h" +#include "TFile.h" +#include +#include +#include "RooGenericPdf.h" +#include "RooPolynomial.h" +#include "RooAddPdf.h" +#include "RooExtendPdf.h" +#include +#include "RooGaussian.h" +#include +#include "RooStats/SPlot.h" +#include "RooDataHist.h" +#include "RooAbsReal.h" +#include "RooMinuit.h" +#include "TLorentzVector.h" + +// use this order for safety on library loading +using namespace RooFit ; +using namespace RooStats ; +using namespace std; + + +int main(int argc, char *argv[]) +{ + if(argc != 2) + { + + cout<<"Wrong number of arguments"< +\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/Lecture1/beamerinnerthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture1/beamerinnerthemeFlip.sty new file mode 100755 index 0000000..8dc12a0 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture1/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/Lecture1/beamerinnerthemeFlip.sty~ b/Lectures_my/NumMet/2016/Lecture1/beamerinnerthemeFlip.sty~ new file mode 100755 index 0000000..38dd47d --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture1/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}% + \vskip1em\par + \begin{beamercolorbox}[sep=7pt,center,#1]{author} + \usebeamerfont{author}\insertauthor + \end{beamercolorbox} + \begin{beamercolorbox}[sep=7pt,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/Lecture1/beamerouterthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture1/beamerouterthemeFlip.sty new file mode 100755 index 0000000..d12f6d6 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture1/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/Lecture1/beamerouterthemedecolines.sty b/Lectures_my/NumMet/2016/Lecture1/beamerouterthemedecolines.sty new file mode 100755 index 0000000..669e493 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture1/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/Lecture1/beamerthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture1/beamerthemeFlip.sty new file mode 100755 index 0000000..a615ff5 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture1/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/Lecture1/images/BG_lower.png b/Lectures_my/NumMet/2016/Lecture1/images/BG_lower.png new file mode 100755 index 0000000..073034a --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture1/images/BG_lower.png Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture1/images/bubble.gif b/Lectures_my/NumMet/2016/Lecture1/images/bubble.gif new file mode 100644 index 0000000..ecff282 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture1/images/bubble.gif Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture1/images/bubble.jpg b/Lectures_my/NumMet/2016/Lecture1/images/bubble.jpg new file mode 100644 index 0000000..ceb584d --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture1/images/bubble.jpg Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture1/images/bubble2.jpg b/Lectures_my/NumMet/2016/Lecture1/images/bubble2.jpg new file mode 100644 index 0000000..0fd03bb --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture1/images/bubble2.jpg Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture1/images/ex1.png b/Lectures_my/NumMet/2016/Lecture1/images/ex1.png new file mode 100644 index 0000000..ca9e7e3 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture1/images/ex1.png Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture1/images/ex2.png b/Lectures_my/NumMet/2016/Lecture1/images/ex2.png new file mode 100644 index 0000000..fa98644 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture1/images/ex2.png Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture1/images/pen.jpg b/Lectures_my/NumMet/2016/Lecture1/images/pen.jpg new file mode 100644 index 0000000..5e7b38d --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture1/images/pen.jpg Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture1/images/prec.png b/Lectures_my/NumMet/2016/Lecture1/images/prec.png new file mode 100644 index 0000000..cd05544 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture1/images/prec.png Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture1/images/table.png b/Lectures_my/NumMet/2016/Lecture1/images/table.png new file mode 100644 index 0000000..81e801e --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture1/images/table.png Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture1/images/uzh-transp.pdf b/Lectures_my/NumMet/2016/Lecture1/images/uzh-transp.pdf new file mode 100644 index 0000000..977da67 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture1/images/uzh-transp.pdf Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture1/mchrzasz+mp.sh b/Lectures_my/NumMet/2016/Lecture1/mchrzasz+mp.sh new file mode 100644 index 0000000..1a24852 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture1/mchrzasz+mp.sh @@ -0,0 +1 @@ +#!/bin/sh diff --git a/Lectures_my/NumMet/2016/Lecture1/mchrzasz-blx.bib b/Lectures_my/NumMet/2016/Lecture1/mchrzasz-blx.bib new file mode 100644 index 0000000..9e405b3 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture1/mchrzasz-blx.bib @@ -0,0 +1,11 @@ +@Comment{$ biblatex control file $} +@Comment{$ biblatex version 2.3 $} +Do not modify this file! + +This is an auxiliary file used by the 'biblatex' package. +This file may safely be deleted. It will be recreated as +required. + +@Control{biblatex-control, + options = {2.3:0:0:1:0:0:1:1:0:0:0:0:1:1:3:1:79:+}, +} diff --git a/Lectures_my/NumMet/2016/Lecture1/mchrzasz.aux b/Lectures_my/NumMet/2016/Lecture1/mchrzasz.aux new file mode 100644 index 0000000..df433bc --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture1/mchrzasz.aux @@ -0,0 +1,172 @@ +\relax +\providecommand\hyper@newdestlabel[2]{} +\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument} +\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined +\global\let\oldcontentsline\contentsline +\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} +\global\let\oldnewlabel\newlabel +\gdef\newlabel#1#2{\newlabelxx{#1}#2} +\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} +\AtEndDocument{\ifx\hyper@anchor\@undefined +\let\contentsline\oldcontentsline +\let\newlabel\oldnewlabel +\fi} +\fi} +\global\let\hyper@last\relax +\gdef\HyperFirstAtBeginDocument#1{#1} +\providecommand*\HyPL@Entry[1]{} +\bibstyle{biblatex} 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Serra, B. Storaci\\Thanks to the theory support from M. Shaposhnikov, D. Gorbunov}\normalsize\\ +\vspace{0.5em} + \textcolor{normal text.fg!50!Comment}{Numerical Methods, \\ 19 September, 2016} +\end{center} +\end{frame} +} + + + +\begin{frame}\frametitle{Course plan} +\begin{small} +\ARROW The course consists of 2 hours lecture and 2 hours of exercise.\\ +\ARROW TA will explain to you how you will get points for the class exercise (you will be coding the algorithms) described on the lecture and applying them to some problems.\\ +\ARROW After passing the class exercise ($>66\%$ of points) you will have an exam (oral).\\ + + +\begin{columns} +\column{0.7\textwidth} +\ARROW The final mark: +\vspace{0.1cm} +\begin{footnotesize} +\begin{equation*} +{\rm mark}= 0.5~ {\rm exam} + 0.5 ~ {\rm class} +\end{equation*} +\ARROW The final exam will be average of exam and class marks. +\end{footnotesize} +\column{0.05\textwidth} +{~} +\column{0.25\textwidth} +\begin{footnotesize} + +\begin{tabular}{|c|c|} +\hline +Mark & Range\\\hline +$6$ & $84-100~\%$ \\ +$5$ & $67-83~\%$ \\ +$4$ & $50-67~\%$ \\ \hline +$3$ & $33-50~\%$ \\ +$2$ & $16-33~\%$ \\ +$1$ & $0-16~\%$ \\ +\hline +\end{tabular} + +\end{footnotesize} + + +\end{columns} +\end{small} +\end{frame} + +\begin{frame}\frametitle{Course plan} +\begin{enumerate} +\item Numerical precision, floating point representation. +\item Numerical stability. +\item Function interpolation, multidim. function interpolation. +\item Function approximation. +\item Linear equation solving with elimination methods and iteration methods. +\item Non-linear system of equation solving. +\item Numerical integration. +\item Differential equations solving. +\item Chaos theorem. +\end{enumerate} + +\end{frame} + + +\begin{frame}\frametitle{Why do we need numerical methods?} +\begin{exampleblock}{Prose:} +\ARROWR Most of the problems that one tackles on daily basis cannot be computed analytically! During the university studies the problems you were solving were tailor suited to be analytically solvable!\\ +\ARROWR Even if the problem is solvable analytically in daily work one needs to repeat the calculations many times changing some conditions. Solving $n^{\rm th}$ time a similar integral on paper can have deadly consequences on your sanity.\\ +\ARROWR Let's face is computers are just much much faster then us in this kind of computations.\\ +\end{exampleblock} +\begin{alertblock}{Cons:} +\ARROW One disadvantage of numerical methods is the fact that they don't give you an exact solution. The reason for that is that the computers don't operate on real numbers but just on their representation which we will learn during today’s lecture. +\end{alertblock} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Errors, fast reminder} +\ARROW As you already know there are two types of errors: +\begin{itemize} +\item Absolute error $\Delta$. +\item Relative error $\delta$. +\end{itemize} + +\begin{align*} +\Delta = \vert A - a \vert~~~~~~~~~~~\delta = \vert \frac{A- a}{A} \vert, ~~A \neq 0, +\end{align*} +where $A$ is the exact number, $a$ its approximation.\\ \pause +\ARROW Now since we know what are errors lets look into the sources of errors:\\ +\ARROWR Input errors.\\ +\ARROWR Cut-off errors.\\ +\ARROWR Rounding errors. + + +\end{frame} + +\begin{frame}\frametitle{Input Errors} +\begin{small} + + +\ARROW Input errors are errors that are associated with the inputs to the computer. We can have different types of this errors: +\begin{columns} +\column{0.6\textwidth} +\begin{itemize} +\item Mathematical model errors. A canonical example of such simplification is the pendulum, where we make an approximation of $\sin x =x$ for small $x$: +\begin{align*} +l \frac{d^2x}{dt^2} + g x =0 +\end{align*} +\item Errors associated to a given numerical algorithm: a choice of a numerical algorithm is indeed an very important step of solving a given problem. As we will see during the course the simplest models that are fast to implement to execute on the machine can lead to large numerical errors. +\end{itemize} + + +\column{0.4\textwidth} +\includegraphics[width=0.75\textwidth]{images/pen.jpg} + +\begin{itemize} +\item Input data errors. For many computations one needs tome inputs: constants, starting points, etc. There are errors that are associated to those as well. This kind of errors are super the easiest to control and usually are negligible. + +\end{itemize} + +\end{columns} + +\end{small} + +\end{frame} + + + +\begin{frame}\frametitle{Cut-off Errors} +\begin{small} +\ARROW This kind of errors arise where the true mathematical problem have some kind of infinite sum.\\ +\ARROWR Computers are stupid creatures and they don't understand what is $\infty$ so we need to cut of computations at some point. Example: +\begin{exampleblock}{Maclaurin series:} +We know that an $e^x$ function can be Taylor expanded: +\begin{align*} +e^x = \sum_{n=0}^{n=\infty} \frac{x^n}{n!}=1 +x +\frac{x^2}{2!} + \frac{x^3}{3!}+\frac{x^4}{4!}+... +\end{align*} +We can replace the infinite sum with a finite one: +\begin{align*} +e^x \approx =1 +x +\frac{x^2}{2!} + \frac{x^3}{3!}+\frac{x^4}{4!}+...+\frac{x^N}{N!} +\end{align*} + + +\end{exampleblock} +\ARROW This kind of errors are unfortunately very common in the field. We will have to deal with them every time we have some kind of $\lim$, $\sum^{\infty}$, etc. + + +\end{small} + +\end{frame} + + +\begin{frame}\frametitle{Rounding Errors} +\begin{small} +\ARROW This kind of errors occur during calculations on machines.\\ +\ARROW Machine represents the number with a final precision.\\ +\ARROW During the calculations the errors accumulate with every operation.\\ +\ARROW This errors can be avoided or reduced by proper algorithm or by changing the precision of computations. +\pause +\begin{center} +\includegraphics[width=0.8\textwidth]{images/prec.png} + +\end{center} + + +\end{small} + +\end{frame} + + +\begin{frame}\frametitle{Integer numbers on our PC} +\begin{small} +\ARROW The integer numbers are very easy to represent on PC: +\begin{align*} +a=\pm (c_1N^0 + c_2N^1 +...+ c_dN^{d-1}), +\end{align*} +where $N$ is the base of the system. Computers of course use $2$. +\begin{columns} +\column{3in} +\ARROW For example: +\begin{align*} +101011 \rightleftarrows & 1 \cdot 2^0 + 1 \cdot 2^1 +0 \cdot 2^2 + 1 \cdot 2^3 +\\ & 0 \cdot 2^4 +1 \cdot 2^5\\ & = 43 +\end{align*} +\ARROW Now the first bit can be used for sign determination ($0$ plus $1$ minus) \texttt{int} or can be used to extend the range of numbers \texttt{unsigned}\\ +\ARROW \texttt{int} - $-2147483648 - 2147483647$\\ +\ARROW \texttt{unsigned} - $0 - 4294967295$ + + +\column{2in} +\includegraphics[width=0.95\textwidth]{images/joke.jpg} + +\end{columns} + +\end{small} + +\end{frame} + + + +\begin{frame}\frametitle{Floating numbers on our PC} +\begin{small} +\ARROW Computers are using so-called ''classical floating point representation'': +\begin{align*} +a=\pm M \cdot N^C,~a \neq 0, +\end{align*} +\begin{itemize} +\item $M$ - mantissa or significand +\item $N$ - base of the system +\item $C$ - exponent +\end{itemize} +\ARROW In such system the mantissa is always normalized: +\begin{align*} +M \in \left[ \frac{1}{N}, 1 \right) +\end{align*} +\ARROW Using the definition we can write the mantissa and exponent in the following way: +\begin{align*} +M=(m_1N^{-1}+m_2N^{-2}+...+m_t N^{-t})\\ +C=\pm(c_1 N^0+ c_2 N^1 + c_3 N^2 + ...+c_d N^{d-1}) +\end{align*} +\ARROW The most often know base are $2,8,10,16$. +\end{small} + +\end{frame} + +\begin{frame}\frametitle{Numbers on our PC: binary system } +\begin{small} +\ARROW For example let's construct numbers using binary system: +\begin{align*} +M=\pm(m_1 2^{-1}+m_2 2^{-2}+...+m_t 2^t)\\ +C=\pm(c_1 2^0+ c_2 2^1 + c_3 2^2 + ...+c_d 2^{d-1}) +\end{align*} +where: +\begin{itemize} +\item $t$ - length of mantissa, $d$ - length of exponent +\item $m_i$ - mantissa digits; $m_i \in \lbrace 0,1\rbrace$ +\item $c_i$ - exponent digits; $c_i \in \lbrace 0,1\rbrace$ +\end{itemize} +\begin{exampleblock}{Example: $11110001~(s)mmmm(s)cc$} +Lets say we are representing a number with a byte. First 5 digits are the mantissa the next 3 are exponent. +\begin{align*} +M=-(1 \cdot 2^{-1} + 1 \cdot 2^{-2} + 1 \cdot 2^{-3} + 0 \cdot 2^{-4} = -\frac{7}{8}\\ +C= + (0 \cdot 2^0 + 1 \cdot 2^1)=2\\ +x=-\frac{7}{8} \cdot 2^2=-3.5 +\end{align*} + +\end{exampleblock} + +\end{small} + +\end{frame} + + +\begin{frame}\frametitle{IEEE754-2008} +\begin{small} +\ARROW The rules of the binary systems are defined by the \texttt{ISO-IEEE754} standard (updated in 2008 of the 1985 standard). + +\begin{center} +\includegraphics[width=0.9\textwidth]{images/table.png} +\end{center} +\ARROW There is a minimum and maximum number we can represent in the current system.\\ +\ARROW There are some tricks you can play: use subnormal \\ +\ARROW In general we can represent numbers from: $\langle -a, -b \rangle \cup \lbrace 0 \rbrace \cup \langle b,a \rangle$\\ +\ARROW The standard also defines the rounding procedures for numbers. + +\end{small} + +\end{frame} + +\begin{frame}\frametitle{Error propagation: sum} +\begin{small} +\ARROW Let's consider we have two numbers $x$ and $y$. \\ +\ARROW Their representation are not exact so: $x=\overline{x} + \epsilon_x$ and $y=\overline{y}+\epsilon_y$\\ +\ARROW Now if we want to sum them: +\begin{align*} +x+y=\overline{x}+\overline{y} + \epsilon_x+\epsilon_y=\overline{x}+\overline{y}+\epsilon +\end{align*} +\ARROW If each of the $\epsilon_i$ numbers have a constant distribution on $\left[-\frac{1}{2} 10^{-d}, \frac{1}{2} 10^{-d} \right]$, where $d$ is the precision.\\ +\ARROW Then $\epsilon$ has a triangular distribution on $\left[-10^{-d}, 10^{-d} \right]$\\ +\ARROW Repeating $N$ times this we will approach the Gaussian distribution with a width of $\sim \sqrt{N} 10^{-d}$ + +\end{small} + +\end{frame} + +\begin{frame}\frametitle{Error propagation: multiplication, division} +\begin{small} +\ARROW Let's consider we have two numbers $x$ and $y$. \\ +\ARROW Their representation are not exact so: $x=\overline{x} + \epsilon_x$ and $y=\overline{y}+\epsilon_y$\\ +\ARROW Now if we want to multiply them (we can neglect $\epsilon_x \epsilon_y$ terms): +\begin{align*} +x \cdot y=\overline{x} \cdot \overline{y} + \epsilon_x \cdot \overline{y}+\epsilon_y \cdot \overline{x} +\end{align*} +\ARROW If $\vert \overline{x} \vert \gg (\ll) \vert \overline{y} \vert$ then the error might explode. \\ + +\ARROW Now if we want to divide them: +\begin{align*} +x / y=\overline{x} / \overline{y} + \frac{\epsilon_x}{\overline{y}}+ \frac{\epsilon_y \overline{x}}{\overline{y}^{ {\color{red} 2}}} +\end{align*} + +\ARROW If $\vert y \vert \ll \vert x \vert$ then the division is will have large errors. +\end{small} + +\end{frame} + + +\begin{frame}\frametitle{Application} +\begin{small} +\ARROW When we implement a current algorithm we need to ensure that our algorithm is ''backward stable'', ''well-conditioned'' and ''numerically stable''.\\ +\begin{exampleblock}{Numerical stability} +We say that the algorithm is numerically stable if the the results does not change if we increase the computation precision. + +\end{exampleblock} +\begin{alertblock}{Backward stability} +Backward stability means that our algorithm will gives us the true answer if we move to infinite precision of the machine. In practice we look if we can conserve the errors of the representation. +\end{alertblock} +\begin{exampleblock}{Well-conditioned} +Each algorithm has some input parameters. If we introduce a slight difference in those parameters (of the order of the representation precision), the results should not change significantly. + +\end{exampleblock} +\ARROWR The numerical precision lead to discovery of chaos. If we have time we will discuss this during our lectures. + +\end{small} + +\end{frame} +\begin{frame}\frametitle{Rounding error} +\begin{small} +\ARROW Imagine we want to calculate: +\begin{align*} +1.0000+\sum_{i=1}^{10} 0.0001 +\end{align*} +\ARROW Now imagine we will carry the calculations with $4$ digit precision.\\ +\ARROW If we calculate the: +\begin{align*} +1.0000+\sum_{i=1}^{10} 0.0001=1.000 +\end{align*} +\ARROW If we calculate the: +\begin{align*} +\sum_{i=1}^{10}0.0001+1.0000=1.001 +\end{align*} +\ARROW The order matters! +\end{small} + +\end{frame} + + +\begin{frame}\frametitle{Condition parameter} +\begin{small} + +\begin{exampleblock}{The condition parameter} +\ARROWR Let $\phi : \mathcal{R}^n \to \mathcal{R}^m$ be a function and $x \in \mathcal{R}^n$ be a precise value and $\overline{x} \in \mathcal{R}^n$ its computer representation.\\ +\ARROWR If there $\kappa \in \mathcal{R}$ exists that: +\begin{align*} +\forall_{x,\overline{x}}: \frac{\Vert \psi(x)- \psi(\overline{x} \Vert}{\Vert \psi(x) \Vert} \leq \kappa \frac{\Vert x- \overline{x} \Vert}{ \Vert x \Vert} +\end{align*} +\ARROWR The $\kappa$ is called the condition parameter. +\end{exampleblock} + +\ARROW If the value of $\kappa$ is large then small difference cause by computer representation will explode in the final result. + + +\end{small} +\end{frame} + + + +\begin{frame}\frametitle{Examples 1} +\begin{small} +\ARROW Let's calculate the $\pi$ number accordingly to the following formula for couple of $i$: +\begin{align*} +G_p=\frac{1}{p}\left[ 10^p \left(1+p\pi 10^{-p} \right) - 10^p \right] + \end{align*} +with a simple program one can see: +\begin{center} +\includegraphics[width=0.5\textwidth]{images/ex1.png} +\end{center} + + +\end{small} + +\end{frame} + + + +\begin{frame}\frametitle{Example 1} +\begin{small} +\ARROWR How to fix this?!\\ +\ARROW Change \texttt{double} to \texttt{long double} + +\begin{center} +\includegraphics[width=0.5\textwidth]{images/ex2.png} +\end{center} + + +\end{small} + +\end{frame} + + + + + +\begin{frame}\frametitle{Example 2} +\begin{small} + + + +\begin{columns} +\column{2.5in} +\begin{align*} +\begin{cases} +x + 3y = 4 \\ +x + 3.00001y = 4.00001 +\end{cases} +\end{align*} + + +\column{2.5in} + +\begin{align*} +\begin{cases} +x + 3y = 4 \\ +x + 2.99999y = 4.00002 +\end{cases} +\end{align*} + + + +\end{columns} +{~}\\{~}\\ + +\ARROW The coefficients of this equations are different by maximum of $0.00002$.\\ +\ARROW The solutions to the first one is $(1,1)$ and to the second $(10,-2)$. \\ +\ARROW So clearly we have a big $\kappa$ as changes $\mathcal{O}(10^{-5})$ are causing differences of $\mathcal{O}(10)$. + + +\end{small} + +\end{frame} + + + + +\begin{frame}\frametitle{Summary} +\begin{small} + +\ARROW Computers use only representations of the floating points!\\ +\ARROW Numerical methods suffer from computer precision!\\ +\ARROW It's YOUR responsibility to ensure that what you are doing will not explode the error.\\ + + + +\end{small} + +\end{frame} + + +\backupbegin + +\begin{frame}\frametitle{Backup} + + +\end{frame} + + + + +\backupend +\end{document} diff --git a/Lectures_my/NumMet/2016/Lecture1/mchrzasz.toc b/Lectures_my/NumMet/2016/Lecture1/mchrzasz.toc new file mode 100644 index 0000000..429917f --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture1/mchrzasz.toc @@ -0,0 +1,5 @@ +\boolfalse {citerequest}\boolfalse {citetracker}\boolfalse {pagetracker}\boolfalse {backtracker}\relax +\defcounter {refsection}{0}\relax +\beamer@endinputifotherversion {3.24pt} +\defcounter {refsection}{0}\relax +\select@language {english} diff --git a/Lectures_my/NumMet/2016/Lecture1/tikzfeynman.sty b/Lectures_my/NumMet/2016/Lecture1/tikzfeynman.sty new file mode 100755 index 0000000..521fc65 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture1/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}, +} + diff --git a/Lectures_my/NumMet/2016/Lecture2/Makefile b/Lectures_my/NumMet/2016/Lecture2/Makefile new file mode 100644 index 0000000..e4cf8e8 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture2/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/Lecture2/beamercolorthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture2/beamercolorthemeFlip.sty new file mode 100755 index 0000000..d6b9c50 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture2/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/Lecture2/beamerinnerthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture2/beamerinnerthemeFlip.sty new file mode 100755 index 0000000..8dc12a0 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture2/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/Lecture2/beamerouterthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture2/beamerouterthemeFlip.sty new file mode 100755 index 0000000..d12f6d6 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture2/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/Lecture2/beamerouterthemedecolines.sty b/Lectures_my/NumMet/2016/Lecture2/beamerouterthemedecolines.sty new file mode 100755 index 0000000..669e493 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture2/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/Lecture2/beamerthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture2/beamerthemeFlip.sty new file mode 100755 index 0000000..a615ff5 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture2/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! 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+ +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/Lecture2/mchrzasz.tex b/Lectures_my/NumMet/2016/Lecture2/mchrzasz.tex new file mode 100644 index 0000000..27e2178 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture2/mchrzasz.tex @@ -0,0 +1,788 @@ +\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 interpolation]{Function Interpolation} +\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 Interpolation} + \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, \\ 21 September, 2016} +\end{center} +\end{frame} +} + + + +\begin{frame}\frametitle{Interpolation - graphical interpretation} +\begin{small} + + +\ARROW Let's assume we have a given function in a tabular form: +\begin{tabular}{c||c|c|c|c|c} +$x_i$ & $x_1$ & $x_2$ & $x_3$ & ... & $x_n$ \\ \hline +$f_i=f(x_i)$ & $f_1$ & $f_2$ & $f_3$ & ... & $f_n$ \\ +\end{tabular}\\ +\ARROWR The $x_i$ are data points.\\ +\ARROW The problem is how to calculate the function values between the points ({\it interpolation}) or outside ({\it extrapolation} - see next lecture!) . +\end{small} +\begin{center} +\includegraphics[angle=-90,width=0.5\textwidth]{images/mass_resolution_Bconstr_afterSel_errBand_scaled.pdf} +\end{center} +\end{frame} + + + +\begin{frame}\frametitle{Interpolation - formal formulation} +\begin{small} + +\ARROW On the interval: $\left[ a, b \right] \subset \mathbb{R}$ and set of points: $D=(x_i, y_i)$, $x_i \neq x_j~ \Leftrightarrow~ i \neq j$.\\ +\ARROW The interpolation is to find a function $F:\left[ a, b \right] \rightarrow \mathbb{R}$ that satisfies: +\begin{align*} +\forall (x_i,y_i) \in D:~~~ F(x_i)=y_i +\end{align*} +\ARROW The above equation is called the interpolation equation.\\ +\ARROW The interpolation error: +\begin{align*} +\epsilon(x)=f(x)-F(x), +\end{align*} +where $f(x)$ is the function that is being interpolated.\\ +\ARROW Each interpolation method has different errors, each of it can be estimated. +\end{small} + +\end{frame} + + + +\begin{frame}\frametitle{Linear Interpolation} +\begin{small} + +\ARROW Let's say we have $n+1$ interpolation points: $(y_i, x_i)$.\\ +\ARROW The linear interpolation is given with with the equation: +\begin{align*} +F(x)=\sum_{j=0}^n a_j \psi_j(x)=a_0 \psi_0(x) + a_1 \psi_1(x) + a_2 \psi_2(x)+ ... + a_n \psi_n(x), +\end{align*} +where: +\begin{itemize} +\item $a_j$ - parameter, +\item $\psi_j(x)$ - base function. +\end{itemize} +\ARROW Now the only thing one needs to do is to find the $a_i$ coefficients. Now there are infinite number such solutions so we need to assume that the number interpolation points is equal to number of base functions. + + +\end{small} + +\end{frame} + + +\begin{frame}\frametitle{Linear Interpolation} +\begin{small} + +\ARROW Now to find all the $a_i$ one just needs to solve the linear equation system: +\begin{align*} +\begin{pmatrix} +\psi_0(x_0) & \psi_1(x_0) & ... & \psi_n(x_0) \\ +\psi_0(x_1) & \psi_1(x_1) & ... & \psi_n(x_1) \\ +& ... \\ +\psi_0(x_0) & \psi_1(x_0) & ... & \psi_n(x_2) +\end{pmatrix} +\begin{pmatrix} +a_0\\ +a_1\\ +...\\ +a_n +\end{pmatrix}= +\begin{pmatrix} +y_0\\ +y_1\\ +...\\ +y_n +\end{pmatrix} +\end{align*} +\ARROW The only necessary condition to solve the equation is that the: +\begin{align*} +\det \left[ \psi_i(x_j) \right] \neq 0 +\end{align*} +\ARROW The polynomial of the order $n$ has $n+1$ base functions, so system has only one solution.\\ +\ARROW We can choose the base functions on many different ways. This depends on the input points and our own judgement. Often use are trigonometric functions and polynomials.\\ +\ARROW The proper selection of the base function can hugely simplify the problem by making the matrix triangular or even diagonal. + +\end{small} + +\end{frame} + +\begin{frame}\frametitle{Linear Interpolation, simplest base} +\begin{small} +\begin{exampleblock}{Theorem:} +If all of the interpolation points $x_0,x_1,...,x_n$ are pair different there exists one and only one solution of the interpolation function of the order max. $n$. +\end{exampleblock} + +The simplest base functions one can imagine to use is the natural base: +\begin{align*} +\psi_0=1,~~~\psi_1=x,~~~\psi_2=x^2,~~~...~~~, \psi_n=x^n +\end{align*} +\begin{alertblock}{Attention/Achtung:} +This kind of interpolation is wrongly conditioned: small changes of input parameters will cause large output differences. +\end{alertblock} + +\ARROW Because of the above it is used almost not used in practice. \\ +\ARROW For education purposes we will analyse it. +\end{small} + +\end{frame} + +\begin{frame}\frametitle{Linear Interpolation, simplest base} +\begin{small} +\ARROW When using natural base the interpolation polynomial will have the structure: +\begin{align*} +F(x)=a_0+a_1 x + a_2 x^2 + a_3 x^3 ... a_n x^n +\end{align*} +\ARROW Now base matrix (so-called Vandermonde matrix) has the form: +\begin{align*} +V=\begin{pmatrix} +1 & x_0 & x_0^2 & ... & x_0^n \\ +1 & x_1 & x_1^2 & ... & x_1^n \\ +& ... \\ +1 & x_n & x_n^2 & ... & x_n^n \\ +\end{pmatrix} +\end{align*} +\ARROW Now the only thing one needs to do is to solve: +\begin{align*} +\begin{pmatrix} +1 & x_0 & x_0^2 & ... & x_0^n \\ +1 & x_1 & x_1^2 & ... & x_1^n \\ +& ... \\ +1 & x_n & x_n^2 & ... & x_n^n \\ +\end{pmatrix} +\begin{pmatrix} +a_0\\ +a_1\\ +...\\ +a_n +\end{pmatrix}= +\begin{pmatrix} +y_0\\ +y_1\\ +...\\ +y_n +\end{pmatrix} +\end{align*} +\ARROW Because the natural base is wrongly conditioned the increase of the interpolation points significantly increases the condition parameter. + +\end{small} + +\end{frame} + + +\begin{frame}\frametitle{Lagrange interpolation} +\begin{small} +\ARROW Now let's choose a better base function that are given by: +\begin{align} +\label{eq:langrange} +l_i(x)= \prod_{j=0,~j \neq i}^n \frac{x-x_j}{x_i-x_j} = \frac{(x-x_0)(x-x_1)...(x-x_n)}{(x_i-x_0)(x_i-x_1)...(x_i-x_n)} +\end{align} +\ARROW It is easy to notice: +\begin{align*} +l_i(x_j)=\begin{cases} +0~~~i \neq j \\ +1~~~i=j +\end{cases} +\end{align*} +\ARROW Now putting this into base matrix we get: +\begin{align*} +\begin{pmatrix} +1 & 0 & 0 & ... & 0 \\ +0 & 1 & 0 & ... & 0 \\ +& ... \\ +0 & 0 & 0 & ... & 1 \\ +\end{pmatrix} +\begin{pmatrix} +a_0\\ +a_1\\ +...\\ +a_n +\end{pmatrix}= +\begin{pmatrix} +y_0\\ +y_1\\ +...\\ +y_n +\end{pmatrix} +\end{align*} +\ARROW Now this is something we like :) The interpolating function then takes the form: +\begin{align*} +F(x)=L_n(x)=\sum_{i=0}^n y_i l_i(x) +\end{align*} + +\end{small} +\end{frame} + + + +\begin{frame}\frametitle{Lagrange interpolation - the algorithm} +\begin{small} +\begin{enumerate} +\item Get the input data $(x_i,y_i),~i=0,...,n$. +\item The coefficients of the polynomial are $y_i$. +\item Calculate the base functions from Eq.~\ref{eq:langrange}. +\item Put everything together to get the $L_n$ Lagrange polynomial. +\end{enumerate} +\begin{alertblock}{Disadvantage:} +The problem with this method is the fact that if you add another interpolation point you need to start over and recalculate everything. +\end{alertblock} + +\begin{exampleblock}{Advantege} +\only<1>{ +It is very popular and simple method. It is used in many different places: differential equations, numerical integrations, etc. Because of this the precision of the method depends on the precision of the interpolation is self: +\begin{align*} +\epsilon(x) = f(x) - F(x) = \frac{f^{(n+1}(\xi) }{(n+1)!} \omega_n(x) +\end{align*} +} +\only<2>{ +where:\\ +$\omega_n(x)=(x-x_0)(x-x_1)...(x-x_n)$\\ +$f$ function of class $C^{n+1}$ on $\left [a,b\right]$\\ +$\xi$ average values.h +} +\end{exampleblock} + + +\end{small} +\end{frame} + + + +\begin{frame}\frametitle{Newton interpolation} +\begin{small} +\ARROW Sir Isaac Newton proposed a different base for the problem: +\begin{align*} +p_0(x) & =1\\ +p_1(x) & =(x-x_0)\\ +p_2(x) & =(x-x_0)(x-x_1)\\ +...\\ +p_n(x) & =(x-x_0)(x-x_1)...(x-x_n) +\end{align*} +\only<1>{ +\ARROW Using the above functions the basis matrix takes a nice form: +\begin{align*} +V=\begin{pmatrix} +1 & 0 & 0 & ... & 0 \\ +1 & p_1(x_1) & 0 & ... & 0 \\ +& ... \\ +1 & p_1(x_n) & p_2(x_n) & ... & p_n(x_n) \\ +\end{pmatrix} +\end{align*} +} +\only<2>{ +\ARROW And the linear equation system: +\begin{align*} +\begin{pmatrix} +1 & 0 & 0 & ... & 0 \\ +1 & p_1(x_1) & 0 & ... & 0 \\ +& ... \\ +1 & p_1(x_n) & p_2(x_n) & ... & p_n(x_n) \\ +\end{pmatrix} +\begin{pmatrix} +a_0\\ +a_1\\ +...\\ +a_n +\end{pmatrix} += +\begin{pmatrix} +y_0\\ +y_1\\ +...\\ +y_n +\end{pmatrix} +\end{align*} + + +} +\end{small} +\end{frame} + + + +\begin{frame}\frametitle{Newton interpolation} +\begin{small} +\ARROW We can solve the aforementioned system by noticing that $a_0$ depends only on $y_0$, $a_1$ depends on $y_0$ and $y_1$, etc.\\ +\ARROW They can be calculated using difference quotient: +\begin{align*} +f\left[ x_0,x_1 \right] =\frac{y_1-y_0}{x_1-x_0},~~f\left[ x_1,x_2 \right] =\frac{y_2-y_1}{x_2-x_1}, \rm~etc. +\end{align*} +\begin{align*} +f\left[ x_0,x_1, x_2 \right] = \frac{ f\left[ x_1,x_2 \right]- f\left[x_0,x_1 \right] }{x_2-x_1} +\end{align*} +\ARROW In general: +\begin{align*} +f\left[ x_i,x_{i+1},..., x_{i+k} \right] = \frac{ f\left[ x_{i+1},x_{i+2},...,x_{i+k} \right] - f\left[ x_{i},x_{i+1},...,x_{i+k-1} \right]}{x_{i+k}-x_i} +\end{align*} +\ARROW Using difference quotient we can calculate the coefficients: +\begin{align*} +a_i=f\left[x_0,x_1,...,x_i\right] +\end{align*} +\end{small} +\end{frame} + + + +\begin{frame}\frametitle{Newton interpolation, the algorithm} +\begin{small} + +\begin{itemize} +\item We read the input interpolating points: $(x_i,y_i)$, $i=0,1,....,n$. +\item Calculate the polynomial coefficients in an iterative way. +\item Calculate the base functions. +\item Put things together to get the Newton interpolation polynomial. +\end{itemize} + +\begin{exampleblock}{Why do we bother?} +\ARROWR Despite the procedure seems more complicated then the Lagrange interpolation it has a huge advantage: adding one more interpolation point does require to repeat the whole procedure, but we can reuse the previous steps. +\end{exampleblock} + +\end{small} +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Runge oscillation} +\begin{small} + +\ARROW If one has many points one needs to use a high order polynomial.\\ +\ARROW The problem with high order polynomials is that they start oscilationg at the edges $\mapsto$ so-called Runge oscillations. + +\begin{center} +\includegraphics[width=0.75\textwidth]{images/Runge.png} +\end{center} + +\ARROW Danny will tell you more about this next lecture. + +\end{small} +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{First degree spline function} +\begin{small} + +\ARROW Till now using couple numerical methods we were able to calculate coefficients of a big single polynomial equation.\\ +\ARROW Now we are smarter then Newton and Lagrange were over 300 years ago!\\ +\ARROW We can use several interpolating functions and then glue them (splice) them together!\\ +\ARROW In order to do so we divide the domain of the $F$ function $\left[ a,b \right]$ into: +\begin{align*} +a=x_0 diff --git a/Lectures_my/NumMet/2016/Lecture3/beamerinnerthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture3/beamerinnerthemeFlip.sty new file mode 100755 index 0000000..8dc12a0 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture3/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/Lecture3/beamerouterthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture3/beamerouterthemeFlip.sty new file mode 100755 index 0000000..d12f6d6 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture3/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/Lecture3/beamerouterthemedecolines.sty b/Lectures_my/NumMet/2016/Lecture3/beamerouterthemedecolines.sty new file mode 100755 index 0000000..669e493 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture3/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/Lecture3/beamerthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture3/beamerthemeFlip.sty new file mode 100755 index 0000000..a615ff5 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture3/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/Lecture3/examples/Makefile b/Lectures_my/NumMet/2016/Lecture3/examples/Makefile new file mode 100644 index 0000000..9a5e050 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture3/examples/Makefile @@ -0,0 +1,2 @@ +ex1: ex1.cc + g++ -o $@ $^ diff --git a/Lectures_my/NumMet/2016/Lecture3/examples/cos.nb b/Lectures_my/NumMet/2016/Lecture3/examples/cos.nb new file mode 100644 index 0000000..d1db6ee --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture3/examples/cos.nb @@ -0,0 +1,1259 @@ +(* Content-type: application/vnd.wolfram.mathematica *) + +(*** Wolfram Notebook File ***) +(* http://www.wolfram.com/nb *) + +(* CreatedBy='Mathematica 10.3' *) + +(*CacheID: 234*) +(* Internal cache information: +NotebookFileLineBreakTest +NotebookFileLineBreakTest +NotebookDataPosition[ 158, 7] +NotebookDataLength[ 46780, 1250] +NotebookOptionsPosition[ 45777, 1211] +NotebookOutlinePosition[ 46113, 1226] +CellTagsIndexPosition[ 46070, 1223] +WindowFrame->Normal*) + +(* Beginning of Notebook Content *) +Notebook[{ +Cell[BoxData[ + RowBox[{ + RowBox[{"f", "[", "x_", "]"}], " ", ":=", " ", + RowBox[{"Cos", "[", "x", "]"}]}]], "Input", + CellChangeTimes->{{3.683213270757375*^9, 3.683213279924851*^9}, { + 3.683213869842869*^9, 3.683213902127639*^9}, {3.683214036747176*^9, + 3.683214048317216*^9}, 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PointSize[0.5], + Opacity[1.], + AbsoluteThickness[1.6], + RGBColor[1, 0, 0]], { + LineBox[{{0, 10}, {20, 10}}]}}, { + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + Opacity[1.], + AbsoluteThickness[1.6], + RGBColor[1, 0, 0]], {}}}, AspectRatio -> Full, + ImageSize -> {20, 10}, PlotRangePadding -> None, + ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}}, + GridBoxAlignment -> { + "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, + AutoDelete -> False, + GridBoxDividers -> { + "Columns" -> {{False}}, "Rows" -> {{False}}}, + GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}}, + GridBoxSpacings -> { + "Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}}, + GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, + AutoDelete -> False, + GridBoxItemSize -> { + "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, + GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], + "Grid"], Alignment -> Left, AppearanceElements -> None, + ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> + "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], { + FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> + False], TraditionalForm]& ), + Editable->True, + InterpretationFunction:>(RowBox[{"LineLegend", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"Directive", "[", + RowBox[{ + RowBox[{"Opacity", "[", "1.`", "]"}], ",", + RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + GrayLevel[0], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> GrayLevel[0.], FrameTicks -> None, + PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], "GrayLevel[0]"], + Appearance -> None, BaseStyle -> {}, BaselinePosition -> + Baseline, DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + GrayLevel[0]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["GrayLevelColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + GrayLevel[0], Editable -> False, Selectable -> False]}], + "]"}], ",", + RowBox[{"Directive", "[", + RowBox[{ + RowBox[{"Opacity", "[", "1.`", "]"}], ",", + RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[1, 0, 0], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> RGBColor[0.6666666666666666, 0., 0.], + FrameTicks -> None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[1, 0, 0]"], Appearance -> None, BaseStyle -> {}, + BaselinePosition -> Baseline, DefaultBaseStyle -> {}, + ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[1, 0, 0]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[1, 0, 0], Editable -> False, Selectable -> + False]}], "]"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{#, ",", #2}], "}"}], ",", + RowBox[{"LegendMarkers", "\[Rule]", "None"}], ",", + RowBox[{"LabelStyle", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& )], + Scaled[{0.75, 0.75}], ImageScaled[{0.5, 0.5}], + BaseStyle->{FontSize -> Larger}, + FormatType->StandardForm]}, + AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], + Axes->{True, True}, + AxesLabel->{None, None}, + AxesOrigin->{0, 0}, + DisplayFunction->Identity, + Frame->{{False, False}, {False, False}}, + FrameLabel->{{None, None}, {None, None}}, + FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, + GridLines->{None, None}, + GridLinesStyle->Directive[ + GrayLevel[0.5, 0.4]], + Method->{ + 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{{1,0,0},{1,0,π/4},{1,π/4,0}} +Out[36]= {{1,0,0},{1,π/8,π/8},{1,π/4,π/4}} +In[14]:= a = {a0, ax, ay}; +In[37]:= ffA = f @@@ pointsA +ffB = f @@@ pointsB +Out[37]= {1,1/Sqrt[2],1/Sqrt[2]} +Out[38]= {1,1/Sqrt[2],0} +In[39]:= Solve[VA.a == ffA, a] +intA = VanderMondeLine[{x, y}].a //. %[[1]] +Out[39]= {{a0->1,ax->(2 (-2+Sqrt[2]))/π,ay->(2 (-2+Sqrt[2]))/π}} +Out[40]= 1+(2 (-2+Sqrt[2]) x)/π+(2 (-2+Sqrt[2]) y)/π +In[44]:= VB.a +Out[44]= {a0,a0+(ax π)/8+(ay π)/8,a0+(ax π)/4+(ay π)/4} +In[43]:= Solve[VB.a == ffB, a] +Out[43]= {} +In[25]:= ContourPlot[ +f[x, y], +{x, 0, π/4}, +{y, 0, π /4} +] + +Out[25]= +In[32]:= ContourPlot[ +intA, +{x, 0, π/4}, +{y, 0, π /4} +] +Out[32]= \ No newline at end of file diff --git a/Lectures_my/NumMet/2016/Lecture3/images/BG_lower.png b/Lectures_my/NumMet/2016/Lecture3/images/BG_lower.png new file mode 100755 index 0000000..073034a --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture3/images/BG_lower.png Binary files differ diff --git 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differ diff --git a/Lectures_my/NumMet/2016/Lecture3/lecture3.tex b/Lectures_my/NumMet/2016/Lecture3/lecture3.tex new file mode 100644 index 0000000..f5a6dff --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture3/lecture3.tex @@ -0,0 +1,822 @@ +% vim: set sts=4 et : +\documentclass[11 pt,xcolor={dvipsnames,svgnames,x11names,table}]{beamer} + +\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} + +\usepackage{tikz,pgfplots} +\usepackage{graphicx} + +% 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}{$#2$}}% + +\graphicspath{{images/}} % Put all images in this directory. Avoids clutter. + +% 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}} +} + +\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 {Interpolation in $D>2$\\ and Extrapolation} + \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 Chrzaszcz, 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, \\ 26. September, 2016} +\end{center} +\end{frame} +} + +\begin{frame}{Plan for today} + \begin{itemize} + \item \alert{When does interpolation fail?}\\ + Marcin showed you how to interpolate in $D=1$. What are the pitfalls? And can we circumvent them? + \vfill + \item \alert{How to interpolate a function of $D>1$ variables?}\\ + Is there are sensible generalization of interpolation to multivariate functions? If yes, + let's apply what we learned before to $D=2$. + \vfill + \item \alert{What happens when I use my interpolation beyond the domain of data?}\\ + Why would I do that? When can I do that? How well does it work, and how can I improve it? + \end{itemize} +\end{frame} + +\begin{frame}{Does interpolation always work?} + \begin{block}{Weierstrass Approximation Theorem} + Suppose $f$  is a continuous real-valued function defined on the real interval $[a, b]$. + For every $\varepsilon > 0$, there exists a polynomial $P(x)$ such that for all $x$ in $[a, b]$, + we have $R[P] \equiv \max_{a \leq x \leq b} |f (x) - P(x)| < \varepsilon$, [\dots] + \end{block} + Using interpolation, we can construct a polynomial $P_n(x)$ of degree $n$ + that approximates $f$ up to an approximation error of $R_n$: + \begin{equation*} + R_n \equiv \max_{a \leq x \leq b} \left|f(x) - P_n(x)\right|\,. + \end{equation*} + + \begin{alert}{Conclusion} + Weierstrass's theorem says that there is \emph{at least one} polynomial + for each choice of the residual error $\varepsilon$. It does not say that either + \begin{itemize} + \item $P_n$ is \emph{in} the set of polynomial for a given $\varepsilon$, or + \item $R_n \to 0$ if $n \to \infty$! + \end{itemize} + \begin{center}{\color{red} Increasing $n$ might be harmful!}\end{center} + \end{alert} +\end{frame} + +\begin{frame}{When Interpolation fails} +So far, you have been confronted with examples in which interpolation +works nicely. Let us now discuss an example, which behaves pathologically.\\ + +\begin{overlayarea}{\textwidth}{7cm} +\begin{columns} +\begin{column}[T]{.5\textwidth} +Consider the classical example by Runge: +\begin{equation*} + f(x) = \left[1 + 25 x^2\right]^{-1} +\end{equation*} + +Let us plot +\begin{itemize} + \item the true function $f(x)$ + \item<2-> {\color{blue}the interpolating polynomial to degree $4$} + \item<3-> {\color{red}the interpolating polynomial to degree $6$} +\end{itemize} +\only<2->{for equidistant interpolation points on $[-1, +1]$.} +\end{column} +\begin{column}[T]{.5\textwidth} +\begin{tikzpicture} + [ + scale=0.75 + ] + \begin{axis}[% + samples=500, + xmin=-1,xmax=+1, + ymin=-0.5,ymax=+1 + ] + \addplot+[black,mark=none] + {1.0 / (1.0 + 25.0 * \x^2)}; + \only<2->{ + \addplot+[blue,domain=-1:+1,y domain=-1:+1,mark=none] + {1 - (3225 * \x^2) / 754 + (1250 * \x^4) / 377}; + } + \only<3->{ + \addplot+[red,domain=-1:+1,y domain=-1:+1,mark=none] + {1 - (211600 * \x^2)/24089 + (2019375 * \x^4)/96356 - (1265625 * \x^6)/96356}; + } + \end{axis} +\end{tikzpicture} + \begin{center}\only<4->{$R_n \to \infty$ as $n \to \infty$}\end{center} +\end{column} +\end{columns} +\end{overlayarea} +\end{frame} + +\begin{frame}{Pieceswise linear/cubic/... interpolations} + \begin{columns} + \begin{column}{.6\textwidth} + This pathological behaviour can be avoided by piecewise interpolation with a small value of + the polynomial degree $n$. + Most popular are linear ($n=1$) or cubic ($n=3$) piecewise interpolations + (``splines''), which do not suffer from the problem that was just described.\\ \medskip + \end{column} + \begin{column}{.4\textwidth} + \includegraphics[width=.9\textwidth]{runge.pdf} + \end{column} + \end{columns} + \medskip + The concrete approaches have been discussed last lecture by Marcin. +\end{frame} + +\begin{frame}{Interpolation in more than $D=1$ dimensions} +In lecture 2 we discussed various ways to interpolate a +univariate function $f(x)$. A very nice fact for +polynomial interpolations in $D=1$ dimension is that the +interpolating polynomial is \emph{unique}: For two polynomials +$g(x)$ and $h(x)$ of identical degree $n$ one has +\begin{equation*} + f_i = g(x_i) = h(x_i) \quad\Rightarrow\quad g(x) \equiv h(x)\,, +\end{equation*} +when considering exactly $\rho_n(D=1) = n + 1$ interpolation points $x_i$, +for $i = 1,\dots, n+1$.\\ +\medskip +We will now investigate if this still holds for $D > 1$ dimensions. +\end{frame} + +\begin{frame}{Interpolation in $D=2$ dimensions} + We will use a bivariate polynomial of degree $n$: + \begin{equation*} + P_n(x, y) = \sum_{i, j}^{i + j \leq n} a_{i, j} x^i y^j\,. + \end{equation*} + This polynomial has exactly $\rho_n(D=2) = \binom{n + 2}{n}$ coefficients, + which need to be computed from the interpolation points.\\ + + If we evaluate exactly $\rho_n(D=2)$ points, the system of linear equations + has exactly one or zero solutions! + + \begin{block}{Examples} + \vspace{-\medskipamount} + \begin{align*} + P_1(x, y) & = a_{0,0} + a_{1,0} x + a_{0,1} y\,, & \binom{1 + 2}{1} = 3\,,\\ + P_2(x, y) & = a_{0,0} + a_{1,0} x + a_{0,1} y\,, & \binom{2 + 2}{2} = 6\,,\\ + & + a_{1,1} x y + a_{2, 0} x^2 + a_{0, 2} y^2 + \end{align*} + \end{block} +\end{frame} + +\begin{frame}{Arrangement of points in $D=2$} + The question is now: How do we choose the $\rho_n(D=2)$ points that shall be + interpolated?\\ + \medskip + In $D=1$, this was easy: all points were on the $x$ axis. In $D=2$ we need to populate + a plane, and this gives us more freedom.\\ + \medskip + How to arrange the interpolation points in the plane? Let's consider two examples + for $D = 2$ dimensions for a $n=1$ polynomial: + + + \begin{overlayarea}{\textwidth}{5cm} + \only<1>{ + \begin{block}{Example \#1} + \begin{columns} + \begin{column}[T]{.35\textwidth} + \begin{center} + \begin{tikzpicture} + \begin{axis}[% + width=3cm,height=3cm, + xmin=0,xmax=1,xtick={0,1},xlabel=$x$, + ymin=0,ymax=1,ytick={0,1},ylabel=$y$ + ] + \addplot+[blue, only marks, mark options={scale=1.75, fill=blue}] coordinates { + (0.0, 0.0) + (0.5, 0.5) + (1.0, 1.0) + }; + \end{axis} + \end{tikzpicture} + \end{center} + \end{column} + \begin{column}[T]{.65\textwidth} + The interpolation equation reads: + \begin{equation*} + \left[\begin{matrix} + 1 & 0 & 0 \\ + 1 & \frac12 & \frac12\\ + 1 & 1 & 1 + \end{matrix}\right] + \cdot + \left[\begin{matrix} + a_{0, 0}\\ + a_{1, 0}\\ + a_{0, 1} + \end{matrix}\right] + = + \left[\begin{matrix} + f(0, 0)\\ + f(\frac12, \frac12)\\ + f(1, 1) + \end{matrix}\right] + \end{equation*} + The Vandermonde matrix is singular, and no polynomial exists + that interpolates the blue points. + \end{column} + \end{columns} + \end{block} + } + \only<2>{ + \begin{block}{Example \#2} + \begin{columns} + \begin{column}[T]{.35\textwidth} + \begin{center} + \begin{tikzpicture} + \begin{axis}[% + width=3cm,height=3cm, + xmin=0,xmax=1,xtick={0,1},xlabel=$x$, + ymin=0,ymax=1,ytick={0,1},ylabel=$y$ + ] + \addplot+[red, only marks, mark options={scale=1.75, fill=red}] coordinates { + (0, 0) + (0, 1) + (1, 0) + }; + \end{axis} + \end{tikzpicture} + \end{center} + \end{column} + \begin{column}[T]{.65\textwidth} + The interpolation equation reads: + \begin{equation*} + \left[\begin{matrix} + 1 & 0 & 0 \\ + 1 & 1 & 0 \\ + 1 & 0 & 1 + \end{matrix}\right] + \cdot + \left[\begin{matrix} + a_{0, 0}\\ + a_{1, 0}\\ + a_{0, 1} + \end{matrix}\right] + = + \left[\begin{matrix} + f(0, 0)\\ + f(\frac12, \frac12)\\ + f(1, 1) + \end{matrix}\right] + \end{equation*} + The Vandermonde matrix is regular, and exactly one polynomial exists + that interpolates the red points. + \end{column} + \end{columns} + \end{block} + } + \end{overlayarea} +\end{frame} + +\begin{frame}{Divide and conquer $D=2$} + We had seen that increasing the degree $n$ does not necessarily reduce the + approximation error $R_n$, even in $D=1$ dimensions.\\ \medskip + + In $D=2$ this problem can become even more serious.\\ \medskip + + It is therefore a good idea to evaluate the function $f$ on a regular grid + in the $(x,y)$ plane. Subequently, one can interpolate within each + cell of the grid. This is the $D=2$ analog to interpolation with splines: + \begin{itemize} + \item linear splines $\to$ bilinear splines + \item cubic splines $\to$ bicubic splines + \end{itemize} +\end{frame} + +\begin{frame}[shrink]{Algorithm for Bilinear Interpolation} + \begin{columns} + \begin{column}[T]{.8\textwidth} + \begin{enumerate} + \item<1-> Create a rectilinear grid in the $(x,y)$ plane + \item<2-> For each rectangle, map the rectangle to the unit square + \item<3-> Evaluate the function $f$ on the four + corners of the (mapped) unit square ${\color{purple}Q_{0,0}}$, + ${\color{red}Q_{1, 0}}$, ${\color{orange}Q_{1, 1}}$, ${\color{Gold}Q_{0, 1}}$. + \item<4-> Make an ansatz: $P(x, y) = a_{0,0} + a_{1,0} x + a_{0,1} y + a_{1,1} x y$. + \end{enumerate} + \end{column} + \begin{column}[T]{.2\textwidth} + \begin{overlayarea}{\textwidth}{.3\textheight} + \resizebox{\textwidth}{!}{ + \begin{tikzpicture} + \draw[black,thick] (0,0) -- (2,0) -- (2,1) -- (0,1) -- (0,0); + \draw[black,thick] (2,0) -- (4,0) -- (4,1) -- (2,1) -- (2,0); + \draw[black,thick] (0,1) -- (2,1) -- (2,2) -- (0,2) -- (0,1); + \draw[black,thick] (2,1) -- (4,1) -- (4,2) -- (2,2) -- (2,1); + \only<2->{ + \fill[gray,thick] (0,1) -- (2,1) -- (2,2) -- (0,2) -- (0,1); + } + \only<3->{ + \fill[purple] (0,1) circle [radius=2pt]; + \fill[red] (2,1) circle [radius=2pt]; + \fill[orange] (2,2) circle [radius=2pt]; + \fill[Gold] (0,2) circle [radius=2pt]; + } + \end{tikzpicture} + }\\ + \only<2->{ + \resizebox{\textwidth}{!}{ + \begin{tikzpicture} + \draw[black,thick] (0,0) -- (1,0) -- (1,1) -- (0,1) -- (0,0); + \only<3->{ + \fill[purple] (0,0) circle [radius=2pt]; + \fill[red] (1,0) circle [radius=2pt]; + \fill[orange] (1,1) circle [radius=2pt]; + \fill[Gold] (0,1) circle [radius=2pt]; + } + \end{tikzpicture} + } + } + \end{overlayarea} + \end{column} + \end{columns} + \begin{enumerate} + \setcounter{enumi}{4} + \item<5-> Solve the interpolation equation + \begin{equation*} + \left[\begin{matrix} + 1 & 0 & 0 & 0\\ + 1 & 1 & 0 & 1\\ + 1 & 0 & 1 & 1\\ + 1 & 1 & 1 & 1 + \end{matrix}\right] + \cdot + \left[\begin{matrix} + a_{0, 0}\\ + a_{1, 0}\\ + a_{0, 1}\\ + a_{1, 1} + \end{matrix}\right] + = + \left[\begin{matrix} + f(Q_{0, 0})\\ + f(Q_{1, 0})\\ + f(Q_{0, 1})\\ + f(Q_{1, 1}) + \end{matrix}\right] + \end{equation*} + We only need to invert the Vandermonde matrix once! + \item<6-> Map the result back from the unit square back to the grid piece in $(x,y)$ plane. + \item<7-> Jump back to \#2. + \end{enumerate} +\end{frame} + +\begin{frame}{Interpolation in $D$ dimensions} + The situation becomes even more complicated if you go to + $D >2$ dimensions: + \begin{description} + \item[$D=3$] You can generalize to with either trilinear or tricubic splines, on + a rectilinear $3D$ grid. The Vandermonde matrix on the unit cube is now + $\binom{n + 3}{n}^2$. + \item[arbitrary $D$] There is no polynomial interpolation for $D$ dimensions. + \end{description} +\end{frame} + +\begin{frame}[shrink]{Extrapolation Basics} + In many numerical applications a common class of problems arises: + Concerning a function $f(x)$ that is expensive to evaluate, we are interested in the value + $f(x_0)$. However, at $x_0$ the function $f(x)$ is numerically instable, + or the problem maybe even ill-posed.\\ \medskip + + Sometime there is an environment around $x_0$, $x \approx x_0 + h$, in which we can evaluate $f$. + Usually, one now discusses $f(h) \equiv f(x_0 + h)$, or rather the limit + $\lim_{h \to 0} f(h)$. [Note: in all generality we can map problems with + limits to either $h \to \infty$ or $h \to \text{finite value}$ onto limits $h \to 0$.]\\ \medskip + + Interpolation, as discussed previously, can not directly help, since $h = 0$ + is not part of the domain of data points. Instead, one can take an interpolation + at finite $h > 0$, $f_\text{int}(h)$, and simply approximate $f(h = 0) \approx f_\text{int}(h = 0)$. + This step of using the interpolation of $f$ outside the domain of data points is + called \emph{extrapolation}.\\ \medskip + + To extrapolate an arbitrary function might work very well, but also might + fail spectacularly. In this part of the course, we will briefly discuss + examples of both cases, and what mathematical requirements make extrapolations + work. +\end{frame} + +\begin{frame}{Working example} +Consider the function $\cos(x)$. Our task at hand is to estimate +$\cos(0)$ through evaluations of $\cos(h_k)$, with $h_k > 0$ but +$h_k \to 0$ with increasing $k$.\\ \medskip + +Let $h_k = 2^{-k}$, and construct interpolating polynomials $P_n$ +that interpolate $\cos(x)$ in $\lbrace h_1, \dots, h_{n + 1}\rbrace$. \\ \medskip + +\begin{overlayarea}{\textwidth}{5cm} + \begin{columns} + \begin{column}[T]{.5\textwidth} + \only<1>{ + \begin{tikzpicture} + [ + scale=0.7 + ] + \begin{axis}[% + domain=0:1, + ymin=0.5, ymax=1.05, + title=$P_n(x)$, + xlabel=$x$ + ] + \addplot[black, thick] { + cos(deg(x)) + }; + \addplot[blue] { + cos(deg(0.5)) + } node [above,pos=1] {$n=0$}; + \addplot[black, mark=x] coordinates { + (0.5000, 0.877583) + }; + \end{axis} + \end{tikzpicture} + } + \only<2>{ + \begin{tikzpicture} + [ + scale=0.7 + ] + \begin{axis}[% + domain=0:1, + ymin=0.5, ymax=1.05, + title=$P_n(x)$, + xlabel=$x$ + ] + \addplot[black, thick] { + cos(deg(x)) + }; + \addplot[blue] { + 1.06 - 0.365 * x + } node [above,pos=1] {$n=1$}; + \addplot[black, mark=x] coordinates { + (0.5000, 0.877583) + (0.2500, 0.968912) + }; + \end{axis} + \end{tikzpicture} + } + \only<3->{ + \begin{tikzpicture} + [ + scale=0.7 + ] + \begin{axis}[% + domain=0:1, + ymin=0.5, ymax=1.05, + title=$P_n(x)$, + xlabel=$x$ + ] + \addplot[black, thick] { + cos(deg(x)) + }; + \addplot[blue] { + 0.99996 + 0.00119746 * x - 0.511201 * x^2 + 0.0385918 * x^3 + } node [above,pos=1] {$n=3$}; + \addplot[black, mark=x] coordinates { + (0.5000, 0.877583) + (0.2500, 0.968912) + (0.1250, 0.992198) + (0.0625, 0.998048) + }; + \end{axis} + \end{tikzpicture} + } + \end{column} + \begin{column}[T]{.5\textwidth} + \only<4->{ + \begin{tikzpicture} + [ + scale=0.7 + ] + \begin{axis}[% + title=$P_n(0)$, + xlabel=$n$ + ] + \addplot+[black, mark=*, only marks] coordinates { + (0, 0.877583) + (1, 1.06024) + (2, 1.00056) + (3, 0.99996) + (4, 1.00000) + (5, 1.00000) + }; + \addplot+[red, mark=none, domain=0:6] { 1 }; + \end{axis} + \end{tikzpicture} + } + \end{column} + \end{columns} +\end{overlayarea} +\end{frame} + +\begin{frame}{Pathological example} + +Consider the example: +\begin{equation*} + f(x) = \exp(-x^{-1/2}) / x^4\,,\quad\text{with}\quad \lim_{x\to 0} f(x) = 0 +\end{equation*} +We use the same procedure as before: + +\begin{overlayarea}{\textwidth}{5cm} + \begin{columns} + \begin{column}[T]{.5\textwidth} + \only<1>{ + \begin{tikzpicture} + [ + scale=0.7 + ] + \begin{axis}[% + domain=0:1, + ymin=0, ymax=120, + title=$P_n(x)$, + xlabel=$x$ + ] + \addplot[black, thick, samples=250] { + exp(-1 / sqrt(x)) / x^3 + }; + \addplot[blue] { + 1.94493 + } node [above,pos=1] {$n=0$}; + \addplot[black, mark=x] coordinates { + (0.5000, 1.94493) + }; + \end{axis} + \end{tikzpicture} + } + \only<2>{ + \begin{tikzpicture} + [ + scale=0.7 + ] + \begin{axis}[% + domain=0:1, + ymin=0, ymax=120, + title=$P_n(x)$, + xlabel=$x$ + ] + \addplot[black, thick, samples=250] { + exp(-1 / sqrt(x)) / x^3 + }; + \addplot[blue] { + 15.378 - 26.8661 * x + } node [above,pos=1] {$n=1$}; + \addplot[black, mark=x] coordinates { + (0.5000, 1.94493) + (0.2500, 8.66146) + }; + \end{axis} + \end{tikzpicture} + } + \only<3->{ + \begin{tikzpicture} + [ + scale=0.7 + ] + \begin{axis}[% + domain=0:1, + ymin=0, ymax=120, + title=$P_n(x)$, + xlabel=$x$ + ] + \addplot[black, thick, samples=250] { + exp(-1 / sqrt(x)) / x^3 + }; + \addplot[blue, samples=50] { + 153.618 - 1573.05 * x + 5406.39 * x^2 - 5733.96 * x^3 + } node [above,pos=1] {$n=3$}; + \addplot[black, mark=x] coordinates { + (0.5000, 1.94493) + (0.2500, 8.66146) + (0.1250, 30.2621) + (0.0625, 75.0209) + }; + \end{axis} + \end{tikzpicture} + } + \end{column} + \begin{column}[T]{.5\textwidth} + \only<4->{ + \begin{tikzpicture} + [ + scale=0.75 + ] + \begin{axis}[% + ymode=log, + title=$\ln |P_n(0) - 1|$, + xlabel=$n$ + ] + \addplot+[black, mark=*, only marks] coordinates { + (0, 1.94493) + (1, 15.3780) + (2, 64.0244) + (3, 153.618) + (4, 169.579) + (5, 4.61491) + (6, 94.4333) + (7, 0.598657) + (8, 9.77146) + (9, 1.16233) + }; + \end{axis} + \end{tikzpicture} + } + \end{column} + \end{columns} +\end{overlayarea} +\end{frame} + +\begin{frame}{Foundations: Necessary prerequisite for extrapolation} + In order for the extrapolation to work, the function $f(x)$ needs + to fulfill a necessary prerequisite: + \begin{itemize} + \item existence of an asymptotic expansion + \end{itemize} + + \begin{block}{Asymptotic Expansion} + A function $f(x)$ can be asymptotically expanded in a sequence $\phi_n(x)$ around $x \simeq x_0$, + \begin{equation*} + f(x) = \sum_n^N a_n \phi_n(x)\,, + \end{equation*} + if + \begin{align*} + f(x) - \sum_n^{N-1} a_n \phi_n(x) = o(\phi_{N-1}(x))\,. + \end{align*} + + Example: The Taylor expansion is an asymptotic expansion with $\phi_n = x^n$. + \end{block} +\end{frame} + +\begin{frame}{Practical Issues} + The pathological example you saw earlier \emph{does have} an asymptotic expansion! + However, for $n \leq 10$ the extrapolation did not yet show convergence.\\ \medskip + + \begin{columns} + \begin{column}[T]{.5\textwidth} + The problem here are + \begin{itemize} + \item the choice of the starting point, + \item the existence of a bump between the starting + point $h_1 = 1/2$ and the point of interest ($h=0$). + \end{itemize} + \end{column} + \begin{column}[T]{.5\textwidth} + \begin{tikzpicture} + [ + scale=0.7 + ] + \begin{axis}[% + domain=0:1, + ymin=0, ymax=120, + title=$f(x)$, + xlabel=$x$ + ] + \addplot[black, thick, samples=250] { + exp(-1 / sqrt(x)) / x^3 + }; + \end{axis} + \end{tikzpicture} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Speeding up extrapolations} + Let's assume you have carried out an extrapolation to some point $x_0$ + for several different values of the degree $n$: + \begin{align*} + P_n(x) & :\,\text{interpolating polynomial} & + p_n & \equiv P_n(x_0)\,. + \end{align*} + The $p_n$ are a sequence that (hopefully) converges to the value you seek.\\ + + For definiteness, let's use the previous example of $f(x) = \cos(x)$. The first + few elements of the sequence $p_n$ were: + \begin{align*} + p_0 & = 0.877583 & + p_1 & = 1.06024 & + p_2 & = 1.00056 \\ + p_3 & = 0.99996 & + p_4 & = 1.00000 + \end{align*} + + Assuming that any sequence $p_n$ is convergent, it would be nice to have a way + to accelerate the sequence without any additional (potentially costly!) evaluations + of the function $f(x)$! +\end{frame} + +\begin{frame}{Delta-Square rule by Aitkens} + Define a new sequence $q_n$ as follows: + \begin{equation*} + q_n \equiv p_n - \frac{\left[\Delta(p)_{n}\right]^2}{\Delta^2(p)_{n}}\,, + \end{equation*} + where + \begin{align*} + \Delta(p)_k & = p_{k + 1} - p_k\,, & + \Delta^2(p)_k & = \Delta(p)_{k + 1} - \Delta(p)_k\,. + \end{align*} + This could be written simpler, but in order to avoid numerical instabilities (floating point numbers!) + the version written here is preferable.\\ \vfill + + [This method has further applications which we will revisit next lecture.] +\end{frame} + +\begin{frame}{Accelerating our example} + \begin{columns} + \begin{column}{.5\textwidth} + \begin{center} + \begin{tikzpicture} + \node[anchor=south] (0, 0) { + \begin{tabular}{lrr} + $n$ & $p_n$ & $q_{n - 2}$\\ + 0 & 0.87758 & --- \\ + 1 & 1.06024 & --- \\ + 2 & 1.00056 & 0.999954 \\ + 3 & 0.99996 & 0.999998 \\ + 4 & 1.00000 & \dots \\ + \end{tabular} + }; + \only<2>{ + \draw[blue,thick] (-0.40, +1.20) rectangle (+0.05, +1.55); + \draw[blue,thick] (+1.30, +1.20) rectangle (+1.90, +1.55); + \draw[draw=none, fill=blue, fill opacity=0.25] (-1.30, +1.20) rectangle (+0.05, 2.55); + } + \only<3>{ + \draw[red, thick] (-0.18, +0.70) rectangle (+0.05, +1.05); + \draw[red, thick] (+1.50, +0.70) rectangle (+1.90, +1.05); + \draw[draw=none, fill=red, fill opacity=0.25] (-1.30, +0.70) rectangle (+0.05, 2.05); + } + \end{tikzpicture} + \end{center} + \end{column} + \begin{column}{.5\textwidth} + \begin{itemize} + \item compare $p_n$ with $q_{n - 2}$ to keep things fair\\ + i.e.: $p_2$ vs $q_0$, $p_3$ vs $q_1$ etc. + \item<2-> {\color{blue}$q_0(p_0, p_1, p_2)$ is competitive with $p_3$!} + \item<3-> {\color{red} $q_1(p_1, p_2, p_3)$ is competitive with $p_4$!} + \end{itemize} + \end{column} + \end{columns} +\end{frame} + +\backupbegin + +\begin{frame}\frametitle{Backup} + + +\end{frame} + + + + +\backupend +\end{document} diff --git a/Lectures_my/NumMet/2016/Lecture3/tikzfeynman.sty b/Lectures_my/NumMet/2016/Lecture3/tikzfeynman.sty new file mode 100755 index 0000000..521fc65 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture3/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}, +} + diff --git a/Lectures_my/NumMet/2016/Lecture4/Makefile b/Lectures_my/NumMet/2016/Lecture4/Makefile new file mode 100644 index 0000000..37f4367 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture4/Makefile @@ -0,0 +1,9 @@ +all: lecture4.pdf + +lecture4.pdf: lecture4.tex + xelatex lecture4.tex +# bibtex lecture3 + xelatex lecture4.tex +# xelatex lecture4.tex +clean: + rm *.aux *.bbl *.blg *.log *.out *.pdf *.sh *.xml *.snm *.toc *.nav diff --git a/Lectures_my/NumMet/2016/Lecture4/beamercolorthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture4/beamercolorthemeFlip.sty new file mode 100755 index 0000000..d6b9c50 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture4/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/Lecture4/beamerinnerthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture4/beamerinnerthemeFlip.sty new file mode 100755 index 0000000..8dc12a0 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture4/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/Lecture4/beamerouterthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture4/beamerouterthemeFlip.sty new file mode 100755 index 0000000..d12f6d6 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture4/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/Lecture4/beamerouterthemedecolines.sty b/Lectures_my/NumMet/2016/Lecture4/beamerouterthemedecolines.sty new file mode 100755 index 0000000..669e493 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture4/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/Lecture4/beamerthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture4/beamerthemeFlip.sty new file mode 100755 index 0000000..a615ff5 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture4/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/Lecture4/images/BG_lower.png b/Lectures_my/NumMet/2016/Lecture4/images/BG_lower.png new file mode 100755 index 0000000..073034a --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture4/images/BG_lower.png Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture4/images/bubble.gif b/Lectures_my/NumMet/2016/Lecture4/images/bubble.gif new file mode 100644 index 0000000..ecff282 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture4/images/bubble.gif Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture4/images/bubble.jpg b/Lectures_my/NumMet/2016/Lecture4/images/bubble.jpg new file mode 100644 index 0000000..ceb584d --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture4/images/bubble.jpg Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture4/images/bubble2.jpg b/Lectures_my/NumMet/2016/Lecture4/images/bubble2.jpg new file mode 100644 index 0000000..0fd03bb --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture4/images/bubble2.jpg Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture4/images/uzh-transp.pdf b/Lectures_my/NumMet/2016/Lecture4/images/uzh-transp.pdf new file mode 100644 index 0000000..977da67 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture4/images/uzh-transp.pdf Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture4/lecture4.tex b/Lectures_my/NumMet/2016/Lecture4/lecture4.tex new file mode 100644 index 0000000..7893275 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture4/lecture4.tex @@ -0,0 +1,605 @@ +% vim: set sts=4 et : +\documentclass[11 pt,xcolor={dvipsnames,svgnames,x11names,table}]{beamer} + +\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} + +\usepackage{bm} +\usepackage{tikz,pgfplots} +\usepackage{graphicx} + +% 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}{$#2$}}% + +\graphicspath{{images/}} % Put all images in this directory. Avoids clutter. + +% 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}} +} + +\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 {Root Finding} + \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 Chrzaszcz, 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} +\vspace{0.5em} + \textcolor{normal text.fg!50!Comment}{Numerical Methods, \\ 26. September, 2016} +\end{center} +\end{frame} +} + +\begin{frame}{Plan for today} + \begin{itemize} + \item \alert{General problem of finding the root of a function}\\ + $\xi$ is a root of $f$ iff $f(\xi) = 0$. + \vfill + \item \alert{Begin with $D=1$}\\ + What properties of $f(x)$ can we use to find one, any, or all roots + of $f$? What are the requirements on $f(x)$? + \vfill + \item \alert{How about $D>1$?}\\ + Can we generalize root finding from $D=1$ do arbitrary $D$? + \end{itemize} +\end{frame} + +\begin{frame}{General iterative procedure} + Let's assume that + \begin{itemize} + \item $f(x)$ is a our function of interest, + \item $\xi$ is the only root of $f$, + \item we have a point $x_0$ close to $\xi$ + \end{itemize} + We now want to find a sequence $\lbrace x_0, x_1, \dots \rbrace$ that + \begin{enumerate} + \item converges toward $\xi$: $\lim_{k\to \infty} x_k = \xi$, + \item is iterative: $x_{k + 1} = \Phi[f](x_k)$ + \end{enumerate} + We can attempt to Taylor expand $f$ around $x_0$ to order $N$, in order + to obtain the generator $\Phi[f]$ for the iteration: + \begin{block}{Expansion around $x_0$} + \begin{equation*} + f(\xi) = 0 = \sum_{n=0}^N \frac{(\xi - x_0)^n}{n!} f^{(n)}(x_0) + \end{equation*} + where $f^{(n)}(x_0)$ is the $n$th derivative of $f$ at the position $x_0$. + \end{block} +\end{frame} + +\begin{frame}{Newton-Raphson method \hfill ($N=1$)} + \begin{block}{Expansion for $N=1$} + \begin{equation} + \tag{*} + f(\xi) = 0 = f(x_0) + (\xi - x_0) \cdot f'(x_0) + \mathcal{O}((\xi - x_0)^2) + \end{equation} + \end{block} + \vfill + Algorithm: + \begin{enumerate} + \item start with index $k=0$ + \item solve equation (*), assuming a vanshing approximation error: + \begin{gather*} + x_{k + 1} \leftarrow x_k - \frac{f(x_k)}{f'(x_k)} \approx \xi + \mathcal{O}((\xi - x_k)^2)\\ + \Phi[f](x) \equiv x - \frac{f(x)}{f'(x)} + \end{gather*} + \item if $f(x_{k + 1}) \leq t$, where $t$ is an a-prior threshold, then stop; otherwise + jump back to step \#2. + \end{enumerate} +\end{frame} + +\begin{frame}{Illustration of Newton-Raphson} + \begin{columns} + \begin{column}[T]{.5\textwidth} + \begin{overlayarea}{\textwidth}{\textheight} + $\bm{k=0}$: + \only<2->{% + \begin{equation*} + x_0 := 1 + \end{equation*} + } + \only<3->{% + $\bm{k=1}$: + \begin{align*} + x_0 & = 1 & + f(x_0) & = +0.54 \\ + & & + f'(x_0) & = -0.84 \\ + \end{align*} + } + \only<4->{% + \begin{equation*} + {\color{red} x_1 \leftarrow 1.64} + \end{equation*} + } + \only<6->{% + $\bm{k=2}$: + \begin{align*} + x_1 & = 1.64 & + f(x_0) & = -0.07 \\ + & & + f'(x_0) & = -0.997 \\ + \end{align*} + } + \only<7->{% + \begin{equation*} + {\color{red} x_2 \leftarrow 1.57} + \end{equation*} + } + \end{overlayarea} + \end{column} + \begin{column}[T]{.5\textwidth} + \hspace{-1cm} + \resizebox{1.1\textwidth}{!}{ + \begin{tikzpicture} + \begin{axis}[% + axis x line=center, + axis y line=center, + ymin=-0.2,ymax=0.8, + xmin=0.0,xmax=1.8, + title=$\cos(x)$ + ] + \addplot[thick,black,domain=0:3.14] { + cos(deg(x)) + }; + \only<2-3>{ + \addplot[thick,blue,only marks,mark=+,mark size=5pt] coordinates { + ( 1, 0.54030 ) + }; + } + \only<3-4>{ + \addplot+[thick,blue,domain=0:3.14,mark=none] { + 0.54030 - 0.84147 * (x - 1) + }; + } + \only<4-5>{ + \addplot[thick,red,only marks,mark=o,mark size=5pt] coordinates { + ( 1.6421, 0.0 ) + }; + \draw[thick,red] (axis cs:1.6421, 0) -- (axis cs:1.6421, -0.0712); + } + \only<5-6>{ + \addplot[thick,blue,only marks,mark=+,mark size=5pt] coordinates { + ( 1.6421, -0.0712 ) + }; + } + \only<6-7>{ + \addplot+[thick,blue,domain=0:3.14,mark=none] { + -0.0712 - 0.99746 * (x - 1.6421) + }; + } + \only<7->{ + \addplot[thick,red,only marks,mark=o,mark size=5pt] coordinates { + ( 1.5707, 7.8e-5 ) + }; + } + \end{axis} + \end{tikzpicture} + } + \vfill + \begin{overlayarea}{\textwidth}{.3\textheight} + \only<8->{ + \begin{tabular}{c|cc} + $k$ & $x_k$ & $f(x_k)$\\ + \hline + $0$ & $1.00$ & $+0.54$\\ + $1$ & $1.64$ & $-0.07$\\ + $2$ & $1.57$ & $+0.00$\\ + \hline + $\xi$&$1.5708$ & $0$ + \end{tabular} + } + \end{overlayarea} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Modified Newton-Raphson method \hfill ($N=2$)} + \begin{block}{Expansion for $N=2$} + \vspace{-2\medskipamount} + \begin{equation} + \tag{*} + f(\xi) = 0 = f(x_0) + (\xi - x_0) \cdot f'(x_0) + \frac{1}{2} (\xi - x_0)^2 f''(x_0) + \mathcal{O}((\xi - x_0)^3) + \end{equation} + \end{block} + \vfill + Algorithm: + \begin{enumerate} + \item start with index $k=0$ + \item solve equation (*), assuming a vanshing approximation error: + \begin{align*} + a_\pm + & \leftarrow x_k - \frac{f'(x_k) \pm \sqrt{[f'(x_k)]^2 - 2 f(x_k) f''(x_k)}}{f''(x_k)}\\ + & \approx \xi + \mathcal{O}((\xi - x_k)^3) + \end{align*} + \item if $|f(a_+)| < |f(a_-)|$, then $x_{k + 1} \leftarrow a_+$; otherwise $x_{k + 1} \leftarrow a_-$ + \item if $f(x_{k + 1}) \leq t$, where $t$ is an a-priori threshold, then stop; otherwise + jump back to step \#2. + \end{enumerate} +\end{frame} + +\begin{frame}{Rate of convergence} + Does this iterative procedure converge? If yes, how fast? How can we quantify the rate of convergence? + + \begin{itemize} + \item we have \alert{local} convergence of order $p \geq 1$, if for all $x \in U(\xi)$ + \begin{equation*} + || \Phi[f](x) - \xi|| \leq C \cdot || x - \xi||^p\,,\quad\text{with}\quad C \geq 0\,. + \end{equation*} + Note: if $p = 1$ then we must have $C < 1$. + \item we have \alert{global} convergence if $U(\xi) = \mathbb{R}$ + \item for $D=1$ we can calculate $p$ if $\Phi[f](x)$ is differentiable to sufficient degree: + \begin{align*} + \Phi(x) - \xi = \Phi(x) - \Phi(\xi) = \frac{(x - \xi)^p}{p!} + o(||x - \xi||^p) + \end{align*} + \end{itemize} +\end{frame} + +\begin{frame}{Rate of convergence for Newton-Raphson} + We have $\Phi(x) \equiv \Phi[f](x)$: + \begin{itemize} + \item $\Phi(\xi) = \xi$ by construction + \item $\Phi'(\xi) = \frac{f(\xi) \cdot f''(\xi)}{[f'(\xi)]^2} = 0$ \alert{(*)} by construction + \item $\Phi''(\xi) = \frac{f''(\xi)}{f'(\xi)}$ + \end{itemize} + We can therefore write + \begin{equation} + \Phi(x) - \Phi(\xi) = \frac{(x - \xi)^2}{2!} \Phi''(\xi) + o(||x - \xi||^2)\,. + \end{equation} + The Newton-Raphson method converges therefore \emph{at least quadratically}, i.e.: it is a + second-order method. + \vfill + \alert{(*): only if $f'(\xi) \neq 0$}, which is equivalent to $\xi$ is a simple root of $f$. +\end{frame} + +\begin{frame}{Pathological Example} + \begin{columns} + \begin{column}[T]{.5\textwidth} + \begin{overlayarea}{\textwidth}{\textheight} + $\bm{k=0}$: + \only<2->{% + \begin{equation*} + x_0 := 0.5 + \end{equation*} + } + \only<3->{% + $\bm{k=1}$: + \begin{align*} + x_0 & = 0.5 & + f(x_0) & = +0.707 \\ + & & + f'(x_0) & = -0.707 \\ + \end{align*} + } + \only<4->{% + \begin{equation*} + {\color{red} x_1 \leftarrow -0.5} + \end{equation*} + } + \only<6->{% + $\bm{k=2}$: + \begin{align*} + x_1 & = -0.5 & + f(x_0) & = +0.707 \\ + & & + f'(x_0) & = -0.707 \\ + \end{align*} + } + \only<7->{% + \begin{equation*} + {\color{red} x_2 \leftarrow +0.5} + \end{equation*} + } + \end{overlayarea} + \end{column} + \begin{column}[T]{.5\textwidth} + \hspace{-1cm} + \resizebox{1.1\textwidth}{!}{ + \begin{tikzpicture} + \begin{axis}[% + axis x line=center, + axis y line=center, + ymin=-0.1,ymax=0.9, + xmin=-0.7,xmax=0.7, + title=$\sqrt(|x|)$, + samples=160 + ] + \addplot[thick,black,domain=-1:+0] { + sqrt(abs(x)) + }; + \addplot[thick,black,domain=-0:+1] { + sqrt(abs(x)) + }; + \only<2-3>{ + \addplot[thick,blue,only marks,mark=+,mark size=5pt] coordinates { + ( +0.5, 0.707 ) + }; + } + \only<3-4>{ + \addplot+[thick,blue,domain=-1:1,mark=none] { + 0.707 + 0.707 * (x - 0.5) + }; + } + \only<4-5>{ + \addplot[thick,red,only marks,mark=o,mark size=5pt] coordinates { + ( -0.5, 0.707 ) + }; + \draw[thick,red] (axis cs:-0.5, 0) -- (axis cs:-0.5, +0.707); + } + \only<5-6>{ + \addplot[thick,blue,only marks,mark=+,mark size=5pt] coordinates { + ( -0.5, 0.707 ) + }; + } + \only<6-7>{ + \addplot+[thick,blue,domain=-1:1,mark=none] { + 0.707 - 0.707 * (x + 0.5) + }; + } + \only<7->{ + \addplot[thick,red,only marks,mark=o,mark size=5pt] coordinates { + ( 0.5, 0.707 ) + }; + \draw[thick,red] (axis cs:+0.5, 0) -- (axis cs:+0.5, +0.707); + } + \end{axis} + \end{tikzpicture} + } + \vfill + \begin{overlayarea}{\textwidth}{.3\textheight} + ~\\\bigskip + endless loop + \end{overlayarea} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Pitfalls of Newton-Raphson} + We had previously discussed that Newton-Raphson is guaranteed to converge + in an environment $U(\xi)$ of the root $\xi$.\\ \medskip + + However, it may fail to converge or converge only very slowly\dots + \begin{itemize} + \item if $U(\xi)$ is a small interval and the initial point lies outside of $U$, + \item if the algorithm encounters a stationary point $\chi$ of $f$ (i.e. $f'(\chi) = 0$), + \item if $\xi$ is a $m$-multiple root of $f$ (i.e. $f(x) \sim (x - \xi)^m \dots$) + \end{itemize} + + The last point can be accomodated for: If you know the mulitplicity $m$ of the root, + modify the Newton-Raphson step to read: + \begin{equation*} + x_{k + 1} \leftarrow x_{k} - m \frac{f(x_k)}{f'(x_k)} + \end{equation*} + Basically, this rescales the derivative from $f'(x) \to f'(x) / m$. +\end{frame} + +\begin{frame}{Honorable mention: Horner Scheme} + If $f(x) \equiv p_n(x)$ is a polynomial of degree $n$ in $x$, there might be multiple roots of $f$, i.e. + roots $\xi_{n}$ with $f'(\xi_n) = 0$.\\ + \vfill + The Horner Scheme allows to efficiently calculate all the (multiple) roots + of the polynomial $p_n(x)$.\\ + \vfill + However, this is of limited use: The polynomials dominantly arise in numerical computations + as the characteric polynomial $\chi_M$ of a matrix $M$. In these cases, the roots of $\chi_M$ + correspond to eigenvalue of $M$. However, the are better/more stables ways to \alert{numerically} compute + all eigenvalues of $M$, instead of finding all root of $\chi_M$. +\end{frame} + +\begin{frame}{Intermission: Derivatives} + Both the original and the modified Newton-Raphson methods involve taking + the derivative $f'$ of our target function $f$ at arbitrary points. Of + course, if we can analytically calculate the derivative, there is no problem.\\ + + \vfill + + What about functions that we can only evaluate numerically? (Think: Experiments, + numerical calculations)\\ + + \vfill + + Enter the field of \emph{numerical differentiation}! +\end{frame} + +\begin{frame}{Intermission: Derivatives} + How can we obtain the derivative $f'(x)$ numerically? Let's start from an expansion of + $f(x)$ close to the point of interest $x_0$: + \begin{tikzpicture} + \node at (0,0) { + \begin{minipage}{\textwidth} + \begin{align*} + f(x_0 + 2 h) & = f(x_0) + f'(x_0) \cdot 2 h + \frac{f''(x_0)}{2} \cdot 4 h^2 + \dots\\ + f(x_0 + \phantom2 h) & = f(x_0) + f'(x_0) \cdot \phantom2 h + \frac{f''(x_0)}{2} \cdot \phantom4 h^2 + \dots\\ + f(x_0 {\color{white}+ 2h}) & = f(x_0)\\ + f(x_0 - \phantom2 h) & = f(x_0) - f'(x_0) \cdot \phantom2 h + \frac{f''(x_0)}{2} \cdot \phantom4 h^2 + \dots\\ + f(x_0 - 2 h) & = f(x_0) - f'(x_0) \cdot 2 h + \frac{f''(x_0)}{2} \cdot 4 h^2 + \dots + \end{align*} + \end{minipage} + }; + %\draw[step=0.50,black,thin] (-4.5,-2.0) grid (4.5,2.0); + \draw[green!75!black,thick,rounded corners=5pt] (-4.5,+0.15) rectangle (+4.5,+1.05); + \only<1>{ + \draw[red, thick,rounded corners=5pt] (-4.5,-0.5) rectangle (+4.5,+0.1); + } + \only<2>{ + \draw[red, thick,rounded corners=5pt] (-4.5,-1.5) rectangle (+4.5,-0.5); + } + \end{tikzpicture} + + + \begin{overlayarea}{\textwidth}{.4\textheight} + \only<1>{ + \begin{block}{Variant \#1: Forward difference quotient} + \begin{equation*} + \frac{{\color{green!75!black}f(x_0 + h)} - {\color{red!90!black}f(x_0)}}{h} = f'(x_0) + \frac{f''(x_0)}{2} \cdot h = f'(x_0) + o(h) + \end{equation*} + \end{block} + } + \only<2>{ + \begin{block}{Variant \#2: Central difference quotient} + \vspace{-1.5\medskipamount} + \begin{equation*} + \frac{{\color{green!75!black}f(x_0 + h)} - {\color{red!90!black}f(x_0 - h)}}{2h} = f'(x_0) + \frac{f'''(x_0)}{3} h^2 = f'(x_0) + o(h^2) + \end{equation*} + \end{block} + } + \end{overlayarea} +\end{frame} + +\begin{frame}{Intermission: How to choose $h$?} + \begin{columns} + \begin{column}{.5\textwidth} + \includegraphics[width=\textwidth]{eps.png}\\ + {\tiny \hfill source: Wikipedia} + \begin{itemize} + \item two sources of numerical errors compete: + \begin{itemize} + \item formula errors, and + \item round-off (finite precision) errors + \end{itemize} + \end{itemize} + \end{column} + \begin{column}{.5\textwidth} + \begin{itemize} + \item formula error can be reduced through ``intelligent formulae'' + \item round-off error can be reduced through (schematically): + \begin{align*} + x_\text{approx} + & \leftarrow x + h\\ + h_\text{approx} + & \leftarrow x_\text{approx} - x\\ + f' & \leftarrow \frac{f(x_\text{approx}) - f(x)}{h_\text{approx}} + \end{align*} + \item optimal choice of $h$ will be close to + \begin{equation*} + h \sim \sqrt{\varepsilon} \cdot x + \end{equation*} + with $\varepsilon$: working precision + \end{itemize} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Intermission: Higher derivatives} + What about $f''(x_0)$, $f^{(3)}(x_0)$ or even higher derivatives?\\ + \medskip + \begin{block}{Central difference quotient for $f^{(n)}$} + \begin{align*} + \sum_{k=0}^n (-1)^k \binom{n}{k} \frac{f(x_0 + (n - 2 k) h)}{(2 h)^n} + & = f^{(n)}(x_0) + o(h^2) + \end{align*} + \end{block} +\end{frame} + +\newcommand{\del}{\partial} +\begin{frame}{Intermission: Multiple partial derivatives} + What about (multiple) partial derivatives $\del_x \del_y f(x, y)$?\\ + \medskip + \begin{block}{Central difference ``stencil'' for $\del_x \del_y f(x, y)$} + Combine what we learned previously: + \begin{multline*} + \frac{\only<1>{a}\only<2>{+} f(+ h_x, + h_y) \only<1>{+b}\only<2>{-} f(+ h_x, - h_y) \only<1>{+c}\only<2>{-} f(- h_x, + h_y) \only<1>{+d}\only<2>{+} f(- h_x, - h_y)}{4 h_x h_y}\\ + = \only<1>{\dots}\only<2>{\del x\del_y f(x,y)|_{x=0,y=0} + o(h_x^2) + o(h_y^2)} + \end{multline*} + \end{block} + \vfill + \only<2>{End of intermission.} +\end{frame} + +\begin{frame}{Newton-Raphson for $D > 1$?} + What happens if we generalize to $D > 1$?\\ + \medskip + Let's consider the case $D=2$ first, for a polynomial of degree $1$ + \begin{equation*} + f(x_1, x_2) = (1 - x) \cdot (2 - y) + \end{equation*} + \medskip + $f$ has infinitely many roots: + \begin{itemize} + \item $x = 1$ and $y$ arbitrary + \item $y = 2$ and $x$ arbitrary + \end{itemize} + In order to pin-point only one point in $D=2$, we need to solve $2$ + equations: + \begin{align*} + f_1(x_1, x_2) & = 0, & + f_2(x_1, x_2) & = 0 + \end{align*} + In $D$ dimensions, we will need to solve $D$ simultaneous equations! +\end{frame} + +\begin{frame}{Generalization to $D > 1$} + Substitute: + \begin{align*} + f(x) \in \mathbb{R} \quad & \to \quad f(x) \in \mathbb{R}^D\\ + x \in \mathbb{R} \quad & \to \quad x \in \mathbb{R}^D\\ + f'(x) \in \mathbb{R} \quad & \to \quad [D_f]_{ij} \equiv \frac{\del f_i(x)}{\del x_j} \in \mathbb{R}^{D\times D} + \end{align*} + + Then the Newton-Raphson steps reads + \begin{equation*} + x^{(k+1)} \leftarrow x^{(k)} - \left[D_f(x^{(k)})\right]^{-1} f(x^{(k)})\,. + \end{equation*} + Problems: + \begin{itemize} + \item the functional matrix $D_f(x^{(k)})$ might be singular, or numerically close to being + singular + \item inverting $D_f$ is generally computationally expensive! + \end{itemize} + + In the next two lectures, Marcin will discuss how to solve systems of linear equations. + These methods will also introduce you to methods to numerically compute the above $x^{(k + 1)}$ + from $D_f(x^{(k)})$. +\end{frame} + +\backupbegin + +\begin{frame}\frametitle{Backup} + +\end{frame} + +\backupend +\end{document} diff --git a/Lectures_my/NumMet/2016/Lecture5/Makefile b/Lectures_my/NumMet/2016/Lecture5/Makefile new file mode 100644 index 0000000..e4cf8e8 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture5/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/Lecture5/beamercolorthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture5/beamercolorthemeFlip.sty new file mode 100755 index 0000000..d6b9c50 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture5/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/Lecture5/beamerinnerthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture5/beamerinnerthemeFlip.sty new file mode 100755 index 0000000..8dc12a0 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture5/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/Lecture5/beamerouterthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture5/beamerouterthemeFlip.sty new file mode 100755 index 0000000..d12f6d6 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture5/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/Lecture5/beamerouterthemedecolines.sty b/Lectures_my/NumMet/2016/Lecture5/beamerouterthemedecolines.sty new file mode 100755 index 0000000..669e493 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture5/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/Lecture5/beamerthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture5/beamerthemeFlip.sty new file mode 100755 index 0000000..a615ff5 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture5/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! 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+ +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/Lecture5/mchrzasz.aux b/Lectures_my/NumMet/2016/Lecture5/mchrzasz.aux new file mode 100644 index 0000000..8f14db5 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture5/mchrzasz.aux @@ -0,0 +1,148 @@ +\relax +\providecommand\hyper@newdestlabel[2]{} +\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument} +\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined +\global\let\oldcontentsline\contentsline +\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} +\global\let\oldnewlabel\newlabel +\gdef\newlabel#1#2{\newlabelxx{#1}#2} +\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} +\AtEndDocument{\ifx\hyper@anchor\@undefined +\let\contentsline\oldcontentsline +\let\newlabel\oldnewlabel +\fi} +\fi} +\global\let\hyper@last\relax +\gdef\HyperFirstAtBeginDocument#1{#1} +\providecommand*\HyPL@Entry[1]{} +\bibstyle{biblatex} 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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{Linear eq. system} + +\ARROW This and the next lecture will focus on a well known problem. Solve the following equation system: +\begin{align*} +A \cdot x =b, +\end{align*} +\ARROWR $A = a_{ij} \in \mathbb{R}^{n\times n}$ and $\det(A) \neq 0$\\ +\ARROWR $b=b_i \in \mathbb{R}^n$.\\ +\ARROW The problem: Find the $x$ vector. + + + +\end{frame} + +\begin{frame}\frametitle{Error digression} +\begin{small} +\ARROW There is enormous amount of ways to solve the linear equation system.\\ +\ARROW The choice of one over the other of them should be gathered by the {\it condition} of the matrix $A$ denoted at $cond(A)$. +\ARROW If the $cond(A)$ is small we say that the problem is well conditioned, otherwise we say it's ill conditioned.\\ +\ARROW The {\it condition} relation is defined as: +\begin{align*} +cond(A) = \Vert A \Vert \cdot \Vert A^{-1} \Vert +\end{align*} +\ARROW Now there are many definitions of different norms... The most popular one (so-called ''column norm''): +\begin{align*} +\Vert A \Vert_1 = \max_{1 \leq j \leq n} \sum_{i=1}^n \vert a_{i,j} \vert, +\end{align*} +where $n$ -is the dimension of $A$, $i,j$ are columns and rows numbers. + + + +\end{small} +\end{frame} + + +\begin{frame}\frametitle{More norms} +\begin{small} +\ARROW A different norm is a spectral norm: +\begin{align*} +\Vert A \Vert_2 &= \sqrt{\rho(A^T A)}\\ +\rho(M) &= \max \lbrace \vert\lambda_i \vert: \det{M- \lambda I} =0,~i=1,...n \rbrace +\end{align*} +where $\rho(M)$ - spectral radius of $M$ matrix, $I$ unit matrix, $\lambda_i$ eigenvalues of $M$.\\ + +\ARROW Row norm: +\begin{align*} +\Vert A \Vert_{\infty} &= \max_{1 \leq i \leq n} \sum_{j=1}^n \vert a_{i,j} \vert, +\end{align*} +\begin{exampleblock}{Digression:} +\ARROWR Calculation of the matrix norms are not a simple process at all. There are certain class of matrices that make the calculations easier.\\ +\ARROWR The spectral norm can be also defined: +\begin{align*} +cond_2(A) = \frac{\max_{1\leq i \leq n}\vert \lambda_i \vert }{\min_{1\leq i \leq n}\vert \lambda_i \vert }, +\end{align*} +\end{exampleblock} + +\end{small} +\end{frame} + + +\begin{frame}\frametitle{Example, ill-conditioned matrix} +\begin{small} +\ARROW The text-book example of wrongly conditioned matrix is the Hilbert matrix: +\begin{align*} +h_{i,j} = \frac{1}{i+j-1} +\end{align*} +\ARROWR Example: +\begin{align*} +h_{i,j}^{4 \times 4} = \begin{pmatrix} +1 & \frac{1}{2} & \frac{1}{3} & \frac{1}{4} \\ +\frac{1}{2} & \frac{1}{3} & \frac{1}{4} & \frac{1}{5} \\ +\frac{1}{3} & \frac{1}{4} & \frac{1}{5} & \frac{1}{6}\\ +\frac{1}{4} & \frac{1}{5} & \frac{1}{6} & \frac{1}{7} +\end{pmatrix} +\end{align*} +\ARROW The condition of this matrix: +\begin{align*} +cond(A)=\mathcal{O}\left(\frac{e^{3.52N}}{\sqrt{N}}\right) +\end{align*} +\ARROW For $8 \times 8$ matrix we get: +\begin{align*} +cond_1(A)=3.387\cdot 10^{10},~~~cond_2(A)=1.526\cdot 10^{10},~~~~~cond_{\infty}(A)=3.387\cdot 10^{10} +\end{align*} +\ARROW Clearly large numbers ;) +\end{small} +\end{frame} + +\begin{frame}\frametitle{Exact methods: Cramer method} +\begin{small} +\ARROW If $\det{A} \neq 0$ then the solutions are given by: +\begin{align*} +x_i =\frac{\det{A_i}}{\det{A}} +\end{align*} +\ARROW So calculate the solutions one needs to calculate $n+1$ determinants. To calculate each determinate one needs $(n-1)n!$ multiplications. \\ +\ARROW Putting it all together one needs $(n+1)(n-1)n! = n^{n+2}$ \\ +\ARROW Brute force but works ;) + + +\end{small} +\end{frame} + + + + + +\begin{frame}\frametitle{Example, ill-conditioned matrix} +\begin{small} +\ARROW The text-book example of wrongly conditioned matrix is the Hilbert matrix: +\begin{align*} +h_{i,j} = \frac{1}{i+j-1} +\end{align*} +\ARROWR Example: +\begin{align*} +h_{i,j}^{4 \times 4} = \begin{pmatrix} +1 & \frac{1}{2} & \frac{1}{3} & \frac{1}{4} \\ +\frac{1}{2} & \frac{1}{3} & \frac{1}{4} & \frac{1}{5} \\ +\frac{1}{3} & \frac{1}{4} & \frac{1}{5} & \frac{1}{6}\\ +\frac{1}{4} & \frac{1}{5} & \frac{1}{6} & \frac{1}{7} +\end{pmatrix} +\end{align*} +\ARROW The condition of this matrix: +\begin{align*} +cond(A)=\mathcal{O}\left(\frac{e^{3.52N}}{\sqrt{N}}\right) +\end{align*} +\ARROW For $8 \times 8$ matrix we get: +\begin{align*} +cond_1(A)=3.387\cdot 10^{10},~~~cond_2(A)=1.526\cdot 10^{10},~~~~~cond_{\infty}(A)=3.387\cdot 10^{10} +\end{align*} +\ARROW Clearly large numbers ;) +\end{small} +\end{frame} + +\begin{frame}\frametitle{Exact methods: Cramer method} +\begin{small} +\ARROW If $\det{A} \neq 0$ then the solutions are given by: +\begin{align*} +x_i =\frac{\det{A_i}}{\det{A}} +\end{align*} +\ARROW So calculate the solutions one needs to calculate $n+1$ determinants. To calculate each determinate one needs $(n-1)n!$ multiplications. \\ +\ARROW Putting it all together one needs $(n+1)(n-1)n! = n^{n+2}$ \\ +\ARROW Brutal force but works ;) + + +\end{small} +\end{frame} + + + + + +\begin{frame}\frametitle{Exact methods: Gauss method} +\begin{small} + +\ARROW The idea besides the Gauss method is simple: transform the $A x =b$ to get the equvalent matrix $A^{\left[n\right]} x = b^{\left[n\right]}$ where $A^{\left[n\right]}$ is triangular matrix: +\begin{align*} +A^{\left[n\right]} = \begin{pmatrix} +a^{\left[n\right]}_{11} & a^{\left[n\right]_{12}} & ... & a^{\left[n\right]}_{1n}\\ +0 & a^{\left[n\right]}_{22} & ... & a^{\left[n\right]}_{2n} \\ +...\\ +0 & 0 & ... & a^{\left[n\right]}_{nn} \\ +\end{pmatrix} +\end{align*} +\ARROWR The algorithm: +\ARROW To do so we calculate the: $d^{\left[1\right]}_{i,1}=\frac{a^{\left[1\right]}_{i1}}{a^{\left[1\right]}_{11}}$ \\ +\ARROW The first row multiplied by the $d^{\left[1\right]}_{i,1}$ we subtract from the $i^{th}$ row. +\ARROW After this we get: + +\begin{align*} +\begin{pmatrix} +a^{\left[ 1 \right]}_{11} & a^{\left[ 1 \right]_{12}} & ... & a^{\left[ 1 \right]}_{1n}\\ +0 & a^{\left[ 1 \right]}_{22} & ... & a^{\left[ 1 \right]}_{2n} \\ +...\\ +0 & a^{\left[ 1 \right]}_{n2} & ... & a^{\left[ 1 \right]}_{nn} \\ +\end{pmatrix} \overrightarrow{x}= +\begin{pmatrix} +b^{\left[ 1 \right]}_{1} \\ +b^{\left[ 1 \right]}_{1} \\ +... \\ +b^{\left[ 1 \right]}_{1} \\ +\end{pmatrix} +\end{align*} + +\end{small} +\end{frame} + + + +\begin{frame}\frametitle{Exact methods: Gauss method 2} +\begin{small} + +\ARROW Now one needs to repeat the above n times moving each time row down. +\begin{alertblock}{Cons:} +\ARROW The algoright can be stooped if you divide by zero.\\ +\ARROW The method is very efficient to accumulate numerical errors. +\end{alertblock} + +\begin{exampleblock}{Pros:} +\ARROWR The number of needed floating point operations is less then Cramer.\\ +\ARROWR Example for 15 equations: $1345$ vs $5 \cdot 10^{12}$. +\end{exampleblock} + +\end{small} +\end{frame} + + + +\begin{frame}\frametitle{Exact methods: modified Gauss method} +\begin{small} + +\ARROW The biggest disadvantage of Gauss method is the fact that we can have zero elements :( \\ +\ARROW The modified method fixes this problem :)\\ +\ARROW The modification is as follows: +\begin{itemize} +\item In each step before we do the elimination we look for main element: +\begin{align*} +\vert a_{mk}^{\vert k \vert } = \max \lbrace \vert a_{jk}^{\vert k \vert} : j=k, k+1,..., n \rbrace +\end{align*} +\item We exchange the rows $m$ and $k$. +\item We do the standard elimination. +\end{itemize} + +\end{small} +\end{frame} + + + +\begin{frame}\frametitle{Exact methods: Jordan elimination method} +\begin{small} + + +\ARROW The Jordan elimination method is similar to Guass method but the idea is to transform the matrix from $Ax =b$ to $I x = b^{\lfloor n+1 \rfloor}$. +\begin{enumerate} +\item We start from eliminating the as in Gauss method in the first row. +\item When we move to the second row we eliminate the $x_2$ element also from the first raw. +\item The third raw we eliminate the first and second raw. +\item We repeat this $n$ times. +\end{enumerate} +\ARROW After this we will get new system $I x = b^{\lfloor n+1 \rfloor}$. \\ +\ARROW The $b^{\lfloor n+1 \rfloor}$ is already the solution! No need to do more. + +\end{small} +\end{frame} + + +\begin{frame}\frametitle{Exact methods: LU method} +\begin{small} + + +\ARROW The most popular of the exact methods is so-called LU method.\\ +\ARROW The idea is very simple; we represent the matrix in a form: +\begin{align*} +A = & \begin{pmatrix} +a_{11} & a_{12} & a_{13} & ... & a_{1n} \\ +a_{21} & a_{22} & a_{23} & ... & a_{2n} \\ +a_{31} & a_{32} & a_{33} & ... & a_{2n} \\ + & & ... & & \\ + _{n1} & a_{n2} & a_{n3} & ... & a_{nn} \\ +\end{pmatrix} = \\ & \begin{pmatrix} +1 & 0 & 0 & ... & 0 \\ +l_{21} & 1 & 0 & ... & 0 \\ +l_{31} & l_{32} & 1 & ... &0 & \\ + & & ... & & \\ +l_{n1} & l_{n2} & l_{n3} & ... & l_{nn}\\ +\end{pmatrix} \cdot +\begin{pmatrix} +u_{11} & u{12} & u_{13} & ... & u_{1n} \\ +0 & u{22} & u_{23} & ... & u_{2n} \\ +0 & 0 & u_{33} & ... & u_{3n} \\ + & & ... & & \\ +0 & 0 & 0 & ... & u_{nn} +\end{pmatrix} = L \cdot U +\end{align*} +\ARROW After this decomposition we need to solve: +\begin{align*} +\begin{cases} +L y & =b\\ +U x & =y +\end{cases} +\end{align*} + +\end{small} +\end{frame} + +\begin{frame}\frametitle{Exact methods: LU method, algorithms} +\begin{small} +\ARROW We solve the following matrix: $A^{\lfloor 1 \rfloor} x = b^{\lfloor1 \rfloor}$\\ +\ARROW We start by preparing the matrix $L^{\lfloor 1 \rfloor}$: +\begin{align*} +L^{\lfloor 1 \rfloor }=\begin{pmatrix} +1 & 0 & 0 & ... & 0 \\ +-l_{21} & 1 & 0 & ... & 0\\ +-l_{31} & 0 & 1 & ... & 0\\ +& & ... & & \\ +-l_{n1} & 0 & 0 & ... & 1 +\end{pmatrix} +\end{align*} +where the $l_{i1}$ are defined: +\begin{align*} +l_{i1} = \frac{a_{i1}^{\lfloor 1 \rfloor}}{a_{11}^{\lfloor 1 \rfloor}} +\end{align*} +\ARROW Now we take our base equation by $L^{\lfloor 1 \rfloor }$: +\begin{align*} +L^{\lfloor 1 \rfloor } A^{\lfloor 1 \rfloor } x = L^{\lfloor 1 \rfloor } b^{\lfloor1 \rfloor} +\end{align*} +\ARROW We get the a new system: +\begin{align*} +A^{\lfloor 2 \rfloor} x = b^{\lfloor2 \rfloor}~~~~~~~~\Leftrightarrow~~~~~~~~~~L^{\lfloor 1 \rfloor } A^{\lfloor 1 \rfloor } x = L^{\lfloor 1 \rfloor } b^{\lfloor1 \rfloor} +\end{align*} + +\end{small} +\end{frame} + +\begin{frame}\frametitle{Exact methods: LU method, algorithms} +\begin{small} +\ARROW In the second step we construct the $L^{\lfloor 2 \rfloor}$ in the form: +\begin{align*} +L^{\lfloor 2 \rfloor}=\begin{pmatrix} +1 & 0 & 0 & ... & 0 \\ +0 & 1 & 0 & ... & 0\\ +0 & -l_{32} & 1 & ... & 0\\ +& & ... & & \\ +0 & -l_{n2} & 0 & ... & 1 +\end{pmatrix} +\end{align*} +where : +\begin{align*} +l_{i2} = \frac{a_{i2}^{\lfloor 2 \rfloor}}{a_{22}^{\lfloor 2 \rfloor}} +\end{align*} + +\ARROW Now we take the $A^{\lfloor 2 \rfloor} x = b^{\lfloor2 \rfloor}$ and multiply it by $L^{\lfloor 2 \rfloor}$: +\begin{align*} +L^{\lfloor 2 \rfloor } A^{\lfloor 2 \rfloor } x = L^{\lfloor 2 \rfloor } b^{\lfloor2 \rfloor} +\end{align*} +\ARROW We get the a new system: +\begin{align*} +A^{\lfloor 3 \rfloor} x = b^{\lfloor3 \rfloor}~~~~~~~~\Leftrightarrow~~~~~~~~~L^{\lfloor 2 \rfloor } L^{\lfloor 1 \rfloor } A^{\lfloor 1 \rfloor } x = L^{\lfloor 2 \rfloor } L^{\lfloor 1 \rfloor } b^{\lfloor1 \rfloor} +\end{align*} + +\end{small} +\end{frame} + + +\begin{frame}\frametitle{Exact methods: LU method, algorithms} +\begin{small} + +\ARROW Now the we repeat the above steps $n-1$ times after which we get: +\begin{align*} +& L^{\lfloor n-1 \rfloor } L^{\lfloor n-2 \rfloor } ... L^{\lfloor 2 \rfloor } L^{\lfloor 1 \rfloor } A^{\lfloor 1 \rfloor } = A^{\lfloor n \rfloor } = U\\ +& L^{\lfloor n-1 \rfloor } L^{\lfloor n-2 \rfloor } ... L^{\lfloor 2 \rfloor } L^{\lfloor 1 \rfloor } b^{\lfloor1 \rfloor} = b^{\lfloor n \rfloor} +\end{align*} +\ARROW From the above we can calculate: +\begin{align*} +A^{\lfloor 1 \rfloor } = \left( L^{\lfloor 1 \rfloor } \right)^{-1} \left( L^{\lfloor 2 \rfloor } \right)^{-1} ... \left( L^{\lfloor n-1 \rfloor } \right)^{-1} A^{\lfloor n \rfloor } +\end{align*} +\ARROW So the matrix $L$ we search for is: +\begin{align*} +L= \left( L^{\lfloor 1 \rfloor } \right)^{-1} \left( L^{\lfloor 2 \rfloor } \right)^{-1} ... \left( L^{\lfloor n-1 \rfloor } \right)^{-1} +\end{align*} +\ARROW The $\left( L^{\lfloor k \rfloor } \right)^{-1}$ can be easy calculated: +\begin{footnotesize} +\begin{align*} +\left( L^{\lfloor k \rfloor } \right)^{-1} = \begin{pmatrix} +1 & 0 & ... & 0 & ... & 0 \\ +0 & 1 & ... & 0 & ... & 0 \\ +& & & ... & & \\ +0 & 0 & ... & 1 & ... & 0 \\ +0 & 0 & ... & l_{k+1 k} & ... & 0 \\ +0 & 0 & ... & l_{k+2 k} & ... & 0 \\ +& & & ... & & \\ +0 & 0 & ... & l_{n k} & ... & 1 \\ +\end{pmatrix} +\end{align*} +\end{footnotesize} + +\end{small} +\end{frame} + + + +\begin{frame}\frametitle{Exact methods: LU method, algorithms} +\begin{small} + +\ARROW Now the only thing left is to solve the simple linear system: +\begin{align*} +\begin{cases} +L y & =b\\ +U x & =y +\end{cases} +\end{align*} +\ARROW Because of the triangular matrix the solution is straightforward: +\begin{align*} +y_1=\frac{b_1}{L_11},~~~~~~~~~y_i=\frac{b_1 - \sum_{j=1^{i-1}} L_{ij} y_j }{L_{ii}}~~{ i\geq 2} +\end{align*} + +\end{small} +\end{frame} + + +\begin{frame}\frametitle{Summary} +\begin{small} + +\ARROW This lecture we learn the exact methods of solving linear equation system.\\ +\ARROW The three most popular one are: Gauss, Jordan, LU.\\ +\ARROW By default the LU method should be used.\\ +\ARROW And remember: be sure the system is well conditioned! + + +\end{small} +\end{frame} + + + + + + +\backupbegin + +\begin{frame}\frametitle{Backup} + + +\end{frame} + + + + + + + +\backupend +\end{document} diff --git a/Lectures_my/NumMet/2016/Lecture5/mchrzasz.toc b/Lectures_my/NumMet/2016/Lecture5/mchrzasz.toc new file mode 100644 index 0000000..429917f --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture5/mchrzasz.toc @@ -0,0 +1,5 @@ +\boolfalse {citerequest}\boolfalse {citetracker}\boolfalse {pagetracker}\boolfalse {backtracker}\relax +\defcounter {refsection}{0}\relax +\beamer@endinputifotherversion {3.24pt} +\defcounter {refsection}{0}\relax +\select@language {english} diff --git a/Lectures_my/NumMet/2016/Lecture5/tikzfeynman.sty b/Lectures_my/NumMet/2016/Lecture5/tikzfeynman.sty new file mode 100755 index 0000000..521fc65 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture5/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}, +} + diff --git a/Lectures_my/NumMet/2016/Lecture6/Makefile b/Lectures_my/NumMet/2016/Lecture6/Makefile new file mode 100644 index 0000000..e4cf8e8 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture6/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/Lecture6/beamercolorthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture6/beamercolorthemeFlip.sty new file mode 100755 index 0000000..d6b9c50 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture6/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/Lecture6/beamerinnerthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture6/beamerinnerthemeFlip.sty new file mode 100755 index 0000000..8dc12a0 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture6/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/Lecture6/beamerouterthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture6/beamerouterthemeFlip.sty new file mode 100755 index 0000000..d12f6d6 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture6/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/Lecture6/beamerouterthemedecolines.sty b/Lectures_my/NumMet/2016/Lecture6/beamerouterthemedecolines.sty new file mode 100755 index 0000000..669e493 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture6/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/Lecture6/beamerthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture6/beamerthemeFlip.sty new file mode 100755 index 0000000..a615ff5 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture6/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/Lecture6/images/BG_lower.png b/Lectures_my/NumMet/2016/Lecture6/images/BG_lower.png new file mode 100755 index 0000000..073034a --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture6/images/BG_lower.png Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture6/images/bubble.gif b/Lectures_my/NumMet/2016/Lecture6/images/bubble.gif new file mode 100644 index 0000000..ecff282 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture6/images/bubble.gif Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture6/images/bubble.jpg b/Lectures_my/NumMet/2016/Lecture6/images/bubble.jpg new file mode 100644 index 0000000..ceb584d --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture6/images/bubble.jpg Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture6/images/bubble2.jpg b/Lectures_my/NumMet/2016/Lecture6/images/bubble2.jpg new file mode 100644 index 0000000..0fd03bb --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture6/images/bubble2.jpg Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture6/images/uzh-transp.pdf b/Lectures_my/NumMet/2016/Lecture6/images/uzh-transp.pdf new file mode 100644 index 0000000..977da67 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture6/images/uzh-transp.pdf Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture6/mchrzasz-blx.bib b/Lectures_my/NumMet/2016/Lecture6/mchrzasz-blx.bib new file mode 100644 index 0000000..9e405b3 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture6/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/Lecture6/mchrzasz.tex b/Lectures_my/NumMet/2016/Lecture6/mchrzasz.tex new file mode 100644 index 0000000..a8f533b --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture6/mchrzasz.tex @@ -0,0 +1,587 @@ +\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[Linear equation systems: iteration methods]{Linear equation systems:iteration methods} +\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 {Linear equation systems: iteration methods} + \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, \\ 17 October, 2016} +\end{center} +\end{frame} +} + + +\begin{frame}\frametitle{Linear eq. system} + +\ARROW This and the next lecture will focus on a well known problem. Solve the following equation system: +\begin{align*} +A \cdot x =b, +\end{align*} +\ARROWR $A = a_{ij} \in \mathbb{R}^{n\times n}$ and $\det(A) \neq 0$\\ +\ARROWR $b=b_i \in \mathbb{R}^n$.\\ +\ARROW The problem: Find the $x$ vector. + + +\end{frame} + + + +\begin{frame}\frametitle{LU method with main element selection} +\begin{small} +\ARROW The algorithm for the LU matrix decomposition from previous lecture doesn't have the main element selection. \\ +\ARROW This might be problematic. For example (backboard example) + + + + +\end{small} +\end{frame} + + + +\begin{frame}\frametitle{Chelosky decomposition} +\begin{small} + +\ARROW If $A \in \textbf{R}^{N \times N}$ is a symmetric ($A^T=A$) and positively defined matrix, then there exits a special case of LU factorization such that: +\begin{align*} +A =C C^T +\end{align*} +where $C$ is a traingular matrixwith diagonal elements greater then zero. \\ +\ARROW Finding the Chelosky decomposition is two times faster the finding the LU decomposition. \\ +\ARROW The Chelosky decomposition has the same algorithm then the LU decomposition. + + + +\end{small} +\end{frame} + + +\begin{frame}\frametitle{LDL factorization} +\begin{small} + +\ARROW If matrix can be Chelosky decomposed it can also be decomposed to: +\begin{align*} +A=LDL^T +\end{align*} +where $L$ is botton triangular matrix such that $\forall_i : l_{ii}=1$ and $D$ is diagonal matrix with positive elements. \\ +\ARROW The advantage of the LDL decomposition compared to Cehlosky decomposition is the fact that we don't need to square root in the calculations. + + + +\end{small} +\end{frame} + + + +\begin{frame}\frametitle{Iterative methods} +\begin{small} + +\ARROW The exact methods are the ones that require more computations to get the solutions.\\ +\ARROWR Because of this they are not really suited to solve big linear systems.\\ +\ARROW The iteration methods are simple and the main goal of them is to transform: +\begin{align*} +Ax=b +\end{align*} +to: +\begin{align*} +x= Mx + c +\end{align*} +where $A$,$M$ are matrices of $n \times n$ size. \\ +$b$ and $c$ are vectors of the size $n$.\\ +\ARROW Once we get the second system (btw. remember MC lectures?) we can use iterative methods to solve them. + +\end{small} +\end{frame} + + +\begin{frame}\frametitle{Expansion} +\begin{small} + +\ARROW If $\overline{x}$ is the solution of the $A x = b$ system then also: +\begin{align*} +\overline{x} = M \overline{x} +c +\end{align*} +\ARROW We construct the a sequence that approximates the $\overline{x}$ in the following way: +\begin{align*} +x^{(k+1)} = M x^{(k)},~~~k=0,1,... +\end{align*} +\ARROW The necessary and sufficient requirement for the convergence of the set is: +\begin{align*} +\rho(M)<1 +\end{align*} + + + +\end{small} +\end{frame} + + +\begin{frame}\frametitle{Jakobi method} +\begin{small} + +\ARROW The simplest method is the Jakobi method. \\ +\ARROW We start from decomposition of $A$ matrix: +\begin{align*} +A = L + U +D +\end{align*} +where +\begin{itemize} +\item $L=(a_{ij})_{i>j}$ - triangular lower matrix. +\item $D=(a_{ik})_{i=j}$ - diagonal matrix. +\item $U=(a_{ij})_{ii}a_{ij}x_{j}^{(k)} \right) + \frac{b_i}{a_{ii}} +\end{align*} +\ARROW The matrix: +\begin{align*} +M_{GS} = -(L+D)^{-1} U +\end{align*} +is so-called Gauss-Seidl matrix. + +\end{small} +\end{frame} + + +\begin{frame}\frametitle{Convergence of Gauss-Seidle and Jacobi methods} +\begin{small} + +\begin{exampleblock}{Reminder:} +The necessary and sufficient condition for the iteration to be convergence is that: +\begin{align*} +\rho(M)<1 +\end{align*} +where $M$ is the matrix of a given method. +\end{exampleblock} + +\ARROW Now calculating the $\rho(M)$ might be already a computationally expensive...\\ +\ARROW A very useful way of getting the $\rho(M_J)$ is: +\begin{align*} +r_J = \frac{\Vert x_{k+1} - x_k \Vert}{\Vert x_k - x_{k-1} \Vert} \approx \vert \rho(M_J) -1 \vert +\end{align*} +\ARROW Another useful equations: +\begin{align*} +\rho(M_{GS}) = \rho(M_J)^2 +\end{align*} + + + +\end{small} +\end{frame} + + +\begin{frame}\frametitle{Convergence of Gauss-Seidle and Jacobi methods} +\begin{small} + +\begin{alertblock}{Theorem:} +If matrix $(a_{ij})$ fulfils one of the conditions:\\ +\ARROW $\vert a_{ii} > \sum_{j \neq i} \vert a_{ij} \vert~~ i=1,...,n$, so-called strong row criteria.\\ +\ARROW $\vert a_{jj} > \sum_{i \neq j} \vert a_{ij} \vert~~ j=1,...,n$, so-called strong column criteria. +\end{alertblock} + +\begin{exampleblock}{Practical note:} +\ARROWR One needs to note that calculating the $\rho(M)$ might be a as time consuming calculation as the solution is self...\\ +\ARROWR If that is the case usually one neglects this steps and computes the solution with extra care at each step checking the convergence. + +\end{exampleblock} + + +\end{small} +\end{frame} + + + + +\begin{frame}\frametitle{SOR method} +\begin{small} + +\ARROW The Successive Over-Relaxation method is an extension of the Gauss-Seidl methods. \\ +\ARROW The modification is that we can reuse the previous step to get a more precise approximation of the solution. \\ +\ARROW The ''hack'' happens when we calculate the $x^{(k+1)}_{GS}$ using the Gauss-Seidl method. Instead assuming that the next step is the $x^{(k+1)}_{GS}$ we ''relax'' the condition using liner combination: +\begin{align*} +x^{(k+1)} =\omega x^{(k+1)}_{GS} + (1-\omega) x^{(k)} +\end{align*} +\ARROW From the above once can see that if $\omega=1$ then we end up with standard Gauss-Seidl method. \\ +\ARROW The iteration method equation has the form: +\begin{align*} +x^{(k+1)} = (D+ \omega L)^{-1} ((1-\omega)D - \omega U)x^{(k)} + (D + \omega L)^{-1} \omega b +\end{align*} + + + + +\end{small} +\end{frame} + + + + +\begin{frame}\frametitle{SOR method, convergence} +\begin{small} + +\ARROW The main difficulty in the SOR method is the fact we need to choose the $\omega$ parameter. \\ +\ARROW One can easily prove that if the method is converging the $\omega \in \left(0, 2 \right)$. \\ +\ARROW This is necessary condition but it's not enough! \\ +\ARROW If the $A$ is symmetric and positively defined then the above condition is also sufficient! + + + + +\end{small} +\end{frame} + + + + + +\begin{frame}\frametitle{Conclusions} +\begin{small} + +\ARROW We learned more exact method of solving the linear system.\\ +\ARROW For big matrix we need to use iterative method which are not exact.\\ +\ARROW My personal experience: Did not have big enough matrices to really need to apply the iterative methods but this is field dependent! + + +\end{small} +\end{frame} + + + + +\backupbegin + +\begin{frame}\frametitle{Backup} + + +\end{frame} + + + + + + + +\backupend +\end{document} diff --git a/Lectures_my/NumMet/2016/Lecture6/tikzfeynman.sty b/Lectures_my/NumMet/2016/Lecture6/tikzfeynman.sty new file mode 100755 index 0000000..521fc65 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture6/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}, +} + diff --git a/Lectures_my/NumMet/2016/Lecture_template/Makefile b/Lectures_my/NumMet/2016/Lecture_template/Makefile new file mode 100644 index 0000000..e4cf8e8 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture_template/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/Lecture_template/beamercolorthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture_template/beamercolorthemeFlip.sty new file mode 100755 index 0000000..d6b9c50 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture_template/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/Lecture_template/beamerinnerthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture_template/beamerinnerthemeFlip.sty new file mode 100755 index 0000000..8dc12a0 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture_template/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/Lecture_template/beamerouterthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture_template/beamerouterthemeFlip.sty new file mode 100755 index 0000000..d12f6d6 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture_template/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/Lecture_template/beamerouterthemedecolines.sty b/Lectures_my/NumMet/2016/Lecture_template/beamerouterthemedecolines.sty new file mode 100755 index 0000000..669e493 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture_template/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/Lecture_template/beamerthemeFlip.sty b/Lectures_my/NumMet/2016/Lecture_template/beamerthemeFlip.sty new file mode 100755 index 0000000..a615ff5 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture_template/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/Lecture_template/images/BG_lower.png b/Lectures_my/NumMet/2016/Lecture_template/images/BG_lower.png new file mode 100755 index 0000000..073034a --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture_template/images/BG_lower.png Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture_template/images/bubble.gif b/Lectures_my/NumMet/2016/Lecture_template/images/bubble.gif new file mode 100644 index 0000000..ecff282 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture_template/images/bubble.gif Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture_template/images/bubble.jpg b/Lectures_my/NumMet/2016/Lecture_template/images/bubble.jpg new file mode 100644 index 0000000..ceb584d --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture_template/images/bubble.jpg Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture_template/images/bubble2.jpg b/Lectures_my/NumMet/2016/Lecture_template/images/bubble2.jpg new file mode 100644 index 0000000..0fd03bb --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture_template/images/bubble2.jpg Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture_template/images/uzh-transp.pdf b/Lectures_my/NumMet/2016/Lecture_template/images/uzh-transp.pdf new file mode 100644 index 0000000..977da67 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture_template/images/uzh-transp.pdf Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture_template/mchrzasz-blx.bib b/Lectures_my/NumMet/2016/Lecture_template/mchrzasz-blx.bib new file mode 100644 index 0000000..9e405b3 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture_template/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/Lecture_template/mchrzasz.synctex.gz b/Lectures_my/NumMet/2016/Lecture_template/mchrzasz.synctex.gz new file mode 100644 index 0000000..d501b18 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture_template/mchrzasz.synctex.gz Binary files differ diff --git a/Lectures_my/NumMet/2016/Lecture_template/mchrzasz.tex b/Lectures_my/NumMet/2016/Lecture_template/mchrzasz.tex new file mode 100644 index 0000000..90d8dcd --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture_template/mchrzasz.tex @@ -0,0 +1,304 @@ +\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[Linear equation systems: exact methods]{Linear equation systems:exact methods} +\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 {Linear equation systems: exact methods} + \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{Linear eq. system} + +\ARROW This and the next lecture will focus on a well known problem. Solve the following equation system: +\begin{align*} +A \cdot x =b, +\end{align*} +\ARROWR $A = a_{ij} \in \mathbb{R}^{n\times n}$ and $\det(A) \neq 0$\\ +\ARROWR $b=b_i \in \mathbb{R}^n$.\\ +\ARROW The problem: Find the $x$ vector. + + + +\end{frame} + +\begin{frame}\frametitle{Error digression} +\begin{small} +\ARROW There is enormous amount of ways to solve the linear equation system.\\ +\ARROW The choice of one over the other of them should be gathered by the {\it condition} of the matrix $A$ denoted at $cond(A)$. +\ARROW If the $cond(A)$ is small we say that the problem is well conditioned, otherwise we say it's ill conditioned.\\ +\ARROW The {\it condition} relation is defined as: +\begin{align*} +cond(A) = \Vert A \Vert \cdot \Vert A^{-1} \Vert +\end{align*} +\ARROW Now there are many definitions of different norms... The most popular one (so-called ''column norm''): +\begin{align*} +\Vert A \vert_1 = \max_{1 \leq j \leq n} \sum_{i=1}^n \vert a_{i,j} \vert, +\end{align*} +where $n$ -is the dimension of $A$, $i,j$ are columns and rows numbers. + + + +\end{small} +\end{frame} + + + + + + +\backupbegin + +\begin{frame}\frametitle{Backup} + + +\end{frame} + + + + + + + +\backupend +\end{document} diff --git a/Lectures_my/NumMet/2016/Lecture_template/tikzfeynman.sty b/Lectures_my/NumMet/2016/Lecture_template/tikzfeynman.sty new file mode 100755 index 0000000..521fc65 --- /dev/null +++ b/Lectures_my/NumMet/2016/Lecture_template/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}, +} + diff --git a/Lectures_my/NumMet/2016/plan.txt b/Lectures_my/NumMet/2016/plan.txt new file mode 100644 index 0000000..22191c6 --- /dev/null +++ b/Lectures_my/NumMet/2016/plan.txt @@ -0,0 +1,37 @@ +Lectures +-------- + +Id Date Title Personnel +01 19.09. Introduction/Precision MC +02 21.09. Interpolation MC +03 26.09. Interpolation+Extrapolation DvD +04 05.10. Root Finding DvD +05 10.10. Solving Linear Equation (I) MC +06 12.10 Solving Linear Equation (II) MC +07 17.10 Solving Non-linear Equations DvD +08 31.10 Numerical Integration (I) MC +09 07.11 Numerical Integration (II) DvD +10 14.11 Ordinary Differential Eqs. (I) DvD +11 21.11 Ordinary Differential Eqs. (II) MC +12 28.11 Chaos Theorem MC +13 05.12 Function Minimization (I) DvD +14 12.12 Function Minimization (II) DvD + +Classes +------- + +Id Date Suggested Topic Personnel +01 28.09 Errors + Numers ? +02 03.10 Interpolation/Extrapolation ? +03 19.10 ? ? +04 24.10 ? ? +05 26.10 ? ? +06 02.10 ? ? +07 09.11 ? ? +08 16.11 ? ? +09 23.11 ? ? +10 30.11 ? ? +11 07.12 ? ? +12 14.12 ? ? +13 19.12 ? ? +44 21.12 ? ? diff --git a/Lectures_my/NumMet/Lecture1/Examples/ex1/Makefile b/Lectures_my/NumMet/Lecture1/Examples/ex1/Makefile deleted file mode 100644 index c7813b2..0000000 --- a/Lectures_my/NumMet/Lecture1/Examples/ex1/Makefile +++ /dev/null @@ -1,70 +0,0 @@ -#---------------------------------------------------------------------- -# Przyklad linkowania bibliotek systemu ROOT z wlasnym programem -#---------------------------------------------------------------------- -.SUFFIXES: .o .c .cxx .cpp .C .f .l .s .sh .h .a .cc -#====================================================================== -# Biblioteki ROOTa dla linkera -# 1) Jawnie: -## Sciezka to systemu ROOT - nalezy ja ustawic odpowiednio -RPATH = /home/mchrzasz/ROOT/root/ -RLIB= -L$(RPATH)lib -lCore -lHist -lGraf -lGraf3d -lGpad -lTree -lRooFitCore -lRooFit -lRooStats \ - -lRint -lPostscript -lMatrix -lPhysics -lm -ldl -lpthread -rdynamic -Wl,--no-as-needed $(ROOTGLIBS) -#2) Niejawnie, przy uzyciu root-config -#RLIB= `root-config --libs` -#====================================================================== -# Nazwa biezacego katalogu -DIRNAME = ./ -#====================================================================== -# Nazwa rdzeniowa modulu programu -NAME1 = ex1 -# Pliki objectowe (po kompilacji) -OBJT1 = $(NAME1).o -# Pliki wykonawcze (po linkowaniu) -EXEC1 = $(NAME1).x -# Nazwa i opcje kompilatora -CXX = g++ -# 1) Jawnie -#CXXFLAGS = -O -Wall -pthread -I$(RPATH)include -# 2) Przy uzyciu root-config -CXXFLAGS = -O2 -Wall `root-config --cflags` -# Nazwa i opcje linkera -LD = $(CXX) -LDFLAGS = `root-config --ldflags` - - -CXXFLAGS += $(shell $(ROOTSYS)/bin/root-config --cflags) -#EXTRALIBS += $(shell $(ROOTSYS)/bin/root-config --libs) -LDFLAGS += $(shell $(ROOTSYS)/bin/root-config --libs) -RLIB += $(shell $(ROOTSYS)/bin/root-config --libs) - -#============================================================================== -# Kompilacja dla modulow z plikami naglowkowymi -%.o: %.cxx %.h - $(CXX) $(CXXFLAGS) -c $< -# Kompilacja dla modulow bez plikow naglowkowych -%.o: %.cxx - $(CXX) $(CXXFLAGS) -c $< -#============================================================================== -.PHONY: all run clean tar -all: ${EXEC1} -#============================================================================== -# Linkowanie -${EXEC1}: ${OBJT1} - $(LD) -o $@ $(LDFLAGS) $^ $(RLIB) - -#============================================================================== -# Uruchamianie -run: ${EXEC1} - ./${EXEC1} -#============================================================================== -clean: - (rm -f *.o *.a *~ *.exe *.x core lmap *.dvi *.aux *.log a.out) -#============================================================================== -tar: clean - (cd ../; tar -cvzf $(DIRNAME).tar.gz $(DIRNAME) ) -#============================================================================== -# Wszelkie akcje jakie należy podjąć aby program zaprezentował swoje działanie: -test: run - @echo 'Test run finished' -#============================================================================== - diff --git a/Lectures_my/NumMet/Lecture1/Examples/ex1/Makefile~ b/Lectures_my/NumMet/Lecture1/Examples/ex1/Makefile~ deleted file mode 100644 index ec55feb..0000000 --- a/Lectures_my/NumMet/Lecture1/Examples/ex1/Makefile~ +++ /dev/null @@ -1,70 +0,0 @@ -#---------------------------------------------------------------------- -# Przyklad linkowania bibliotek systemu ROOT z wlasnym programem -#---------------------------------------------------------------------- -.SUFFIXES: .o .c .cxx .cpp .C .f .l .s .sh .h .a .cc -#====================================================================== -# Biblioteki ROOTa dla linkera -# 1) Jawnie: -## Sciezka to systemu ROOT - nalezy ja ustawic odpowiednio -RPATH = /home/mchrzasz/ROOT/root/ -RLIB= -L$(RPATH)lib -lCore -lHist -lGraf -lGraf3d -lGpad -lTree -lRooFitCore -lRooFit -lRooStats \ - -lRint -lPostscript -lMatrix -lPhysics -lm -ldl -lpthread -rdynamic -Wl,--no-as-needed $(ROOTGLIBS) -#2) Niejawnie, przy uzyciu root-config -#RLIB= `root-config --libs` -#====================================================================== -# Nazwa biezacego katalogu -DIRNAME = ./ -#====================================================================== -# Nazwa rdzeniowa modulu programu -NAME1 = Add_variables -# Pliki objectowe (po kompilacji) -OBJT1 = $(NAME1).o -# Pliki wykonawcze (po linkowaniu) -EXEC1 = $(NAME1).x -# Nazwa i opcje kompilatora -CXX = g++ -# 1) Jawnie -#CXXFLAGS = -O -Wall -pthread -I$(RPATH)include -# 2) Przy uzyciu root-config -CXXFLAGS = -O2 -Wall `root-config --cflags` -# Nazwa i opcje linkera -LD = $(CXX) -LDFLAGS = `root-config --ldflags` - - -CXXFLAGS += $(shell $(ROOTSYS)/bin/root-config --cflags) -#EXTRALIBS += $(shell $(ROOTSYS)/bin/root-config --libs) -LDFLAGS += $(shell $(ROOTSYS)/bin/root-config --libs) -RLIB += $(shell $(ROOTSYS)/bin/root-config --libs) - -#============================================================================== -# Kompilacja dla modulow z plikami naglowkowymi -%.o: %.cxx %.h - $(CXX) $(CXXFLAGS) -c $< -# Kompilacja dla modulow bez plikow naglowkowych -%.o: %.cxx - $(CXX) $(CXXFLAGS) -c $< -#============================================================================== -.PHONY: all run clean tar -all: ${EXEC1} -#============================================================================== -# Linkowanie -${EXEC1}: ${OBJT1} - $(LD) -o $@ $(LDFLAGS) $^ $(RLIB) - -#============================================================================== -# Uruchamianie -run: ${EXEC1} - ./${EXEC1} -#============================================================================== -clean: - (rm -f *.o *.a *~ *.exe *.x core lmap *.dvi *.aux *.log a.out) -#============================================================================== -tar: clean - (cd ../; tar -cvzf $(DIRNAME).tar.gz $(DIRNAME) ) -#============================================================================== -# Wszelkie akcje jakie należy podjąć aby program zaprezentował swoje działanie: -test: run - @echo 'Test run finished' -#============================================================================== - diff --git a/Lectures_my/NumMet/Lecture1/Examples/ex1/ex1.cc b/Lectures_my/NumMet/Lecture1/Examples/ex1/ex1.cc deleted file mode 100644 index 82364cd..0000000 --- a/Lectures_my/NumMet/Lecture1/Examples/ex1/ex1.cc +++ /dev/null @@ -1,99 +0,0 @@ -#include "RooRealVar.h" -#include "RooDataSet.h" -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include "math.h" -#include "RooCBShape.h" -#include "RooRealVar.h" -#include "RooAbsReal.h" -#include "RooExponential.h" -#include "RooDataSet.h" -#include "RooPlot.h" -#include "TFile.h" -#include -#include -#include "RooGenericPdf.h" -#include "RooPolynomial.h" -#include "RooAddPdf.h" -#include "RooExtendPdf.h" -#include -#include "RooGaussian.h" -#include -#include "RooStats/SPlot.h" -#include "RooDataHist.h" -#include "RooAbsReal.h" -#include "RooMinuit.h" -#include "TLorentzVector.h" - -// use this order for safety on library loading -using namespace RooFit ; -using namespace RooStats ; -using namespace std; - - -const double PI=3.14159265358979323846264338327950288419716939937510; -const long double PIdd=3.14159265358979323846264338327950288419716939937510; - - - - -double calc(int a) -{ - return (1./a)*(pow(10.,a)*(1.+a*PI*pow(10,-a))-pow(10,a)); -} - -double calc2d(int a) -{ - long double const1=1.; - long double const10=10.; - return (const1/a)*(pow(const10, a)*(const1+a*PIdd*pow(const10,-a))-pow(const10,a)); -} - - -int main(int argc, char *argv[]) -{ - if(argc != 2) - { - - cout<<"Wrong number of arguments"< -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include "math.h" -#include "RooCBShape.h" -#include "RooRealVar.h" -#include "RooAbsReal.h" -#include "RooExponential.h" -#include "RooDataSet.h" -#include "RooPlot.h" -#include "TFile.h" -#include -#include -#include "RooGenericPdf.h" -#include "RooPolynomial.h" -#include "RooAddPdf.h" -#include "RooExtendPdf.h" -#include -#include "RooGaussian.h" -#include -#include "RooStats/SPlot.h" -#include "RooDataHist.h" -#include "RooAbsReal.h" -#include "RooMinuit.h" -#include "TLorentzVector.h" - -// use this order for safety on library loading -using namespace RooFit ; -using namespace RooStats ; -using namespace std; - - -int main(int argc, char *argv[]) -{ - if(argc != 2) - { - - cout<<"Wrong number of arguments"< -\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/Lecture1/beamerinnerthemeFlip.sty b/Lectures_my/NumMet/Lecture1/beamerinnerthemeFlip.sty deleted file mode 100755 index 8dc12a0..0000000 --- a/Lectures_my/NumMet/Lecture1/beamerinnerthemeFlip.sty +++ /dev/null @@ -1,95 +0,0 @@ -% 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/Lecture1/beamerinnerthemeFlip.sty~ b/Lectures_my/NumMet/Lecture1/beamerinnerthemeFlip.sty~ deleted file mode 100755 index 38dd47d..0000000 --- a/Lectures_my/NumMet/Lecture1/beamerinnerthemeFlip.sty~ +++ /dev/null @@ -1,95 +0,0 @@ -% 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}% - \vskip1em\par - \begin{beamercolorbox}[sep=7pt,center,#1]{author} - \usebeamerfont{author}\insertauthor - \end{beamercolorbox} - \begin{beamercolorbox}[sep=7pt,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/Lecture1/beamerouterthemeFlip.sty b/Lectures_my/NumMet/Lecture1/beamerouterthemeFlip.sty deleted file mode 100755 index d12f6d6..0000000 --- a/Lectures_my/NumMet/Lecture1/beamerouterthemeFlip.sty +++ /dev/null @@ -1,189 +0,0 @@ -% 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/Lecture1/beamerouterthemedecolines.sty b/Lectures_my/NumMet/Lecture1/beamerouterthemedecolines.sty deleted file mode 100755 index 669e493..0000000 --- a/Lectures_my/NumMet/Lecture1/beamerouterthemedecolines.sty +++ /dev/null @@ -1,168 +0,0 @@ -% 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/Lecture1/beamerthemeFlip.sty b/Lectures_my/NumMet/Lecture1/beamerthemeFlip.sty deleted file mode 100755 index a615ff5..0000000 --- a/Lectures_my/NumMet/Lecture1/beamerthemeFlip.sty +++ /dev/null @@ -1,59 +0,0 @@ -% 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! 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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, \\ 19 September, 2016} -\end{center} -\end{frame} -} - - - -\begin{frame}\frametitle{Course plan} -\begin{small} -\ARROW The course consists of 2 hours lecture and 2 hours of exercise.\\ -\ARROW TA will explain to you how you will get points for the class exercise (you will be coding the algorithms) described on the lecture and applying them to some problems.\\ -\ARROW After passing the class exercise ($>66\%$ of points) you will have an exam (oral).\\ - - -\begin{columns} -\column{0.7\textwidth} -\ARROW The final mark: -\vspace{0.1cm} -\begin{footnotesize} -\begin{equation*} -{\rm mark}= 0.5~ {\rm exam} + 0.5 ~ {\rm class} -\end{equation*} -\ARROW The final exam will be average of exam and class marks. -\end{footnotesize} -\column{0.05\textwidth} -{~} -\column{0.25\textwidth} -\begin{footnotesize} - -\begin{tabular}{|c|c|} -\hline -Mark & Range\\\hline -$6$ & $84-100~\%$ \\ -$5$ & $67-83~\%$ \\ -$4$ & $50-67~\%$ \\ \hline -$3$ & $33-50~\%$ \\ -$2$ & $16-33~\%$ \\ -$1$ & $0-16~\%$ \\ -\hline -\end{tabular} - -\end{footnotesize} - - -\end{columns} -\end{small} -\end{frame} - -\begin{frame}\frametitle{Course plan} -\begin{enumerate} -\item Numerical precision, floating point representation. -\item Numerical stability. -\item Function interpolation, multidim. function interpolation. -\item Function approximation. -\item Linear equation solving with elimination methods and iteration methods. -\item Non-linear system of equation solving. -\item Numerical integration. -\item Differential equations solving. -\item Chaos theorem. -\end{enumerate} - -\end{frame} - - -\begin{frame}\frametitle{Why do we need numerical methods?} -\begin{exampleblock}{Prose:} -\ARROWR Most of the problems that one tackles on daily basis cannot be computed analytically! During the university studies the problems you were solving were tailor suited to be analytically solvable!\\ -\ARROWR Even if the problem is solvable analytically in daily work one needs to repeat the calculations many times changing some conditions. Solving $n^{\rm th}$ time a similar integral on paper can have deadly consequences on your sanity.\\ -\ARROWR Let's face is computers are just much much faster then us in this kind of computations.\\ -\end{exampleblock} -\begin{alertblock}{Cons:} -\ARROW One disadvantage of numerical methods is the fact that they don't give you an exact solution. The reason for that is that the computers don't operate on real numbers but just on their representation which we will learn during today’s lecture. -\end{alertblock} -\end{frame} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame}\frametitle{Errors, fast reminder} -\ARROW As you already know there are two types of errors: -\begin{itemize} -\item Absolute error $\Delta$. -\item Relative error $\delta$. -\end{itemize} - -\begin{align*} -\Delta = \vert A - a \vert~~~~~~~~~~~\delta = \vert \frac{A- a}{A} \vert, ~~A \neq 0, -\end{align*} -where $A$ is the exact number, $a$ its approximation.\\ \pause -\ARROW Now since we know what are errors lets look into the sources of errors:\\ -\ARROWR Input errors.\\ -\ARROWR Cut-off errors.\\ -\ARROWR Rounding errors. - - -\end{frame} - -\begin{frame}\frametitle{Input Errors} -\begin{small} - - -\ARROW Input errors are errors that are associated with the inputs to the computer. We can have different types of this errors: -\begin{columns} -\column{0.6\textwidth} -\begin{itemize} -\item Mathematical model errors. A canonical example of such simplification is the pendulum, where we make an approximation of $\sin x =x$ for small $x$: -\begin{align*} -l \frac{d^2x}{dt^2} + g x =0 -\end{align*} -\item Errors associated to a given numerical algorithm: a choice of a numerical algorithm is indeed an very important step of solving a given problem. As we will see during the course the simplest models that are fast to implement to execute on the machine can lead to large numerical errors. -\end{itemize} - - -\column{0.4\textwidth} -\includegraphics[width=0.75\textwidth]{images/pen.jpg} - -\begin{itemize} -\item Input data errors. For many computations one needs tome inputs: constants, starting points, etc. There are errors that are associated to those as well. This kind of errors are super the easiest to control and usually are negligible. - -\end{itemize} - -\end{columns} - -\end{small} - -\end{frame} - - - -\begin{frame}\frametitle{Cut-off Errors} -\begin{small} -\ARROW This kind of errors arise where the true mathematical problem have some kind of infinite sum.\\ -\ARROWR Computers are stupid creatures and they don't understand what is $\infty$ so we need to cut of computations at some point. Example: -\begin{exampleblock}{Maclaurin series:} -We know that an $e^x$ function can be Taylor expanded: -\begin{align*} -e^x = \sum_{n=0}^{n=\infty} \frac{x^n}{n!}=1 +x +\frac{x^2}{2!} + \frac{x^3}{3!}+\frac{x^4}{4!}+... -\end{align*} -We can replace the infinite sum with a finite one: -\begin{align*} -e^x \approx =1 +x +\frac{x^2}{2!} + \frac{x^3}{3!}+\frac{x^4}{4!}+...+\frac{x^N}{N!} -\end{align*} - - -\end{exampleblock} -\ARROW This kind of errors are unfortunately very common in the field. We will have to deal with them every time we have some kind of $\lim$, $\sum^{\infty}$, etc. - - -\end{small} - -\end{frame} - - -\begin{frame}\frametitle{Rounding Errors} -\begin{small} -\ARROW This kind of errors occur during calculations on machines.\\ -\ARROW Machine represents the number with a final precision.\\ -\ARROW During the calculations the errors accumulate with every operation.\\ -\ARROW This errors can be avoided or reduced by proper algorithm or by changing the precision of computations. -\pause -\begin{center} -\includegraphics[width=0.8\textwidth]{images/prec.png} - -\end{center} - - -\end{small} - -\end{frame} - - -\begin{frame}\frametitle{Integer numbers on our PC} -\begin{small} -\ARROW The integer numbers are very easy to represent on PC: -\begin{align*} -a=\pm (c_1N^0 + c_2N^1 +...+ c_dN^{d-1}), -\end{align*} -where $N$ is the base of the system. Computers of course use $2$. -\begin{columns} -\column{3in} -\ARROW For example: -\begin{align*} -101011 \rightleftarrows & 1 \cdot 2^0 + 1 \cdot 2^1 +0 \cdot 2^2 + 1 \cdot 2^3 +\\ & 0 \cdot 2^4 +1 \cdot 2^5\\ & = 43 -\end{align*} -\ARROW Now the first bit can be used for sign determination ($0$ plus $1$ minus) \texttt{int} or can be used to extend the range of numbers \texttt{unsigned}\\ -\ARROW \texttt{int} - $-2147483648 - 2147483647$\\ -\ARROW \texttt{unsigned} - $0 - 4294967295$ - - -\column{2in} -\includegraphics[width=0.95\textwidth]{images/joke.jpg} - -\end{columns} - -\end{small} - -\end{frame} - - - -\begin{frame}\frametitle{Floating numbers on our PC} -\begin{small} -\ARROW Computers are using so-called ''classical floating point representation'': -\begin{align*} -a=\pm M \cdot N^C,~a \neq 0, -\end{align*} -\begin{itemize} -\item $M$ - mantissa or significand -\item $N$ - base of the system -\item $C$ - exponent -\end{itemize} -\ARROW In such system the mantissa is always normalized: -\begin{align*} -M \in \left[ \frac{1}{N}, 1 \right) -\end{align*} -\ARROW Using the definition we can write the mantissa and exponent in the following way: -\begin{align*} -M=(m_1N^{-1}+m_2N^{-2}+...+m_t N^{-t})\\ -C=\pm(c_1 N^0+ c_2 N^1 + c_3 N^2 + ...+c_d N^{d-1}) -\end{align*} -\ARROW The most often know base are $2,8,10,16$. -\end{small} - -\end{frame} - -\begin{frame}\frametitle{Numbers on our PC: binary system } -\begin{small} -\ARROW For example let's construct numbers using binary system: -\begin{align*} -M=\pm(m_1 2^{-1}+m_2 2^{-2}+...+m_t 2^t)\\ -C=\pm(c_1 2^0+ c_2 2^1 + c_3 2^2 + ...+c_d 2^{d-1}) -\end{align*} -where: -\begin{itemize} -\item $t$ - length of mantissa, $d$ - length of exponent -\item $m_i$ - mantissa digits; $m_i \in \lbrace 0,1\rbrace$ -\item $c_i$ - exponent digits; $c_i \in \lbrace 0,1\rbrace$ -\end{itemize} -\begin{exampleblock}{Example: $11110001~(s)mmmm(s)cc$} -Lets say we are representing a number with a byte. First 5 digits are the mantissa the next 3 are exponent. -\begin{align*} -M=-(1 \cdot 2^{-1} + 1 \cdot 2^{-2} + 1 \cdot 2^{-3} + 0 \cdot 2^{-4} = -\frac{7}{8}\\ -C= + (0 \cdot 2^0 + 1 \cdot 2^1)=2\\ -x=-\frac{7}{8} \cdot 2^2=-3.5 -\end{align*} - -\end{exampleblock} - -\end{small} - -\end{frame} - - -\begin{frame}\frametitle{IEEE754-2008} -\begin{small} -\ARROW The rules of the binary systems are defined by the \texttt{ISO-IEEE754} standard (updated in 2008 of the 1985 standard). - -\begin{center} -\includegraphics[width=0.9\textwidth]{images/table.png} -\end{center} -\ARROW There is a minimum and maximum number we can represent in the current system.\\ -\ARROW There are some tricks you can play: use subnormal \\ -\ARROW In general we can represent numbers from: $\langle -a, -b \rangle \cup \lbrace 0 \rbrace \cup \langle b,a \rangle$\\ -\ARROW The standard also defines the rounding procedures for numbers. - -\end{small} - -\end{frame} - -\begin{frame}\frametitle{Error propagation: sum} -\begin{small} -\ARROW Let's consider we have two numbers $x$ and $y$. \\ -\ARROW Their representation are not exact so: $x=\overline{x} + \epsilon_x$ and $y=\overline{y}+\epsilon_y$\\ -\ARROW Now if we want to sum them: -\begin{align*} -x+y=\overline{x}+\overline{y} + \epsilon_x+\epsilon_y=\overline{x}+\overline{y}+\epsilon -\end{align*} -\ARROW If each of the $\epsilon_i$ numbers have a constant distribution on $\left[-\frac{1}{2} 10^{-d}, \frac{1}{2} 10^{-d} \right]$, where $d$ is the precision.\\ -\ARROW Then $\epsilon$ has a triangular distribution on $\left[-10^{-d}, 10^{-d} \right]$\\ -\ARROW Repeating $N$ times this we will approach the Gaussian distribution with a width of $\sim \sqrt{N} 10^{-d}$ - -\end{small} - -\end{frame} - -\begin{frame}\frametitle{Error propagation: multiplication, division} -\begin{small} -\ARROW Let's consider we have two numbers $x$ and $y$. \\ -\ARROW Their representation are not exact so: $x=\overline{x} + \epsilon_x$ and $y=\overline{y}+\epsilon_y$\\ -\ARROW Now if we want to multiply them (we can neglect $\epsilon_x \epsilon_y$ terms): -\begin{align*} -x \cdot y=\overline{x} \cdot \overline{y} + \epsilon_x \cdot \overline{y}+\epsilon_y \cdot \overline{x} -\end{align*} -\ARROW If $\vert \overline{x} \vert \gg (\ll) \vert \overline{y} \vert$ then the error might explode. \\ - -\ARROW Now if we want to divide them: -\begin{align*} -x / y=\overline{x} / \overline{y} + \frac{\epsilon_x}{\overline{y}}+ \frac{\epsilon_y \overline{x}}{\overline{y}^{ {\color{red} 2}}} -\end{align*} - -\ARROW If $\vert y \vert \ll \vert x \vert$ then the division is will have large errors. -\end{small} - -\end{frame} - - -\begin{frame}\frametitle{Application} -\begin{small} -\ARROW When we implement a current algorithm we need to ensure that our algorithm is ''backward stable'', ''well-conditioned'' and ''numerically stable''.\\ -\begin{exampleblock}{Numerical stability} -We say that the algorithm is numerically stable if the the results does not change if we increase the computation precision. - -\end{exampleblock} -\begin{alertblock}{Backward stability} -Backward stability means that our algorithm will gives us the true answer if we move to infinite precision of the machine. In practice we look if we can conserve the errors of the representation. -\end{alertblock} -\begin{exampleblock}{Well-conditioned} -Each algorithm has some input parameters. If we introduce a slight difference in those parameters (of the order of the representation precision), the results should not change significantly. - -\end{exampleblock} -\ARROWR The numerical precision lead to discovery of chaos. If we have time we will discuss this during our lectures. - -\end{small} - -\end{frame} -\begin{frame}\frametitle{Rounding error} -\begin{small} -\ARROW Imagine we want to calculate: -\begin{align*} -1.0000+\sum_{i=1}^{10} 0.0001 -\end{align*} -\ARROW Now imagine we will carry the calculations with $4$ digit precision.\\ -\ARROW If we calculate the: -\begin{align*} -1.0000+\sum_{i=1}^{10} 0.0001=1.000 -\end{align*} -\ARROW If we calculate the: -\begin{align*} -\sum_{i=1}^{10}0.0001+1.0000=1.001 -\end{align*} -\ARROW The order matters! -\end{small} - -\end{frame} - - -\begin{frame}\frametitle{Condition parameter} -\begin{small} - -\begin{exampleblock}{The condition parameter} -\ARROWR Let $\phi : \mathcal{R}^n \to \mathcal{R}^m$ be a function and $x \in \mathcal{R}^n$ be a precise value and $\overline{x} \in \mathcal{R}^n$ its computer representation.\\ -\ARROWR If there $\kappa \in \mathcal{R}$ exists that: -\begin{align*} -\forall_{x,\overline{x}}: \frac{\Vert \psi(x)- \psi(\overline{x} \Vert}{\Vert \psi(x) \Vert} \leq \kappa \frac{\Vert x- \overline{x} \Vert}{ \Vert x \Vert} -\end{align*} -\ARROWR The $\kappa$ is called the condition parameter. -\end{exampleblock} - -\ARROW If the value of $\kappa$ is large then small difference cause by computer representation will explode in the final result. - - -\end{small} -\end{frame} - - - -\begin{frame}\frametitle{Examples 1} -\begin{small} -\ARROW Let's calculate the $\pi$ number accordingly to the following formula for couple of $i$: -\begin{align*} -G_p=\frac{1}{p}\left[ 10^p \left(1+p\pi 10^{-p} \right) - 10^p \right] - \end{align*} -with a simple program one can see: -\begin{center} -\includegraphics[width=0.5\textwidth]{images/ex1.png} -\end{center} - - -\end{small} - -\end{frame} - - - -\begin{frame}\frametitle{Example 1} -\begin{small} -\ARROWR How to fix this?!\\ -\ARROW Change \texttt{double} to \texttt{long double} - -\begin{center} -\includegraphics[width=0.5\textwidth]{images/ex2.png} -\end{center} - - -\end{small} - -\end{frame} - - - - - -\begin{frame}\frametitle{Example 2} -\begin{small} - - - -\begin{columns} -\column{2.5in} -\begin{align*} -\begin{cases} -x + 3y = 4 \\ -x + 3.00001y = 4.00001 -\end{cases} -\end{align*} - - -\column{2.5in} - -\begin{align*} -\begin{cases} -x + 3y = 4 \\ -x + 2.99999y = 4.00002 -\end{cases} -\end{align*} - - - -\end{columns} -{~}\\{~}\\ - -\ARROW The coefficients of this equations are different by maximum of $0.00002$.\\ -\ARROW The solutions to the first one is $(1,1)$ and to the second $(10,-2)$. \\ -\ARROW So clearly we have a big $\kappa$ as changes $\mathcal{O}(10^{-5})$ are causing differences of $\mathcal{O}(10)$. - - -\end{small} - -\end{frame} - - - - -\begin{frame}\frametitle{Summary} -\begin{small} - -\ARROW Computers use only representations of the floating points!\\ -\ARROW Numerical methods suffer from computer precision!\\ -\ARROW It's YOUR responsibility to ensure that what you are doing will not explode the error.\\ - - - -\end{small} - -\end{frame} - - -\backupbegin - -\begin{frame}\frametitle{Backup} - - -\end{frame} - - - - -\backupend -\end{document} diff --git a/Lectures_my/NumMet/Lecture1/mchrzasz.toc b/Lectures_my/NumMet/Lecture1/mchrzasz.toc deleted file mode 100644 index 429917f..0000000 --- a/Lectures_my/NumMet/Lecture1/mchrzasz.toc +++ /dev/null @@ -1,5 +0,0 @@ -\boolfalse {citerequest}\boolfalse {citetracker}\boolfalse {pagetracker}\boolfalse {backtracker}\relax -\defcounter {refsection}{0}\relax -\beamer@endinputifotherversion {3.24pt} -\defcounter {refsection}{0}\relax -\select@language {english} diff --git a/Lectures_my/NumMet/Lecture1/tikzfeynman.sty b/Lectures_my/NumMet/Lecture1/tikzfeynman.sty deleted file mode 100755 index 521fc65..0000000 --- a/Lectures_my/NumMet/Lecture1/tikzfeynman.sty +++ /dev/null @@ -1,43 +0,0 @@ -% 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}, -} - diff --git a/Lectures_my/NumMet/Lecture2/Makefile b/Lectures_my/NumMet/Lecture2/Makefile deleted file mode 100644 index e4cf8e8..0000000 --- a/Lectures_my/NumMet/Lecture2/Makefile +++ /dev/null @@ -1,9 +0,0 @@ -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/Lecture2/beamercolorthemeFlip.sty b/Lectures_my/NumMet/Lecture2/beamercolorthemeFlip.sty deleted file mode 100755 index d6b9c50..0000000 --- a/Lectures_my/NumMet/Lecture2/beamercolorthemeFlip.sty +++ /dev/null @@ -1,179 +0,0 @@ -% 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/Lecture2/beamerinnerthemeFlip.sty b/Lectures_my/NumMet/Lecture2/beamerinnerthemeFlip.sty deleted file mode 100755 index 8dc12a0..0000000 --- a/Lectures_my/NumMet/Lecture2/beamerinnerthemeFlip.sty +++ /dev/null @@ -1,95 +0,0 @@ -% 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/Lecture2/beamerouterthemeFlip.sty b/Lectures_my/NumMet/Lecture2/beamerouterthemeFlip.sty deleted file mode 100755 index d12f6d6..0000000 --- a/Lectures_my/NumMet/Lecture2/beamerouterthemeFlip.sty +++ /dev/null @@ -1,189 +0,0 @@ -% 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/Lecture2/beamerouterthemedecolines.sty b/Lectures_my/NumMet/Lecture2/beamerouterthemedecolines.sty deleted file mode 100755 index 669e493..0000000 --- a/Lectures_my/NumMet/Lecture2/beamerouterthemedecolines.sty +++ /dev/null @@ -1,168 +0,0 @@ -% 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/Lecture2/beamerthemeFlip.sty b/Lectures_my/NumMet/Lecture2/beamerthemeFlip.sty deleted file mode 100755 index a615ff5..0000000 --- a/Lectures_my/NumMet/Lecture2/beamerthemeFlip.sty +++ /dev/null @@ -1,59 +0,0 @@ -% 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! 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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 interpolation]{Function Interpolation} -\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 Interpolation} - \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, \\ 21 September, 2016} -\end{center} -\end{frame} -} - - - -\begin{frame}\frametitle{Interpolation - graphical interpretation} -\begin{small} - - -\ARROW Let's assume we have a given function in a tabular form: -\begin{tabular}{c||c|c|c|c|c} -$x_i$ & $x_1$ & $x_2$ & $x_3$ & ... & $x_n$ \\ \hline -$f_i=f(x_i)$ & $f_1$ & $f_2$ & $f_3$ & ... & $f_n$ \\ -\end{tabular}\\ -\ARROWR The $x_i$ are data points.\\ -\ARROW The problem is how to calculate the function values between the points ({\it interpolation}) or outside ({\it extrapolation} - see next lecture!) . -\end{small} -\begin{center} -\includegraphics[angle=-90,width=0.5\textwidth]{images/mass_resolution_Bconstr_afterSel_errBand_scaled.pdf} -\end{center} -\end{frame} - - - -\begin{frame}\frametitle{Interpolation - formal formulation} -\begin{small} - -\ARROW On the interval: $\left[ a, b \right] \subset \mathbb{R}$ and set of points: $D=(x_i, y_i)$, $x_i \neq x_j~ \Leftrightarrow~ i \neq j$.\\ -\ARROW The interpolation is to find a function $F:\left[ a, b \right] \rightarrow \mathbb{R}$ that satisfies: -\begin{align*} -\forall (x_i,y_i) \in D:~~~ F(x_i)=y_i -\end{align*} -\ARROW The above equation is called the interpolation equation.\\ -\ARROW The interpolation error: -\begin{align*} -\epsilon(x)=f(x)-F(x), -\end{align*} -where $f(x)$ is the function that is being interpolated.\\ -\ARROW Each interpolation method has different errors, each of it can be estimated. -\end{small} - -\end{frame} - - - -\begin{frame}\frametitle{Linear Interpolation} -\begin{small} - -\ARROW Let's say we have $n+1$ interpolation points: $(y_i, x_i)$.\\ -\ARROW The linear interpolation is given with with the equation: -\begin{align*} -F(x)=\sum_{j=0}^n a_j \psi_j(x)=a_0 \psi_0(x) + a_1 \psi_1(x) + a_2 \psi_2(x)+ ... + a_n \psi_n(x), -\end{align*} -where: -\begin{itemize} -\item $a_j$ - parameter, -\item $\psi_j(x)$ - base function. -\end{itemize} -\ARROW Now the only thing one needs to do is to find the $a_i$ coefficients. Now there are infinite number such solutions so we need to assume that the number interpolation points is equal to number of base functions. - - -\end{small} - -\end{frame} - - -\begin{frame}\frametitle{Linear Interpolation} -\begin{small} - -\ARROW Now to find all the $a_i$ one just needs to solve the linear equation system: -\begin{align*} -\begin{pmatrix} -\psi_0(x_0) & \psi_1(x_0) & ... & \psi_n(x_0) \\ -\psi_0(x_1) & \psi_1(x_1) & ... & \psi_n(x_1) \\ -& ... \\ -\psi_0(x_0) & \psi_1(x_0) & ... & \psi_n(x_2) -\end{pmatrix} -\begin{pmatrix} -a_0\\ -a_1\\ -...\\ -a_n -\end{pmatrix}= -\begin{pmatrix} -y_0\\ -y_1\\ -...\\ -y_n -\end{pmatrix} -\end{align*} -\ARROW The only necessary condition to solve the equation is that the: -\begin{align*} -\det \left[ \psi_i(x_j) \right] \neq 0 -\end{align*} -\ARROW The polynomial of the order $n$ has $n+1$ base functions, so system has only one solution.\\ -\ARROW We can choose the base functions on many different ways. This depends on the input points and our own judgement. Often use are trigonometric functions and polynomials.\\ -\ARROW The proper selection of the base function can hugely simplify the problem by making the matrix triangular or even diagonal. - -\end{small} - -\end{frame} - -\begin{frame}\frametitle{Linear Interpolation, simplest base} -\begin{small} -\begin{exampleblock}{Theorem:} -If all of the interpolation points $x_0,x_1,...,x_n$ are pair different there exists one and only one solution of the interpolation function of the order max. $n$. -\end{exampleblock} - -The simplest base functions one can imagine to use is the natural base: -\begin{align*} -\psi_0=1,~~~\psi_1=x,~~~\psi_2=x^2,~~~...~~~, \psi_n=x^n -\end{align*} -\begin{alertblock}{Attention/Achtung:} -This kind of interpolation is wrongly conditioned: small changes of input parameters will cause large output differences. -\end{alertblock} - -\ARROW Because of the above it is used almost not used in practice. \\ -\ARROW For education purposes we will analyse it. -\end{small} - -\end{frame} - -\begin{frame}\frametitle{Linear Interpolation, simplest base} -\begin{small} -\ARROW When using natural base the interpolation polynomial will have the structure: -\begin{align*} -F(x)=a_0+a_1 x + a_2 x^2 + a_3 x^3 ... a_n x^n -\end{align*} -\ARROW Now base matrix (so-called Vandermonde matrix) has the form: -\begin{align*} -V=\begin{pmatrix} -1 & x_0 & x_0^2 & ... & x_0^n \\ -1 & x_1 & x_1^2 & ... & x_1^n \\ -& ... \\ -1 & x_n & x_n^2 & ... & x_n^n \\ -\end{pmatrix} -\end{align*} -\ARROW Now the only thing one needs to do is to solve: -\begin{align*} -\begin{pmatrix} -1 & x_0 & x_0^2 & ... & x_0^n \\ -1 & x_1 & x_1^2 & ... & x_1^n \\ -& ... \\ -1 & x_n & x_n^2 & ... & x_n^n \\ -\end{pmatrix} -\begin{pmatrix} -a_0\\ -a_1\\ -...\\ -a_n -\end{pmatrix}= -\begin{pmatrix} -y_0\\ -y_1\\ -...\\ -y_n -\end{pmatrix} -\end{align*} -\ARROW Because the natural base is wrongly conditioned the increase of the interpolation points significantly increases the condition parameter. - -\end{small} - -\end{frame} - - -\begin{frame}\frametitle{Lagrange interpolation} -\begin{small} -\ARROW Now let's choose a better base function that are given by: -\begin{align} -\label{eq:langrange} -l_i(x)= \prod_{j=0,~j \neq i}^n \frac{x-x_j}{x_i-x_j} = \frac{(x-x_0)(x-x_1)...(x-x_n)}{(x_i-x_0)(x_i-x_1)...(x_i-x_n)} -\end{align} -\ARROW It is easy to notice: -\begin{align*} -l_i(x_j)=\begin{cases} -0~~~i \neq j \\ -1~~~i=j -\end{cases} -\end{align*} -\ARROW Now putting this into base matrix we get: -\begin{align*} -\begin{pmatrix} -1 & 0 & 0 & ... & 0 \\ -0 & 1 & 0 & ... & 0 \\ -& ... \\ -0 & 0 & 0 & ... & 1 \\ -\end{pmatrix} -\begin{pmatrix} -a_0\\ -a_1\\ -...\\ -a_n -\end{pmatrix}= -\begin{pmatrix} -y_0\\ -y_1\\ -...\\ -y_n -\end{pmatrix} -\end{align*} -\ARROW Now this is something we like :) The interpolating function then takes the form: -\begin{align*} -F(x)=L_n(x)=\sum_{i=0}^n y_i l_i(x) -\end{align*} - -\end{small} -\end{frame} - - - -\begin{frame}\frametitle{Lagrange interpolation - the algorithm} -\begin{small} -\begin{enumerate} -\item Get the input data $(x_i,y_i),~i=0,...,n$. -\item The coefficients of the polynomial are $y_i$. -\item Calculate the base functions from Eq.~\ref{eq:langrange}. -\item Put everything together to get the $L_n$ Lagrange polynomial. -\end{enumerate} -\begin{alertblock}{Disadvantage:} -The problem with this method is the fact that if you add another interpolation point you need to start over and recalculate everything. -\end{alertblock} - -\begin{exampleblock}{Advantege} -\only<1>{ -It is very popular and simple method. It is used in many different places: differential equations, numerical integrations, etc. Because of this the precision of the method depends on the precision of the interpolation is self: -\begin{align*} -\epsilon(x) = f(x) - F(x) = \frac{f^{(n+1}(\xi) }{(n+1)!} \omega_n(x) -\end{align*} -} -\only<2>{ -where:\\ -$\omega_n(x)=(x-x_0)(x-x_1)...(x-x_n)$\\ -$f$ function of class $C^{n+1}$ on $\left [a,b\right]$\\ -$\xi$ average values.h -} -\end{exampleblock} - - -\end{small} -\end{frame} - - - -\begin{frame}\frametitle{Newton interpolation} -\begin{small} -\ARROW Sir Isaac Newton proposed a different base for the problem: -\begin{align*} -p_0(x) & =1\\ -p_1(x) & =(x-x_0)\\ -p_2(x) & =(x-x_0)(x-x_1)\\ -...\\ -p_n(x) & =(x-x_0)(x-x_1)...(x-x_n) -\end{align*} -\only<1>{ -\ARROW Using the above functions the basis matrix takes a nice form: -\begin{align*} -V=\begin{pmatrix} -1 & 0 & 0 & ... & 0 \\ -1 & p_1(x_1) & 0 & ... & 0 \\ -& ... \\ -1 & p_1(x_n) & p_2(x_n) & ... & p_n(x_n) \\ -\end{pmatrix} -\end{align*} -} -\only<2>{ -\ARROW And the linear equation system: -\begin{align*} -\begin{pmatrix} -1 & 0 & 0 & ... & 0 \\ -1 & p_1(x_1) & 0 & ... & 0 \\ -& ... \\ -1 & p_1(x_n) & p_2(x_n) & ... & p_n(x_n) \\ -\end{pmatrix} -\begin{pmatrix} -a_0\\ -a_1\\ -...\\ -a_n -\end{pmatrix} -= -\begin{pmatrix} -y_0\\ -y_1\\ -...\\ -y_n -\end{pmatrix} -\end{align*} - - -} -\end{small} -\end{frame} - - - -\begin{frame}\frametitle{Newton interpolation} -\begin{small} -\ARROW We can solve the aforementioned system by noticing that $a_0$ depends only on $y_0$, $a_1$ depends on $y_0$ and $y_1$, etc.\\ -\ARROW They can be calculated using difference quotient: -\begin{align*} -f\left[ x_0,x_1 \right] =\frac{y_1-y_0}{x_1-x_0},~~f\left[ x_1,x_2 \right] =\frac{y_2-y_1}{x_2-x_1}, \rm~etc. -\end{align*} -\begin{align*} -f\left[ x_0,x_1, x_2 \right] = \frac{ f\left[ x_1,x_2 \right]- f\left[x_0,x_1 \right] }{x_2-x_1} -\end{align*} -\ARROW In general: -\begin{align*} -f\left[ x_i,x_{i+1},..., x_{i+k} \right] = \frac{ f\left[ x_{i+1},x_{i+2},...,x_{i+k} \right] - f\left[ x_{i},x_{i+1},...,x_{i+k-1} \right]}{x_{i+k}-x_i} -\end{align*} -\ARROW Using difference quotient we can calculate the coefficients: -\begin{align*} -a_i=f\left[x_0,x_1,...,x_i\right] -\end{align*} -\end{small} -\end{frame} - - - -\begin{frame}\frametitle{Newton interpolation, the algorithm} -\begin{small} - -\begin{itemize} -\item We read the input interpolating points: $(x_i,y_i)$, $i=0,1,....,n$. -\item Calculate the polynomial coefficients in an iterative way. -\item Calculate the base functions. -\item Put things together to get the Newton interpolation polynomial. -\end{itemize} - -\begin{exampleblock}{Why do we bother?} -\ARROWR Despite the procedure seems more complicated then the Lagrange interpolation it has a huge advantage: adding one more interpolation point does require to repeat the whole procedure, but we can reuse the previous steps. -\end{exampleblock} - -\end{small} -\end{frame} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame}\frametitle{Runge oscillation} -\begin{small} - -\ARROW If one has many points one needs to use a high order polynomial.\\ -\ARROW The problem with high order polynomials is that they start oscilationg at the edges $\mapsto$ so-called Runge oscillations. - -\begin{center} -\includegraphics[width=0.75\textwidth]{images/Runge.png} -\end{center} - -\ARROW Danny will tell you more about this next lecture. - -\end{small} -\end{frame} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame}\frametitle{First degree spline function} -\begin{small} - -\ARROW Till now using couple numerical methods we were able to calculate coefficients of a big single polynomial equation.\\ -\ARROW Now we are smarter then Newton and Lagrange were over 300 years ago!\\ -\ARROW We can use several interpolating functions and then glue them (splice) them together!\\ -\ARROW In order to do so we divide the domain of the $F$ function $\left[ a,b \right]$ into: -\begin{align*} -a=x_0 diff --git a/Lectures_my/NumMet/Lecture3/beamerinnerthemeFlip.sty b/Lectures_my/NumMet/Lecture3/beamerinnerthemeFlip.sty deleted file mode 100755 index 8dc12a0..0000000 --- a/Lectures_my/NumMet/Lecture3/beamerinnerthemeFlip.sty +++ /dev/null @@ -1,95 +0,0 @@ -% 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/Lecture3/beamerouterthemeFlip.sty b/Lectures_my/NumMet/Lecture3/beamerouterthemeFlip.sty deleted file mode 100755 index d12f6d6..0000000 --- a/Lectures_my/NumMet/Lecture3/beamerouterthemeFlip.sty +++ /dev/null @@ -1,189 +0,0 @@ -% 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/Lecture3/beamerouterthemedecolines.sty b/Lectures_my/NumMet/Lecture3/beamerouterthemedecolines.sty deleted file mode 100755 index 669e493..0000000 --- a/Lectures_my/NumMet/Lecture3/beamerouterthemedecolines.sty +++ /dev/null @@ -1,168 +0,0 @@ -% 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. 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\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/Lecture3/beamerthemeFlip.sty b/Lectures_my/NumMet/Lecture3/beamerthemeFlip.sty deleted file mode 100755 index a615ff5..0000000 --- a/Lectures_my/NumMet/Lecture3/beamerthemeFlip.sty +++ /dev/null @@ -1,59 +0,0 @@ -% 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/Lecture3/examples/Makefile b/Lectures_my/NumMet/Lecture3/examples/Makefile deleted file mode 100644 index 9a5e050..0000000 --- a/Lectures_my/NumMet/Lecture3/examples/Makefile +++ /dev/null @@ -1,2 +0,0 @@ -ex1: ex1.cc - g++ -o $@ $^ diff --git a/Lectures_my/NumMet/Lecture3/examples/cos.nb b/Lectures_my/NumMet/Lecture3/examples/cos.nb deleted file 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PointSize[0.5], - Opacity[1.], - AbsoluteThickness[1.6], - RGBColor[1, 0, 0]], { - LineBox[{{0, 10}, {20, 10}}]}}, { - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - Opacity[1.], - AbsoluteThickness[1.6], - RGBColor[1, 0, 0]], {}}}, AspectRatio -> Full, - ImageSize -> {20, 10}, PlotRangePadding -> None, - ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}}, - GridBoxAlignment -> { - "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, - AutoDelete -> False, - GridBoxDividers -> { - "Columns" -> {{False}}, "Rows" -> {{False}}}, - GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}}, - GridBoxSpacings -> { - "Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}}, - GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, - AutoDelete -> False, - GridBoxItemSize -> { - "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, - GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], - "Grid"], Alignment 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{{1,0,0},{1,π/8,π/8},{1,π/4,π/4}} -In[14]:= a = {a0, ax, ay}; -In[37]:= ffA = f @@@ pointsA -ffB = f @@@ pointsB -Out[37]= {1,1/Sqrt[2],1/Sqrt[2]} -Out[38]= {1,1/Sqrt[2],0} -In[39]:= Solve[VA.a == ffA, a] -intA = VanderMondeLine[{x, y}].a //. %[[1]] -Out[39]= {{a0->1,ax->(2 (-2+Sqrt[2]))/π,ay->(2 (-2+Sqrt[2]))/π}} -Out[40]= 1+(2 (-2+Sqrt[2]) x)/π+(2 (-2+Sqrt[2]) y)/π -In[44]:= VB.a -Out[44]= {a0,a0+(ax π)/8+(ay π)/8,a0+(ax π)/4+(ay π)/4} -In[43]:= Solve[VB.a == ffB, a] -Out[43]= {} -In[25]:= ContourPlot[ -f[x, y], -{x, 0, π/4}, -{y, 0, π /4} -] - -Out[25]= -In[32]:= ContourPlot[ -intA, -{x, 0, π/4}, -{y, 0, π /4} -] -Out[32]= \ No newline at end of file diff --git a/Lectures_my/NumMet/Lecture3/images/BG_lower.png b/Lectures_my/NumMet/Lecture3/images/BG_lower.png deleted file mode 100755 index 073034a..0000000 --- a/Lectures_my/NumMet/Lecture3/images/BG_lower.png +++ /dev/null Binary files differ diff --git a/Lectures_my/NumMet/Lecture3/images/bubble.gif 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b/Lectures_my/NumMet/Lecture3/lecture3.tex deleted file mode 100644 index f5a6dff..0000000 --- a/Lectures_my/NumMet/Lecture3/lecture3.tex +++ /dev/null @@ -1,822 +0,0 @@ -% vim: set sts=4 et : -\documentclass[11 pt,xcolor={dvipsnames,svgnames,x11names,table}]{beamer} - -\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} - -\usepackage{tikz,pgfplots} -\usepackage{graphicx} - -% 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$}}% - -\graphicspath{{images/}} % Put all images in this directory. Avoids clutter. - -% 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}} -} - -\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 {Interpolation in $D>2$\\ and Extrapolation} - \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 Chrzaszcz, 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, \\ 26. September, 2016} -\end{center} -\end{frame} -} - -\begin{frame}{Plan for today} - \begin{itemize} - \item \alert{When does interpolation fail?}\\ - Marcin showed you how to interpolate in $D=1$. What are the pitfalls? And can we circumvent them? - \vfill - \item \alert{How to interpolate a function of $D>1$ variables?}\\ - Is there are sensible generalization of interpolation to multivariate functions? If yes, - let's apply what we learned before to $D=2$. - \vfill - \item \alert{What happens when I use my interpolation beyond the domain of data?}\\ - Why would I do that? When can I do that? How well does it work, and how can I improve it? - \end{itemize} -\end{frame} - -\begin{frame}{Does interpolation always work?} - \begin{block}{Weierstrass Approximation Theorem} - Suppose $f$  is a continuous real-valued function defined on the real interval $[a, b]$. - For every $\varepsilon > 0$, there exists a polynomial $P(x)$ such that for all $x$ in $[a, b]$, - we have $R[P] \equiv \max_{a \leq x \leq b} |f (x) - P(x)| < \varepsilon$, [\dots] - \end{block} - Using interpolation, we can construct a polynomial $P_n(x)$ of degree $n$ - that approximates $f$ up to an approximation error of $R_n$: - \begin{equation*} - R_n \equiv \max_{a \leq x \leq b} \left|f(x) - P_n(x)\right|\,. - \end{equation*} - - \begin{alert}{Conclusion} - Weierstrass's theorem says that there is \emph{at least one} polynomial - for each choice of the residual error $\varepsilon$. It does not say that either - \begin{itemize} - \item $P_n$ is \emph{in} the set of polynomial for a given $\varepsilon$, or - \item $R_n \to 0$ if $n \to \infty$! - \end{itemize} - \begin{center}{\color{red} Increasing $n$ might be harmful!}\end{center} - \end{alert} -\end{frame} - -\begin{frame}{When Interpolation fails} -So far, you have been confronted with examples in which interpolation -works nicely. Let us now discuss an example, which behaves pathologically.\\ - -\begin{overlayarea}{\textwidth}{7cm} -\begin{columns} -\begin{column}[T]{.5\textwidth} -Consider the classical example by Runge: -\begin{equation*} - f(x) = \left[1 + 25 x^2\right]^{-1} -\end{equation*} - -Let us plot -\begin{itemize} - \item the true function $f(x)$ - \item<2-> {\color{blue}the interpolating polynomial to degree $4$} - \item<3-> {\color{red}the interpolating polynomial to degree $6$} -\end{itemize} -\only<2->{for equidistant interpolation points on $[-1, +1]$.} -\end{column} -\begin{column}[T]{.5\textwidth} -\begin{tikzpicture} - [ - scale=0.75 - ] - \begin{axis}[% - samples=500, - xmin=-1,xmax=+1, - ymin=-0.5,ymax=+1 - ] - \addplot+[black,mark=none] - {1.0 / (1.0 + 25.0 * \x^2)}; - \only<2->{ - \addplot+[blue,domain=-1:+1,y domain=-1:+1,mark=none] - {1 - (3225 * \x^2) / 754 + (1250 * \x^4) / 377}; - } - \only<3->{ - \addplot+[red,domain=-1:+1,y domain=-1:+1,mark=none] - {1 - (211600 * \x^2)/24089 + (2019375 * \x^4)/96356 - (1265625 * \x^6)/96356}; - } - \end{axis} -\end{tikzpicture} - \begin{center}\only<4->{$R_n \to \infty$ as $n \to \infty$}\end{center} -\end{column} -\end{columns} -\end{overlayarea} -\end{frame} - -\begin{frame}{Pieceswise linear/cubic/... interpolations} - \begin{columns} - \begin{column}{.6\textwidth} - This pathological behaviour can be avoided by piecewise interpolation with a small value of - the polynomial degree $n$. - Most popular are linear ($n=1$) or cubic ($n=3$) piecewise interpolations - (``splines''), which do not suffer from the problem that was just described.\\ \medskip - \end{column} - \begin{column}{.4\textwidth} - \includegraphics[width=.9\textwidth]{runge.pdf} - \end{column} - \end{columns} - \medskip - The concrete approaches have been discussed last lecture by Marcin. -\end{frame} - -\begin{frame}{Interpolation in more than $D=1$ dimensions} -In lecture 2 we discussed various ways to interpolate a -univariate function $f(x)$. A very nice fact for -polynomial interpolations in $D=1$ dimension is that the -interpolating polynomial is \emph{unique}: For two polynomials -$g(x)$ and $h(x)$ of identical degree $n$ one has -\begin{equation*} - f_i = g(x_i) = h(x_i) \quad\Rightarrow\quad g(x) \equiv h(x)\,, -\end{equation*} -when considering exactly $\rho_n(D=1) = n + 1$ interpolation points $x_i$, -for $i = 1,\dots, n+1$.\\ -\medskip -We will now investigate if this still holds for $D > 1$ dimensions. -\end{frame} - -\begin{frame}{Interpolation in $D=2$ dimensions} - We will use a bivariate polynomial of degree $n$: - \begin{equation*} - P_n(x, y) = \sum_{i, j}^{i + j \leq n} a_{i, j} x^i y^j\,. - \end{equation*} - This polynomial has exactly $\rho_n(D=2) = \binom{n + 2}{n}$ coefficients, - which need to be computed from the interpolation points.\\ - - If we evaluate exactly $\rho_n(D=2)$ points, the system of linear equations - has exactly one or zero solutions! - - \begin{block}{Examples} - \vspace{-\medskipamount} - \begin{align*} - P_1(x, y) & = a_{0,0} + a_{1,0} x + a_{0,1} y\,, & \binom{1 + 2}{1} = 3\,,\\ - P_2(x, y) & = a_{0,0} + a_{1,0} x + a_{0,1} y\,, & \binom{2 + 2}{2} = 6\,,\\ - & + a_{1,1} x y + a_{2, 0} x^2 + a_{0, 2} y^2 - \end{align*} - \end{block} -\end{frame} - -\begin{frame}{Arrangement of points in $D=2$} - The question is now: How do we choose the $\rho_n(D=2)$ points that shall be - interpolated?\\ - \medskip - In $D=1$, this was easy: all points were on the $x$ axis. In $D=2$ we need to populate - a plane, and this gives us more freedom.\\ - \medskip - How to arrange the interpolation points in the plane? Let's consider two examples - for $D = 2$ dimensions for a $n=1$ polynomial: - - - \begin{overlayarea}{\textwidth}{5cm} - \only<1>{ - \begin{block}{Example \#1} - \begin{columns} - \begin{column}[T]{.35\textwidth} - \begin{center} - \begin{tikzpicture} - \begin{axis}[% - width=3cm,height=3cm, - xmin=0,xmax=1,xtick={0,1},xlabel=$x$, - ymin=0,ymax=1,ytick={0,1},ylabel=$y$ - ] - \addplot+[blue, only marks, mark options={scale=1.75, fill=blue}] coordinates { - (0.0, 0.0) - (0.5, 0.5) - (1.0, 1.0) - }; - \end{axis} - \end{tikzpicture} - \end{center} - \end{column} - \begin{column}[T]{.65\textwidth} - The interpolation equation reads: - \begin{equation*} - \left[\begin{matrix} - 1 & 0 & 0 \\ - 1 & \frac12 & \frac12\\ - 1 & 1 & 1 - \end{matrix}\right] - \cdot - \left[\begin{matrix} - a_{0, 0}\\ - a_{1, 0}\\ - a_{0, 1} - \end{matrix}\right] - = - \left[\begin{matrix} - f(0, 0)\\ - f(\frac12, \frac12)\\ - f(1, 1) - \end{matrix}\right] - \end{equation*} - The Vandermonde matrix is singular, and no polynomial exists - that interpolates the blue points. - \end{column} - \end{columns} - \end{block} - } - \only<2>{ - \begin{block}{Example \#2} - \begin{columns} - \begin{column}[T]{.35\textwidth} - \begin{center} - \begin{tikzpicture} - \begin{axis}[% - width=3cm,height=3cm, - xmin=0,xmax=1,xtick={0,1},xlabel=$x$, - ymin=0,ymax=1,ytick={0,1},ylabel=$y$ - ] - \addplot+[red, only marks, mark options={scale=1.75, fill=red}] coordinates { - (0, 0) - (0, 1) - (1, 0) - }; - \end{axis} - \end{tikzpicture} - \end{center} - \end{column} - \begin{column}[T]{.65\textwidth} - The interpolation equation reads: - \begin{equation*} - \left[\begin{matrix} - 1 & 0 & 0 \\ - 1 & 1 & 0 \\ - 1 & 0 & 1 - \end{matrix}\right] - \cdot - \left[\begin{matrix} - a_{0, 0}\\ - a_{1, 0}\\ - a_{0, 1} - \end{matrix}\right] - = - \left[\begin{matrix} - f(0, 0)\\ - f(\frac12, \frac12)\\ - f(1, 1) - \end{matrix}\right] - \end{equation*} - The Vandermonde matrix is regular, and exactly one polynomial exists - that interpolates the red points. - \end{column} - \end{columns} - \end{block} - } - \end{overlayarea} -\end{frame} - -\begin{frame}{Divide and conquer $D=2$} - We had seen that increasing the degree $n$ does not necessarily reduce the - approximation error $R_n$, even in $D=1$ dimensions.\\ \medskip - - In $D=2$ this problem can become even more serious.\\ \medskip - - It is therefore a good idea to evaluate the function $f$ on a regular grid - in the $(x,y)$ plane. Subequently, one can interpolate within each - cell of the grid. This is the $D=2$ analog to interpolation with splines: - \begin{itemize} - \item linear splines $\to$ bilinear splines - \item cubic splines $\to$ bicubic splines - \end{itemize} -\end{frame} - -\begin{frame}[shrink]{Algorithm for Bilinear Interpolation} - \begin{columns} - \begin{column}[T]{.8\textwidth} - \begin{enumerate} - \item<1-> Create a rectilinear grid in the $(x,y)$ plane - \item<2-> For each rectangle, map the rectangle to the unit square - \item<3-> Evaluate the function $f$ on the four - corners of the (mapped) unit square ${\color{purple}Q_{0,0}}$, - ${\color{red}Q_{1, 0}}$, ${\color{orange}Q_{1, 1}}$, ${\color{Gold}Q_{0, 1}}$. - \item<4-> Make an ansatz: $P(x, y) = a_{0,0} + a_{1,0} x + a_{0,1} y + a_{1,1} x y$. - \end{enumerate} - \end{column} - \begin{column}[T]{.2\textwidth} - \begin{overlayarea}{\textwidth}{.3\textheight} - \resizebox{\textwidth}{!}{ - \begin{tikzpicture} - \draw[black,thick] (0,0) -- (2,0) -- (2,1) -- (0,1) -- (0,0); - \draw[black,thick] (2,0) -- (4,0) -- (4,1) -- (2,1) -- (2,0); - \draw[black,thick] (0,1) -- (2,1) -- (2,2) -- (0,2) -- (0,1); - \draw[black,thick] (2,1) -- (4,1) -- (4,2) -- (2,2) -- (2,1); - \only<2->{ - \fill[gray,thick] (0,1) -- (2,1) -- (2,2) -- (0,2) -- (0,1); - } - \only<3->{ - \fill[purple] (0,1) circle [radius=2pt]; - \fill[red] (2,1) circle [radius=2pt]; - \fill[orange] (2,2) circle [radius=2pt]; - \fill[Gold] (0,2) circle [radius=2pt]; - } - \end{tikzpicture} - }\\ - \only<2->{ - \resizebox{\textwidth}{!}{ - \begin{tikzpicture} - \draw[black,thick] (0,0) -- (1,0) -- (1,1) -- (0,1) -- (0,0); - \only<3->{ - \fill[purple] (0,0) circle [radius=2pt]; - \fill[red] (1,0) circle [radius=2pt]; - \fill[orange] (1,1) circle [radius=2pt]; - \fill[Gold] (0,1) circle [radius=2pt]; - } - \end{tikzpicture} - } - } - \end{overlayarea} - \end{column} - \end{columns} - \begin{enumerate} - \setcounter{enumi}{4} - \item<5-> Solve the interpolation equation - \begin{equation*} - \left[\begin{matrix} - 1 & 0 & 0 & 0\\ - 1 & 1 & 0 & 1\\ - 1 & 0 & 1 & 1\\ - 1 & 1 & 1 & 1 - \end{matrix}\right] - \cdot - \left[\begin{matrix} - a_{0, 0}\\ - a_{1, 0}\\ - a_{0, 1}\\ - a_{1, 1} - \end{matrix}\right] - = - \left[\begin{matrix} - f(Q_{0, 0})\\ - f(Q_{1, 0})\\ - f(Q_{0, 1})\\ - f(Q_{1, 1}) - \end{matrix}\right] - \end{equation*} - We only need to invert the Vandermonde matrix once! - \item<6-> Map the result back from the unit square back to the grid piece in $(x,y)$ plane. - \item<7-> Jump back to \#2. - \end{enumerate} -\end{frame} - -\begin{frame}{Interpolation in $D$ dimensions} - The situation becomes even more complicated if you go to - $D >2$ dimensions: - \begin{description} - \item[$D=3$] You can generalize to with either trilinear or tricubic splines, on - a rectilinear $3D$ grid. The Vandermonde matrix on the unit cube is now - $\binom{n + 3}{n}^2$. - \item[arbitrary $D$] There is no polynomial interpolation for $D$ dimensions. - \end{description} -\end{frame} - -\begin{frame}[shrink]{Extrapolation Basics} - In many numerical applications a common class of problems arises: - Concerning a function $f(x)$ that is expensive to evaluate, we are interested in the value - $f(x_0)$. However, at $x_0$ the function $f(x)$ is numerically instable, - or the problem maybe even ill-posed.\\ \medskip - - Sometime there is an environment around $x_0$, $x \approx x_0 + h$, in which we can evaluate $f$. - Usually, one now discusses $f(h) \equiv f(x_0 + h)$, or rather the limit - $\lim_{h \to 0} f(h)$. [Note: in all generality we can map problems with - limits to either $h \to \infty$ or $h \to \text{finite value}$ onto limits $h \to 0$.]\\ \medskip - - Interpolation, as discussed previously, can not directly help, since $h = 0$ - is not part of the domain of data points. Instead, one can take an interpolation - at finite $h > 0$, $f_\text{int}(h)$, and simply approximate $f(h = 0) \approx f_\text{int}(h = 0)$. - This step of using the interpolation of $f$ outside the domain of data points is - called \emph{extrapolation}.\\ \medskip - - To extrapolate an arbitrary function might work very well, but also might - fail spectacularly. In this part of the course, we will briefly discuss - examples of both cases, and what mathematical requirements make extrapolations - work. -\end{frame} - -\begin{frame}{Working example} -Consider the function $\cos(x)$. Our task at hand is to estimate -$\cos(0)$ through evaluations of $\cos(h_k)$, with $h_k > 0$ but -$h_k \to 0$ with increasing $k$.\\ \medskip - -Let $h_k = 2^{-k}$, and construct interpolating polynomials $P_n$ -that interpolate $\cos(x)$ in $\lbrace h_1, \dots, h_{n + 1}\rbrace$. \\ \medskip - -\begin{overlayarea}{\textwidth}{5cm} - \begin{columns} - \begin{column}[T]{.5\textwidth} - \only<1>{ - \begin{tikzpicture} - [ - scale=0.7 - ] - \begin{axis}[% - domain=0:1, - ymin=0.5, ymax=1.05, - title=$P_n(x)$, - xlabel=$x$ - ] - \addplot[black, thick] { - cos(deg(x)) - }; - \addplot[blue] { - cos(deg(0.5)) - } node [above,pos=1] {$n=0$}; - \addplot[black, mark=x] coordinates { - (0.5000, 0.877583) - }; - \end{axis} - \end{tikzpicture} - } - \only<2>{ - \begin{tikzpicture} - [ - scale=0.7 - ] - \begin{axis}[% - domain=0:1, - ymin=0.5, ymax=1.05, - title=$P_n(x)$, - xlabel=$x$ - ] - \addplot[black, thick] { - cos(deg(x)) - }; - \addplot[blue] { - 1.06 - 0.365 * x - } node [above,pos=1] {$n=1$}; - \addplot[black, mark=x] coordinates { - (0.5000, 0.877583) - (0.2500, 0.968912) - }; - \end{axis} - \end{tikzpicture} - } - \only<3->{ - \begin{tikzpicture} - [ - scale=0.7 - ] - \begin{axis}[% - domain=0:1, - ymin=0.5, ymax=1.05, - title=$P_n(x)$, - xlabel=$x$ - ] - \addplot[black, thick] { - cos(deg(x)) - }; - \addplot[blue] { - 0.99996 + 0.00119746 * x - 0.511201 * x^2 + 0.0385918 * x^3 - } node [above,pos=1] {$n=3$}; - \addplot[black, mark=x] coordinates { - (0.5000, 0.877583) - (0.2500, 0.968912) - (0.1250, 0.992198) - (0.0625, 0.998048) - }; - \end{axis} - \end{tikzpicture} - } - \end{column} - \begin{column}[T]{.5\textwidth} - \only<4->{ - \begin{tikzpicture} - [ - scale=0.7 - ] - \begin{axis}[% - title=$P_n(0)$, - xlabel=$n$ - ] - \addplot+[black, mark=*, only marks] coordinates { - (0, 0.877583) - (1, 1.06024) - (2, 1.00056) - (3, 0.99996) - (4, 1.00000) - (5, 1.00000) - }; - \addplot+[red, mark=none, domain=0:6] { 1 }; - \end{axis} - \end{tikzpicture} - } - \end{column} - \end{columns} -\end{overlayarea} -\end{frame} - -\begin{frame}{Pathological example} - -Consider the example: -\begin{equation*} - f(x) = \exp(-x^{-1/2}) / x^4\,,\quad\text{with}\quad \lim_{x\to 0} f(x) = 0 -\end{equation*} -We use the same procedure as before: - -\begin{overlayarea}{\textwidth}{5cm} - \begin{columns} - \begin{column}[T]{.5\textwidth} - \only<1>{ - \begin{tikzpicture} - [ - scale=0.7 - ] - \begin{axis}[% - domain=0:1, - ymin=0, ymax=120, - title=$P_n(x)$, - xlabel=$x$ - ] - \addplot[black, thick, samples=250] { - exp(-1 / sqrt(x)) / x^3 - }; - \addplot[blue] { - 1.94493 - } node [above,pos=1] {$n=0$}; - \addplot[black, mark=x] coordinates { - (0.5000, 1.94493) - }; - \end{axis} - \end{tikzpicture} - } - \only<2>{ - \begin{tikzpicture} - [ - scale=0.7 - ] - \begin{axis}[% - domain=0:1, - ymin=0, ymax=120, - title=$P_n(x)$, - xlabel=$x$ - ] - \addplot[black, thick, samples=250] { - exp(-1 / sqrt(x)) / x^3 - }; - \addplot[blue] { - 15.378 - 26.8661 * x - } node [above,pos=1] {$n=1$}; - \addplot[black, mark=x] coordinates { - (0.5000, 1.94493) - (0.2500, 8.66146) - }; - \end{axis} - \end{tikzpicture} - } - \only<3->{ - \begin{tikzpicture} - [ - scale=0.7 - ] - \begin{axis}[% - domain=0:1, - ymin=0, ymax=120, - title=$P_n(x)$, - xlabel=$x$ - ] - \addplot[black, thick, samples=250] { - exp(-1 / sqrt(x)) / x^3 - }; - \addplot[blue, samples=50] { - 153.618 - 1573.05 * x + 5406.39 * x^2 - 5733.96 * x^3 - } node [above,pos=1] {$n=3$}; - \addplot[black, mark=x] coordinates { - (0.5000, 1.94493) - (0.2500, 8.66146) - (0.1250, 30.2621) - (0.0625, 75.0209) - }; - \end{axis} - \end{tikzpicture} - } - \end{column} - \begin{column}[T]{.5\textwidth} - \only<4->{ - \begin{tikzpicture} - [ - scale=0.75 - ] - \begin{axis}[% - ymode=log, - title=$\ln |P_n(0) - 1|$, - xlabel=$n$ - ] - \addplot+[black, mark=*, only marks] coordinates { - (0, 1.94493) - (1, 15.3780) - (2, 64.0244) - (3, 153.618) - (4, 169.579) - (5, 4.61491) - (6, 94.4333) - (7, 0.598657) - (8, 9.77146) - (9, 1.16233) - }; - \end{axis} - \end{tikzpicture} - } - \end{column} - \end{columns} -\end{overlayarea} -\end{frame} - -\begin{frame}{Foundations: Necessary prerequisite for extrapolation} - In order for the extrapolation to work, the function $f(x)$ needs - to fulfill a necessary prerequisite: - \begin{itemize} - \item existence of an asymptotic expansion - \end{itemize} - - \begin{block}{Asymptotic Expansion} - A function $f(x)$ can be asymptotically expanded in a sequence $\phi_n(x)$ around $x \simeq x_0$, - \begin{equation*} - f(x) = \sum_n^N a_n \phi_n(x)\,, - \end{equation*} - if - \begin{align*} - f(x) - \sum_n^{N-1} a_n \phi_n(x) = o(\phi_{N-1}(x))\,. - \end{align*} - - Example: The Taylor expansion is an asymptotic expansion with $\phi_n = x^n$. - \end{block} -\end{frame} - -\begin{frame}{Practical Issues} - The pathological example you saw earlier \emph{does have} an asymptotic expansion! - However, for $n \leq 10$ the extrapolation did not yet show convergence.\\ \medskip - - \begin{columns} - \begin{column}[T]{.5\textwidth} - The problem here are - \begin{itemize} - \item the choice of the starting point, - \item the existence of a bump between the starting - point $h_1 = 1/2$ and the point of interest ($h=0$). - \end{itemize} - \end{column} - \begin{column}[T]{.5\textwidth} - \begin{tikzpicture} - [ - scale=0.7 - ] - \begin{axis}[% - domain=0:1, - ymin=0, ymax=120, - title=$f(x)$, - xlabel=$x$ - ] - \addplot[black, thick, samples=250] { - exp(-1 / sqrt(x)) / x^3 - }; - \end{axis} - \end{tikzpicture} - \end{column} - \end{columns} -\end{frame} - -\begin{frame}{Speeding up extrapolations} - Let's assume you have carried out an extrapolation to some point $x_0$ - for several different values of the degree $n$: - \begin{align*} - P_n(x) & :\,\text{interpolating polynomial} & - p_n & \equiv P_n(x_0)\,. - \end{align*} - The $p_n$ are a sequence that (hopefully) converges to the value you seek.\\ - - For definiteness, let's use the previous example of $f(x) = \cos(x)$. The first - few elements of the sequence $p_n$ were: - \begin{align*} - p_0 & = 0.877583 & - p_1 & = 1.06024 & - p_2 & = 1.00056 \\ - p_3 & = 0.99996 & - p_4 & = 1.00000 - \end{align*} - - Assuming that any sequence $p_n$ is convergent, it would be nice to have a way - to accelerate the sequence without any additional (potentially costly!) evaluations - of the function $f(x)$! -\end{frame} - -\begin{frame}{Delta-Square rule by Aitkens} - Define a new sequence $q_n$ as follows: - \begin{equation*} - q_n \equiv p_n - \frac{\left[\Delta(p)_{n}\right]^2}{\Delta^2(p)_{n}}\,, - \end{equation*} - where - \begin{align*} - \Delta(p)_k & = p_{k + 1} - p_k\,, & - \Delta^2(p)_k & = \Delta(p)_{k + 1} - \Delta(p)_k\,. - \end{align*} - This could be written simpler, but in order to avoid numerical instabilities (floating point numbers!) - the version written here is preferable.\\ \vfill - - [This method has further applications which we will revisit next lecture.] -\end{frame} - -\begin{frame}{Accelerating our example} - \begin{columns} - \begin{column}{.5\textwidth} - \begin{center} - \begin{tikzpicture} - \node[anchor=south] (0, 0) { - \begin{tabular}{lrr} - $n$ & $p_n$ & $q_{n - 2}$\\ - 0 & 0.87758 & --- \\ - 1 & 1.06024 & --- \\ - 2 & 1.00056 & 0.999954 \\ - 3 & 0.99996 & 0.999998 \\ - 4 & 1.00000 & \dots \\ - \end{tabular} - }; - \only<2>{ - \draw[blue,thick] (-0.40, +1.20) rectangle (+0.05, +1.55); - \draw[blue,thick] (+1.30, +1.20) rectangle (+1.90, +1.55); - \draw[draw=none, fill=blue, fill opacity=0.25] (-1.30, +1.20) rectangle (+0.05, 2.55); - } - \only<3>{ - \draw[red, thick] (-0.18, +0.70) rectangle (+0.05, +1.05); - \draw[red, thick] (+1.50, +0.70) rectangle (+1.90, +1.05); - \draw[draw=none, fill=red, fill opacity=0.25] (-1.30, +0.70) rectangle (+0.05, 2.05); - } - \end{tikzpicture} - \end{center} - \end{column} - \begin{column}{.5\textwidth} - \begin{itemize} - \item compare $p_n$ with $q_{n - 2}$ to keep things fair\\ - i.e.: $p_2$ vs $q_0$, $p_3$ vs $q_1$ etc. - \item<2-> {\color{blue}$q_0(p_0, p_1, p_2)$ is competitive with $p_3$!} - \item<3-> {\color{red} $q_1(p_1, p_2, p_3)$ is competitive with $p_4$!} - \end{itemize} - \end{column} - \end{columns} -\end{frame} - -\backupbegin - -\begin{frame}\frametitle{Backup} - - -\end{frame} - - - - -\backupend -\end{document} diff --git a/Lectures_my/NumMet/Lecture3/tikzfeynman.sty b/Lectures_my/NumMet/Lecture3/tikzfeynman.sty deleted file mode 100755 index 521fc65..0000000 --- a/Lectures_my/NumMet/Lecture3/tikzfeynman.sty +++ /dev/null @@ -1,43 +0,0 @@ -% 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}, -} - diff --git a/Lectures_my/NumMet/Lecture4/Makefile b/Lectures_my/NumMet/Lecture4/Makefile deleted file mode 100644 index 37f4367..0000000 --- a/Lectures_my/NumMet/Lecture4/Makefile +++ /dev/null @@ -1,9 +0,0 @@ -all: lecture4.pdf - -lecture4.pdf: lecture4.tex - xelatex lecture4.tex -# bibtex lecture3 - xelatex lecture4.tex -# xelatex lecture4.tex -clean: - rm *.aux *.bbl *.blg *.log *.out *.pdf *.sh *.xml *.snm *.toc *.nav diff --git a/Lectures_my/NumMet/Lecture4/beamercolorthemeFlip.sty b/Lectures_my/NumMet/Lecture4/beamercolorthemeFlip.sty deleted file mode 100755 index d6b9c50..0000000 --- a/Lectures_my/NumMet/Lecture4/beamercolorthemeFlip.sty +++ /dev/null @@ -1,179 +0,0 @@ -% 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/Lecture4/beamerinnerthemeFlip.sty b/Lectures_my/NumMet/Lecture4/beamerinnerthemeFlip.sty deleted file mode 100755 index 8dc12a0..0000000 --- a/Lectures_my/NumMet/Lecture4/beamerinnerthemeFlip.sty +++ /dev/null @@ -1,95 +0,0 @@ -% 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/Lecture4/beamerouterthemeFlip.sty b/Lectures_my/NumMet/Lecture4/beamerouterthemeFlip.sty deleted file mode 100755 index d12f6d6..0000000 --- a/Lectures_my/NumMet/Lecture4/beamerouterthemeFlip.sty +++ /dev/null @@ -1,189 +0,0 @@ -% 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/Lecture4/beamerouterthemedecolines.sty b/Lectures_my/NumMet/Lecture4/beamerouterthemedecolines.sty deleted file mode 100755 index 669e493..0000000 --- a/Lectures_my/NumMet/Lecture4/beamerouterthemedecolines.sty +++ /dev/null @@ -1,168 +0,0 @@ -% 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/Lecture4/beamerthemeFlip.sty b/Lectures_my/NumMet/Lecture4/beamerthemeFlip.sty deleted file mode 100755 index a615ff5..0000000 --- a/Lectures_my/NumMet/Lecture4/beamerthemeFlip.sty +++ /dev/null @@ -1,59 +0,0 @@ -% 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/Lecture4/images/BG_lower.png b/Lectures_my/NumMet/Lecture4/images/BG_lower.png deleted file mode 100755 index 073034a..0000000 --- a/Lectures_my/NumMet/Lecture4/images/BG_lower.png +++ /dev/null Binary files differ diff --git a/Lectures_my/NumMet/Lecture4/images/bubble.gif b/Lectures_my/NumMet/Lecture4/images/bubble.gif deleted file mode 100644 index ecff282..0000000 --- a/Lectures_my/NumMet/Lecture4/images/bubble.gif +++ /dev/null Binary files differ diff --git a/Lectures_my/NumMet/Lecture4/images/bubble.jpg b/Lectures_my/NumMet/Lecture4/images/bubble.jpg deleted file mode 100644 index ceb584d..0000000 --- a/Lectures_my/NumMet/Lecture4/images/bubble.jpg +++ /dev/null Binary files differ diff --git a/Lectures_my/NumMet/Lecture4/images/bubble2.jpg b/Lectures_my/NumMet/Lecture4/images/bubble2.jpg deleted file mode 100644 index 0fd03bb..0000000 --- a/Lectures_my/NumMet/Lecture4/images/bubble2.jpg +++ /dev/null Binary files differ diff --git a/Lectures_my/NumMet/Lecture4/images/uzh-transp.pdf b/Lectures_my/NumMet/Lecture4/images/uzh-transp.pdf deleted file mode 100644 index 977da67..0000000 --- a/Lectures_my/NumMet/Lecture4/images/uzh-transp.pdf +++ /dev/null Binary files differ diff --git a/Lectures_my/NumMet/Lecture4/lecture4.tex b/Lectures_my/NumMet/Lecture4/lecture4.tex deleted file mode 100644 index 7893275..0000000 --- a/Lectures_my/NumMet/Lecture4/lecture4.tex +++ /dev/null @@ -1,605 +0,0 @@ -% vim: set sts=4 et : -\documentclass[11 pt,xcolor={dvipsnames,svgnames,x11names,table}]{beamer} - -\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} - -\usepackage{bm} -\usepackage{tikz,pgfplots} -\usepackage{graphicx} - -% 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}{$#2$}}% - -\graphicspath{{images/}} % Put all images in this directory. Avoids clutter. - -% 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}} -} - -\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 {Root Finding} - \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 Chrzaszcz, 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} -\vspace{0.5em} - \textcolor{normal text.fg!50!Comment}{Numerical Methods, \\ 26. September, 2016} -\end{center} -\end{frame} -} - -\begin{frame}{Plan for today} - \begin{itemize} - \item \alert{General problem of finding the root of a function}\\ - $\xi$ is a root of $f$ iff $f(\xi) = 0$. - \vfill - \item \alert{Begin with $D=1$}\\ - What properties of $f(x)$ can we use to find one, any, or all roots - of $f$? What are the requirements on $f(x)$? - \vfill - \item \alert{How about $D>1$?}\\ - Can we generalize root finding from $D=1$ do arbitrary $D$? - \end{itemize} -\end{frame} - -\begin{frame}{General iterative procedure} - Let's assume that - \begin{itemize} - \item $f(x)$ is a our function of interest, - \item $\xi$ is the only root of $f$, - \item we have a point $x_0$ close to $\xi$ - \end{itemize} - We now want to find a sequence $\lbrace x_0, x_1, \dots \rbrace$ that - \begin{enumerate} - \item converges toward $\xi$: $\lim_{k\to \infty} x_k = \xi$, - \item is iterative: $x_{k + 1} = \Phi[f](x_k)$ - \end{enumerate} - We can attempt to Taylor expand $f$ around $x_0$ to order $N$, in order - to obtain the generator $\Phi[f]$ for the iteration: - \begin{block}{Expansion around $x_0$} - \begin{equation*} - f(\xi) = 0 = \sum_{n=0}^N \frac{(\xi - x_0)^n}{n!} f^{(n)}(x_0) - \end{equation*} - where $f^{(n)}(x_0)$ is the $n$th derivative of $f$ at the position $x_0$. - \end{block} -\end{frame} - -\begin{frame}{Newton-Raphson method \hfill ($N=1$)} - \begin{block}{Expansion for $N=1$} - \begin{equation} - \tag{*} - f(\xi) = 0 = f(x_0) + (\xi - x_0) \cdot f'(x_0) + \mathcal{O}((\xi - x_0)^2) - \end{equation} - \end{block} - \vfill - Algorithm: - \begin{enumerate} - \item start with index $k=0$ - \item solve equation (*), assuming a vanshing approximation error: - \begin{gather*} - x_{k + 1} \leftarrow x_k - \frac{f(x_k)}{f'(x_k)} \approx \xi + \mathcal{O}((\xi - x_k)^2)\\ - \Phi[f](x) \equiv x - \frac{f(x)}{f'(x)} - \end{gather*} - \item if $f(x_{k + 1}) \leq t$, where $t$ is an a-prior threshold, then stop; otherwise - jump back to step \#2. - \end{enumerate} -\end{frame} - -\begin{frame}{Illustration of Newton-Raphson} - \begin{columns} - \begin{column}[T]{.5\textwidth} - \begin{overlayarea}{\textwidth}{\textheight} - $\bm{k=0}$: - \only<2->{% - \begin{equation*} - x_0 := 1 - \end{equation*} - } - \only<3->{% - $\bm{k=1}$: - \begin{align*} - x_0 & = 1 & - f(x_0) & = +0.54 \\ - & & - f'(x_0) & = -0.84 \\ - \end{align*} - } - \only<4->{% - \begin{equation*} - {\color{red} x_1 \leftarrow 1.64} - \end{equation*} - } - \only<6->{% - $\bm{k=2}$: - \begin{align*} - x_1 & = 1.64 & - f(x_0) & = -0.07 \\ - & & - f'(x_0) & = -0.997 \\ - \end{align*} - } - \only<7->{% - \begin{equation*} - {\color{red} x_2 \leftarrow 1.57} - \end{equation*} - } - \end{overlayarea} - \end{column} - \begin{column}[T]{.5\textwidth} - \hspace{-1cm} - \resizebox{1.1\textwidth}{!}{ - \begin{tikzpicture} - \begin{axis}[% - axis x line=center, - axis y line=center, - ymin=-0.2,ymax=0.8, - xmin=0.0,xmax=1.8, - title=$\cos(x)$ - ] - \addplot[thick,black,domain=0:3.14] { - cos(deg(x)) - }; - \only<2-3>{ - \addplot[thick,blue,only marks,mark=+,mark size=5pt] coordinates { - ( 1, 0.54030 ) - }; - } - \only<3-4>{ - \addplot+[thick,blue,domain=0:3.14,mark=none] { - 0.54030 - 0.84147 * (x - 1) - }; - } - \only<4-5>{ - \addplot[thick,red,only marks,mark=o,mark size=5pt] coordinates { - ( 1.6421, 0.0 ) - }; - \draw[thick,red] (axis cs:1.6421, 0) -- (axis cs:1.6421, -0.0712); - } - \only<5-6>{ - \addplot[thick,blue,only marks,mark=+,mark size=5pt] coordinates { - ( 1.6421, -0.0712 ) - }; - } - \only<6-7>{ - \addplot+[thick,blue,domain=0:3.14,mark=none] { - -0.0712 - 0.99746 * (x - 1.6421) - }; - } - \only<7->{ - \addplot[thick,red,only marks,mark=o,mark size=5pt] coordinates { - ( 1.5707, 7.8e-5 ) - }; - } - \end{axis} - \end{tikzpicture} - } - \vfill - \begin{overlayarea}{\textwidth}{.3\textheight} - \only<8->{ - \begin{tabular}{c|cc} - $k$ & $x_k$ & $f(x_k)$\\ - \hline - $0$ & $1.00$ & $+0.54$\\ - $1$ & $1.64$ & $-0.07$\\ - $2$ & $1.57$ & $+0.00$\\ - \hline - $\xi$&$1.5708$ & $0$ - \end{tabular} - } - \end{overlayarea} - \end{column} - \end{columns} -\end{frame} - -\begin{frame}{Modified Newton-Raphson method \hfill ($N=2$)} - \begin{block}{Expansion for $N=2$} - \vspace{-2\medskipamount} - \begin{equation} - \tag{*} - f(\xi) = 0 = f(x_0) + (\xi - x_0) \cdot f'(x_0) + \frac{1}{2} (\xi - x_0)^2 f''(x_0) + \mathcal{O}((\xi - x_0)^3) - \end{equation} - \end{block} - \vfill - Algorithm: - \begin{enumerate} - \item start with index $k=0$ - \item solve equation (*), assuming a vanshing approximation error: - \begin{align*} - a_\pm - & \leftarrow x_k - \frac{f'(x_k) \pm \sqrt{[f'(x_k)]^2 - 2 f(x_k) f''(x_k)}}{f''(x_k)}\\ - & \approx \xi + \mathcal{O}((\xi - x_k)^3) - \end{align*} - \item if $|f(a_+)| < |f(a_-)|$, then $x_{k + 1} \leftarrow a_+$; otherwise $x_{k + 1} \leftarrow a_-$ - \item if $f(x_{k + 1}) \leq t$, where $t$ is an a-priori threshold, then stop; otherwise - jump back to step \#2. - \end{enumerate} -\end{frame} - -\begin{frame}{Rate of convergence} - Does this iterative procedure converge? If yes, how fast? How can we quantify the rate of convergence? - - \begin{itemize} - \item we have \alert{local} convergence of order $p \geq 1$, if for all $x \in U(\xi)$ - \begin{equation*} - || \Phi[f](x) - \xi|| \leq C \cdot || x - \xi||^p\,,\quad\text{with}\quad C \geq 0\,. - \end{equation*} - Note: if $p = 1$ then we must have $C < 1$. - \item we have \alert{global} convergence if $U(\xi) = \mathbb{R}$ - \item for $D=1$ we can calculate $p$ if $\Phi[f](x)$ is differentiable to sufficient degree: - \begin{align*} - \Phi(x) - \xi = \Phi(x) - \Phi(\xi) = \frac{(x - \xi)^p}{p!} + o(||x - \xi||^p) - \end{align*} - \end{itemize} -\end{frame} - -\begin{frame}{Rate of convergence for Newton-Raphson} - We have $\Phi(x) \equiv \Phi[f](x)$: - \begin{itemize} - \item $\Phi(\xi) = \xi$ by construction - \item $\Phi'(\xi) = \frac{f(\xi) \cdot f''(\xi)}{[f'(\xi)]^2} = 0$ \alert{(*)} by construction - \item $\Phi''(\xi) = \frac{f''(\xi)}{f'(\xi)}$ - \end{itemize} - We can therefore write - \begin{equation} - \Phi(x) - \Phi(\xi) = \frac{(x - \xi)^2}{2!} \Phi''(\xi) + o(||x - \xi||^2)\,. - \end{equation} - The Newton-Raphson method converges therefore \emph{at least quadratically}, i.e.: it is a - second-order method. - \vfill - \alert{(*): only if $f'(\xi) \neq 0$}, which is equivalent to $\xi$ is a simple root of $f$. -\end{frame} - -\begin{frame}{Pathological Example} - \begin{columns} - \begin{column}[T]{.5\textwidth} - \begin{overlayarea}{\textwidth}{\textheight} - $\bm{k=0}$: - \only<2->{% - \begin{equation*} - x_0 := 0.5 - \end{equation*} - } - \only<3->{% - $\bm{k=1}$: - \begin{align*} - x_0 & = 0.5 & - f(x_0) & = +0.707 \\ - & & - f'(x_0) & = -0.707 \\ - \end{align*} - } - \only<4->{% - \begin{equation*} - {\color{red} x_1 \leftarrow -0.5} - \end{equation*} - } - \only<6->{% - $\bm{k=2}$: - \begin{align*} - x_1 & = -0.5 & - f(x_0) & = +0.707 \\ - & & - f'(x_0) & = -0.707 \\ - \end{align*} - } - \only<7->{% - \begin{equation*} - {\color{red} x_2 \leftarrow +0.5} - \end{equation*} - } - \end{overlayarea} - \end{column} - \begin{column}[T]{.5\textwidth} - \hspace{-1cm} - \resizebox{1.1\textwidth}{!}{ - \begin{tikzpicture} - \begin{axis}[% - axis x line=center, - axis y line=center, - ymin=-0.1,ymax=0.9, - xmin=-0.7,xmax=0.7, - title=$\sqrt(|x|)$, - samples=160 - ] - \addplot[thick,black,domain=-1:+0] { - sqrt(abs(x)) - }; - \addplot[thick,black,domain=-0:+1] { - sqrt(abs(x)) - }; - \only<2-3>{ - \addplot[thick,blue,only marks,mark=+,mark size=5pt] coordinates { - ( +0.5, 0.707 ) - }; - } - \only<3-4>{ - \addplot+[thick,blue,domain=-1:1,mark=none] { - 0.707 + 0.707 * (x - 0.5) - }; - } - \only<4-5>{ - \addplot[thick,red,only marks,mark=o,mark size=5pt] coordinates { - ( -0.5, 0.707 ) - }; - \draw[thick,red] (axis cs:-0.5, 0) -- (axis cs:-0.5, +0.707); - } - \only<5-6>{ - \addplot[thick,blue,only marks,mark=+,mark size=5pt] coordinates { - ( -0.5, 0.707 ) - }; - } - \only<6-7>{ - \addplot+[thick,blue,domain=-1:1,mark=none] { - 0.707 - 0.707 * (x + 0.5) - }; - } - \only<7->{ - \addplot[thick,red,only marks,mark=o,mark size=5pt] coordinates { - ( 0.5, 0.707 ) - }; - \draw[thick,red] (axis cs:+0.5, 0) -- (axis cs:+0.5, +0.707); - } - \end{axis} - \end{tikzpicture} - } - \vfill - \begin{overlayarea}{\textwidth}{.3\textheight} - ~\\\bigskip - endless loop - \end{overlayarea} - \end{column} - \end{columns} -\end{frame} - -\begin{frame}{Pitfalls of Newton-Raphson} - We had previously discussed that Newton-Raphson is guaranteed to converge - in an environment $U(\xi)$ of the root $\xi$.\\ \medskip - - However, it may fail to converge or converge only very slowly\dots - \begin{itemize} - \item if $U(\xi)$ is a small interval and the initial point lies outside of $U$, - \item if the algorithm encounters a stationary point $\chi$ of $f$ (i.e. $f'(\chi) = 0$), - \item if $\xi$ is a $m$-multiple root of $f$ (i.e. $f(x) \sim (x - \xi)^m \dots$) - \end{itemize} - - The last point can be accomodated for: If you know the mulitplicity $m$ of the root, - modify the Newton-Raphson step to read: - \begin{equation*} - x_{k + 1} \leftarrow x_{k} - m \frac{f(x_k)}{f'(x_k)} - \end{equation*} - Basically, this rescales the derivative from $f'(x) \to f'(x) / m$. -\end{frame} - -\begin{frame}{Honorable mention: Horner Scheme} - If $f(x) \equiv p_n(x)$ is a polynomial of degree $n$ in $x$, there might be multiple roots of $f$, i.e. - roots $\xi_{n}$ with $f'(\xi_n) = 0$.\\ - \vfill - The Horner Scheme allows to efficiently calculate all the (multiple) roots - of the polynomial $p_n(x)$.\\ - \vfill - However, this is of limited use: The polynomials dominantly arise in numerical computations - as the characteric polynomial $\chi_M$ of a matrix $M$. In these cases, the roots of $\chi_M$ - correspond to eigenvalue of $M$. However, the are better/more stables ways to \alert{numerically} compute - all eigenvalues of $M$, instead of finding all root of $\chi_M$. -\end{frame} - -\begin{frame}{Intermission: Derivatives} - Both the original and the modified Newton-Raphson methods involve taking - the derivative $f'$ of our target function $f$ at arbitrary points. Of - course, if we can analytically calculate the derivative, there is no problem.\\ - - \vfill - - What about functions that we can only evaluate numerically? (Think: Experiments, - numerical calculations)\\ - - \vfill - - Enter the field of \emph{numerical differentiation}! -\end{frame} - -\begin{frame}{Intermission: Derivatives} - How can we obtain the derivative $f'(x)$ numerically? Let's start from an expansion of - $f(x)$ close to the point of interest $x_0$: - \begin{tikzpicture} - \node at (0,0) { - \begin{minipage}{\textwidth} - \begin{align*} - f(x_0 + 2 h) & = f(x_0) + f'(x_0) \cdot 2 h + \frac{f''(x_0)}{2} \cdot 4 h^2 + \dots\\ - f(x_0 + \phantom2 h) & = f(x_0) + f'(x_0) \cdot \phantom2 h + \frac{f''(x_0)}{2} \cdot \phantom4 h^2 + \dots\\ - f(x_0 {\color{white}+ 2h}) & = f(x_0)\\ - f(x_0 - \phantom2 h) & = f(x_0) - f'(x_0) \cdot \phantom2 h + \frac{f''(x_0)}{2} \cdot \phantom4 h^2 + \dots\\ - f(x_0 - 2 h) & = f(x_0) - f'(x_0) \cdot 2 h + \frac{f''(x_0)}{2} \cdot 4 h^2 + \dots - \end{align*} - \end{minipage} - }; - %\draw[step=0.50,black,thin] (-4.5,-2.0) grid (4.5,2.0); - \draw[green!75!black,thick,rounded corners=5pt] (-4.5,+0.15) rectangle (+4.5,+1.05); - \only<1>{ - \draw[red, thick,rounded corners=5pt] (-4.5,-0.5) rectangle (+4.5,+0.1); - } - \only<2>{ - \draw[red, thick,rounded corners=5pt] (-4.5,-1.5) rectangle (+4.5,-0.5); - } - \end{tikzpicture} - - - \begin{overlayarea}{\textwidth}{.4\textheight} - \only<1>{ - \begin{block}{Variant \#1: Forward difference quotient} - \begin{equation*} - \frac{{\color{green!75!black}f(x_0 + h)} - {\color{red!90!black}f(x_0)}}{h} = f'(x_0) + \frac{f''(x_0)}{2} \cdot h = f'(x_0) + o(h) - \end{equation*} - \end{block} - } - \only<2>{ - \begin{block}{Variant \#2: Central difference quotient} - \vspace{-1.5\medskipamount} - \begin{equation*} - \frac{{\color{green!75!black}f(x_0 + h)} - {\color{red!90!black}f(x_0 - h)}}{2h} = f'(x_0) + \frac{f'''(x_0)}{3} h^2 = f'(x_0) + o(h^2) - \end{equation*} - \end{block} - } - \end{overlayarea} -\end{frame} - -\begin{frame}{Intermission: How to choose $h$?} - \begin{columns} - \begin{column}{.5\textwidth} - \includegraphics[width=\textwidth]{eps.png}\\ - {\tiny \hfill source: Wikipedia} - \begin{itemize} - \item two sources of numerical errors compete: - \begin{itemize} - \item formula errors, and - \item round-off (finite precision) errors - \end{itemize} - \end{itemize} - \end{column} - \begin{column}{.5\textwidth} - \begin{itemize} - \item formula error can be reduced through ``intelligent formulae'' - \item round-off error can be reduced through (schematically): - \begin{align*} - x_\text{approx} - & \leftarrow x + h\\ - h_\text{approx} - & \leftarrow x_\text{approx} - x\\ - f' & \leftarrow \frac{f(x_\text{approx}) - f(x)}{h_\text{approx}} - \end{align*} - \item optimal choice of $h$ will be close to - \begin{equation*} - h \sim \sqrt{\varepsilon} \cdot x - \end{equation*} - with $\varepsilon$: working precision - \end{itemize} - \end{column} - \end{columns} -\end{frame} - -\begin{frame}{Intermission: Higher derivatives} - What about $f''(x_0)$, $f^{(3)}(x_0)$ or even higher derivatives?\\ - \medskip - \begin{block}{Central difference quotient for $f^{(n)}$} - \begin{align*} - \sum_{k=0}^n (-1)^k \binom{n}{k} \frac{f(x_0 + (n - 2 k) h)}{(2 h)^n} - & = f^{(n)}(x_0) + o(h^2) - \end{align*} - \end{block} -\end{frame} - -\newcommand{\del}{\partial} -\begin{frame}{Intermission: Multiple partial derivatives} - What about (multiple) partial derivatives $\del_x \del_y f(x, y)$?\\ - \medskip - \begin{block}{Central difference ``stencil'' for $\del_x \del_y f(x, y)$} - Combine what we learned previously: - \begin{multline*} - \frac{\only<1>{a}\only<2>{+} f(+ h_x, + h_y) \only<1>{+b}\only<2>{-} f(+ h_x, - h_y) \only<1>{+c}\only<2>{-} f(- h_x, + h_y) \only<1>{+d}\only<2>{+} f(- h_x, - h_y)}{4 h_x h_y}\\ - = \only<1>{\dots}\only<2>{\del x\del_y f(x,y)|_{x=0,y=0} + o(h_x^2) + o(h_y^2)} - \end{multline*} - \end{block} - \vfill - \only<2>{End of intermission.} -\end{frame} - -\begin{frame}{Newton-Raphson for $D > 1$?} - What happens if we generalize to $D > 1$?\\ - \medskip - Let's consider the case $D=2$ first, for a polynomial of degree $1$ - \begin{equation*} - f(x_1, x_2) = (1 - x) \cdot (2 - y) - \end{equation*} - \medskip - $f$ has infinitely many roots: - \begin{itemize} - \item $x = 1$ and $y$ arbitrary - \item $y = 2$ and $x$ arbitrary - \end{itemize} - In order to pin-point only one point in $D=2$, we need to solve $2$ - equations: - \begin{align*} - f_1(x_1, x_2) & = 0, & - f_2(x_1, x_2) & = 0 - \end{align*} - In $D$ dimensions, we will need to solve $D$ simultaneous equations! -\end{frame} - -\begin{frame}{Generalization to $D > 1$} - Substitute: - \begin{align*} - f(x) \in \mathbb{R} \quad & \to \quad f(x) \in \mathbb{R}^D\\ - x \in \mathbb{R} \quad & \to \quad x \in \mathbb{R}^D\\ - f'(x) \in \mathbb{R} \quad & \to \quad [D_f]_{ij} \equiv \frac{\del f_i(x)}{\del x_j} \in \mathbb{R}^{D\times D} - \end{align*} - - Then the Newton-Raphson steps reads - \begin{equation*} - x^{(k+1)} \leftarrow x^{(k)} - \left[D_f(x^{(k)})\right]^{-1} f(x^{(k)})\,. - \end{equation*} - Problems: - \begin{itemize} - \item the functional matrix $D_f(x^{(k)})$ might be singular, or numerically close to being - singular - \item inverting $D_f$ is generally computationally expensive! - \end{itemize} - - In the next two lectures, Marcin will discuss how to solve systems of linear equations. - These methods will also introduce you to methods to numerically compute the above $x^{(k + 1)}$ - from $D_f(x^{(k)})$. -\end{frame} - -\backupbegin - -\begin{frame}\frametitle{Backup} - -\end{frame} - -\backupend -\end{document} diff --git a/Lectures_my/NumMet/Lecture5/Makefile b/Lectures_my/NumMet/Lecture5/Makefile deleted file mode 100644 index e4cf8e8..0000000 --- a/Lectures_my/NumMet/Lecture5/Makefile +++ /dev/null @@ -1,9 +0,0 @@ -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/Lecture5/beamercolorthemeFlip.sty b/Lectures_my/NumMet/Lecture5/beamercolorthemeFlip.sty deleted file mode 100755 index d6b9c50..0000000 --- a/Lectures_my/NumMet/Lecture5/beamercolorthemeFlip.sty +++ /dev/null @@ -1,179 +0,0 @@ -% 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/Lecture5/beamerinnerthemeFlip.sty b/Lectures_my/NumMet/Lecture5/beamerinnerthemeFlip.sty deleted file mode 100755 index 8dc12a0..0000000 --- a/Lectures_my/NumMet/Lecture5/beamerinnerthemeFlip.sty +++ /dev/null @@ -1,95 +0,0 @@ -% 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/Lecture5/beamerouterthemeFlip.sty b/Lectures_my/NumMet/Lecture5/beamerouterthemeFlip.sty deleted file mode 100755 index d12f6d6..0000000 --- a/Lectures_my/NumMet/Lecture5/beamerouterthemeFlip.sty +++ /dev/null @@ -1,189 +0,0 @@ -% 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/Lecture5/beamerouterthemedecolines.sty b/Lectures_my/NumMet/Lecture5/beamerouterthemedecolines.sty deleted file mode 100755 index 669e493..0000000 --- a/Lectures_my/NumMet/Lecture5/beamerouterthemedecolines.sty +++ /dev/null @@ -1,168 +0,0 @@ -% 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/Lecture5/beamerthemeFlip.sty b/Lectures_my/NumMet/Lecture5/beamerthemeFlip.sty deleted file mode 100755 index a615ff5..0000000 --- a/Lectures_my/NumMet/Lecture5/beamerthemeFlip.sty +++ /dev/null @@ -1,59 +0,0 @@ -% 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! 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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{Linear eq. system} - -\ARROW This and the next lecture will focus on a well known problem. Solve the following equation system: -\begin{align*} -A \cdot x =b, -\end{align*} -\ARROWR $A = a_{ij} \in \mathbb{R}^{n\times n}$ and $\det(A) \neq 0$\\ -\ARROWR $b=b_i \in \mathbb{R}^n$.\\ -\ARROW The problem: Find the $x$ vector. - - - -\end{frame} - -\begin{frame}\frametitle{Error digression} -\begin{small} -\ARROW There is enormous amount of ways to solve the linear equation system.\\ -\ARROW The choice of one over the other of them should be gathered by the {\it condition} of the matrix $A$ denoted at $cond(A)$. -\ARROW If the $cond(A)$ is small we say that the problem is well conditioned, otherwise we say it's ill conditioned.\\ -\ARROW The {\it condition} relation is defined as: -\begin{align*} -cond(A) = \Vert A \Vert \cdot \Vert A^{-1} \Vert -\end{align*} -\ARROW Now there are many definitions of different norms... The most popular one (so-called ''column norm''): -\begin{align*} -\Vert A \Vert_1 = \max_{1 \leq j \leq n} \sum_{i=1}^n \vert a_{i,j} \vert, -\end{align*} -where $n$ -is the dimension of $A$, $i,j$ are columns and rows numbers. - - - -\end{small} -\end{frame} - - -\begin{frame}\frametitle{More norms} -\begin{small} -\ARROW A different norm is a spectral norm: -\begin{align*} -\Vert A \Vert_2 &= \sqrt{\rho(A^T A)}\\ -\rho(M) &= \max \lbrace \vert\lambda_i \vert: \det{M- \lambda I} =0,~i=1,...n \rbrace -\end{align*} -where $\rho(M)$ - spectral radius of $M$ matrix, $I$ unit matrix, $\lambda_i$ eigenvalues of $M$.\\ - -\ARROW Row norm: -\begin{align*} -\Vert A \Vert_{\infty} &= \max_{1 \leq i \leq n} \sum_{j=1}^n \vert a_{i,j} \vert, -\end{align*} -\begin{exampleblock}{Digression:} -\ARROWR Calculation of the matrix norms are not a simple process at all. There are certain class of matrices that make the calculations easier.\\ -\ARROWR The spectral norm can be also defined: -\begin{align*} -cond_2(A) = \frac{\max_{1\leq i \leq n}\vert \lambda_i \vert }{\min_{1\leq i \leq n}\vert \lambda_i \vert }, -\end{align*} -\end{exampleblock} - -\end{small} -\end{frame} - - -\begin{frame}\frametitle{Example, ill-conditioned matrix} -\begin{small} -\ARROW The text-book example of wrongly conditioned matrix is the Hilbert matrix: -\begin{align*} -h_{i,j} = \frac{1}{i+j-1} -\end{align*} -\ARROWR Example: -\begin{align*} -h_{i,j}^{4 \times 4} = \begin{pmatrix} -1 & \frac{1}{2} & \frac{1}{3} & \frac{1}{4} \\ -\frac{1}{2} & \frac{1}{3} & \frac{1}{4} & \frac{1}{5} \\ -\frac{1}{3} & \frac{1}{4} & \frac{1}{5} & \frac{1}{6}\\ -\frac{1}{4} & \frac{1}{5} & \frac{1}{6} & \frac{1}{7} -\end{pmatrix} -\end{align*} -\ARROW The condition of this matrix: -\begin{align*} -cond(A)=\mathcal{O}\left(\frac{e^{3.52N}}{\sqrt{N}}\right) -\end{align*} -\ARROW For $8 \times 8$ matrix we get: -\begin{align*} -cond_1(A)=3.387\cdot 10^{10},~~~cond_2(A)=1.526\cdot 10^{10},~~~~~cond_{\infty}(A)=3.387\cdot 10^{10} -\end{align*} -\ARROW Clearly large numbers ;) -\end{small} -\end{frame} - -\begin{frame}\frametitle{Exact methods: Cramer method} -\begin{small} -\ARROW If $\det{A} \neq 0$ then the solutions are given by: -\begin{align*} -x_i =\frac{\det{A_i}}{\det{A}} -\end{align*} -\ARROW So calculate the solutions one needs to calculate $n+1$ determinants. To calculate each determinate one needs $(n-1)n!$ multiplications. \\ -\ARROW Putting it all together one needs $(n+1)(n-1)n! = n^{n+2}$ \\ -\ARROW Brute force but works ;) - - -\end{small} -\end{frame} - - - - - -\begin{frame}\frametitle{Example, ill-conditioned matrix} -\begin{small} -\ARROW The text-book example of wrongly conditioned matrix is the Hilbert matrix: -\begin{align*} -h_{i,j} = \frac{1}{i+j-1} -\end{align*} -\ARROWR Example: -\begin{align*} -h_{i,j}^{4 \times 4} = \begin{pmatrix} -1 & \frac{1}{2} & \frac{1}{3} & \frac{1}{4} \\ -\frac{1}{2} & \frac{1}{3} & \frac{1}{4} & \frac{1}{5} \\ -\frac{1}{3} & \frac{1}{4} & \frac{1}{5} & \frac{1}{6}\\ -\frac{1}{4} & \frac{1}{5} & \frac{1}{6} & \frac{1}{7} -\end{pmatrix} -\end{align*} -\ARROW The condition of this matrix: -\begin{align*} -cond(A)=\mathcal{O}\left(\frac{e^{3.52N}}{\sqrt{N}}\right) -\end{align*} -\ARROW For $8 \times 8$ matrix we get: -\begin{align*} -cond_1(A)=3.387\cdot 10^{10},~~~cond_2(A)=1.526\cdot 10^{10},~~~~~cond_{\infty}(A)=3.387\cdot 10^{10} -\end{align*} -\ARROW Clearly large numbers ;) -\end{small} -\end{frame} - -\begin{frame}\frametitle{Exact methods: Cramer method} -\begin{small} -\ARROW If $\det{A} \neq 0$ then the solutions are given by: -\begin{align*} -x_i =\frac{\det{A_i}}{\det{A}} -\end{align*} -\ARROW So calculate the solutions one needs to calculate $n+1$ determinants. To calculate each determinate one needs $(n-1)n!$ multiplications. \\ -\ARROW Putting it all together one needs $(n+1)(n-1)n! = n^{n+2}$ \\ -\ARROW Brutal force but works ;) - - -\end{small} -\end{frame} - - - - - -\begin{frame}\frametitle{Exact methods: Gauss method} -\begin{small} - -\ARROW The idea besides the Gauss method is simple: transform the $A x =b$ to get the equvalent matrix $A^{\left[n\right]} x = b^{\left[n\right]}$ where $A^{\left[n\right]}$ is triangular matrix: -\begin{align*} -A^{\left[n\right]} = \begin{pmatrix} -a^{\left[n\right]}_{11} & a^{\left[n\right]_{12}} & ... & a^{\left[n\right]}_{1n}\\ -0 & a^{\left[n\right]}_{22} & ... & a^{\left[n\right]}_{2n} \\ -...\\ -0 & 0 & ... & a^{\left[n\right]}_{nn} \\ -\end{pmatrix} -\end{align*} -\ARROWR The algorithm: -\ARROW To do so we calculate the: $d^{\left[1\right]}_{i,1}=\frac{a^{\left[1\right]}_{i1}}{a^{\left[1\right]}_{11}}$ \\ -\ARROW The first row multiplied by the $d^{\left[1\right]}_{i,1}$ we subtract from the $i^{th}$ row. -\ARROW After this we get: - -\begin{align*} -\begin{pmatrix} -a^{\left[ 1 \right]}_{11} & a^{\left[ 1 \right]_{12}} & ... & a^{\left[ 1 \right]}_{1n}\\ -0 & a^{\left[ 1 \right]}_{22} & ... & a^{\left[ 1 \right]}_{2n} \\ -...\\ -0 & a^{\left[ 1 \right]}_{n2} & ... & a^{\left[ 1 \right]}_{nn} \\ -\end{pmatrix} \overrightarrow{x}= -\begin{pmatrix} -b^{\left[ 1 \right]}_{1} \\ -b^{\left[ 1 \right]}_{1} \\ -... \\ -b^{\left[ 1 \right]}_{1} \\ -\end{pmatrix} -\end{align*} - -\end{small} -\end{frame} - - - -\begin{frame}\frametitle{Exact methods: Gauss method 2} -\begin{small} - -\ARROW Now one needs to repeat the above n times moving each time row down. -\begin{alertblock}{Cons:} -\ARROW The algoright can be stooped if you divide by zero.\\ -\ARROW The method is very efficient to accumulate numerical errors. -\end{alertblock} - -\begin{exampleblock}{Pros:} -\ARROWR The number of needed floating point operations is less then Cramer.\\ -\ARROWR Example for 15 equations: $1345$ vs $5 \cdot 10^{12}$. -\end{exampleblock} - -\end{small} -\end{frame} - - - -\begin{frame}\frametitle{Exact methods: modified Gauss method} -\begin{small} - -\ARROW The biggest disadvantage of Gauss method is the fact that we can have zero elements :( \\ -\ARROW The modified method fixes this problem :)\\ -\ARROW The modification is as follows: -\begin{itemize} -\item In each step before we do the elimination we look for main element: -\begin{align*} -\vert a_{mk}^{\vert k \vert } = \max \lbrace \vert a_{jk}^{\vert k \vert} : j=k, k+1,..., n \rbrace -\end{align*} -\item We exchange the rows $m$ and $k$. -\item We do the standard elimination. -\end{itemize} - -\end{small} -\end{frame} - - - -\begin{frame}\frametitle{Exact methods: Jordan elimination method} -\begin{small} - - -\ARROW The Jordan elimination method is similar to Guass method but the idea is to transform the matrix from $Ax =b$ to $I x = b^{\lfloor n+1 \rfloor}$. -\begin{enumerate} -\item We start from eliminating the as in Gauss method in the first row. -\item When we move to the second row we eliminate the $x_2$ element also from the first raw. -\item The third raw we eliminate the first and second raw. -\item We repeat this $n$ times. -\end{enumerate} -\ARROW After this we will get new system $I x = b^{\lfloor n+1 \rfloor}$. \\ -\ARROW The $b^{\lfloor n+1 \rfloor}$ is already the solution! No need to do more. - -\end{small} -\end{frame} - - -\begin{frame}\frametitle{Exact methods: LU method} -\begin{small} - - -\ARROW The most popular of the exact methods is so-called LU method.\\ -\ARROW The idea is very simple; we represent the matrix in a form: -\begin{align*} -A = & \begin{pmatrix} -a_{11} & a_{12} & a_{13} & ... & a_{1n} \\ -a_{21} & a_{22} & a_{23} & ... & a_{2n} \\ -a_{31} & a_{32} & a_{33} & ... & a_{2n} \\ - & & ... & & \\ - _{n1} & a_{n2} & a_{n3} & ... & a_{nn} \\ -\end{pmatrix} = \\ & \begin{pmatrix} -1 & 0 & 0 & ... & 0 \\ -l_{21} & 1 & 0 & ... & 0 \\ -l_{31} & l_{32} & 1 & ... &0 & \\ - & & ... & & \\ -l_{n1} & l_{n2} & l_{n3} & ... & l_{nn}\\ -\end{pmatrix} \cdot -\begin{pmatrix} -u_{11} & u{12} & u_{13} & ... & u_{1n} \\ -0 & u{22} & u_{23} & ... & u_{2n} \\ -0 & 0 & u_{33} & ... & u_{3n} \\ - & & ... & & \\ -0 & 0 & 0 & ... & u_{nn} -\end{pmatrix} = L \cdot U -\end{align*} -\ARROW After this decomposition we need to solve: -\begin{align*} -\begin{cases} -L y & =b\\ -U x & =y -\end{cases} -\end{align*} - -\end{small} -\end{frame} - -\begin{frame}\frametitle{Exact methods: LU method, algorithms} -\begin{small} -\ARROW We solve the following matrix: $A^{\lfloor 1 \rfloor} x = b^{\lfloor1 \rfloor}$\\ -\ARROW We start by preparing the matrix $L^{\lfloor 1 \rfloor}$: -\begin{align*} -L^{\lfloor 1 \rfloor }=\begin{pmatrix} -1 & 0 & 0 & ... & 0 \\ --l_{21} & 1 & 0 & ... & 0\\ --l_{31} & 0 & 1 & ... & 0\\ -& & ... & & \\ --l_{n1} & 0 & 0 & ... & 1 -\end{pmatrix} -\end{align*} -where the $l_{i1}$ are defined: -\begin{align*} -l_{i1} = \frac{a_{i1}^{\lfloor 1 \rfloor}}{a_{11}^{\lfloor 1 \rfloor}} -\end{align*} -\ARROW Now we take our base equation by $L^{\lfloor 1 \rfloor }$: -\begin{align*} -L^{\lfloor 1 \rfloor } A^{\lfloor 1 \rfloor } x = L^{\lfloor 1 \rfloor } b^{\lfloor1 \rfloor} -\end{align*} -\ARROW We get the a new system: -\begin{align*} -A^{\lfloor 2 \rfloor} x = b^{\lfloor2 \rfloor}~~~~~~~~\Leftrightarrow~~~~~~~~~~L^{\lfloor 1 \rfloor } A^{\lfloor 1 \rfloor } x = L^{\lfloor 1 \rfloor } b^{\lfloor1 \rfloor} -\end{align*} - -\end{small} -\end{frame} - -\begin{frame}\frametitle{Exact methods: LU method, algorithms} -\begin{small} -\ARROW In the second step we construct the $L^{\lfloor 2 \rfloor}$ in the form: -\begin{align*} -L^{\lfloor 2 \rfloor}=\begin{pmatrix} -1 & 0 & 0 & ... & 0 \\ -0 & 1 & 0 & ... & 0\\ -0 & -l_{32} & 1 & ... & 0\\ -& & ... & & \\ -0 & -l_{n2} & 0 & ... & 1 -\end{pmatrix} -\end{align*} -where : -\begin{align*} -l_{i2} = \frac{a_{i2}^{\lfloor 2 \rfloor}}{a_{22}^{\lfloor 2 \rfloor}} -\end{align*} - -\ARROW Now we take the $A^{\lfloor 2 \rfloor} x = b^{\lfloor2 \rfloor}$ and multiply it by $L^{\lfloor 2 \rfloor}$: -\begin{align*} -L^{\lfloor 2 \rfloor } A^{\lfloor 2 \rfloor } x = L^{\lfloor 2 \rfloor } b^{\lfloor2 \rfloor} -\end{align*} -\ARROW We get the a new system: -\begin{align*} -A^{\lfloor 3 \rfloor} x = b^{\lfloor3 \rfloor}~~~~~~~~\Leftrightarrow~~~~~~~~~L^{\lfloor 2 \rfloor } L^{\lfloor 1 \rfloor } A^{\lfloor 1 \rfloor } x = L^{\lfloor 2 \rfloor } L^{\lfloor 1 \rfloor } b^{\lfloor1 \rfloor} -\end{align*} - -\end{small} -\end{frame} - - -\begin{frame}\frametitle{Exact methods: LU method, algorithms} -\begin{small} - -\ARROW Now the we repeat the above steps $n-1$ times after which we get: -\begin{align*} -& L^{\lfloor n-1 \rfloor } L^{\lfloor n-2 \rfloor } ... L^{\lfloor 2 \rfloor } L^{\lfloor 1 \rfloor } A^{\lfloor 1 \rfloor } = A^{\lfloor n \rfloor } = U\\ -& L^{\lfloor n-1 \rfloor } L^{\lfloor n-2 \rfloor } ... L^{\lfloor 2 \rfloor } L^{\lfloor 1 \rfloor } b^{\lfloor1 \rfloor} = b^{\lfloor n \rfloor} -\end{align*} -\ARROW From the above we can calculate: -\begin{align*} -A^{\lfloor 1 \rfloor } = \left( L^{\lfloor 1 \rfloor } \right)^{-1} \left( L^{\lfloor 2 \rfloor } \right)^{-1} ... \left( L^{\lfloor n-1 \rfloor } \right)^{-1} A^{\lfloor n \rfloor } -\end{align*} -\ARROW So the matrix $L$ we search for is: -\begin{align*} -L= \left( L^{\lfloor 1 \rfloor } \right)^{-1} \left( L^{\lfloor 2 \rfloor } \right)^{-1} ... \left( L^{\lfloor n-1 \rfloor } \right)^{-1} -\end{align*} -\ARROW The $\left( L^{\lfloor k \rfloor } \right)^{-1}$ can be easy calculated: -\begin{footnotesize} -\begin{align*} -\left( L^{\lfloor k \rfloor } \right)^{-1} = \begin{pmatrix} -1 & 0 & ... & 0 & ... & 0 \\ -0 & 1 & ... & 0 & ... & 0 \\ -& & & ... & & \\ -0 & 0 & ... & 1 & ... & 0 \\ -0 & 0 & ... & l_{k+1 k} & ... & 0 \\ -0 & 0 & ... & l_{k+2 k} & ... & 0 \\ -& & & ... & & \\ -0 & 0 & ... & l_{n k} & ... & 1 \\ -\end{pmatrix} -\end{align*} -\end{footnotesize} - -\end{small} -\end{frame} - - - -\begin{frame}\frametitle{Exact methods: LU method, algorithms} -\begin{small} - -\ARROW Now the only thing left is to solve the simple linear system: -\begin{align*} -\begin{cases} -L y & =b\\ -U x & =y -\end{cases} -\end{align*} -\ARROW Because of the triangular matrix the solution is straightforward: -\begin{align*} -y_1=\frac{b_1}{L_11},~~~~~~~~~y_i=\frac{b_1 - \sum_{j=1^{i-1}} L_{ij} y_j }{L_{ii}}~~{ i\geq 2} -\end{align*} - -\end{small} -\end{frame} - - -\begin{frame}\frametitle{Summary} -\begin{small} - -\ARROW This lecture we learn the exact methods of solving linear equation system.\\ -\ARROW The three most popular one are: Gauss, Jordan, LU.\\ -\ARROW By default the LU method should be used.\\ -\ARROW And remember: be sure the system is well conditioned! - - -\end{small} -\end{frame} - - - - - - -\backupbegin - -\begin{frame}\frametitle{Backup} - - -\end{frame} - - - - - - - -\backupend -\end{document} diff --git a/Lectures_my/NumMet/Lecture5/mchrzasz.toc b/Lectures_my/NumMet/Lecture5/mchrzasz.toc deleted file mode 100644 index 429917f..0000000 --- a/Lectures_my/NumMet/Lecture5/mchrzasz.toc +++ /dev/null @@ -1,5 +0,0 @@ -\boolfalse {citerequest}\boolfalse {citetracker}\boolfalse {pagetracker}\boolfalse {backtracker}\relax -\defcounter {refsection}{0}\relax -\beamer@endinputifotherversion {3.24pt} -\defcounter {refsection}{0}\relax -\select@language {english} diff --git a/Lectures_my/NumMet/Lecture5/tikzfeynman.sty b/Lectures_my/NumMet/Lecture5/tikzfeynman.sty deleted file mode 100755 index 521fc65..0000000 --- a/Lectures_my/NumMet/Lecture5/tikzfeynman.sty +++ /dev/null @@ -1,43 +0,0 @@ -% 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}, -} - diff --git a/Lectures_my/NumMet/Lecture6/Makefile b/Lectures_my/NumMet/Lecture6/Makefile deleted file mode 100644 index e4cf8e8..0000000 --- a/Lectures_my/NumMet/Lecture6/Makefile +++ /dev/null @@ -1,9 +0,0 @@ -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/Lecture6/beamercolorthemeFlip.sty b/Lectures_my/NumMet/Lecture6/beamercolorthemeFlip.sty deleted file mode 100755 index d6b9c50..0000000 --- a/Lectures_my/NumMet/Lecture6/beamercolorthemeFlip.sty +++ /dev/null @@ -1,179 +0,0 @@ -% 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/Lecture6/beamerinnerthemeFlip.sty b/Lectures_my/NumMet/Lecture6/beamerinnerthemeFlip.sty deleted file mode 100755 index 8dc12a0..0000000 --- a/Lectures_my/NumMet/Lecture6/beamerinnerthemeFlip.sty +++ /dev/null @@ -1,95 +0,0 @@ -% 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/Lecture6/beamerouterthemeFlip.sty b/Lectures_my/NumMet/Lecture6/beamerouterthemeFlip.sty deleted file mode 100755 index d12f6d6..0000000 --- a/Lectures_my/NumMet/Lecture6/beamerouterthemeFlip.sty +++ /dev/null @@ -1,189 +0,0 @@ -% 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/Lecture6/beamerouterthemedecolines.sty b/Lectures_my/NumMet/Lecture6/beamerouterthemedecolines.sty deleted file mode 100755 index 669e493..0000000 --- a/Lectures_my/NumMet/Lecture6/beamerouterthemedecolines.sty +++ /dev/null @@ -1,168 +0,0 @@ -% 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/Lecture6/beamerthemeFlip.sty b/Lectures_my/NumMet/Lecture6/beamerthemeFlip.sty deleted file mode 100755 index a615ff5..0000000 --- a/Lectures_my/NumMet/Lecture6/beamerthemeFlip.sty +++ /dev/null @@ -1,59 +0,0 @@ -% 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/Lecture6/images/BG_lower.png b/Lectures_my/NumMet/Lecture6/images/BG_lower.png deleted file mode 100755 index 073034a..0000000 --- a/Lectures_my/NumMet/Lecture6/images/BG_lower.png +++ /dev/null Binary files differ diff --git a/Lectures_my/NumMet/Lecture6/images/bubble.gif b/Lectures_my/NumMet/Lecture6/images/bubble.gif deleted file mode 100644 index ecff282..0000000 --- a/Lectures_my/NumMet/Lecture6/images/bubble.gif +++ /dev/null Binary files differ diff --git a/Lectures_my/NumMet/Lecture6/images/bubble.jpg b/Lectures_my/NumMet/Lecture6/images/bubble.jpg deleted file mode 100644 index ceb584d..0000000 --- a/Lectures_my/NumMet/Lecture6/images/bubble.jpg +++ /dev/null Binary files differ diff --git a/Lectures_my/NumMet/Lecture6/images/bubble2.jpg b/Lectures_my/NumMet/Lecture6/images/bubble2.jpg deleted file mode 100644 index 0fd03bb..0000000 --- a/Lectures_my/NumMet/Lecture6/images/bubble2.jpg +++ /dev/null Binary files differ diff --git a/Lectures_my/NumMet/Lecture6/images/uzh-transp.pdf b/Lectures_my/NumMet/Lecture6/images/uzh-transp.pdf deleted file mode 100644 index 977da67..0000000 --- a/Lectures_my/NumMet/Lecture6/images/uzh-transp.pdf +++ /dev/null Binary files differ diff --git a/Lectures_my/NumMet/Lecture6/mchrzasz-blx.bib b/Lectures_my/NumMet/Lecture6/mchrzasz-blx.bib deleted file mode 100644 index 9e405b3..0000000 --- a/Lectures_my/NumMet/Lecture6/mchrzasz-blx.bib +++ /dev/null @@ -1,11 +0,0 @@ -@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/Lecture6/mchrzasz.tex b/Lectures_my/NumMet/Lecture6/mchrzasz.tex deleted file mode 100644 index 4b958d9..0000000 --- a/Lectures_my/NumMet/Lecture6/mchrzasz.tex +++ /dev/null @@ -1,589 +0,0 @@ -\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[Linear equation systems: iteration methods]{Linear equation systems:iteration methods} -\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 {Linear equation systems: iteration methods} - \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, \\ 17 October, 2016} -\end{center} -\end{frame} -} - - -\begin{frame}\frametitle{Linear eq. system} - -\ARROW This and the next lecture will focus on a well known problem. Solve the following equation system: -\begin{align*} -A \cdot x =b, -\end{align*} -\ARROWR $A = a_{ij} \in \mathbb{R}^{n\times n}$ and $\det(A) \neq 0$\\ -\ARROWR $b=b_i \in \mathbb{R}^n$.\\ -\ARROW The problem: Find the $x$ vector. - - -\end{frame} - - - -\begin{frame}\frametitle{LU method with main element selection} -\begin{small} -\ARROW The algorithm for the LU matrix decomposition from previous lecture doesn't have the main element selection. \\ -\ARROW This might be problematic. For example: - -\fixme - - - - -\end{small} -\end{frame} - - - -\begin{frame}\frametitle{Chelosky decomposition} -\begin{small} - -\ARROW If $A \in \textbf{R}^{N \times N}$ is a symmetric ($A^T=A$) and positively defined matrix, then there exits a special case of LU factorization such that: -\begin{align*} -A =C C^T -\end{align*} -where $C$ is a traingular matrixwith diagonal elements greater then zero. \\ -\ARROW Finding the Chelosky decomposition is two times faster the finding the LU decomposition. \\ -\ARROW The Chelosky decomposition has the same algorithm then the LU decomposition. - - - -\end{small} -\end{frame} - - -\begin{frame}\frametitle{LDL factorization} -\begin{small} - -\ARROW If matrix can be Chelosky decomposed it can also be decomposed to: -\begin{align*} -A=LDL^T -\end{align*} -where $L$ is botton triangular matrix such that $\forall_i : l_{ii}=1$ and $D$ is diagonal matrix with positive elements. \\ -\ARROW The advantage of the LDL decomposition compared to Cehlosky decomposition is the fact that we don't need to square root in the calculations. - - - -\end{small} -\end{frame} - - - -\begin{frame}\frametitle{Iterative methods} -\begin{small} - -\ARROW The exact methods are the ones that require more computations to get the solutions.\\ -\ARROWR Because of this they are not really suited to solve big linear systems.\\ -\ARROW The iteration methods are simple and the main goal of them is to transform: -\begin{align*} -Ax=b -\end{align*} -to: -\begin{align*} -x= Mx + c -\end{align*} -where $A$,$M$ are matrices of $n \times n$ size. \\ -$b$ and $c$ are vectors of the size $n$.\\ -\ARROW Once we get the second system (btw. remember MC lectures?) we can use iterative methods to solve them. - -\end{small} -\end{frame} - - -\begin{frame}\frametitle{Expansion} -\begin{small} - -\ARROW If $\overline{x}$ is the solution of the $A x = b$ system then also: -\begin{align*} -\overline{x} = M \overline{x} +c -\end{align*} -\ARROW We construct the a sequence that approximates the $\overline{x}$ in the following way: -\begin{align*} -x^{(k+1)} = M x^{(k)},~~~k=0,1,... -\end{align*} -\ARROW The necessary and sufficient requirement for the convergence of the set is: -\begin{align*} -\rho(M)<1 -\end{align*} - - - -\end{small} -\end{frame} - - -\begin{frame}\frametitle{Jakobi method} -\begin{small} - -\ARROW The simplest method is the Jakobi method. \\ -\ARROW We start from decomposition of $A$ matrix: -\begin{align*} -A = L + U +D -\end{align*} -where -\begin{itemize} -\item $L=(a_{ij})_{i>j}$ - triangular lower matrix. -\item $D=(a_{ik})_{i=j}$ - diagonal matrix. -\item $U=(a_{ij})_{ii}a_{ij}x_{j}^{(k)} \right) + \frac{b_i}{a_{ii}} -\end{align*} -\ARROW The matrix: -\begin{align*} -M_{GS} = -(L+D)^{-1} U -\end{align*} -is so-called Gauss-Seidl matrix. - -\end{small} -\end{frame} - - -\begin{frame}\frametitle{Convergence of Gauss-Seidle and Jacobi methods} -\begin{small} - -\begin{exampleblock}{Reminder:} -The necessary and sufficient condition for the iteration to be convergence is that: -\begin{align*} -\rho(M)<1 -\end{align*} -where $M$ is the matrix of a given method. -\end{exampleblock} - -\ARROW Now calculating the $\rho(M)$ might be already a computationally expensive...\\ -\ARROW A very useful way of getting the $\rho(M_J)$ is: -\begin{align*} -r_J = \frac{\Vert x_{k+1} - x_k \Vert}{\Vert x_k - x_{k-1} \Vert} \approx \vert \rho(M_J) -1 \vert -\end{align*} -\ARROW Another useful equations: -\begin{align*} -\rho(M_{GS}) = \rho(M_J)^2 -\end{align*} - - - -\end{small} -\end{frame} - - -\begin{frame}\frametitle{Convergence of Gauss-Seidle and Jacobi methods} -\begin{small} - -\begin{alertblock}{Theorem:} -If matrix $(a_{ij})$ fulfils one of the conditions:\\ -\ARROW $\vert a_{ii} > \sum_{j \neq i} \vert a_{ij} \vert~~ i=1,...,n$, so-called strong row criteria.\\ -\ARROW $\vert a_{jj} > \sum_{i \neq j} \vert a_{ij} \vert~~ j=1,...,n$, so-called strong column criteria. -\end{alertblock} - -\begin{exampleblock}{Practical note:} -\ARROWR One needs to note that calculating the $\rho(M)$ might be a as time consuming calculation as the solution is self...\\ -\ARROWR If that is the case usually one neglects this steps and computes the solution with extra care at each step checking the convergence. - -\end{exampleblock} - - -\end{small} -\end{frame} - - - - -\begin{frame}\frametitle{SOR method} -\begin{small} - -\ARROW The Successive Over-Relaxation method is an extension of the Gauss-Seidl methods. \\ -\ARROW The modification is that we can reuse the previous step to get a more precise approximation of the solution. \\ -\ARROW The ''hack'' happens when we calculate the $x^{(k+1)}_{GS}$ using the Gauss-Seidl method. Instead assuming that the next step is the $x^{(k+1)}_{GS}$ we ''relax'' the condition using liner combination: -\begin{align*} -x^{(k+1)} =\omega x^{(k+1)}_{GS} + (1-\omega) x^{(k)} -\end{align*} -\ARROW From the above once can see that if $\omega=1$ then we end up with standard Gauss-Seidl method. \\ -\ARROW The iteration method equation has the form: -\begin{align*} -x^{(k+1)} = (D+ \omega L)^{-1} ((1-\omega)D - \omega U)x^{(k)} + (D + \omega L)^{-1} \omega b -\end{align*} - - - - -\end{small} -\end{frame} - - - - -\begin{frame}\frametitle{SOR method, convergence} -\begin{small} - -\ARROW The main difficulty in the SOR method is the fact we need to choose the $\omega$ parameter. \\ -\ARROW One can easily prove that if the method is converging the $\omega \in \left(0, 2 \right)$. \\ -\ARROW This is necessary condition but it's not enough! \\ -\ARROW If the $A$ is symmetric and positively defined then the above condition is also sufficient! - - - - -\end{small} -\end{frame} - - - - - -\begin{frame}\frametitle{Conclusions} -\begin{small} - -\ARROW We learned more exact method of solving the linear system.\\ -\ARROW For big matrix we need to use iterative method which are not exact.\\ -\ARROW My personal experience: Did not have big enough matrices to really need to apply the iterative methods but this is field dependent! - - -\end{small} -\end{frame} - - - - -\backupbegin - -\begin{frame}\frametitle{Backup} - - -\end{frame} - - - - - - - -\backupend -\end{document} diff --git a/Lectures_my/NumMet/Lecture6/tikzfeynman.sty b/Lectures_my/NumMet/Lecture6/tikzfeynman.sty deleted file mode 100755 index 521fc65..0000000 --- a/Lectures_my/NumMet/Lecture6/tikzfeynman.sty +++ /dev/null @@ -1,43 +0,0 @@ -% 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}, -} - diff --git a/Lectures_my/NumMet/Lecture_template/Makefile b/Lectures_my/NumMet/Lecture_template/Makefile deleted file mode 100644 index e4cf8e8..0000000 --- a/Lectures_my/NumMet/Lecture_template/Makefile +++ /dev/null @@ -1,9 +0,0 @@ -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/Lecture_template/beamercolorthemeFlip.sty b/Lectures_my/NumMet/Lecture_template/beamercolorthemeFlip.sty deleted file mode 100755 index d6b9c50..0000000 --- a/Lectures_my/NumMet/Lecture_template/beamercolorthemeFlip.sty +++ /dev/null @@ -1,179 +0,0 @@ -% 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/Lecture_template/beamerinnerthemeFlip.sty b/Lectures_my/NumMet/Lecture_template/beamerinnerthemeFlip.sty deleted file mode 100755 index 8dc12a0..0000000 --- a/Lectures_my/NumMet/Lecture_template/beamerinnerthemeFlip.sty +++ /dev/null @@ -1,95 +0,0 @@ -% 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/Lecture_template/beamerouterthemeFlip.sty b/Lectures_my/NumMet/Lecture_template/beamerouterthemeFlip.sty deleted file mode 100755 index d12f6d6..0000000 --- a/Lectures_my/NumMet/Lecture_template/beamerouterthemeFlip.sty +++ /dev/null @@ -1,189 +0,0 @@ -% 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/Lecture_template/beamerouterthemedecolines.sty b/Lectures_my/NumMet/Lecture_template/beamerouterthemedecolines.sty deleted file mode 100755 index 669e493..0000000 --- a/Lectures_my/NumMet/Lecture_template/beamerouterthemedecolines.sty +++ /dev/null @@ -1,168 +0,0 @@ -% 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/Lecture_template/beamerthemeFlip.sty b/Lectures_my/NumMet/Lecture_template/beamerthemeFlip.sty deleted file mode 100755 index a615ff5..0000000 --- a/Lectures_my/NumMet/Lecture_template/beamerthemeFlip.sty +++ /dev/null @@ -1,59 +0,0 @@ -% 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/Lecture_template/images/BG_lower.png b/Lectures_my/NumMet/Lecture_template/images/BG_lower.png deleted file mode 100755 index 073034a..0000000 --- a/Lectures_my/NumMet/Lecture_template/images/BG_lower.png +++ /dev/null Binary files differ diff --git a/Lectures_my/NumMet/Lecture_template/images/bubble.gif b/Lectures_my/NumMet/Lecture_template/images/bubble.gif deleted file mode 100644 index ecff282..0000000 --- a/Lectures_my/NumMet/Lecture_template/images/bubble.gif +++ /dev/null Binary files differ diff --git a/Lectures_my/NumMet/Lecture_template/images/bubble.jpg b/Lectures_my/NumMet/Lecture_template/images/bubble.jpg deleted file mode 100644 index ceb584d..0000000 --- a/Lectures_my/NumMet/Lecture_template/images/bubble.jpg +++ /dev/null Binary files differ diff --git a/Lectures_my/NumMet/Lecture_template/images/bubble2.jpg b/Lectures_my/NumMet/Lecture_template/images/bubble2.jpg deleted file mode 100644 index 0fd03bb..0000000 --- a/Lectures_my/NumMet/Lecture_template/images/bubble2.jpg +++ /dev/null Binary files differ diff --git a/Lectures_my/NumMet/Lecture_template/images/uzh-transp.pdf b/Lectures_my/NumMet/Lecture_template/images/uzh-transp.pdf deleted file mode 100644 index 977da67..0000000 --- a/Lectures_my/NumMet/Lecture_template/images/uzh-transp.pdf +++ /dev/null Binary files differ diff --git a/Lectures_my/NumMet/Lecture_template/mchrzasz-blx.bib b/Lectures_my/NumMet/Lecture_template/mchrzasz-blx.bib deleted file mode 100644 index 9e405b3..0000000 --- a/Lectures_my/NumMet/Lecture_template/mchrzasz-blx.bib +++ /dev/null @@ -1,11 +0,0 @@ -@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/Lecture_template/mchrzasz.synctex.gz b/Lectures_my/NumMet/Lecture_template/mchrzasz.synctex.gz deleted file mode 100644 index d501b18..0000000 --- a/Lectures_my/NumMet/Lecture_template/mchrzasz.synctex.gz +++ /dev/null Binary files differ diff --git a/Lectures_my/NumMet/Lecture_template/mchrzasz.tex b/Lectures_my/NumMet/Lecture_template/mchrzasz.tex deleted file mode 100644 index 90d8dcd..0000000 --- a/Lectures_my/NumMet/Lecture_template/mchrzasz.tex +++ /dev/null @@ -1,304 +0,0 @@ -\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[Linear equation systems: exact methods]{Linear equation systems:exact methods} -\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 {Linear equation systems: exact methods} - \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{Linear eq. system} - -\ARROW This and the next lecture will focus on a well known problem. Solve the following equation system: -\begin{align*} -A \cdot x =b, -\end{align*} -\ARROWR $A = a_{ij} \in \mathbb{R}^{n\times n}$ and $\det(A) \neq 0$\\ -\ARROWR $b=b_i \in \mathbb{R}^n$.\\ -\ARROW The problem: Find the $x$ vector. - - - -\end{frame} - -\begin{frame}\frametitle{Error digression} -\begin{small} -\ARROW There is enormous amount of ways to solve the linear equation system.\\ -\ARROW The choice of one over the other of them should be gathered by the {\it condition} of the matrix $A$ denoted at $cond(A)$. -\ARROW If the $cond(A)$ is small we say that the problem is well conditioned, otherwise we say it's ill conditioned.\\ -\ARROW The {\it condition} relation is defined as: -\begin{align*} -cond(A) = \Vert A \Vert \cdot \Vert A^{-1} \Vert -\end{align*} -\ARROW Now there are many definitions of different norms... The most popular one (so-called ''column norm''): -\begin{align*} -\Vert A \vert_1 = \max_{1 \leq j \leq n} \sum_{i=1}^n \vert a_{i,j} \vert, -\end{align*} -where $n$ -is the dimension of $A$, $i,j$ are columns and rows numbers. - - - -\end{small} -\end{frame} - - - - - - -\backupbegin - -\begin{frame}\frametitle{Backup} - - -\end{frame} - - - - - - - -\backupend -\end{document} diff --git a/Lectures_my/NumMet/Lecture_template/tikzfeynman.sty b/Lectures_my/NumMet/Lecture_template/tikzfeynman.sty deleted file mode 100755 index 521fc65..0000000 --- a/Lectures_my/NumMet/Lecture_template/tikzfeynman.sty +++ /dev/null @@ -1,43 +0,0 @@ -% 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}, -} - diff --git a/Lectures_my/NumMet/plan.txt b/Lectures_my/NumMet/plan.txt deleted file mode 100644 index 22191c6..0000000 --- a/Lectures_my/NumMet/plan.txt +++ /dev/null @@ -1,37 +0,0 @@ -Lectures --------- - -Id Date Title Personnel -01 19.09. Introduction/Precision MC -02 21.09. Interpolation MC -03 26.09. Interpolation+Extrapolation DvD -04 05.10. Root Finding DvD -05 10.10. Solving Linear Equation (I) MC -06 12.10 Solving Linear Equation (II) MC -07 17.10 Solving Non-linear Equations DvD -08 31.10 Numerical Integration (I) MC -09 07.11 Numerical Integration (II) DvD -10 14.11 Ordinary Differential Eqs. (I) DvD -11 21.11 Ordinary Differential Eqs. (II) MC -12 28.11 Chaos Theorem MC -13 05.12 Function Minimization (I) DvD -14 12.12 Function Minimization (II) DvD - -Classes -------- - -Id Date Suggested Topic Personnel -01 28.09 Errors + Numers ? -02 03.10 Interpolation/Extrapolation ? -03 19.10 ? ? -04 24.10 ? ? -05 26.10 ? ? -06 02.10 ? ? -07 09.11 ? ? -08 16.11 ? ? -09 23.11 ? ? -10 30.11 ? ? -11 07.12 ? ? -12 14.12 ? ? -13 19.12 ? ? -44 21.12 ? ?