Merge branch 'master' of https://github.com/daHugen/SeminarSpezielleFunktionen

3 files changed, 131 insertions, 101 deletions

diff --git a/buch/papers/dreieck/images/beta.pdf b/buch/papers/dreieck/images/beta.pdf
index c3ab4f6..cd5ed80 100644
--- a/buch/papers/dreieck/images/beta.pdf
+++ b/buch/papers/dreieck/images/beta.pdf
diff --git a/buch/papers/dreieck/images/beta.tex b/buch/papers/dreieck/images/beta.tex
index 50509ee..f0ffdf0 100644
--- a/buch/papers/dreieck/images/beta.tex
+++ b/buch/papers/dreieck/images/beta.tex
@@ -23,7 +23,8 @@
 \definecolor{coloreight}{rgb}{0.0,0.8,0.8}
 \definecolor{colornine}{rgb}{0.0,0.8,0.2}
 \definecolor{colorten}{rgb}{0.2,0.4,0.0}
-\definecolor{coloreleven}{rgb}{1.0,0.8,0.4}
+\definecolor{coloreleven}{rgb}{0.6,1.0,0.0}
+\definecolor{colortwelve}{rgb}{1.0,0.8,0.4}
 
 \def\achsen{
 	\foreach \x in {0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9}{
@@ -47,24 +48,24 @@
 }
 
 \def\farbcoord#1#2{
-	({\dx*(0.7+((#1-1)/4)*0.27)},{\dx*(0.15+((#2-1)/4)*0.27)})
+	({\dx*(0.63+((#1)/5)*0.27)},{\dx*(0.18+((#2)/5)*0.27)})
 }
 \def\farbviereck{
-	\foreach \x in {1,2,3,4,5}{
-		\draw[color=gray!30] \farbcoord{\x}{1} -- \farbcoord{\x}{5};
-		\draw[color=gray!30] \farbcoord{1}{\x} -- \farbcoord{5}{\x};
+	\foreach \x in {1,2,3,4}{
+		\draw[color=gray!30] \farbcoord{\x}{0} -- \farbcoord{\x}{4};
+		\draw[color=gray!30] \farbcoord{0}{\x} -- \farbcoord{4}{\x};
 	}
-	\draw[->] \farbcoord{1}{1} -- \farbcoord{5.4}{1}
+	\draw[->] \farbcoord{0}{0} -- \farbcoord{4.4}{0}
 		coordinate[label={$a$}];
-	\draw[->] \farbcoord{1}{1} -- \farbcoord{1}{5.4}
+	\draw[->] \farbcoord{0}{0} -- \farbcoord{0}{4.4}
 		coordinate[label={left: $b$}];
-	\foreach \x in {1,2,3,4,5}{
-		\node[color=gray] at \farbcoord{5}{\x} [right] {\tiny $b=\x$};
-		\fill[color=white,opacity=0.7] 
-			\farbcoord{(\x-0.1)}{4.3}
-			rectangle
-			\farbcoord{(\x+0.1)}{5};
-		\node[color=gray] at \farbcoord{\x}{5} [left,rotate=90]
+	\foreach \x in {1,2,3,4}{
+		\node[color=gray] at \farbcoord{4}{\x} [right] {\tiny $b=\x$};
+		%\fill[color=white,opacity=0.7] 
+		%	\farbcoord{(\x-0.1)}{3.3}
+		%	rectangle
+		%	\farbcoord{(\x+0.1)}{4};
+		\node[color=gray] at \farbcoord{\x}{4} [right,rotate=90]
 			{\tiny $a=\x$};
 	}
 }
@@ -74,23 +75,26 @@
 
 \begin{tikzpicture}[>=latex,thick,scale=\skala]
 
-\def\dx{1}
+\def\dx{1.1}
 \def\dy{0.1}
 \def\opa{0.1}
 
-\def\betamax{4.2}
-
-\fill[color=colorone,opacity=\opa] (0,0) -- \betaaa -- (\dx,0) -- cycle;
-\fill[color=colortwo,opacity=\opa] (0,0) -- \betabb -- (\dx,0) -- cycle;
-\fill[color=colorthree,opacity=\opa] (0,0) -- \betacc -- (\dx,0) -- cycle;
-\fill[color=colorfour,opacity=\opa] (0,0) -- \betadd -- (\dx,0) -- cycle;
-\fill[color=colorfive,opacity=\opa] (0,0) -- \betaee -- (\dx,0) -- cycle;
-\fill[color=colorsix,opacity=\opa] (0,0) -- \betaff -- (\dx,0) -- cycle;
-\fill[color=colorseven,opacity=\opa] (0,0) -- \betagg -- (\dx,0) -- cycle;
-\fill[color=coloreight,opacity=\opa] (0,0) -- \betahh -- (\dx,0) -- cycle;
-\fill[color=colornine,opacity=\opa] (0,0) -- \betaii -- (\dx,0) -- cycle;
-\fill[color=colorten,opacity=\opa] (0,0) -- \betajj -- (\dx,0) -- cycle;
+\def\betamax{4.9}
+
+\begin{scope}
+\clip (0,0) rectangle ({1*\dx},{\betamax*\dy});
+\fill[color=colorone,opacity=\opa]    (0,0) -- \betaaa -- (\dx,0) -- cycle;
+\fill[color=colortwo,opacity=\opa]    (0,0) -- \betabb -- (\dx,0) -- cycle;
+\fill[color=colorthree,opacity=\opa]  (0,0) -- \betacc -- (\dx,0) -- cycle;
+\fill[color=colorfour,opacity=\opa]   (0,0) -- \betadd -- (\dx,0) -- cycle;
+\fill[color=colorfive,opacity=\opa]   (0,0) -- \betaee -- (\dx,0) -- cycle;
+\fill[color=colorsix,opacity=\opa]    (0,0) -- \betaff -- (\dx,0) -- cycle;
+\fill[color=colorseven,opacity=\opa]  (0,0) -- \betagg -- (\dx,0) -- cycle;
+\fill[color=coloreight,opacity=\opa]  (0,0) -- \betahh -- (\dx,0) -- cycle;
+\fill[color=colornine,opacity=\opa]   (0,0) -- \betaii -- (\dx,0) -- cycle;
+\fill[color=colorten,opacity=\opa]    (0,0) -- \betajj -- (\dx,0) -- cycle;
 \fill[color=coloreleven,opacity=\opa] (0,0) -- \betakk -- (\dx,0) -- cycle;
+\fill[color=colortwelve,opacity=\opa] (0,0) -- \betall -- (\dx,0) -- cycle;
 
 \draw[color=colorone]    \betaaa;
 \draw[color=colortwo]    \betabb;
@@ -103,11 +107,15 @@
 \draw[color=colornine]   \betaii;
 \draw[color=colorten]    \betajj;
 \draw[color=coloreleven] \betakk;
+\draw[color=colortwelve] \betall;
+
+\end{scope}
 
 \achsen
 
 \farbviereck
 
+\farbpunkt{\alphatwelve}{\betatwelve}{colortwelve}
 \farbpunkt{\alphaeleven}{\betaeleven}{coloreleven}
 \farbpunkt{\alphaten}{\betaten}{colorten}
 \farbpunkt{\alphanine}{\betanine}{colornine}
@@ -124,88 +132,102 @@
 \def\betamax{4.9}
 
 \begin{scope}[yshift=-0.6cm]
-\fill[color=colorone,opacity=\opa] (0,0) -- \betaaa -- (\dx,0) -- cycle;
-\fill[color=colortwo,opacity=\opa] (0,0) -- \betaab -- (\dx,0) -- cycle;
-\fill[color=colorthree,opacity=\opa] (0,0) -- \betaac -- (\dx,0) -- cycle;
-\fill[color=colorfour,opacity=\opa] (0,0) -- \betaad -- (\dx,0) -- cycle;
-\fill[color=colorfive,opacity=\opa] (0,0) -- \betaae -- (\dx,0) -- cycle;
-\fill[color=colorsix,opacity=\opa] (0,0) -- \betaaf -- (\dx,0) -- cycle;
-\fill[color=colorseven,opacity=\opa] (0,0) -- \betaag -- (\dx,0) -- cycle;
-\fill[color=coloreight,opacity=\opa] (0,0) -- \betaah -- (\dx,0) -- cycle;
-\fill[color=colornine,opacity=\opa] (0,0) -- \betaai -- (\dx,0) -- cycle;
-\fill[color=colorten,opacity=\opa] (0,0) -- \betaaj -- (\dx,0) -- cycle;
-\fill[color=coloreleven,opacity=\opa] (0,0) -- \betaak -- (\dx,0) -- cycle;
 
-\draw[color=colorone]    \betaaa;
-\draw[color=colortwo]    \betaab;
-\draw[color=colorthree]  \betaac;
-\draw[color=colorfour]   \betaad;
-\draw[color=colorfive]   \betaae;
-\draw[color=colorsix]    \betaaf;
-\draw[color=colorseven]  \betaag;
-\draw[color=coloreight]  \betaah;
-\draw[color=colornine]   \betaai;
-\draw[color=colorten]    \betaaj;
-\draw[color=coloreleven] \betaak;
+\begin{scope}
+\clip (0,0) rectangle ({1*\dx},{\betamax*\dy});
+\fill[color=colorone,opacity=\opa]    (0,0) -- \betaea -- (\dx,0) -- cycle;
+\fill[color=colortwo,opacity=\opa]    (0,0) -- \betaeb -- (\dx,0) -- cycle;
+\fill[color=colorthree,opacity=\opa]  (0,0) -- \betaec -- (\dx,0) -- cycle;
+\fill[color=colorfour,opacity=\opa]   (0,0) -- \betaed -- (\dx,0) -- cycle;
+\fill[color=colorfive,opacity=\opa]   (0,0) -- \betaee -- (\dx,0) -- cycle;
+\fill[color=colorsix,opacity=\opa]    (0,0) -- \betaef -- (\dx,0) -- cycle;
+\fill[color=colorseven,opacity=\opa]  (0,0) -- \betaeg -- (\dx,0) -- cycle;
+\fill[color=coloreight,opacity=\opa]  (0,0) -- \betaeh -- (\dx,0) -- cycle;
+\fill[color=colornine,opacity=\opa]   (0,0) -- \betaei -- (\dx,0) -- cycle;
+\fill[color=colorten,opacity=\opa]    (0,0) -- \betaej -- (\dx,0) -- cycle;
+\fill[color=coloreleven,opacity=\opa] (0,0) -- \betaek -- (\dx,0) -- cycle;
+\fill[color=colortwelve,opacity=\opa] (0,0) -- \betael -- (\dx,0) -- cycle;
+
+\draw[color=colorone]    \betaea;
+\draw[color=colortwo]    \betaeb;
+\draw[color=colorthree]  \betaec;
+\draw[color=colorfour]   \betaed;
+\draw[color=colorfive]   \betaee;
+\draw[color=colorsix]    \betaef;
+\draw[color=colorseven]  \betaeg;
+\draw[color=coloreight]  \betaeh;
+\draw[color=colornine]   \betaei;
+\draw[color=colorten]    \betaej;
+\draw[color=coloreleven] \betaek;
+\draw[color=colortwelve] \betael;
+\end{scope}
 
 \achsen
 
 \farbviereck
 
-\farbpunkt{\alphaone}{\betaeleven}{coloreleven}
-\farbpunkt{\alphaone}{\betaten}{colorten}
-\farbpunkt{\alphaone}{\betanine}{colornine}
-\farbpunkt{\alphaone}{\betaeight}{coloreight}
-\farbpunkt{\alphaone}{\betaseven}{colorseven}
-\farbpunkt{\alphaone}{\betasix}{colorsix}
-\farbpunkt{\alphaone}{\betafive}{colorfive}
-\farbpunkt{\alphaone}{\betafour}{colorfour}
-\farbpunkt{\alphaone}{\betathree}{colorthree}
-\farbpunkt{\alphaone}{\betatwo}{colortwo}
-\farbpunkt{\alphaone}{\betaone}{colorone}
+\farbpunkt{\alphafive}{\betatwelve}{colortwelve}
+\farbpunkt{\alphafive}{\betaeleven}{coloreleven}
+\farbpunkt{\alphafive}{\betaten}{colorten}
+\farbpunkt{\alphafive}{\betanine}{colornine}
+\farbpunkt{\alphafive}{\betaeight}{coloreight}
+\farbpunkt{\alphafive}{\betaseven}{colorseven}
+\farbpunkt{\alphafive}{\betasix}{colorsix}
+\farbpunkt{\alphafive}{\betafive}{colorfive}
+\farbpunkt{\alphafive}{\betafour}{colorfour}
+\farbpunkt{\alphafive}{\betathree}{colorthree}
+\farbpunkt{\alphafive}{\betatwo}{colortwo}
+\farbpunkt{\alphafive}{\betaone}{colorone}
 
 \end{scope}
 
 \begin{scope}[yshift=-1.2cm]
-\fill[color=colorone,opacity=\opa]    (0,0) -- \betaak -- (\dx,0) -- cycle;
-\fill[color=colortwo,opacity=\opa]    (0,0) -- \betabk -- (\dx,0) -- cycle;
-\fill[color=colorthree,opacity=\opa]  (0,0) -- \betack -- (\dx,0) -- cycle;
-\fill[color=colorfour,opacity=\opa]   (0,0) -- \betadk -- (\dx,0) -- cycle;
-\fill[color=colorfive,opacity=\opa]   (0,0) -- \betaek -- (\dx,0) -- cycle;
-\fill[color=colorsix,opacity=\opa]    (0,0) -- \betafk -- (\dx,0) -- cycle;
-\fill[color=colorseven,opacity=\opa]  (0,0) -- \betagk -- (\dx,0) -- cycle;
-\fill[color=coloreight,opacity=\opa]  (0,0) -- \betahk -- (\dx,0) -- cycle;
-\fill[color=colornine,opacity=\opa]   (0,0) -- \betaik -- (\dx,0) -- cycle;
-\fill[color=colorten,opacity=\opa]    (0,0) -- \betajk -- (\dx,0) -- cycle;
-\fill[color=coloreleven,opacity=\opa] (0,0) -- \betakk -- (\dx,0) -- cycle;
 
-\draw[color=colorone]    \betaak;
-\draw[color=colortwo]    \betabk;
-\draw[color=colorthree]  \betack;
-\draw[color=colorfour]   \betadk;
-\draw[color=colorfive]   \betaek;
-\draw[color=colorsix]    \betafk;
-\draw[color=colorseven]  \betagk;
-\draw[color=coloreight]  \betahk;
-\draw[color=colornine]   \betaik;
-\draw[color=colorten]    \betajk;
-\draw[color=coloreleven] \betakk;
+\begin{scope}
+\clip (0,0) rectangle ({1*\dx},{\betamax*\dy});
+\fill[color=colorone,opacity=\opa]    (0,0) -- \betaal -- (\dx,0) -- cycle;
+\fill[color=colortwo,opacity=\opa]    (0,0) -- \betabl -- (\dx,0) -- cycle;
+\fill[color=colorthree,opacity=\opa]  (0,0) -- \betacl -- (\dx,0) -- cycle;
+\fill[color=colorfour,opacity=\opa]   (0,0) -- \betadl -- (\dx,0) -- cycle;
+\fill[color=colorfive,opacity=\opa]   (0,0) -- \betael -- (\dx,0) -- cycle;
+\fill[color=colorsix,opacity=\opa]    (0,0) -- \betafl -- (\dx,0) -- cycle;
+\fill[color=colorseven,opacity=\opa]  (0,0) -- \betagl -- (\dx,0) -- cycle;
+\fill[color=coloreight,opacity=\opa]  (0,0) -- \betahl -- (\dx,0) -- cycle;
+\fill[color=colornine,opacity=\opa]   (0,0) -- \betail -- (\dx,0) -- cycle;
+\fill[color=colorten,opacity=\opa]    (0,0) -- \betajl -- (\dx,0) -- cycle;
+\fill[color=coloreleven,opacity=\opa] (0,0) -- \betakl -- (\dx,0) -- cycle;
+\fill[color=colortwelve,opacity=\opa] (0,0) -- \betall -- (\dx,0) -- cycle;
+
+\draw[color=colorone]    \betaal;
+\draw[color=colortwo]    \betabl;
+\draw[color=colorthree]  \betacl;
+\draw[color=colorfour]   \betadl;
+\draw[color=colorfive]   \betael;
+\draw[color=colorsix]    \betafl;
+\draw[color=colorseven]  \betagl;
+\draw[color=coloreight]  \betahl;
+\draw[color=colornine]   \betail;
+\draw[color=colorten]    \betajl;
+\draw[color=coloreleven] \betakl;
+\draw[color=colortwelve] \betall;
+\end{scope}
 
 \achsen
 
 \farbviereck
 
-\farbpunkt{\alphaeleven}{\betaeleven}{coloreleven}
-\farbpunkt{\alphaten}{\betaeleven}{colorten}
-\farbpunkt{\alphanine}{\betaeleven}{colornine}
-\farbpunkt{\alphaeight}{\betaeleven}{coloreight}
-\farbpunkt{\alphaseven}{\betaeleven}{colorseven}
-\farbpunkt{\alphasix}{\betaeleven}{colorsix}
-\farbpunkt{\alphafive}{\betaeleven}{colorfive}
-\farbpunkt{\alphafour}{\betaeleven}{colorfour}
-\farbpunkt{\alphathree}{\betaeleven}{colorthree}
-\farbpunkt{\alphatwo}{\betaeleven}{colortwo}
-\farbpunkt{\alphaone}{\betaeleven}{colorone}
+\farbpunkt{\alphatwelve}{\betatwelve}{colortwelve}
+\farbpunkt{\alphaeleven}{\betatwelve}{coloreleven}
+\farbpunkt{\alphaten}{\betatwelve}{colorten}
+\farbpunkt{\alphanine}{\betatwelve}{colornine}
+\farbpunkt{\alphaeight}{\betatwelve}{coloreight}
+\farbpunkt{\alphaseven}{\betatwelve}{colorseven}
+\farbpunkt{\alphasix}{\betatwelve}{colorsix}
+\farbpunkt{\alphafive}{\betatwelve}{colorfive}
+\farbpunkt{\alphafour}{\betatwelve}{colorfour}
+\farbpunkt{\alphathree}{\betatwelve}{colorthree}
+\farbpunkt{\alphatwo}{\betatwelve}{colortwo}
+\farbpunkt{\alphaone}{\betatwelve}{colorone}
 
 \end{scope}
 
diff --git a/buch/papers/dreieck/images/betadist.m b/buch/papers/dreieck/images/betadist.m
index 9ff78ed..5b466a6 100644
--- a/buch/papers/dreieck/images/betadist.m
+++ b/buch/papers/dreieck/images/betadist.m
@@ -5,24 +5,32 @@
 #
 global N;
 N = 201;
-global n;
-n = 11;
+global nmin;
+global nmax;
+nmin = -4;
+nmax = 7;
+n = nmax - nmin + 1
+A = 3;
 
-t = (0:n-1) / (n-1)
-alpha = 1 + 4 * t.^2
+t = (nmin:nmax) / nmax;
+alpha = 1 + A * t .* abs(t)
+#alpha(1) = 0.01;
 
 #alpha = [ 1, 1.03, 1.05, 1.1, 1.25, 1.5, 2, 2.5, 3, 4, 5 ];
 beta = alpha;
 names = [ "one"; "two"; "three"; "four"; "five"; "six"; "seven"; "eight";
-	  "nine"; "ten"; "eleven" ]
+	  "nine"; "ten"; "eleven"; "twelve" ]
 
 function retval = Beta(a, b, x)
 	retval = x^(a-1) * (1-x)^(b-1) / beta(a, b);
+	if (retval > 100)
+		retval = 100
+	end
 end
 
 function plotbeta(fn, a, b, name)
 	global N;
-	fprintf(fn, "\\def\\beta%s{\n", name);
+	fprintf(fn, "\\def\\beta%s{\n", strtrim(name));
 	fprintf(fn, "\t({%.4f*\\dx},{%.4f*\\dy})", 0, Beta(a, b, 0));
 	for x = (1:N-1)/(N-1)
 		X = (1-cos(pi * x))/2;
@@ -35,8 +43,8 @@ end
 fn = fopen("betapaths.tex", "w");
 
 for i = (1:n)
-	fprintf(fn, "\\def\\alpha%s{%f}\n", names(i,:), alpha(i));
-	fprintf(fn, "\\def\\beta%s{%f}\n", names(i,:), beta(i));
+	fprintf(fn, "\\def\\alpha%s{%f}\n", strtrim(names(i,:)), alpha(i));
+	fprintf(fn, "\\def\\beta%s{%f}\n", strtrim(names(i,:)), beta(i));
 end
 
 for i = (1:n)