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authorLordMcFungus <mceagle117@gmail.com>2022-07-22 21:28:45 +0200
committerGitHub <noreply@github.com>2022-07-22 21:28:45 +0200
commit23f17598c1742c70f442b94044a20aa821022c5a (patch)
treea945540ee6a4e86b37df2f01e3a91584b4797c4f /buch/chapters/040-rekursion/images
parentMerge pull request #2 from AndreasFMueller/master (diff)
parentMerge pull request #25 from JODBaer/master (diff)
downloadSeminarSpezielleFunktionen-23f17598c1742c70f442b94044a20aa821022c5a.tar.gz
SeminarSpezielleFunktionen-23f17598c1742c70f442b94044a20aa821022c5a.zip
Merge pull request #3 from AndreasFMueller/master
update
Diffstat (limited to 'buch/chapters/040-rekursion/images')
-rw-r--r--buch/chapters/040-rekursion/images/0f1.cpp94
-rw-r--r--buch/chapters/040-rekursion/images/0f1.pdfbin0 -> 49497 bytes
-rw-r--r--buch/chapters/040-rekursion/images/0f1.tex86
-rw-r--r--buch/chapters/040-rekursion/images/Makefile16
-rw-r--r--buch/chapters/040-rekursion/images/loggammaplot.m43
-rw-r--r--buch/chapters/040-rekursion/images/loggammaplot.pdfbin0 -> 30943 bytes
-rw-r--r--buch/chapters/040-rekursion/images/loggammaplot.tex89
-rw-r--r--buch/chapters/040-rekursion/images/order.pdfbin32692 -> 32688 bytes
-rw-r--r--buch/chapters/040-rekursion/images/order.tex2
9 files changed, 328 insertions, 2 deletions
diff --git a/buch/chapters/040-rekursion/images/0f1.cpp b/buch/chapters/040-rekursion/images/0f1.cpp
new file mode 100644
index 0000000..24ca3f1
--- /dev/null
+++ b/buch/chapters/040-rekursion/images/0f1.cpp
@@ -0,0 +1,94 @@
+/*
+ * 0f1.cpp
+ *
+ * (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+ */
+#include <cstring>
+#include <cstdio>
+#include <cstdlib>
+#include <cmath>
+#include <string>
+#include <iostream>
+#include <fstream>
+
+static int N = 100;
+static double xmin = -50;
+static double xmax = 30;
+static int points = 200;
+
+double f(double b, double x) {
+ double s = 1;
+ double p = 1;
+ for (int k = 1; k < N; k++) {
+ p = p * x / (k * (b + k - 1.));
+ s += p;
+ }
+ return s;
+}
+
+typedef std::pair<double, double> point_t;
+
+point_t F(double b, double x) {
+ return std::make_pair(x, f(b, x));
+}
+
+std::string ff(double f) {
+ if (f > 1000) { f = 1000; }
+ if (f < -1000) { f = -1000; }
+ char b[128];
+ snprintf(b, sizeof(b), "%.4f", f);
+ return std::string(b);
+}
+
+std::ostream& operator<<(std::ostream& out, const point_t& p) {
+ char b[128];
+ out << "({" << ff(p.first) << "*\\dx},{" << ff(p.second) << "*\\dy})";
+ return out;
+}
+
+void curve(std::ostream& out, double b, const std::string& name) {
+ double h = (xmax - xmin) / points;
+ out << "\\def\\kurve" << name << "{";
+ out << std::endl << "\t" << F(b, xmin);
+ for (int i = 1; i <= points; i++) {
+ double x = xmin + h * i;
+ out << std::endl << "\t-- " << F(b, x);
+ }
+ out << std::endl;
+ out << "}" << std::endl;
+}
+
+int main(int argc, char *argv[]) {
+ std::ofstream out("0f1data.tex");
+
+ double s = 13/(xmax-xmin);
+ out << "\\def\\dx{" << ff(s) << "}" << std::endl;
+ out << "\\def\\dy{" << ff(s) << "}" << std::endl;
+ out << "\\def\\xmin{" << ff(s * xmin) << "}" << std::endl;
+ out << "\\def\\xmax{" << ff(s * xmax) << "}" << std::endl;
+
+ curve(out, 0.5, "one");
+ curve(out, 1.5, "two");
+ curve(out, 2.5, "three");
+ curve(out, 3.5, "four");
+ curve(out, 4.5, "five");
+ curve(out, 5.5, "six");
+ curve(out, 6.5, "seven");
+ curve(out, 7.5, "eight");
+ curve(out, 8.5, "nine");
+ curve(out, 9.5, "ten");
+
+ curve(out,-0.5, "none");
+ curve(out,-1.5, "ntwo");
+ curve(out,-2.5, "nthree");
+ curve(out,-3.5, "nfour");
+ curve(out,-4.5, "nfive");
+ curve(out,-5.5, "nsix");
+ curve(out,-6.5, "nseven");
+ curve(out,-7.5, "neight");
+ curve(out,-8.5, "nnine");
+ curve(out,-9.5, "nten");
+
+ out.close();
+ return EXIT_SUCCESS;
+}
diff --git a/buch/chapters/040-rekursion/images/0f1.pdf b/buch/chapters/040-rekursion/images/0f1.pdf
new file mode 100644
index 0000000..2c35813
--- /dev/null
+++ b/buch/chapters/040-rekursion/images/0f1.pdf
Binary files differ
diff --git a/buch/chapters/040-rekursion/images/0f1.tex b/buch/chapters/040-rekursion/images/0f1.tex
new file mode 100644
index 0000000..1bc8b87
--- /dev/null
+++ b/buch/chapters/040-rekursion/images/0f1.tex
@@ -0,0 +1,86 @@
+%
+% 0f1.tex -- template for standalon tikz images
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math}
+\begin{document}
+\def\skala{1}
+\input{0f1data.tex}
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\begin{scope}
+\clip (\xmin,-1) rectangle (\xmax,5);
+\draw[color=blue!5!red,line width=1.4pt] \kurveone;
+\draw[color=blue!16!red,line width=1.4pt] \kurvetwo;
+\draw[color=blue!26!red,line width=1.4pt] \kurvethree;
+\draw[color=blue!37!red,line width=1.4pt] \kurvefour;
+\draw[color=blue!47!red,line width=1.4pt] \kurvefive;
+\draw[color=blue!57!red,line width=1.4pt] \kurvesix;
+\draw[color=blue!68!red,line width=1.4pt] \kurveseven;
+\draw[color=blue!78!red,line width=1.4pt] \kurveeight;
+\draw[color=blue!89!red,line width=1.4pt] \kurvenine;
+\draw[color=blue!100!red,line width=1.4pt] \kurveten;
+\def\ds{0.4}
+\begin{scope}[yshift=0.5cm]
+\node[color=blue!5!red] at (\xmin,{1*\ds}) [right] {$\alpha=0.5$};
+\node[color=blue!16!red] at (\xmin,{2*\ds}) [right] {$\alpha=1.5$};
+\node[color=blue!26!red] at (\xmin,{3*\ds}) [right] {$\alpha=2.5$};
+\node[color=blue!37!red] at (\xmin,{4*\ds}) [right] {$\alpha=2.5$};
+\node[color=blue!47!red] at (\xmin,{5*\ds}) [right] {$\alpha=3.5$};
+\node[color=blue!57!red] at (\xmin,{6*\ds}) [right] {$\alpha=5.5$};
+\node[color=blue!68!red] at (\xmin,{7*\ds}) [right] {$\alpha=6.5$};
+\node[color=blue!78!red] at (\xmin,{8*\ds}) [right] {$\alpha=7.5$};
+\node[color=blue!89!red] at (\xmin,{9*\ds}) [right] {$\alpha=8.5$};
+\node[color=blue!100!red]at (\xmin,{10*\ds}) [right] {$\alpha=9.5$};
+\end{scope}
+\node at (-1.7,4.5) {$\displaystyle
+y=\mathstrut_0F_1\biggl(\begin{matrix}\text{---}\\\alpha\end{matrix};x\biggr)$};
+\end{scope}
+
+\draw[->] (\xmin-0.2,0) -- (\xmax+0.3,0) coordinate[label=$x$];
+\draw[->] (0,-0.5) -- (0,5.3) coordinate[label={right:$y$}];
+
+\begin{scope}[yshift=-6.5cm]
+\begin{scope}
+\clip (\xmin,-5) rectangle (\xmax,5);
+
+\draw[color=darkgreen!5!red,line width=1.4pt] \kurvenone;
+\draw[color=darkgreen!16!red,line width=1.4pt] \kurventwo;
+\draw[color=darkgreen!26!red,line width=1.4pt] \kurventhree;
+\draw[color=darkgreen!37!red,line width=1.4pt] \kurvenfour;
+\draw[color=darkgreen!47!red,line width=1.4pt] \kurvenfive;
+\draw[color=darkgreen!57!red,line width=1.4pt] \kurvensix;
+\draw[color=darkgreen!68!red,line width=1.4pt] \kurvenseven;
+\draw[color=darkgreen!78!red,line width=1.4pt] \kurveneight;
+\draw[color=darkgreen!89!red,line width=1.4pt] \kurvennine;
+\draw[color=darkgreen!100!red,line width=1.4pt] \kurventen;
+\end{scope}
+
+\draw[->] (\xmin-0.2,0) -- (\xmax+0.3,0) coordinate[label=$x$];
+\draw[->] (0,-5.2) -- (0,5.3) coordinate[label={right:$y$}];
+\def\ds{-0.4}
+\begin{scope}[yshift=-0.5cm]
+\node[color=darkgreen!5!red] at (\xmax,{1*\ds}) [left] {$\alpha=-0.5$};
+\node[color=darkgreen!16!red] at (\xmax,{2*\ds}) [left] {$\alpha=-1.5$};
+\node[color=darkgreen!26!red] at (\xmax,{3*\ds}) [left] {$\alpha=-2.5$};
+\node[color=darkgreen!37!red] at (\xmax,{4*\ds}) [left] {$\alpha=-2.5$};
+\node[color=darkgreen!47!red] at (\xmax,{5*\ds}) [left] {$\alpha=-3.5$};
+\node[color=darkgreen!57!red] at (\xmax,{6*\ds}) [left] {$\alpha=-5.5$};
+\node[color=darkgreen!68!red] at (\xmax,{7*\ds}) [left] {$\alpha=-6.5$};
+\node[color=darkgreen!78!red] at (\xmax,{8*\ds}) [left] {$\alpha=-7.5$};
+\node[color=darkgreen!89!red] at (\xmax,{9*\ds}) [left] {$\alpha=-8.5$};
+\node[color=darkgreen!100!red]at (\xmax,{10*\ds}) [left] {$\alpha=-9.5$};
+\end{scope}
+\end{scope}
+
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/chapters/040-rekursion/images/Makefile b/buch/chapters/040-rekursion/images/Makefile
index 86dfa1e..54ed23b 100644
--- a/buch/chapters/040-rekursion/images/Makefile
+++ b/buch/chapters/040-rekursion/images/Makefile
@@ -3,7 +3,8 @@
#
# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
#
-all: gammaplot.pdf fibonacci.pdf order.pdf beta.pdf
+all: gammaplot.pdf fibonacci.pdf order.pdf beta.pdf loggammaplot.pdf \
+ 0f1.pdf
gammaplot.pdf: gammaplot.tex gammapaths.tex
pdflatex gammaplot.tex
@@ -29,4 +30,17 @@ beta.pdf: beta.tex betapaths.tex
betapaths.tex: betadist.m
octave betadist.m
+loggammaplot.pdf: loggammaplot.tex loggammadata.tex
+ pdflatex loggammaplot.tex
+loggammadata.tex: loggammaplot.m
+ octave loggammaplot.m
+
+0f1: 0f1.cpp
+ g++ -O -Wall -g -o 0f1 0f1.cpp
+
+0f1data.tex: 0f1
+ ./0f1
+
+0f1.pdf: 0f1.tex 0f1data.tex
+ pdflatex 0f1.tex
diff --git a/buch/chapters/040-rekursion/images/loggammaplot.m b/buch/chapters/040-rekursion/images/loggammaplot.m
new file mode 100644
index 0000000..5456e4f
--- /dev/null
+++ b/buch/chapters/040-rekursion/images/loggammaplot.m
@@ -0,0 +1,43 @@
+#
+# loggammaplot.m
+#
+# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+xmax = 10;
+xmin = 0.1;
+N = 500;
+
+fn = fopen("loggammadata.tex", "w");
+
+fprintf(fn, "\\def\\loggammapath{\n ({%.4f*\\dx},{%.4f*\\dy})",
+ xmax, log(gamma(xmax)));
+xstep = (xmax - 1) / N;
+for x = (xmax:-xstep:1)
+ fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", x, log(gamma(x)));
+endfor
+for k = (0:0.2:10)
+ x = exp(-k);
+ fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", x, log(gamma(x)));
+endfor
+fprintf(fn, "\n}\n");
+
+function retval = lgp(fn, x0, name)
+ fprintf(fn, "\\def\\loggammaplot%s{\n", name);
+ fprintf(fn, "\\draw[color=red,line width=1pt] ");
+ for k = (-7:0.1:7)
+ x = x0 + 0.5 * tanh(k);
+ if (k > -5)
+ fprintf(fn, "\n\t-- ");
+ end
+ fprintf(fn, "({%.4f*\\dx},{%.4f*\\dy})", x, log(gamma(x)));
+ endfor
+ fprintf(fn, ";\n}\n");
+endfunction
+
+lgp(fn, -0.5, "zero");
+lgp(fn, -1.5, "one");
+lgp(fn, -2.5, "two");
+lgp(fn, -3.5, "three");
+lgp(fn, -4.5, "four");
+
+fclose(fn);
diff --git a/buch/chapters/040-rekursion/images/loggammaplot.pdf b/buch/chapters/040-rekursion/images/loggammaplot.pdf
new file mode 100644
index 0000000..a2963f2
--- /dev/null
+++ b/buch/chapters/040-rekursion/images/loggammaplot.pdf
Binary files differ
diff --git a/buch/chapters/040-rekursion/images/loggammaplot.tex b/buch/chapters/040-rekursion/images/loggammaplot.tex
new file mode 100644
index 0000000..8ca4e1c
--- /dev/null
+++ b/buch/chapters/040-rekursion/images/loggammaplot.tex
@@ -0,0 +1,89 @@
+%
+% tikztemplate.tex -- template for standalon tikz images
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math}
+\begin{document}
+\def\skala{1}
+\input{loggammadata.tex}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+% add image content here
+
+\def\dx{1}
+\def\dy{0.6}
+\def\xmax{8}
+\def\xmin{-4.9}
+\def\ymax{8}
+\def\ymin{-3.1}
+
+\fill[color=blue!20] ({\xmin*\dx},{\ymin*\dy}) rectangle ({-4*\dx},{\ymax*\dy});
+\fill[color=blue!20] ({-3*\dx},{\ymin*\dy}) rectangle ({-2*\dx},{\ymax*\dy});
+\fill[color=blue!20] ({-1*\dx},{\ymin*\dy}) rectangle ({-0*\dx},{\ymax*\dy});
+
+\draw[->] ({\xmin*\dx-0.1},0) -- ({\xmax*\dx+0.3},0)
+ coordinate[label={$x$}];
+\draw[->] (0,{\ymin*\dy-0.1}) -- (0,{\ymax*\dy+0.3})
+ coordinate[label={right:$y$}];
+
+\begin{scope}
+\clip ({\xmin*\dx},{\ymin*\dy}) rectangle ({\xmax*\dx},{\ymax*\dy});
+
+\foreach \x in {-1,-2,-3,-4}{
+ \draw[color=blue,line width=0.3pt]
+ ({\x*\dx},{\ymin*\dy}) -- ({\x*\dx},{\ymax*\dy});
+}
+
+\draw[color=red,line width=1pt] \loggammapath;
+
+\loggammaplotzero
+\loggammaplotone
+\loggammaplottwo
+\loggammaplotthree
+\loggammaplotfour
+
+\end{scope}
+
+\foreach \y in {0.1,10,100,1000,1000}{
+ \draw[line width=0.3pt]
+ ({\xmin*\dx},{ln(\y)*\dy})
+ --
+ ({\xmax*\dx},{ln(\y)*\dy}) ;
+}
+
+\foreach \x in {1,...,8}{
+ \draw ({\x*\dx},{-0.05}) -- ({\x*\dx},{0.05});
+ \node at ({\x*\dx},0) [below] {$\x$};
+}
+
+\foreach \x in {-1,...,-4}{
+ \draw ({\x*\dx},{-0.05}) -- ({\x*\dx},{0.05});
+}
+\foreach \x in {-1,...,-3}{
+ \node at ({\x*\dx},0) [below right] {$\x$};
+}
+\node at ({-4*\dx},0) [below left] {$-4$};
+
+\def\htick#1#2{
+ \draw (-0.05,{ln(#1)*\dy}) -- (0.05,{ln(#1)*\dy});
+ \node at (0,{ln(#1)*\dy}) [above right] {#2};
+}
+
+\htick{10}{$10^1$}
+\htick{100}{$10^2$}
+\htick{1000}{$10^3$}
+\htick{0.1}{$10^{-1}$}
+
+\node[color=red] at ({3*\dx},{ln(30)*\dy}) {$y=\log|\Gamma(x)|$};
+
+
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/chapters/040-rekursion/images/order.pdf b/buch/chapters/040-rekursion/images/order.pdf
index cc175a9..88b2b08 100644
--- a/buch/chapters/040-rekursion/images/order.pdf
+++ b/buch/chapters/040-rekursion/images/order.pdf
Binary files differ
diff --git a/buch/chapters/040-rekursion/images/order.tex b/buch/chapters/040-rekursion/images/order.tex
index 9a2511c..0284735 100644
--- a/buch/chapters/040-rekursion/images/order.tex
+++ b/buch/chapters/040-rekursion/images/order.tex
@@ -65,7 +65,7 @@
\node at ({-0.1/\skala},{\y*\dy}) [left] {$\y$};
}
-\node[color=darkgreen] at (0.65,{0.5*\dy}) [above,rotate=55] {$k=7$};
+\node[color=darkgreen] at ({0.64*\dx},{0.56*\dy}) [rotate=42] {$k=7$};
\begin{scope}[yshift=-0.7cm]
\def\dy{0.125}