many changes in the orthogonality chapter

5 files changed, 148 insertions, 1 deletions

diff --git a/buch/chapters/070-orthogonalitaet/images/Makefile b/buch/chapters/070-orthogonalitaet/images/Makefile
index efe5d36..83f6762 100644
--- a/buch/chapters/070-orthogonalitaet/images/Makefile
+++ b/buch/chapters/070-orthogonalitaet/images/Makefile
@@ -4,7 +4,7 @@
 #
 # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
 #
-all:	legendre.pdf orthogonal.pdf weight.pdf jacobi.pdf
+all:	legendre.pdf orthogonal.pdf weight.pdf jacobi.pdf laguerre.pdf
 
 legendrepaths.tex:	legendre.m
 	octave legendre.m
@@ -22,6 +22,11 @@ weightfunction.tex:	weight.m
 jacobi:	jacobi.cpp
 	g++ --std=c++11 -O -Wall -g -o jacobi jacobi.cpp
 
+laguerre.pdf:	laguerre.tex laguerrepaths.tex
+	pdflatex laguerre.tex
+laguerrepaths.tex:	laguerre.m
+	octave laguerre.m
+
 jacobipaths.tex:	jacobi Makefile
 	./jacobi --a=0 --b=0 --prefix=legendre --outfile=jacobipaths.tex
 	./jacobi --a=1 --b=0 --degree=14 --prefix=aone >> jacobipaths.tex
diff --git a/buch/chapters/070-orthogonalitaet/images/jacobi.pdf b/buch/chapters/070-orthogonalitaet/images/jacobi.pdf
index d1977f0..7fdc702 100644
--- a/buch/chapters/070-orthogonalitaet/images/jacobi.pdf
+++ b/buch/chapters/070-orthogonalitaet/images/jacobi.pdf
diff --git a/buch/chapters/070-orthogonalitaet/images/laguerre.m b/buch/chapters/070-orthogonalitaet/images/laguerre.m
new file mode 100644
index 0000000..0a9c18c
--- /dev/null
+++ b/buch/chapters/070-orthogonalitaet/images/laguerre.m
@@ -0,0 +1,55 @@
+#
+# laguerre.m
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+pkg load miscellaneous
+global N;
+N = 120;
+
+function retval = laguerre(n, x)
+	s = 1;
+	p = 1;
+	if (n == 0)
+		retval = p;
+	else
+		for k = (1:n)
+			p = p * x * (-n-1+k) / (k * k);
+			s = s + p;
+		endfor
+		retval = s;
+	end
+endfunction
+
+function retval = laguerrepath(fn, n, name)
+	global N;
+	h = 12 / N;
+	fprintf(fn, "\\def\\laguerre%s{\n", name)
+	fprintf(fn, "\t   ({%.5f*\\dx},{%.5f*\\dy})", 0, 1);
+	for i = (1:N)
+		x = h * i;
+		y = laguerre(n, x);
+		if (abs(y) > 100)
+			y = 100 * sign(y);
+		end
+		fprintf(fn, "\n\t-- ({%.5f*\\dx},{%.5f*\\dy})", x, y);
+	endfor
+	fprintf(fn, "\n}\n");
+endfunction
+
+fn = fopen("laguerrepaths.tex", "w");
+
+laguerrepath(fn,  0, "zero");
+laguerrepath(fn,  1, "one");
+laguerrepath(fn,  2, "two");
+laguerrepath(fn,  3, "three");
+laguerrepath(fn,  4, "four");
+laguerrepath(fn,  5, "five");
+laguerrepath(fn,  6, "six");
+laguerrepath(fn,  7, "seven");
+laguerrepath(fn,  8, "eight");
+laguerrepath(fn,  9, "nine");
+
+fclose(fn);
+
+
diff --git a/buch/chapters/070-orthogonalitaet/images/laguerre.pdf b/buch/chapters/070-orthogonalitaet/images/laguerre.pdf
new file mode 100644
index 0000000..c16698e
--- /dev/null
+++ b/buch/chapters/070-orthogonalitaet/images/laguerre.pdf
diff --git a/buch/chapters/070-orthogonalitaet/images/laguerre.tex b/buch/chapters/070-orthogonalitaet/images/laguerre.tex
new file mode 100644
index 0000000..537c4af
--- /dev/null
+++ b/buch/chapters/070-orthogonalitaet/images/laguerre.tex
@@ -0,0 +1,87 @@
+%
+% laguerre.tex -- Laguerre-Polynome
+%
+% (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\dx{1}
+\def\dy{0.33333}
+\input{laguerrepaths.tex}
+
+\definecolor{fone}{rgb}{1,0,0}
+\definecolor{ftwo}{rgb}{1.0,0,0.8}
+\definecolor{fthree}{rgb}{0.8,0,1}
+\definecolor{ffour}{rgb}{0,0,1}
+\definecolor{ffive}{rgb}{0,0.8,1}
+\definecolor{fsix}{rgb}{0,1,1}
+\definecolor{fseven}{rgb}{0,0.6,0}
+\definecolor{feight}{rgb}{0.2,1,0.6}
+\definecolor{fnine}{rgb}{0.6,0.8,0.2}
+\definecolor{ften}{rgb}{1,0.4,0}
+
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+
+\begin{scope}
+\clip (0,-5) rectangle (12,5);
+
+\draw[color=fone] \laguerrezero;
+\draw[color=ftwo] \laguerreone;
+\draw[color=fthree] \laguerretwo;
+\draw[color=ffour] \laguerrethree;
+\draw[color=ffive] \laguerrefour;
+\draw[color=fsix] \laguerrefive;
+\draw[color=fseven] \laguerresix;
+\draw[color=feight] \laguerreseven;
+\draw[color=fnine] \laguerreeight;
+\draw[color=ften] \laguerrenine;
+
+\end{scope}
+
+\draw[->] (-0.1,0) -- (12.4,0) coordinate[label={$x$}];
+\draw[->] (0,{-5.1}) -- (0,{5.3}) coordinate[label={$y$}];
+
+\def\marke#1#2{
+	\node[color=#1] at (0.5,{5-0.42*#2}) [right] {$n=#2$};
+}
+
+\marke{fone}{0}
+\marke{ftwo}{1}
+\marke{fthree}{2}
+\marke{ffour}{3}
+\marke{ffive}{4}
+\marke{fsix}{5}
+\marke{fseven}{6}
+\marke{feight}{7}
+\marke{fnine}{8}
+\marke{ften}{9}
+
+\foreach \x in {1,...,12}{
+	\draw ({\x},-0.05) -- ({\x},0.05);
+}
+\node at (5,-0.05) [below] {$5$};
+\node at (10,-0.05) [below] {$10$};
+
+\foreach \y in {1,...,15}{
+	\draw (-0.05,{\y*\dy}) -- (0.05,{\y*\dy});
+	\draw (-0.05,{-\y*\dy}) -- (0.05,{-\y*\dy});
+}
+\node at (-0.05,{1*\dy}) [left] {$1$};
+\node at (-0.05,{5*\dy}) [left] {$5$};
+\node at (-0.05,{10*\dy}) [left] {$10$};
+\node at (-0.05,{15*\dy}) [left] {$15$};
+\node at (-0.05,{-5*\dy}) [left] {$-5$};
+\node at (-0.05,{-10*\dy}) [left] {$-10$};
+\node at (-0.05,{-15*\dy}) [left] {$-15$};
+
+\end{tikzpicture}
+\end{document}
+