added solutions to function erecises

pointprocesses/lecture/pointprocessscetchA.eps

@@ -1,7 +1,7 @@
 %!PS-Adobe-2.0 EPSF-2.0
 %%Title: pointprocessscetchA.tex
 %%Creator: gnuplot 4.6 patchlevel 4
-%%CreationDate: Fri Sep 30 10:14:40 2016
+%%CreationDate: Sat Nov 19 10:17:42 2016
 %%DocumentFonts: 
 %%BoundingBox: 50 50 373 135
 %%EndComments
@@ -430,10 +430,10 @@ SDict begin [
   /Title (pointprocessscetchA.tex)
   /Subject (gnuplot plot)
   /Creator (gnuplot 4.6 patchlevel 4)
-  /Author (grewe)
+  /Author (jan)
 %  /Producer (gnuplot)
 %  /Keywords ()
-  /CreationDate (Fri Sep 30 10:14:40 2016)
+  /CreationDate (Sat Nov 19 10:17:42 2016)
   /DOCINFO pdfmark
 end
 } ifelse

pointprocesses/lecture/pointprocessscetchB.eps

@@ -1,7 +1,7 @@
 %!PS-Adobe-2.0 EPSF-2.0
 %%Title: pointprocessscetchB.tex
 %%Creator: gnuplot 4.6 patchlevel 4
-%%CreationDate: Fri Sep 30 10:14:40 2016
+%%CreationDate: Sat Nov 19 10:17:43 2016
 %%DocumentFonts: 
 %%BoundingBox: 50 50 373 237
 %%EndComments
@@ -430,10 +430,10 @@ SDict begin [
   /Title (pointprocessscetchB.tex)
   /Subject (gnuplot plot)
   /Creator (gnuplot 4.6 patchlevel 4)
-  /Author (grewe)
+  /Author (jan)
 %  /Producer (gnuplot)
 %  /Keywords ()
-  /CreationDate (Fri Sep 30 10:14:40 2016)
+  /CreationDate (Sat Nov 19 10:17:43 2016)
   /DOCINFO pdfmark
 end
 } ifelse

programming/code/boltzmann.m

@@ -0,0 +1,8 @@
+function y = boltzmann( x, k )
+% computes the boltzmann function
+% x: scalar or vector of x values
+% k: slope parameter of boltzman function
+% returns y-values of boltzmann function
+y = 1./(1+exp(-k*x));
+end
+

programming/code/plotboltzmann.m

@@ -0,0 +1,3 @@
+p = boltzmann(voltage, a);
+plot(voltage, p)
+y = -1;

programming/exercises/faculty.m

@@ -0,0 +1,8 @@
+function x = faculty(n)
+% return the faculty of n
+x = 1;
+for i = 1:n
+    x = x * i;
+end
+% x = prod(1:n)  % this is a one line alternative to the for loop!
+end

programming/exercises/facultyscripta.m

@@ -0,0 +1,6 @@
+n = 5;
+x = 1;
+for i = 1:n
+    x = x * i;
+end 
+fprintf('Faculty of %i is: %i\n', n, x)

programming/exercises/facultyscriptb.m

@@ -0,0 +1 @@
+printfaculty(5);

programming/exercises/facultyscriptc.m

@@ -0,0 +1,3 @@
+n = 5
+a = faculty(n);
+fprintf('Faculty of %i is: %i\n', n, x)

programming/exercises/plotsine.m

@@ -0,0 +1,19 @@
+function plotsine(freq, ampl, duration, step)
+% plot a sine wave
+% freq: frequency of the sinewave in Hertz
+% ampl: amplitude of the sinewave
+% duration: duration of the sinewave in seconds
+% step: stepsize for plotting in seconds
+time = 0:step:duration;
+sine = ampl*sin(2*pi*freq*time);
+if duration <= 1.0
+	plot(1000.0*time, sine);
+	xlabel('Time [ms]');
+else
+	plot(time, sine);
+	xlabel('Time [s]');
+end
+ylim([-1.2*ampl 1.2*ampl]);
+ylabel('Sinewave');
+title(sprintf('Frequency %g Hz', freq));
+end

programming/exercises/plotsine50.m

@@ -0,0 +1,9 @@
+function plotsine50()
+% plot a sine wave of 50Hz
+time = 0:0.0001:0.2;
+sine = sin(2*pi*50.0*time);
+plot(1000.0*time, sine);
+xlabel('Time [ms]');
+ylim([-1.2 1.2]);
+ylabel('Sinewave');
+end

programming/exercises/plotsinea.m

@@ -0,0 +1 @@
+plotsine50()

programming/exercises/plotsineb.m

@@ -0,0 +1 @@
+plotsine(5.0, 2.0, 1.5, 0.001)

programming/exercises/plotsinec.m

@@ -0,0 +1,14 @@
+freq = 5.0;
+ampl = 2.0;
+[time, sine] = sinewave(freq, ampl, 1.5, 0.001);
+
+if duration <= 1.0
+	plot(1000.0*time, sine);
+	xlabel('Time [ms]');
+else
+	plot(time, sine);
+	xlabel('Time [s]');
+end
+ylim([-1.2*ampl 1.2*ampl]);
+ylabel('Sinewave');
+title(sprintf('Frequency %g Hz', freq));

programming/exercises/plotsined.m

@@ -0,0 +1,4 @@
+freq = 5.0;
+ampl = 2.0;
+[time, sine] = sinewave(freq, ampl, 1.5, 0.001);
+plotsinewave(time, sine);

programming/exercises/plotsinewave.m

@@ -0,0 +1,13 @@
+function plotsinewave(time, sine)
+% plot precomputed sinewave
+% time: vector with timepoints
+% sine: corresponding vector with sinewave 
+if time(end)-time(1) <= 1.0
+	plot(1000.0*time, sine);
+	xlabel('Time [ms]');
+else
+	plot(time, sine);
+	xlabel('Time [s]');
+end
+ylim([1.2*min(sine) 1.2*max(sine)]);
+ylabel('Sinewave');

programming/exercises/printfaculty.m

@@ -0,0 +1,8 @@
+function printfaculty(n)
+% compute the faculty of n and print it
+x = 1;
+for i = 1:n
+    x = x * i;
+end 
+fprintf('Faculty of %i is: %i\n', n, x)
+end

programming/exercises/randomwalk.m

@@ -0,0 +1,13 @@
+function [time, position] = randomwalk(numbersteps)
+% 1-D random walk for numbersteps time steps
+time = 1:numbersteps;
+position = zeros(numbersteps, 1);
+for i = time(2:end)
+	r = rand(1);
+	if r > 0.5
+		position(i) = position(i-1) + 1;
+	else
+		position(i) = position(i-1) - 1;
+	end
+end
+end

programming/exercises/randomwalkscript.m

@@ -0,0 +1,7 @@
+n = 2000;
+hold on
+for k = 1:10
+	[t, x] = randomwalk(n);
+	plot(t, x)
+end
+hold off

programming/exercises/randomwalkscriptb.m

@@ -0,0 +1,8 @@
+p = 0.5;
+thresh = 50.0;
+hold on
+for k = 1:30
+	x = randomwalkthresh(p, thresh);
+	plot(x)
+end
+hold off

programming/exercises/randomwalkscriptc.m

@@ -0,0 +1,20 @@
+thresh = 50.0;
+probs = [0.5 0.52 0.55 0.6];
+maxt = 0;
+for sp = 1:4
+	p = probs(sp);
+	subplot(2, 2, sp);
+	hold on
+	for k = 1:30
+		x = randomwalkthresh(p, thresh);
+		if maxt < length(x)
+			maxt = length(x);
+		end
+		plot(x)
+	end
+	hold off
+	title(sprintf('p=%g', p))
+	xlabel('Time')
+	xlim([0 maxt])
+	ylabel('Position')
+end

programming/exercises/randomwalkscriptd.m

@@ -0,0 +1,23 @@
+thresh = 50.0;
+probs = 0.5:0.01:1.0;
+reps = 1000;
+meancount = zeros(length(probs), 1);
+stdcount = zeros(length(probs), 1);
+for sp = 1:length(probs)
+	p = probs(sp);
+	positions = zeros(reps, 1);
+	for k = 1:reps
+		x = randomwalkthresh(p, thresh);
+		positions(k) = length(x);
+	end
+	meancount(sp) = mean(positions);
+	stdcount(sp) = std(positions);
+end
+semilogy(probs, meancount, 'displayname', 'mean');
+hold on;
+semilogy(probs, stdcount, 'displayname', 'std');
+hold off;
+xlabel('p');
+xlim([0.5 1.0])
+ylabel('number of steps');
+legend('show');

programming/exercises/randomwalkthresh.m

@@ -0,0 +1,25 @@
+function positions = randomwalkthresh(p, thresh)
+% computes a single random walk
+%
+% Arguments:
+% p: the probability for an upward step
+% thresh: compute the random walk until abs(pos) is larger than thresh
+%
+% Returns:
+% positions: vector with positions of the random walker
+
+positions = [0.0];
+i = 2;
+while true
+	r = rand(1);
+	if r < p
+		positions(i) = positions(i-1) + 1;
+	else
+		positions(i) = positions(i-1) - 1;
+	end
+	if abs(positions(i)) > thresh
+		break
+	end
+	i = i + 1;
+end
+end

programming/exercises/scripts_functions.tex

@@ -1,7 +1,9 @@
-\documentclass[12pt,a4paper,pdftex]{exam}
+%\documentclass[12pt,a4paper,pdftex]{exam}
+\documentclass[answers,12pt,a4paper,pdftex]{exam}
 
 \usepackage[german]{babel}
 \usepackage{natbib}
+\usepackage{xcolor}
 \usepackage{graphicx}
 \usepackage[small]{caption}
 \usepackage{sidecap}
@@ -24,6 +26,27 @@
 \setlength{\parskip}{0.3cm}
 \renewcommand{\baselinestretch}{1.15}
 
+
+%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage{listings}
+\lstset{
+  language=Matlab,
+  basicstyle=\ttfamily\footnotesize,
+  numbers=left,
+  numberstyle=\tiny,
+  title=\lstname,
+  showstringspaces=false,
+  commentstyle=\itshape\color{darkgray},
+  breaklines=true,
+  breakautoindent=true,
+  columns=flexible,
+  frame=single,
+  xleftmargin=1em,
+  xrightmargin=1em,
+  aboveskip=10pt
+}
+
+
 \newcommand{\code}[1]{\texttt{#1}}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
@@ -49,19 +72,52 @@ also als zip-Archiv auf ILIAS hochladen. Das Archiv sollte nach dem Muster:
   \begin{parts}
     \part Version 1: berechnet die Fakult\"at von 5 und gib das
     Resultat auf dem Bildschirm aus.
+    \begin{solution}
+      \lstinputlisting{facultyscripta.m}
+    \end{solution}
+
     \part Version 2: Wie 1 aber die Funktion \"ubernimmt als Argument
     die Zahl, von der die Fakult\"at berechnet werden soll.
+    \begin{solution}
+      \lstinputlisting{printfaculty.m}
+      \lstinputlisting{facultyscriptb.m}
+    \end{solution}
+
     \part Version 3: Wie 2 aber mit R\"uckgabe des berechneten Wertes.
+    \begin{solution}
+      \lstinputlisting{faculty.m}
+      \lstinputlisting{facultyscriptc.m}
+    \end{solution}
+
   \end{parts}
 
   \question Implementiere eine Funktion, die einen Sinus mit der
   Amplitude 1 und der Frequenz $f = $ 50\,Hz plottet ($sin(2\pi \cdot
   f \cdot t)$):
+  \begin{solution}
+    \lstinputlisting{plotsine50.m}
+    \lstinputlisting{plotsinea.m}
+  \end{solution}
   \begin{parts}
     \part Erweitere die Funktion sodass die L\"ange der Zeitachse, die
     Schrittweite, Amplitude, Frequenz als Argumente
     \"ubergeben werden k\"onnen.
+    \begin{solution}
+      \lstinputlisting{plotsine.m}
+      \lstinputlisting{plotsineb.m}
+    \end{solution}
+
     \part Gib sowohl den Sinus als auch die Zeitachse zur\"uck.
+    \begin{solution}
+      \lstinputlisting{sinewave.m}
+      \lstinputlisting{plotsinec.m}
+    \end{solution}
+
+    \part Extra plot Funktion.
+    \begin{solution}
+      \lstinputlisting{plotsinewave.m}
+      \lstinputlisting{plotsined.m}
+    \end{solution}
   \end{parts}
 
   %\question Schreibe eine Funktion, die bin\"are Datens\"atze
@@ -80,15 +136,33 @@ also als zip-Archiv auf ILIAS hochladen. Das Archiv sollte nach dem Muster:
   \begin{parts}
     \part \"Uberlege Dir ein geeignetes ``Programmlayout'' aus
     Funktionen und Skripten.
+    \begin{solution}
+      One function that computes one realisation of a random walk.
+      Scripts for plotting and analysis.
+    \end{solution}
+
     \part Implementiere die L\"osung.
+    \begin{solution}
+      \lstinputlisting{randomwalkthresh.m}
+      \lstinputlisting{randomwalkscriptb.m}
+    \end{solution}
+
     \part Simuliere 30 Realisationen des random walk pro
     Wahrscheinlichkeit.
+
     \part Es sollen die Positionen als Funktion der Schrittanzahl
     geplottet werden. Erstelle einen Plot mit den je 30
     Wiederholungen pro Wahrscheinlichkeitsstufe.
+    \begin{solution}
+      \lstinputlisting{randomwalkscriptc.m}
+    \end{solution}
+
     \part Wie entwickelt sich die mittlere ben\"otigte Schrittanzahl
     in Abh\"angigkeit der Wahrscheinlichkeit?  Stelle die Mittelwerte
     und die Standardabweichungen graphisch dar.
+    \begin{solution}
+      \lstinputlisting{randomwalkscriptd.m}
+    \end{solution}
   \end{parts}
 
   %\question Modellierung des exponentiellen Wachstums einer isolierten

programming/exercises/sinewave.m

@@ -0,0 +1,12 @@
+function [time, sine] = sinewave(freq, ampl, duration, step)
+% compute sine wave with time axis
+% freq: frequency of the sinewave in Hertz
+% ampl: amplitude of the sinewave
+% duration: duration of the sinewave in seconds
+% step: stepsize for plotting in seconds
+% returns:
+% time: vector of time points
+% sine: corresponding vector with the sine wave
+time = 0:step:duration;
+sine = ampl*sin(2*pi*freq*time);
+end

scientificcomputing-script.tex

@@ -2,7 +2,7 @@
 
 \input{header}
 
-\setcounter{maxexercise}{0}  % show listings up to exercise maxexercise
+\setcounter{maxexercise}{1000}  % show listings up to exercise maxexercise
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%