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fixed page breaking of code and exercises

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Jan Benda
2020-12-11 23:22:40 +01:00
parent 0380b7a96f
commit 0e30a01a45
13 changed files with 362 additions and 538 deletions
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69
designpattern/lecture/designpattern.tex
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@@ -10,7 +10,8 @@ pattern]{design pattern}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Looping over vector elements}
Iterating over vector elements by means of a \mcode{for}-loop is a very commen pattern:
\begin{lstlisting}[caption={\varcode{for}-loop for accessing vector elements by indices}]
\begin{pagelisting}[caption={\varcode{for}-loop for accessing vector elements by indices}]
x = [2:3:20]; % Some vector.
for i=1:length(x) % For loop over the indices of the vector.
i % This is the index (an integer number)
@@ -22,12 +23,14 @@ for i=1:length(x) % For loop over the indices of the vector.
% as an argument to a function:
do_something(x(i));
end
\end{lstlisting}
\end{pagelisting}
\noindent
If the result of the computation within the loop are single numbers
that are to be stored in a vector, you should create this vector with
the right size before the loop:
\begin{lstlisting}[caption={\varcode{for}-loop for writing a vector}]
\begin{pagelisting}[caption={\varcode{for}-loop for writing a vector}]
x = [1.2 2.3 2.6 3.1]; % Some vector.
% Create a vector for the results, as long as the number of loops:
y = zeros(length(x),1);
@@ -38,13 +41,15 @@ for i=1:length(x)
end
% Now the result vector can be further processed:
mean(y);
\end{lstlisting}
\end{pagelisting}
\noindent
The computation within the loop could also result in a vector of some
length and not just a single number. If the length of this vector
(here 10) is known beforehand, then you should create a matrix of
appropriate size for storing the results:
\begin{lstlisting}[caption={\varcode{for}-loop for writing rows of a matrix}]
\begin{pagelisting}[caption={\varcode{for}-loop for writing rows of a matrix}]
x = [2:3:20]; % Some vector.
% Create space for results -
% as many rows as loops, as many columns as needed:
@@ -56,11 +61,13 @@ for i=1:length(x)
end
% Process the results stored in matrix y:
mean(y, 1)
\end{lstlisting}
\end{pagelisting}
\noindent
Another possibility is that the result vectors (here of unknown size)
need to be combined into a single large vector:
\begin{lstlisting}[caption={\varcode{for}-loop for appending vectors}]
\begin{pagelisting}[caption={\varcode{for}-loop for appending vectors}]
x = [2:3:20]; % Some vector.
y = []; % Empty vector for storing the results.
for i=1:length(x)
@@ -72,14 +79,15 @@ for i=1:length(x)
end
% Process the results stored in the vector z:
mean(y)
\end{lstlisting}
\end{pagelisting}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Scaling and shifting random numbers, zeros, and ones}
Random number generators usually return random numbers of a given mean
and standard deviation. Multiply those numbers by a factor to change their standard deviation and add a number to shift the mean.
\begin{lstlisting}[caption={Scaling and shifting of random numbers}]
\begin{pagelisting}[caption={Scaling and shifting of random numbers}]
% 100 random numbers drawn from a normal distribution
% with mean 0 and standard deviation 1:
x = randn(100, 1);
@@ -89,18 +97,20 @@ x = randn(100, 1);
mu = 4.8;
sigma = 2.3;
y = randn(100, 1)*sigma + mu;
\end{lstlisting}
\end{pagelisting}
\noindent
The same principle can be useful for in the context of the functions
\mcode{zeros()} or \mcode{ones()}:
\begin{lstlisting}[caption={Scaling and shifting of \varcode{zeros()} and \varcode{ones()}}]
\begin{pagelisting}[caption={Scaling and shifting of \varcode{zeros()} and \varcode{ones()}}]
x = -1:0.01:2; % Vector of x-values for plotting
plot(x, exp(-x.*x));
% Plot for the same x-values a horizontal line with y=0.8:
plot(x, zeros(size(x))+0.8);
% ... or a line with y=0.5:
plot(x, ones(size(x))*0.5);
\end{lstlisting}
\end{pagelisting}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -119,25 +129,26 @@ can plot the values of the $y$ vector against the ones of the $x$
vector.
The following scripts compute and plot the function $f(x)=e^{-x^2}$:
\begin{lstlisting}[caption={Plotting a mathematical function --- very detailed}]
\begin{pagelisting}[caption={Plotting a mathematical function --- very detailed}]
xmin = -1.0;
xmax = 2.0;
dx = 0.01; % Step size
x = xmin:dx:xmax; % Vector with x-values.
y = exp(-x.*x); % No for loop! '.*' for multiplying the vector elements.
plot(x, y);
\end{lstlisting}
\end{pagelisting}
\begin{lstlisting}[caption={Plotting a mathematical function --- shorter}]
\begin{pagelisting}[caption={Plotting a mathematical function --- shorter}]
x = -1:0.01:2;
y = exp(-x.*x);
plot(x, y);
\end{lstlisting}
\end{pagelisting}
\begin{lstlisting}[caption={Plotting a mathematical function --- compact}]
\begin{pagelisting}[caption={Plotting a mathematical function --- compact}]
x = -1:0.01:2;
plot(x, exp(-x.*x));
\end{lstlisting}
\end{pagelisting}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -146,28 +157,34 @@ For estimating probabilities or probability densities from histograms
we need to normalize them appropriately.
The \mcode{histogram()} function does this automatically with the appropriate arguments:
\begin{lstlisting}[caption={Probability density with the \varcode{histogram()}-function}]
\begin{pagelisting}[caption={Probability density with the \varcode{histogram()}-function}]
x = randn(100, 1); % Some real-valued data.
histogram(x, 'Normalization', 'pdf');
\end{lstlisting}
\begin{lstlisting}[caption={Probability with the \varcode{histogram()}-function}]
\end{pagelisting}
\begin{pagelisting}[caption={Probability with the \varcode{histogram()}-function}]
x = randi(6, 100, 1); % Some integer-valued data.
histogram(x, 'Normalization', 'probability');
\end{lstlisting}
\end{pagelisting}
\noindent
Alternatively one can normalize the histogram data as returned by the
\code{hist()}-function manually:
\begin{lstlisting}[caption={Probability density with the \varcode{hist()}- and \varcode{bar()}-function}]
\begin{pagelisting}[caption={Probability density with the \varcode{hist()}- and \varcode{bar()}-function}]
x = randn(100, 1); % Some real-valued data.
[h, b] = hist(x); % Compute histogram.
h = h/sum(h)/(b(2)-b(1)); % Normalization to a probability density.
bar(b, h); % Plot the probability density.
\end{lstlisting}
\begin{lstlisting}[caption={Probability with the \varcode{hist()}- and \varcode{bar()}-function}]
\end{pagelisting}
\begin{pagelisting}[caption={Probability with the \varcode{hist()}- and \varcode{bar()}-function}]
x = randi(6, 100, 1); % Some integer-valued data.
[h, b] = hist(x); % Compute histogram.
h = h/sum(h); % Normalize to probability.
bar(b, h); % Plot the probabilities.
\end{lstlisting}
\end{pagelisting}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%