Misc style cleanup of matrix and vector algebra functions and constru…

…ctors

chapters/arrays.tex

@@ -493,59 +493,75 @@ \subsubsection{Reduction Expressions}\doublelabel{reduction-expressions}
 
 \subsection{Matrix and Vector Algebra Functions}\doublelabel{matrix-and-vector-algebra-functions}
 
-The following set of built-in matrix and vector algebra functions are
-available. The function transpose and symmetric can be applied to any matrix. The
-functions outerProduct, cross and skew require Real/Integer
-vector(s) or matrix as input(s) and returns a Real/Integer vector or matrix (the result is only Integer
-if the input/all inputs are Integer):
+The following set of built-in matrix and vector algebra functions are available.  The function transpose and symmetric can be applied to any matrix.
+The functions \lstinline!outerProduct!, \lstinline!cross! and \lstinline!skew! require \lstinline!Real!/\lstinline!Integer! vector(s) or matrix as input(s)
+and returns a \lstinline!Real!/\lstinline!Integer! vector or matrix (the result is only \lstinline!Integer! if the input/all inputs are \lstinline!Integer!):
 \begin{longtable}[]{|p{3.5cm}|p{11.5cm}|}
 \caption{Matrix and vector algebra functions.}\\
 \hline
 \tablehead{Modelica} & \tablehead{Explanation}\\ \hline
 \endhead
 \lstinline!transpose(A)!
-& Permutes the first two dimensions of array A. It is an error, if array A
+& Permutes the first two dimensions of array \lstinline!A!. It is an error, if array \lstinline!A!
 does not have at least 2 dimensions.\\ \hline
-\lstinline!outerProduct(v1,v2)!
-& Returns the outer product of vectors v1 and v2 ( = matrix(v1)*transpose(
-matrix(v2) ) ).\\ \hline
+\lstinline!outerProduct(v1, v2)!
+&
+\begin{tabular}{@{}p{10cm}@{}}
+Returns the outer product of vectors \lstinline!v1! and \lstinline!v2!:\\
+\lstinline!= matrix(v1) * transpose(matrix(v2))!
+\end{tabular}\\ \hline
 \lstinline!symmetric(A)!
 & Returns a symmetric matrix which is identical to the square matrix \lstinline!A!
-on and above the diagonal, i.e., \lstinline!B := symmetric(A) ->!
-  \lstinline!B[i,j] := A[i,j], if i <= j, ! \lstinline! B[i,j] := A[j,i], if i > j!.\\ \hline
-\lstinline!cross(x,y)!
-& Returns the cross product of the 3-vectors x and y, i.e.
-\lstinline!cross(x,y) = vector( [ x[2]*y[3]-x[3]*y[2];  x[3]*y[1]-x[1]*y[3]; x[1]*y[2]-x[2]*y[1]  ] );!\\ \hline
+on and above the diagonal, i.e., \lstinline!B := symmetric(A)! implies
+\begin{equation*}
+\text{\lstinline[mathescape=true]!B[$i$, $j$]!} =
+\begin{cases}
+\text{\lstinline[mathescape=true]!A[$i$, $j$]!} & \text{if $i \leq j$}\\
+\text{\lstinline[mathescape=true]!A[$j$, $i$]!} & \text{if $i > j$}
+\end{cases}
+\end{equation*}\\ \hline
+\lstinline!cross(x, y)!
+&
+\begin{tabular}{@{}p{10cm}@{}}
+Returns the cross product of the 3-vectors \lstinline!x! and \lstinline!y!:
+\begin{lstlisting}[frame=none,aboveskip=-\parskip,belowskip=-\medskipamount]
+= vector([ x[2] * y[3] - x[3] * y[2];
+           x[3] * y[1] - x[1] * y[3];
+           x[1] * y[2] - x[2] * y[1] ])
+\end{lstlisting}
+\end{tabular}\\ \hline
 \lstinline!skew(x)!
-& Returns the 3 x 3 skew symmetric matrix associated with a 3-vector,
-  i.e., \lstinline!cross(x,y) = skew(x)*y; skew(x) = [0, -x[3], x[2]; x[3], 0, -x[1]; -x[2], x[1], 0];!\\ \hline
+&
+\begin{tabular}{@{}p{10cm}@{}}
+Returns the $3 \times 3$ skew symmetric matrix associated with a 3-vector, i.e., \lstinline!cross(x, y) = skew(x) * y!, or --- equivalently --- \lstinline!skew(x)!
+\begin{lstlisting}[frame=none,aboveskip=-\parskip,belowskip=-\medskipamount]
+= [ 0,   -x[3], x[2] ;
+    x[3], 0,   -x[1] ;
+   -x[2], x[1], 0    ]
+\end{lstlisting}
+\end{tabular}\\ \hline
 \end{longtable}
 
 \section{Vector, Matrix and Array Constructors}\doublelabel{vector-matrix-and-array-constructors}
 
-The constructor function \lstinline!array(A,B,C,...)! constructs an array from its
-arguments according to the following rules:
+The constructor function \lstinline[mathescape=true]!array(A, B, C, $\ldots$)! constructs an array from its arguments according to the following rules:
 \begin{itemize}
 \item
   Size matching: All arguments must have the same sizes, i.e.,
-  \lstinline!size(A)=size(B)=size(C)=!...
+  \lstinline!size(A)! = \lstinline!size(B)! = \lstinline!size(C)! = \ldots
 \item
-  All arguments must be type compatible expressions (\autoref{type-compatible-expressions}) giving
-  the type of the elements. The data type of the result array is the
-  maximally expanded type of the arguments. Real and Integer subtypes
-  can be mixed resulting in a Real result array where the Integer
-  numbers have been transformed to Real numbers.
+  All arguments must be type compatible expressions (\autoref{type-compatible-expressions}) giving the type of the elements.  The data type of the result array is the
+  maximally expanded type of the arguments. \lstinline!Real! and \lstinline!Integer! subtypes can be mixed resulting in a \lstinline!Real! result array where the
+  \lstinline!Integer! numbers have been transformed to \lstinline!Real! numbers.
 \item
-  Each application of this constructor function adds a one-sized
-  dimension to the left in the result compared to the dimensions of the
-  argument arrays, i.e., \lstinline!ndims(array(A,B,C)) = ndims(A) + 1 = ndims(B) + 1, ...!
+  Each application of this constructor function adds a one-sized dimension to the left in the result compared to the dimensions of the argument arrays, i.e.,
+  \lstinline[mathescape=true]!ndims(array(A, B, C)) = ndims(A) + 1 = ndims(B) + 1, $\ldots$!
 \item
-  \lstinline!{A, B, C, ...}! is a shorthand notation for \lstinline!array(A, B, C, ...)!.
+  \lstinline[mathescape=true]!{A, B, C, $\ldots$}! is a shorthand notation for \lstinline[mathescape=true]!array(A, B, C, $\ldots$)!.
 \item
   There must be at least one argument.
   \begin{nonnormative}
-  The reason \lstinline!array()! or \lstinline!{}! is not defined is that at least one argument is
-  needed to determine the type of the resulting array.
+  The reason \lstinline!array()! or \lstinline!{}! is not defined is that at least one argument is needed to determine the type of the resulting array.
   \end{nonnormative}
 \end{itemize}
 

preamble.tex

@@ -213,7 +213,8 @@
 
 \lstset{ %
   backgroundcolor=\color{white},   % choose the background color
-  breaklines=true,                % automatic line breaking only at whitespace
+  breaklines=true,                 % automatic line breaking only at whitespace
+  keepspaces,                      % don't remove space such as those after closing parenthesis
   captionpos=b,                    % sets the caption-position to bottom
   commentstyle=\color[rgb]{0,0.4,0}\sffamily,    % comment style
   keywordstyle=\color{blue}\ttfamily\bfseries,       % keyword style