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Work around broken tables #3205

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136 changes: 68 additions & 68 deletions chapters/arrays.tex
Original file line number Diff line number Diff line change
Expand Up @@ -70,12 +70,12 @@ \section{Array Declarations}\label{array-declarations}
\tablehead{Modelica form 1} & \tablehead{Modelica form 2} & \tablehead{\# dims} & \tablehead{Designation} & \tablehead{Explanation}\\
\hline
\hline
\lstinline!C x!; & \lstinline!C x!; & $0$ & Scalar & Scalar\\
\lstinline!C[$n$] x;! & \lstinline!C x[$n$];! & $1$ & Vector & $n$-vector\\
\lstinline!C[EB] x;! & \lstinline!C x[EB]! & $1$ & Vector & Vector indexed by \lstinline!EB!\\
\lstinline!C[$n$, $m$] x;! & \lstinline!C x[$n$, $m$];! & $2$ & Matrix & $n \times m$ matrix\\
\lstinline!C[$n_1$, $n_{2}$, $\ldots$, $n_k$] x;! &
\lstinline!C x[$n_{1}$, $n_{2}$, $\ldots$, $n_{k}$];! & $k$ & Array & General array\\
{\lstinline!C x!}; & {\lstinline!C x!}; & $0$ & Scalar & Scalar\\
{\lstinline!C[$n$] x;!} & {\lstinline!C x[$n$];!} & $1$ & Vector & $n$-vector\\
{\lstinline!C[EB] x;!} & {\lstinline!C x[EB]!} & $1$ & Vector & Vector indexed by {\lstinline!EB!}\\
{\lstinline!C[$n$, $m$] x;!} & {\lstinline!C x[$n$, $m$];!} & $2$ & Matrix & $n \times m$ matrix\\
{\lstinline!C[$n_1$, $n_{2}$, $\ldots$, $n_k$] x;!} &
{\lstinline!C x[$n_{1}$, $n_{2}$, $\ldots$, $n_{k}$];!} & $k$ & Array & General array\\
\hline
\end{tabular}
\end{center}
Expand Down Expand Up @@ -137,10 +137,10 @@ \section{Array Declarations}\label{array-declarations}
\tablehead{Modelica form 1} & \tablehead{Modelica form 2} & \tablehead{\# dims} & \tablehead{Designation} & \tablehead{Explanation}\\
\hline
\hline
\lstinline!C[1] x;! & \lstinline!C x[1];! & $1$ & Vector & 1-vector, representing a scalar\\
\lstinline!C[1, 1] x;! & \lstinline!C x[1, 1];! & $2$ & Matrix & $(1 \times 1)$-matrix, representing a scalar\\
\lstinline!C[$n$, 1] x;! & \lstinline!C x[$n$, 1];! & $2$ & Matrix & $(n \times 1)$-matrix, representing a column\\
\lstinline!C[1, $n$] x;! & \lstinline!C x[1, $n$];! & $2$ & Matrix & $(1 \times n)$-matrix, representing a row\\
{\lstinline!C[1] x;!} & {\lstinline!C x[1];!} & $1$ & Vector & 1-vector, representing a scalar\\
{\lstinline!C[1, 1] x;!} & {\lstinline!C x[1, 1];!} & $2$ & Matrix & $(1 \times 1)$-matrix, representing a scalar\\
{\lstinline!C[$n$, 1] x;!} & {\lstinline!C x[$n$, 1];!} & $2$ & Matrix & $(n \times 1)$-matrix, representing a column\\
{\lstinline!C[1, $n$] x;!} & {\lstinline!C x[1, $n$];!} & $2$ & Matrix & $(1 \times n)$-matrix, representing a row\\
\hline
\end{tabular}
\end{center}
Expand Down Expand Up @@ -601,10 +601,10 @@ \subsubsection{Reduction Expressions}\label{reduction-expressions}
\tablehead{Reduction} & \tablehead{Restriction on \lstinline!expression1!} & \tablehead{Result for empty \lstinline!expression2!}\\
\hline
\hline
\lstinline!sum! & \lstinline!Integer! or \lstinline!Real! & \lstinline!zeros($\ldots$)!\\
\lstinline!product! & Scalar \lstinline!Integer! or \lstinline!Real! & 1\\
\lstinline!min! & Scalar enumeration, \lstinline!Boolean!, \lstinline!Integer! or \lstinline!Real! & Greatest value of type\\
\lstinline!max! & Scalar enumeration, \lstinline!Boolean!, \lstinline!Integer! or \lstinline!Real! & Least value of type\\
{\lstinline!sum!} & {\lstinline!Integer!} or {\lstinline!Real!} & {\lstinline!zeros($\ldots$)!}\\
{\lstinline!product!} & Scalar {\lstinline!Integer!} or {\lstinline!Real!} & 1\\
{\lstinline!min!} & Scalar enumeration, {\lstinline!Boolean!}, {\lstinline!Integer!} or {\lstinline!Real!} & Greatest value of type\\
{\lstinline!max!} & Scalar enumeration, {\lstinline!Boolean!}, {\lstinline!Integer!} or {\lstinline!Real!} & Least value of type\\
\hline
\end{tabular}
\end{center}
Expand All @@ -630,11 +630,11 @@ \subsection{Matrix and Vector Algebra Functions}\label{matrix-and-vector-algebra
\tablehead{Expression} & \tablehead{Description} & \tablehead{Details}\\
\hline
\hline
\lstinline!transpose($A$)! & Matrix transpose & \Cref{modelica:transpose} \\
\lstinline!outerProduct($x$, $y$)! & Vector outer product & \Cref{modelica:outerProduct} \\
\lstinline!symmetric($A$)! & Symmetric matrix, keeping upper part & \Cref{modelica:symmetric} \\
\lstinline!cross($x$, $y$)! & Cross product & \Cref{modelica:cross} \\
\lstinline!skew($x$)! & Skew symmetric matrix associated with vector & \Cref{modelica:skew} \\
{\lstinline!transpose($A$)!} & Matrix transpose & \Cref{modelica:transpose} \\
{\lstinline!outerProduct($x$, $y$)!} & Vector outer product & \Cref{modelica:outerProduct} \\
{\lstinline!symmetric($A$)!} & Symmetric matrix, keeping upper part & \Cref{modelica:symmetric} \\
{\lstinline!cross($x$, $y$)!} & Cross product & \Cref{modelica:cross} \\
{\lstinline!skew($x$)!} & Skew symmetric matrix associated with vector & \Cref{modelica:skew} \\
\hline
\end{tabular}
\end{center}
Expand Down Expand Up @@ -994,17 +994,17 @@ \section{Indexing}\label{array-indexing}\label{indexing}
\tablehead{Expression} & \tablehead{\# dims} & \tablehead{Description}\\
\hline
\hline
\lstinline!x[1, 1]! & 0 & Scalar\\
\lstinline!x[:, 1]! & 1 & $n$-vector\\
\lstinline!x[1, :]! or \lstinline!x[1]! & 1 & $m$-vector\\
\lstinline!v[1:$p$]! & 1 & $p$-vector\\
\lstinline!x[1:$p$, :]! & 2 & $p \times m$ matrix\\
\lstinline!x[1:1, :]! & 2 & $1 \times m$ ``row'' matrix\\
\lstinline!x[{1, 3, 5}, :]! & 2 & $3 \times m$ matrix\\
\lstinline!x[:, v]! & 2 & $n \times k$ matrix\\
\lstinline!z[:, 3, :]! & 2 & $i \times p$ matrix\\
\lstinline!x[scalar([1]), :]! & 1 & $m$-vector\\
\lstinline!x[vector([1]), :]! & 2 & $1 \times m$ ``row'' matrix\\
{\lstinline!x[1, 1]!} & 0 & Scalar\\
{\lstinline!x[:, 1]!} & 1 & $n$-vector\\
{\lstinline!x[1, :]!} or {\lstinline!x[1]!} & 1 & $m$-vector\\
{\lstinline!v[1:$p$]!} & 1 & $p$-vector\\
{\lstinline!x[1:$p$, :]!} & 2 & $p \times m$ matrix\\
{\lstinline!x[1:1, :]!} & 2 & $1 \times m$ ``row'' matrix\\
{\lstinline!x[{1, 3, 5}, :]!} & 2 & $3 \times m$ matrix\\
{\lstinline!x[:, v]!} & 2 & $n \times k$ matrix\\
{\lstinline!z[:, 3, :]!} & 2 & $i \times p$ matrix\\
{\lstinline!x[scalar([1]), :]!} & 1 & $m$-vector\\
{\lstinline!x[vector([1]), :]!} & 2 & $1 \times m$ ``row'' matrix\\
\hline
\end{tabular}
\end{center}
Expand Down Expand Up @@ -1070,10 +1070,10 @@ \subsection{Equality and Assignment}\label{equality-and-assignment}
\tablehead{Size of \lstinline!a!} & \tablehead{Size of \lstinline!b!} & \tablehead{Size of \lstinline!a = b!} & \tablehead{Operation}\\
\hline
\hline
Scalar & Scalar & Scalar & \lstinline!a = b!\\
$n$-vector & $n$-vector & $n$-vector & \lstinline!a[$j$] = b[$j$]!\\
$n \times m$ matrix & $n \times m$ matrix & $n \times m$ matrix & \lstinline!a[$j$, $k$] = b[$j$, $k$]!\\
$n \times m \times \ldots$ & $n \times m \times \ldots$ & $n \times m \times \ldots$ & \lstinline!a[$j$, $k$, $\ldots$] = b[$j$, $k$, $\ldots$]!\\
Scalar & Scalar & Scalar & {\lstinline!a = b!}\\
$n$-vector & $n$-vector & $n$-vector & {\lstinline!a[$j$] = b[$j$]!}\\
$n \times m$ matrix & $n \times m$ matrix & $n \times m$ matrix & {\lstinline!a[$j$, $k$] = b[$j$, $k$]!}\\
$n \times m \times \ldots$ & $n \times m \times \ldots$ & $n \times m \times \ldots$ & {\lstinline!a[$j$, $k$, $\ldots$] = b[$j$, $k$, $\ldots$]!}\\
\hline
\end{tabular}
\end{center}
Expand All @@ -1098,10 +1098,10 @@ \subsection{Addition, Subtraction, and String Concatenation}\label{array-element
\tablehead{Operation} \lstinline!c := a $\pm$ b!\\
\hline
\hline
Scalar & Scalar & Scalar & \lstinline!c := a $\pm$ b!\\
$n$-vector & $n$-vector & $n$-vector & \lstinline!c[$j$] := a[$j$] $\pm$ b[$j$]!\\
$n \times m$ matrix & $n \times m$ matrix & $n \times m$ matrix & \lstinline!c[$j$, $k$] := a[$j$, $k$] $\pm$ b[$j$, $k$]!\\
$n \times m \times \ldots$ & $n \times m \times \ldots$ & $n \times m \times \ldots$ & \lstinline!c[$j$, $k$, $\ldots$] := a[$j$, $k$, $\ldots$] $\pm$ b[$j$, $k$, $\ldots$]!\\
Scalar & Scalar & Scalar & {\lstinline!c := a $\pm$ b!}\\
$n$-vector & $n$-vector & $n$-vector & {\lstinline!c[$j$] := a[$j$] $\pm$ b[$j$]!}\\
$n \times m$ matrix & $n \times m$ matrix & $n \times m$ matrix & {\lstinline!c[$j$, $k$] := a[$j$, $k$] $\pm$ b[$j$, $k$]!}\\
$n \times m \times \ldots$ & $n \times m \times \ldots$ & $n \times m \times \ldots$ & {\lstinline!c[$j$, $k$, $\ldots$] := a[$j$, $k$, $\ldots$] $\pm$ b[$j$, $k$, $\ldots$]!}\\
\hline
\end{tabular}
\end{center}
Expand All @@ -1121,10 +1121,10 @@ \subsection{Addition, Subtraction, and String Concatenation}\label{array-element
& \tablehead{Operation \lstinline!c := a .$\pm$ b!}\\
\hline
\hline
Scalar & Scalar & Scalar & \lstinline!c := a $\pm$ b!\\
Scalar & $n \times m \times \ldots$ & $n \times m \times \ldots$ & \lstinline!c[$j$, $k$, $\ldots$] := a $\pm$ b[$j$, $k$, $\ldots$]!\\
$n \times m \times \ldots$ & Scalar & $n \times m \times \ldots$ & \lstinline!c[$j$, $k$, $\ldots$] := a[$j$, $k$, $\ldots$] $\pm$ b!\\
$n \times m \times \ldots$ & $n \times m \times \ldots$ & $n \times m \times \ldots$ & \lstinline!c[$j$, $k$, $\ldots$] := a[$j$, $k$, $\ldots$] $\pm$ b[$j$, $k$, $\ldots$]!\\
Scalar & Scalar & Scalar & {\lstinline!c := a $\pm$ b!}\\
Scalar & $n \times m \times \ldots$ & $n \times m \times \ldots$ & {\lstinline!c[$j$, $k$, $\ldots$] := a $\pm$ b[$j$, $k$, $\ldots$]!}\\
$n \times m \times \ldots$ & Scalar & $n \times m \times \ldots$ & {\lstinline!c[$j$, $k$, $\ldots$] := a[$j$, $k$, $\ldots$] $\pm$ b!}\\
$n \times m \times \ldots$ & $n \times m \times \ldots$ & $n \times m \times \ldots$ & {\lstinline!c[$j$, $k$, $\ldots$] := a[$j$, $k$, $\ldots$] $\pm$ b[$j$, $k$, $\ldots$]!}\\
\hline
\end{tabular}
\end{center}
Expand All @@ -1140,8 +1140,8 @@ \subsection{Addition, Subtraction, and String Concatenation}\label{array-element
\tablehead{Operation} \lstinline!c := $\pm$ a!\\
\hline
\hline
Scalar & Scalar & \lstinline!c := $\pm$ a!\\
$n \times m \times \ldots$ & $n \times m \times \ldots$ & \lstinline!c[$j$, $k$, $\ldots$] := $\pm$ a[$j$, $k$, $\ldots$]!\\
Scalar & Scalar & {\lstinline!c := $\pm$ a!}\\
$n \times m \times \ldots$ & $n \times m \times \ldots$ & {\lstinline!c[$j$, $k$, $\ldots$] := $\pm$ a[$j$, $k$, $\ldots$]!}\\
\hline
\end{tabular}
\end{center}
Expand All @@ -1160,10 +1160,10 @@ \subsection{Element-wise Multiplication}\label{array-element-wise-multiplication
\tablehead{Operation \lstinline!c := s * a! or \lstinline!c := a * s!}\\
\hline
\hline
Scalar & Scalar & Scalar & \lstinline!c := s * a!\\
Scalar & $n$-vector & $n$-vector & \lstinline!c[$j$] := s * a[$j$]!\\
Scalar & $n \times m$ matrix & $n \times m$ matrix & \lstinline!c[$j$, $k$] := s * a[$j$, $k$]!\\
Scalar & $n \times m \times \ldots$ & $n \times m \times \ldots$ & \lstinline!c[$j$, $k$, $\ldots$] := s * a[$j$, $k$, $\ldots$]!\\
Scalar & Scalar & Scalar & {\lstinline!c := s * a!}\\
Scalar & $n$-vector & $n$-vector & {\lstinline!c[$j$] := s * a[$j$]!}\\
Scalar & $n \times m$ matrix & $n \times m$ matrix & {\lstinline!c[$j$, $k$] := s * a[$j$, $k$]!}\\
Scalar & $n \times m \times \ldots$ & $n \times m \times \ldots$ & {\lstinline!c[$j$, $k$, $\ldots$] := s * a[$j$, $k$, $\ldots$]!}\\
\hline
\end{tabular}
\end{center}
Expand All @@ -1181,10 +1181,10 @@ \subsection{Element-wise Multiplication}\label{array-element-wise-multiplication
\tablehead{Operation} \lstinline!c := a .* b!\\
\hline
\hline
Scalar & Scalar & Scalar & \lstinline!c := a * b!\\
Scalar & $n \times m \times \ldots$ & $n \times m \times \ldots$ & \lstinline!c[$j$, $k$, $\ldots$] := a * b[$j$, $k$, $\ldots$]!\\
$n \times m \times \ldots$ & Scalar & $n \times m \times \ldots$ & \lstinline!c[$j$, $k$, $\ldots$] := a[$j$, $k$, $\ldots$] * b!\\
$n \times m \times \ldots$ & $n \times m \times \ldots$ & $n \times m \times \ldots$ & \lstinline!c[$j$, $k$, $\ldots$] := a[$j$, $k$, $\ldots$] * b[$j$, $k$, $\ldots$]!\\
Scalar & Scalar & Scalar & {\lstinline!c := a * b!}\\
Scalar & $n \times m \times \ldots$ & $n \times m \times \ldots$ & {\lstinline!c[$j$, $k$, $\ldots$] := a * b[$j$, $k$, $\ldots$]!}\\
$n \times m \times \ldots$ & Scalar & $n \times m \times \ldots$ & {\lstinline!c[$j$, $k$, $\ldots$] := a[$j$, $k$, $\ldots$] * b!}\\
$n \times m \times \ldots$ & $n \times m \times \ldots$ & $n \times m \times \ldots$ & {\lstinline!c[$j$, $k$, $\ldots$] := a[$j$, $k$, $\ldots$] * b[$j$, $k$, $\ldots$]!}\\
\hline
\end{tabular}
\end{center}
Expand All @@ -1202,10 +1202,10 @@ \subsection{Multiplication of Matrices and Vectors}\label{matrix-and-vector-mult
\tablehead{Operation \lstinline!c := a * b!}\\
\hline
\hline
$m$-vector & $m$-vector & Scalar & \lstinline!c := $\sum_{k}$ a[$k$] * b[$k$]!\\
$m$-vector & $m \times n$ matrix & $n$-vector & \lstinline!c[$j$] := $\sum_{k}$ a[$k$] * b[$k$, $j$]!\\
$l \times m$ matrix & $m$-vector & $l$-vector & \lstinline!c[$i$] := $\sum_{k}$ a[$i$, $k$] * b[$k$]!\\
$l \times m$ matrix & $m \times n$ matrix & $l \times n$ matrix & \lstinline!c[$i$, $j$] := $\sum_{k}$ a[$i$, $k$] * b[$k$, $j$]!\\
$m$-vector & $m$-vector & Scalar & {\lstinline!c := $\sum_{k}$ a[$k$] * b[$k$]!}\\
$m$-vector & $m \times n$ matrix & $n$-vector & {\lstinline!c[$j$] := $\sum_{k}$ a[$k$] * b[$k$, $j$]!}\\
$l \times m$ matrix & $m$-vector & $l$-vector & {\lstinline!c[$i$] := $\sum_{k}$ a[$i$, $k$] * b[$k$]!}\\
$l \times m$ matrix & $m \times n$ matrix & $l \times n$ matrix & {\lstinline!c[$i$, $j$] := $\sum_{k}$ a[$i$, $k$] * b[$k$, $j$]!}\\
\hline
\end{tabular}
\end{center}
Expand Down Expand Up @@ -1236,10 +1236,10 @@ \subsection{Division by Numeric Scalars}\label{division-by-numeric-scalars}
\tablehead{Operation \lstinline!c := a / s!}\\
\hline
\hline
Scalar & Scalar & Scalar & \lstinline!c := a / s!\\
$n$-vector & Scalar & $n$-vector & \lstinline!c[$k$] := a[$k$] / s!\\
$n \times m$ matrix & Scalar & $n \times m$ matrix & \lstinline!c[$j$, $k$] := a[$j$, $k$] / s!\\
$n \times m \times \ldots$ & Scalar & $n \times m \times \ldots$ & \lstinline!c[$j$, $k$, $\ldots$] := a[$j$, $k$, $\ldots$] / s!\\
Scalar & Scalar & Scalar & {\lstinline!c := a / s!}\\
$n$-vector & Scalar & $n$-vector & {\lstinline!c[$k$] := a[$k$] / s!}\\
$n \times m$ matrix & Scalar & $n \times m$ matrix & {\lstinline!c[$j$, $k$] := a[$j$, $k$] / s!}\\
$n \times m \times \ldots$ & Scalar & $n \times m \times \ldots$ & {\lstinline!c[$j$, $k$, $\ldots$] := a[$j$, $k$, $\ldots$] / s!}\\
\hline
\end{tabular}
\end{center}
Expand All @@ -1260,10 +1260,10 @@ \subsection{Element-wise Division}\label{array-element-wise-division}\label{elem
\tablehead{Operation} \lstinline!c := a ./ b!\\
\hline
\hline
Scalar & Scalar & Scalar & \lstinline!c := a / b!\\
Scalar & $n \times m \times \ldots$ & $n \times m \times \ldots$ & \lstinline!c[$j$, $k$, $\ldots$] := a / b[$j$, $k$, $\ldots$]!\\
$n \times m \times \ldots$ & Scalar & $n \times m \times \ldots$ & \lstinline!c[$j$, $k$, $\ldots$] := a[$j$, $k$, $\ldots$] / b!\\
$n \times m \times \ldots$ & $n \times m \times \ldots$ & $n \times m \times \ldots$ & \lstinline!c[$j$, $k$, $\ldots$] := a[$j$, $k$, $\ldots$] / b[$j$, $k$, $\ldots$]!\\
Scalar & Scalar & Scalar & {\lstinline!c := a / b!}\\
Scalar & $n \times m \times \ldots$ & $n \times m \times \ldots$ & {\lstinline!c[$j$, $k$, $\ldots$] := a / b[$j$, $k$, $\ldots$]!}\\
$n \times m \times \ldots$ & Scalar & $n \times m \times \ldots$ & {\lstinline!c[$j$, $k$, $\ldots$] := a[$j$, $k$, $\ldots$] / b!}\\
$n \times m \times \ldots$ & $n \times m \times \ldots$ & $n \times m \times \ldots$ & {\lstinline!c[$j$, $k$, $\ldots$] := a[$j$, $k$, $\ldots$] / b[$j$, $k$, $\ldots$]!}\\
\hline
\end{tabular}
\end{center}
Expand Down Expand Up @@ -1297,10 +1297,10 @@ \subsection{Element-wise Exponentiation}\label{element-wise-exponentiation}
\tablehead{Operation} \lstinline!c := a .^ b!\\
\hline
\hline
Scalar & Scalar & Scalar & \lstinline!c := a ^ b!\\
Scalar & $n \times m \times \ldots$ & $n \times m \times \ldots$ & \lstinline!c[$j$, $k$, $\ldots$] := a ^ b[$j$, $k$, $\ldots$]!\\
$n \times m \times \ldots$ & Scalar & $n \times m \times \ldots$ & \lstinline!c[$j$, $k$, $\ldots$] := a[$j$, $k$, $\ldots$] ^ b!\\
$n \times m \times \ldots$ & $n \times m \times \ldots$ & $n \times m \times \ldots$ & \lstinline!c[$j$, $k$, $\ldots$] := a[$j$, $k$, $\ldots$] ^ b[$j$, $k$, $\ldots$]!\\
Scalar & Scalar & Scalar & {\lstinline!c := a ^ b!}\\
Scalar & $n \times m \times \ldots$ & $n \times m \times \ldots$ & {\lstinline!c[$j$, $k$, $\ldots$] := a ^ b[$j$, $k$, $\ldots$]!}\\
$n \times m \times \ldots$ & Scalar & $n \times m \times \ldots$ & {\lstinline!c[$j$, $k$, $\ldots$] := a[$j$, $k$, $\ldots$] ^ b!}\\
$n \times m \times \ldots$ & $n \times m \times \ldots$ & $n \times m \times \ldots$ & {\lstinline!c[$j$, $k$, $\ldots$] := a[$j$, $k$, $\ldots$] ^ b[$j$, $k$, $\ldots$]!}\\
\hline
\end{tabular}
\end{center}
Expand Down
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