From f5f943d0bc02d1207590227b17aaaebeb0a4be1b Mon Sep 17 00:00:00 2001 From: Henrik Tidefelt Date: Thu, 23 Apr 2020 23:22:53 +0200 Subject: [PATCH] Clean up non-normative content in annotations.tex --- chapters/arrays.tex | 88 ++++++++++++++++++++++----------------------- 1 file changed, 44 insertions(+), 44 deletions(-) diff --git a/chapters/arrays.tex b/chapters/arrays.tex index b27165781..7b5227e58 100644 --- a/chapters/arrays.tex +++ b/chapters/arrays.tex @@ -8,22 +8,25 @@ \chapter{Arrays}\doublelabel{arrays} Each array has a certain dimensionality, i.e., number of dimensions. The degenerate case of a scalar variable is not really an array, but can be regarded as an array with zero dimensions. Vectors have one dimension, -matrices have two dimensions, etc. {[}\emph{So-called row vectors and -column vectors do not exist in Modelica and cannot be distinguished -since vectors have only one dimension. If distinguishing these is -desired, row matrices and column matrices are available, being the -corresponding two-dimensional entities. However, in practice this is -seldom needed since the usual matrix arithmetic and linear algebra -operations have been defined to give the expected behavior when -operating on Modelica vectors and matrices.}{]} +matrices have two dimensions, etc. + +\begin{nonnormative} +So-called row vectors and column vectors do not exist in Modelica and cannot be distinguished since vectors have only one +dimension. If distinguishing these is desired, row matrices and column matrices are available, being the corresponding +two-dimensional entities. However, in practice this is seldom needed since the usual matrix arithmetic and linear algebra +operations have been defined to give the expected behavior when operating on Modelica vectors and matrices. +\end{nonnormative} Modelica is a strongly typed language, which also applies to array types. The number of dimensions of an array is fixed and cannot be -changed at run-time {[}\emph{in order to permit strong type checking and -efficient implementation.}{]} However, the sizes of array dimensions can -be computed at run-time, {[}\emph{allowing fairly generic array -manipulation code to be written as well as interfacing to standard -numeric libraries implemented in other programming languages}.{]} +changed at run-time. However, the sizes of array dimensions can +be computed at run-time. + +\begin{nonnormative} +The fixed number of array dimensions permits strong type checking and efficient implementation. The non-fixed sizes of array +dimensions on the other hand, allow fairly generic array manipulation code to be written as well as interfacing to standard +numeric libraries implemented in other programming languages. +\end{nonnormative} An array is allocated by declaring an array variable or calling an array constructor. Elements of an array can be indexed by \lstinline!Integer!, \lstinline!Boolean!, or @@ -33,18 +36,20 @@ \section{Array Declarations}\doublelabel{array-declarations} The Modelica type system includes scalar number, vector, matrix (number of dimensions, ndim=2), and arrays of more than two dimensions. -{[}\emph{There is no distinguishing between a row and column vector}.{]} + +\begin{nonnormative} +There is no distinguishing between a row and column vector. +\end{nonnormative} The following table shows the two possible forms of declarations and defines the terminology. C is a placeholder for any class, including the -built-in type classes Real, Integer, Boolean, String, and enumeration +built-in type classes \lstinline!Real!, \lstinline!Integer!, \lstinline!Boolean!, \lstinline!String!, and enumeration types. The type of a dimension upper bound expression, e.g. n, m, p,... -in the table below, need to be a subtype of Integer or EB for a class EB -that is an enumeration type or subtype of the Boolean type. +in the table below, need to be a subtype of \lstinline!Integer! or EB for a class EB +that is an enumeration type or subtype of the \lstinline!Boolean! type. -Colon (:) -indicates that the dimension upper bound is unknown and is a subtype of -Integer. The size of such a variable can be determined from its binding equation, or the size +Colon (:) indicates that the dimension upper bound is unknown and is a subtype of +\lstinline!Integer!. The size of such a variable can be determined from its binding equation, or the size of any of its array attributes - see also \autoref{flexible-array-sizes-and-resizing-of-arrays-in-functions}. The size cannot be determined from other equations or algorithm. @@ -80,45 +85,41 @@ \section{Array Declarations}\doublelabel{array-declarations} ($k \geq 0$).\\ \hline \end{longtable} -{[}\emph{The number of dimensions and the dimensions sizes are part of +\begin{example} +The number of dimensions and the dimensions sizes are part of the type, and shall be checked for example at redeclarations. Declaration form 1 displays clearly the type of an array, whereas declaration form 2 is the traditional way of array declarations in -languages such as Fortran, C, C++.} +languages such as Fortran, C, C++. \begin{lstlisting}[language=modelica] Real[:] v1, v2 // vectors v1 and v2 have unknown sizes. The actual sizes may be different. \end{lstlisting} - -\emph{It is possible to mix the two declaration forms although it might -be confusing.} - +It is possible to mix the two declaration forms although it might be confusing. \begin{lstlisting}[language=modelica] Real[3,2] x[4,5]; // x has type Real[4,5,3,2]; \end{lstlisting} -\emph{The reason for this order is given by examples such as:} - +The reason for this order is given by examples such as: \begin{lstlisting}[language=modelica] type R3=Real[3]; R3 a; R3 b[1]={a}; Real[3] c[1]=b; \end{lstlisting} -\emph{Using a type for \lstinline!a! and \lstinline!b! in this way is normal, and -substituting a type by its definition allow \lstinline!c!.} - -\emph{A vector \lstinline!y! indexed by enumeration values} +Using a type for \lstinline!a! and \lstinline!b! in this way is normal, and +substituting a type by its definition allow \lstinline!c!. +A vector \lstinline!y! indexed by enumeration values \begin{lstlisting}[language=modelica] type TwoEnums = enumeration(one,two); Real[TwoEnums] y; \end{lstlisting} -{]} +\end{example} -Zero-valued dimensions are allowed, so: \lstinline!C x[0];! declares an empty - vector and: \lstinline!C x[0,3]!; an empty matrix. -{[}\emph{Special cases}: +Zero-valued dimensions are allowed, so: \lstinline!C x[0];! declares an empty vector and: \lstinline!C x[0,3]!; an empty matrix. +\begin{nonnormative} +Special cases: \begin{longtable}{|l|l|l|l|p{3cm}|} \caption{Declaration of arrays as 1-vectors, row-vectors, or column-vectors of arrays.}\\ @@ -131,8 +132,7 @@ \section{Array Declarations}\doublelabel{array-declarations} C{[}n,1{]} x; & C x{[}n, 1{]}; & 2 & Matrix & n x 1 -- Matrix, representing a column\\ \hline C{[}1,n{]} x; & C x{[}1, n{]}; & 2 & Matrix & 1 x n -- Matrix, representing a row\\ \hline \end{longtable} - -{]} +\end{nonnormative} The type of an array of array is the multidimensional array which is constructed by taking the first dimensions from the component @@ -537,7 +537,6 @@ \section{Vector, Matrix and Array Constructors}\doublelabel{vector-matrix-and-ar The constructor function \lstinline!array(A,B,C,...)! 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., @@ -796,11 +795,8 @@ \section{Array Indexing}\doublelabel{array-indexing} The array indexing operator \emph{name}\lstinline![!\emph{...}\lstinline!]! is used to access array elements for retrieval of their values or for updating these values. An indexing operation is subject to upper and lower array -dimension index bounds (\autoref{array-dimension-lower-and-upper-index-bounds}). {[}\emph{An indexing operation -is assumed to take constant time, i.e., largely independent of the size -of the array.}{]} The indexing operator takes two or more operands, -where the first operand is the array to be indexed and the rest of the -operands are index expressions: +dimension index bounds (\autoref{array-dimension-lower-and-upper-index-bounds}). The indexing operator takes two or more +operands, where the first operand is the array to be indexed and the rest of the operands are index expressions: arrayname{[}\emph{indexexpr1}, \emph{indexexpr2}, ...{]} @@ -818,6 +814,10 @@ \section{Array Indexing}\doublelabel{array-indexing} side and the index on the left-hand side are evaluated before any element is assigned a new value. +\begin{nonnormative} +An indexing operation is assumed to take constant time, i.e., largely independent of the size of the array. +\end{nonnormative} + \begin{example} \begin{lstlisting}[language=modelica, escapechar=!] a[:, j] !\emph{is a vector of the j-th column of a,}!