Commit b1450981 authored by Oliver Sander's avatar Oliver Sander

Minor fixes in Chapter 4

I am happy with it now.
parent 5fad945d
......@@ -2406,20 +2406,19 @@ returns the
path of the subtree associated to the \cpp{SubspaceBasis}
within the full tree.
For convenience a global basis behaves like a trivial \cpp{SubspaceBasis},
i.e., it has the method \cpp{rootBasis()} returning the basis itself
and \cpp{prefixPath()} returns an empty tree-path.
Notice that a \cpp{SubspaceBasis} differs from a classical
global basis, because the global multi-indices are the
same as the ones of the root basis and thus in general
neither consecutive nor zero-based. As a consequence those multi-indices
i.e., it has the method \cpp{rootBasis()} returning the basis itself,
and \cpp{prefixPath()} returning an empty tree-path.
Note that a \cpp{SubspaceBasis} differs from a full
global basis because the global multi-indices are the
same as the ones of the root basis, and thus they are in general
neither consecutive nor zero-based. Instead, those multi-indices
allow to access containers storing coefficients for the
full root basis.
\cpp{SubspaceBasis} objects are created using a global
factory function from the root basis and the path
to the desired subtree. The path can either be passed
as a single \cpp{HybridTreePath} object (see Section~\ref{sec:multi_indices}) or
as a single \cpp{HybridTreePath} object (see Section~\ref{sec:multi_indices}), or
as a sequence of individual indices.
\begin{lstlisting}[style=Interface]
......@@ -2430,7 +2429,7 @@ auto subspaceBasis(const RootBasis& rootBasis,
template<class RootBasis, class... PathIndices>
auto subspaceBasis(const RootBasis& rootBasis, const PathIndices&... indices);
\end{lstlisting}
%
For example, suppose that \cpp{taylorHoodBasis} is any one of the implementations
of the Taylor--Hood basis defined in Section~\ref{sec:composed_bases}.
Then
......@@ -2448,9 +2447,11 @@ best illustrated by extracting a single velocity component
auto velocityZBasis = subspaceBasis(taylorHoodBasis, _0, 2);
\end{lstlisting}
For this example the following table shows the multi-indices
of the \cpp{SubspaceBasis} extracted from the full basis
(cf.\ Table~\ref{tab:th_indexing_variants})
with different columns representing different index merging strategies:
of the \cpp{SubspaceBasis} extracted from the full basis,
with columns representing the different index merging strategies also
used in Table~\ref{tab:th_indexing_variants}:
\medskip
\noindent
\makebox[\textwidth][c]{
......@@ -2513,9 +2514,10 @@ with different columns representing different index merging strategies:
\end{tabular}
}
\medskip
\cpp{SubspaceBasis} objects can be combined with
coefficient vectors to represent the corresponding vector and scalar fields.
coefficient vectors to represent vector- and scalar-valued discrete functions.
The interface for this construction is discussed in the next section.
......
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