This class implements the limited hyperbolic cut shape. More...
#include <shape_hyperbolic.hpp>
Public Member Functions | |
| LimitedHyperbolicCutShape (int S, const std::array< int, D > &limits) | |
| General constructor to define sparsity parameter and limits. More... | |
| LimitedHyperbolicCutShape (int S, int size) | |
| Specialized constructor to set all limits \( K_d \) to the same value \( K^\star \). More... | |
| LimitedHyperbolicCutShape (int S, std::initializer_list< int > list) | |
| General constructor to define sparsity parameter and limits. More... | |
| virtual int | bbox (dim_t axis) const override |
| Retrieves the length of the minimum bounding box in one direction. More... | |
| virtual int | limit (int const *base_node, dim_t axis) const override |
| Evaluates one surface function on a base node. More... | |
| virtual void | print (std::ostream &out) const override |
| Prints a pretty description of the shape. More... | |
 Public Member Functions inherited from waveblocks::wavepackets::shapes::AbstractShape< D > | |
| virtual | ~AbstractShape () |
Private Attributes | |
| int | S_ |
| std::array< int, D > | limits_ |
Detailed Description
template<dim_t D>
class waveblocks::wavepackets::shapes::LimitedHyperbolicCutShape< D >
This class implements the limited hyperbolic cut shape.
This class implements the limited hyperbolic cut basis shape which is a special type of a sparse basis shape. The limited hyperbolic cut shape in \( D \) dimensions with sparsity \(S\) and limits \( \boldsymbol{K} = (K_1,\ldots,K_D) \) is defined as the set
\[ \mathfrak{K}(D,S,\boldsymbol{K}) := \left\{(k_1,\dots,k_D) \in \mathbb{N}_0^D \mid 0 \leq k_d < K_d \; \land \displaystyle\prod_{d=1}^{D} (1+k_d) \leq S \right\} \]
It is an intersection of the hyperbolic cut shape with a hypercubic shape.
- Template Parameters
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D basis shape dimensionality
Constructor & Destructor Documentation
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inline |
General constructor to define sparsity parameter and limits.
- Parameters
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S The sparsity parameter \( S \). limits Tuple of all limits \( \boldsymbol{K} \).
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inline |
Specialized constructor to set all limits \( K_d \) to the same value \( K^\star \).
- Parameters
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S The sparsity parameter \( S \). size The limit \( K^\star \).
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inline |
General constructor to define sparsity parameter and limits.
- Parameters
-
S The sparsity parameter \( S \). list List of all limits \( \boldsymbol{K} \).
Member Function Documentation
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inlineoverridevirtual |
Retrieves the length of the minimum bounding box in one direction.
The minimum bounding box is given by
\[ L_{\alpha}=\max_{k_{\alpha}}\left\{\underline{k} \in \mathfrak{K}\right\} \]
- Parameters
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axis The direction \( \alpha \).
- Returns
- Length of the bbox.
Implements waveblocks::wavepackets::shapes::AbstractShape< D >.
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inlineoverridevirtual |
Evaluates one surface function on a base node.
The surface function to direction \( \alpha \) is given by
\[ s_{\alpha}(\underline{n})=\max_{k_{\alpha}} \left\{\underline{k} \in \mathfrak{K} \;|\; k_d = n_d \; \forall d \neq \alpha \right\} \]
Notice that the \( \alpha \)-th entry of \( \underline{n} \) does not influence return value. It can be of any value since it is simply ignored.
- Parameters
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base_node The basis node \( \underline{n} \). It contains D indices. axis The direction \( \alpha \).
- Returns
- Value of the surface function.
Implements waveblocks::wavepackets::shapes::AbstractShape< D >.
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inlineoverridevirtual |
Prints a pretty description of the shape.
- Parameters
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out The output stream.
Implements waveblocks::wavepackets::shapes::AbstractShape< D >.
Member Data Documentation
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private |
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private |
The documentation for this class was generated from the following file:
- /userdata/raoulb/LWB/libwaveblocks/waveblocks/wavepackets/shapes/shape_hyperbolic.hpp
