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WaveBlocksND
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Classes | |
| class | ContinuousSqrt |
| This class deals with the issue, that the square root of complex numbers is not unique. More... | |
| class | KahanSum |
| The Kahan's algorithm achieves O(1) error growth for summing N numbers. More... | |
Typedefs | |
| template<int D> | |
| using | partition_t = std::array< int, D > |
| template<int D> | |
| using | partitions_t = std::list< partition_t< D >> |
| template<int D> | |
| using | point_t = std::array< int, D > |
| template<int D> | |
| using | latticepoints_t = std::list< point_t< D >> |
| template<int D> | |
| using | permutation_t = std::array< int, D > |
| template<int D> | |
| using | permutations_t = std::list< permutation_t< D >> |
Functions | |
| template<int D> | |
| int | sum (const point_t< D > Z) |
| Sum of the components of the point Z. More... | |
| template<int D> | |
| int | nz (const point_t< D > Z) |
| template<int D> | |
| int | nnz (const point_t< D > Z) |
| template<int D> | |
| partitions_t< D > | partitions (const int K) |
| template<int D> | |
| latticepoints_t< D > | lattice_points (const int N) |
| template<int D> | |
| permutations_t< D > | permutations (const permutation_t< D > permutation) |
| template<class T > | |
| constexpr T | pi () |
| using waveblocks::math::latticepoints_t = typedef std::list<point_t<D>> |
| using waveblocks::math::partition_t = typedef std::array<int, D> |
| using waveblocks::math::partitions_t = typedef std::list<partition_t<D>> |
| using waveblocks::math::permutation_t = typedef std::array<int, D> |
| using waveblocks::math::permutations_t = typedef std::list<permutation_t<D>> |
| using waveblocks::math::point_t = typedef std::array<int, D> |
| latticepoints_t<D> waveblocks::math::lattice_points | ( | const int | N | ) |
This method enumerates all lattice points of a lattice \(\Lambda \subset \mathbb{N}^D\) in \(D\) dimensions having fixed \(l_1\) norm \(N\).
| N | The \(l_1\) norm of the lattice points. |
| int waveblocks::math::nnz | ( | const point_t< D > | Z | ) |
Number of non-zero components of the point Z.
| int waveblocks::math::nz | ( | const point_t< D > | Z | ) |
Number of zero components of the point Z.
| partitions_t<D> waveblocks::math::partitions | ( | const int | K | ) |
Enumerate integer partitions in anti-lexocographic order for integers up to some limit K. All partitions have exactly D parts, some may be zero.
| K | The Level |
| permutations_t<D> waveblocks::math::permutations | ( | const permutation_t< D > | permutation | ) |
Enumerate all permutations in anti-lexicographical order follwing the given permutation \(P\).
| permutation | A permutation. |
| constexpr T waveblocks::math::pi | ( | ) |
| int waveblocks::math::sum | ( | const point_t< D > | Z | ) |
Sum of the components of the point Z.
1.8.11