Imaginary frequency discrete Lehmann representation (DLR) mesh type.
An imaginary frequency DLR mesh is defined by the inverse temperature \( \beta > 0 \), the particle statistics, a DLR energy cutoff \( \omega_{\text{max}} \), an error tolerance \( \epsilon \) and a boolean flag specifying if the mesh should be symmetric around \( i\omega_n = 0 \) (a symmetric mesh enforces the DLR rank to be even for Fermions and odd for Bosons).
An imaginary frequency DLR mesh has the following properties:
- Each mesh point is identified by a unique index \( l \in \{0, 1, \ldots, N-1\} \).
- The size of the mesh \( N \) depends on \( \beta \) and the choice of \( \omega_{\text{max}} \) and \( \epsilon \). It is equal to the DLR rank \( r \) and the number of DLR basis functions \( K(i\omega_n, \omega_l) \).
- An index \( l \) is mapped to the corresponding data index \( d \) by the identity function \( d(l) = l \) and vice versa.
- An index \( l \) is mapped to the corresponding value \( i\omega_{n_l} \), where \( i\omega_{n_l} \) is the l-th DLR interpolation node in imaginary frequency space.
- Note
- The index \( l \), which is used to access a certain mesh point, is different from the Matsubara index \( n_l \) that is stored in the mesh point object. That means, if m is an instance of imaginary-frequency DLR mesh, then m(l).index() != l in general.
Green's function containers that are based on an imaginary frequency DLR mesh store the function values at the discrete frequency points \( i\omega_{n_l} \), i.e. \( f_l = f(i\omega_{n_l}) \). In contrast to DLR and imaginary-frequency meshes, the GF container cannot evaluate the function at an arbitrary Matsubara frequency \( i\omega_n \) (evaluation at arbitrary points is intentionally unsupported).
Definition at line 80 of file dlr_imfreq.hpp.
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| dlr_imfreq ()=default |
| | Default constructor constructs an empty mesh.
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| | dlr_imfreq (double beta, statistic_enum statistic, double w_max, double eps, bool symmetrize=true) |
| | Construct an imaginary frequency DLR mesh with a given energy cutoff \( \omega_{\text{max}} \) and error tolerance \( \epsilon \).
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| template<nda::AnyOf< dlr_imtime, dlr > M> |
| | dlr_imfreq (M const &m) |
| | Construct an imaginary frequency DLR mesh from another DLR type mesh.
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auto | begin () const |
| | Get an iterator to the beginning of the mesh.
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double | beta () const noexcept |
| | Get the inverse temperature \( \beta \).
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auto | cbegin () const |
| | Get a const iterator to the beginning of the mesh.
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auto | cend () const |
| | Get a const iterator to the end of the mesh.
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| void | deserialize (auto &ar) |
| | Deserialize the mesh from a generic archive.
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auto const & | dlr_freq () const |
| | Get the array of DLR frequencies \( \omega_l \).
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auto const & | dlr_if () const |
| | Get the Matsubara frequency DLR operations object (see also cppdlr::imfreq_ops).
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auto const & | dlr_it () const |
| | Get the imaginary time DLR operations object (see also cppdlr::imtime_ops).
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auto | end () const |
| | Get an iterator to the end of the mesh.
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double | eps () const noexcept |
| | Get the DLR error tolerance \( \epsilon \).
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| bool | is_index_valid (long l) const noexcept |
| | Check if an index \( l \) is valid.
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uint64_t | mesh_hash () const noexcept |
| | Get the hash value of the mesh.
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auto | min_max_frequencies () const noexcept |
| | Get a pair containing the smallest and largest Matsubara frequency in the mesh.
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| mesh_point_t | operator() (long l) const |
| | Function call operator to access a mesh point by its index \( l \in \{0, 1, \ldots, N-1\} \).
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bool | operator== (dlr_imfreq const &m) const |
| | Equal-to comparison operator compares the hash values.
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| mesh_point_t | operator[] (long d) const |
| | Subscript operator to access a mesh point by its data index \( d \in \{0, 1, \ldots, N-1\} \).
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| void | serialize (auto &ar) const |
| | Serialize the mesh to a generic archive.
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long | size () const noexcept |
| | Get the size \( N \) of the mesh, i.e. the DLR rank \( r \).
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statistic_enum | statistic () const noexcept |
| | Get the particle statistics.
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bool | symmetrize () const noexcept |
| | Is the mesh symmetric around \( i\omega_n = 0 \)?
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| long | to_data_index (long l) const noexcept |
| | Map an index \( l \in \{0, 1, \ldots, N-1\} \) to its corresponding data index \( d(l) \).
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| long | to_index (long d) const noexcept |
| | Map a data index \( d \in \{0, 1, \ldots, N-1\} \) to the corresponding index \( l(d) \).
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| matsubara_freq | to_value (long l) const noexcept |
| | Map an index \( l \in \{0, 1, \ldots, N-1\} \) to its corresponding Matsubara frequency \( i\omega_{n_l} \).
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double | w_max () const noexcept |
| | Get the DLR energy cutoff \( \omega_{\text{max}} = \Lambda / \beta \).
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1.15.0