Mesh utilities

Detailed Description

Various utilities used with Meshes.

Classes
struct	triqs::mesh::closest_mesh_point_t< T >
	Lazy struct used in various function overloads as a placeholder for the closest mesh point to a given value. More...
struct	triqs::mesh::energy_t
	Represents an energy value to distinguish constructors in imaginary-frequency mesh. More...
struct	triqs::mesh::mesh_iterator< M >
	A generic random access iterator for 1D meshes. More...

Enumerations
enum	triqs::mesh::statistic_enum
	Enum to specify particle statistics. More...

Functions
template<typename... Ts>
auto	triqs::mesh::closest_mesh_pt (Ts &&...ts)
	Construct a triqs::mesh::closest_mesh_point_t object for a single value or a std::tuple of triqs::mesh::closest_mesh_point_t objects for multiple values.
template<Mesh M>
M	triqs::mesh::copy (M const &m)
	Get a copy of a mesh (for Python bindings).
template<Mesh M>
void	triqs::mesh::copy_from (M &m1, M const &m2)
	Copy one mesh into another (for Python bindings).
template<Mesh M>
__inline__ auto	triqs::mesh::evaluate (M const &, auto const &f, typename M::index_t const &n)
	Evaluate a function \( f \) at the index of a mesh point of the given mesh.
template<Mesh M>
__inline__ auto	triqs::mesh::evaluate (M const &m, auto const &f, typename M::mesh_point_t const &mp)
	Evaluate a function \( f \) at a specific mesh point of the given mesh.
template<typename T>
__inline__ auto	triqs::mesh::evaluate (Mesh auto const &, auto const &f, mesh::closest_mesh_point_t< T > const &cmp)
	Evaluate a function \( f \) at a triqs::mesh::closest_mesh_point_t object.
__inline__ auto	triqs::mesh::evaluate (Mesh auto const &, auto const &f, nda::range::all_t)
	Evaluate a function \( f \) for nda::range::all.
template<Mesh... Ms, typename... Xs>
__inline__ auto	triqs::mesh::evaluate (mesh::prod< Ms... > const &m, auto const &f, Xs const &...xs)
	Evaluate a multivariate function \( f \) defined on the given product mesh at the given arguments.
template<typename... Ds, typename X1, typename... Xs>
__inline__ auto	triqs::mesh::evaluate (std::tuple< Ds... > const &tup, auto const &f, X1 const &x1, Xs const &...xs)
	Evaluate a multivariate function \( f \) defined on the given domains (meshes) at the given arguments.
template<typename... Ts>
uint64_t	triqs::mesh::hash (Ts &&...ts)
	Generic hash function for multiple arguments.
template<nda::MemoryArray R>
std::size_t	triqs::mesh::hash_bytes (R const &r)
	Hash the raw bytes of a contiguous nda array's elements (forwards to the byte-span overload).
std::size_t	triqs::mesh::hash_bytes (std::span< std::byte const > bytes)
	Hash the raw bytes of a span via the standard library's std::hash<std::string_view>.
auto	triqs::mesh::operator* (statistic_enum s1, statistic_enum s2)
	Multiplication operator for two triqs::mesh::statistic_enum objects.
long	triqs::mesh::positive_modulo (long x, long y)
	Calculate the positive modulo of two integer numbers.
int	triqs::mesh::sign (statistic_enum s)
	Get the sign associated with the given particle statistics.
template<MeshWithValues M>
auto	triqs::mesh::values (M const &m)
	Get the values of all mesh points in a mesh.

Variables
template<Mesh M>
static constexpr bool	triqs::mesh::is_product = false
	Constexpr bool that is true if the given triqs::mesh::Mesh type is a product of meshes, i.e. a triqs::mesh::prod.
template<Mesh M>
static constexpr int	triqs::mesh::n_variables = 1
	Constexpr variable that holds the number of meshes in a triqs::mesh::Mesh type ( \( 1 \) for non-product meshes).

Enumeration Type Documentation

statistic_enum

enum triqs::mesh::statistic_enum

#include <triqs/mesh/utils.hpp>

Enum to specify particle statistics.

The following statistics are supported:

• Boson and
• Fermion.

Definition at line 163 of file utils.hpp.

Function Documentation

closest_mesh_pt()

template<typename... Ts>

auto triqs::mesh::closest_mesh_pt ( Ts &&... ts )

nodiscard

#include <triqs/mesh/utils.hpp>

Construct a triqs::mesh::closest_mesh_point_t object for a single value or a std::tuple of triqs::mesh::closest_mesh_point_t objects for multiple values.

Template Parameters

Ts	Value types.

Parameters

ts	Values to be wrapped in triqs::mesh::closest_mesh_point_t objects.

Returns

Either a triqs::mesh::closest_mesh_point_t object or a tuple of such objects.

Definition at line 199 of file utils.hpp.

copy()

template<Mesh M>

M triqs::mesh::copy ( M const & m )

nodiscard

#include <triqs/mesh/utils.hpp>

Get a copy of a mesh (for Python bindings).

Template Parameters

M	A mesh type.

Parameters

m	The mesh object to copy.

Returns

Copy of the given mesh.

Definition at line 137 of file utils.hpp.

copy_from()

template<Mesh M>

void triqs::mesh::copy_from	(	M &	m1,
		M const &	m2 )

#include <triqs/mesh/utils.hpp>

Copy one mesh into another (for Python bindings).

Simply calls the copy assignment operator of the mesh.

Template Parameters

M	A mesh type.

Parameters

m1	The mesh object to copy into.
m2	The mesh object to copy from.

Definition at line 148 of file utils.hpp.

evaluate() [1/6]

template<Mesh M>

__inline__ auto triqs::mesh::evaluate	(	M const &	,
		auto const &	f,
		typename M::index_t const &	n )

#include <triqs/mesh/evaluate.hpp>

Evaluate a function \( f \) at the index of a mesh point of the given mesh.

It simply forwards the index to the function object \( f \).

Template Parameters

M	triqs::mesh::Mesh type.

Parameters

f	Callable object \( f \) representing the function to be evaluated.
n	Mesh point index \( n \).

Returns

Result of the function call.

Definition at line 63 of file evaluate.hpp.

evaluate() [2/6]

template<Mesh M>

__inline__ auto triqs::mesh::evaluate	(	M const &	m,
		auto const &	f,
		typename M::mesh_point_t const &	mp )

#include <triqs/mesh/evaluate.hpp>

Evaluate a function \( f \) at a specific mesh point of the given mesh.

If the given mesh satisfies the triqs::mesh::MeshWithValues concept, it calls evaluate with the mesh, the function object \( f \) and the value of the mesh point. Otherwise, it calls \( f \) with the mesh point itself.

Template Parameters

M	triqs::mesh::Mesh type.

Parameters

m	Mesh object.
f	Callable object \( f \) representing the function to be evaluated.
mp	Mesh point of the mesh.

Returns

Result of the evaluation.

Definition at line 100 of file evaluate.hpp.

evaluate() [3/6]

template<typename T>

__inline__ auto triqs::mesh::evaluate	(	Mesh auto const &	,
		auto const &	f,
		mesh::closest_mesh_point_t< T > const &	cmp )

#include <triqs/mesh/evaluate.hpp>

Evaluate a function \( f \) at a triqs::mesh::closest_mesh_point_t object.

It simply forwards the given object to the function object \( f \).

Template Parameters

T	Value type of triqs::mesh::closest_mesh_point_t.

Parameters

f	Callable object \( f \) representing the function to be evaluated.
cmp	triqs::mesh::closest_mesh_point_t object.

Returns

Result of the function call.

Definition at line 75 of file evaluate.hpp.

evaluate() [4/6]

__inline__ auto triqs::mesh::evaluate	(	Mesh auto const &	,
		auto const &	f,
		nda::range::all_t	)

#include <triqs/mesh/evaluate.hpp>

Evaluate a function \( f \) for nda::range::all.

It simply calls the function object \( f \) with nda::range::all.

Parameters

f	Callable object \( f \) representing the function to be evaluated.

Returns

Result of the function call.

Definition at line 85 of file evaluate.hpp.

evaluate() [5/6]

template<Mesh... Ms, typename... Xs>

__inline__ auto triqs::mesh::evaluate	(	mesh::prod< Ms... > const &	m,
		auto const &	f,
		Xs const &...	xs )

#include <triqs/mesh/evaluate.hpp>

Evaluate a multivariate function \( f \) defined on the given product mesh at the given arguments.

It simply forwards the arguments and the components of the product mesh to triqs::mesh::evaluate.

Template Parameters

Ms	triqs::mesh::Mesh types of the product mesh.
Xs	Argument types.

Parameters

m	Product mesh.
f	Callable object \( f \) representing the function to be evaluated.
xs	Arguments \( x_1, \dots, x_n \).

Returns

Result of the evaluation \( f(x_1, \dots, x_n) \).

Definition at line 177 of file evaluate.hpp.

evaluate() [6/6]

template<typename... Ds, typename X1, typename... Xs>

__inline__ auto triqs::mesh::evaluate	(	std::tuple< Ds... > const &	tup,
		auto const &	f,
		X1 const &	x1,
		Xs const &...	xs )

#include <triqs/mesh/evaluate.hpp>

Evaluate a multivariate function \( f \) defined on the given domains (meshes) at the given arguments.

The function is evaluated by currying, i.e. it is evaluated step by step for each domain.

Suppose that we want to evaluate the function \( f : \mathrm{D}_1 \times \dots \times \mathrm{D}_n \to \mathrm{R} \) at the points \( x_1 \in \mathrm{D}_1, \dots, x_n \in \mathrm{D}_n \). Then currying works by creating a sequence of functions each taking one argument:

\[ \mathrm{curry}(f) : \mathrm{D}_n \to ( \mathrm{D_{n-1}} \to ( \dots \to ( \mathrm{D}_1 \to \mathrm{R} ) ) ) \; . \]

Here, \( \mathrm{curry}(f) \) is a function that

• takes an argument \( x_n \in \mathrm{D}_n \) and returns a new function \( f_{x_n} \) that
• takes an argument \( x_{n-1} \in \mathrm{D}_{n-1} \) and returns a new function \( f_{x_n, x_{n-1}} \) that
• . . .
• takes an argument \( x_{2} \in \mathrm{D}_2 \) and returns a new function \( f_{x_n, x_{n-1}, \dots, x_2} \) that
• takes an argument \( x_1 \in \mathrm{D}_1 \) and returns the final result \( f(x_1, \dots, x_n) \).

This is used to evaluate Green's functions defined on product meshes.

Note

The intermediate functions objects \( f_{x_n, \dots} \) are hidden by nested evaluate calls.

#include <triqs/mesh.hpp>
#include <iostream>
 
// Dummy domain.
struct domain {};
 
// Overload evaluate for a single dummy domain.
auto evaluate(domain d, auto f, double x) { return f(x); }
 
int main() {
  // function to evaluate by currying
  auto f = [](double x, double y, double z) { return x + y + z; };
 
  // calculate f(1, 2, 3) = 6 using triqs::mesh::evaluate
  std::cout << triqs::mesh::evaluate(std::make_tuple(domain{}, domain{}, domain{}), f, 1, 2, 3) << std::endl;
}

Output:

6

Template Parameters

Ds	Domain (Mesh) types.
X1	First argument type.
Xs	Remaining argument types.

Parameters

tup	Tuple of the domains (meshes) \( \mathrm{D}_1, \dots, \mathrm{D}_n \).
f	Callable object \( f \) representing the function to be evaluated.
x1	First argument \( x_1 \in \mathrm{D}_1 \).
xs	Remaining arguments \( x_2 \in \mathrm{D}_2, \dots, x_n \in \mathrm{D}_n \).

Returns

Result of the evaluation \( f(x_1, \dots, x_n) \).

Definition at line 149 of file evaluate.hpp.

hash()

template<typename... Ts>

uint64_t triqs::mesh::hash ( Ts &&... ts )

nodiscard

#include <triqs/mesh/utils.hpp>

Generic hash function for multiple arguments.

It simply uses std::hash for each argument and adds the results.

Template Parameters

Ts	Argument types.

Parameters

ts	Objects to be hashed.

Returns

Combined hash value of all arguments.

Definition at line 70 of file utils.hpp.

hash_bytes() [1/2]

template<nda::MemoryArray R>

std::size_t triqs::mesh::hash_bytes ( R const & r )

nodiscard

#include <triqs/mesh/utils.hpp>

Hash the raw bytes of a contiguous nda array's elements (forwards to the byte-span overload).

Contiguity is asserted at runtime, since nda views may be strided.

Template Parameters

R	An nda::MemoryArray type.

Parameters

r	Array to hash; must be contiguous (stride 1).

Returns

Hash value of the array's element bytes.

Definition at line 93 of file utils.hpp.

hash_bytes() [2/2]

std::size_t triqs::mesh::hash_bytes ( std::span< std::byte const > bytes )

inlinenodiscard

#include <triqs/mesh/utils.hpp>

Hash the raw bytes of a span via the standard library's std::hash<std::string_view>.

A proper byte mixer, sensitive to every element and their ordering.

Parameters

bytes

Byte span to be hashed.

Returns

Hash value of the byte sequence.

Definition at line 80 of file utils.hpp.

operator*()

auto triqs::mesh::operator* ( statistic_enum s1, statistic_enum s2 )

inlinenodiscard

#include <triqs/mesh/utils.hpp>

Multiplication operator for two triqs::mesh::statistic_enum objects.

Parameters

s1	Left-hand side operand.
s2	Right-hand side operand.

Returns

Boson statistics if s1 == s2, otherwise Fermion statistics.

Definition at line 180 of file utils.hpp.

positive_modulo()

long triqs::mesh::positive_modulo ( long x, long y )

inlinenodiscard

#include <triqs/mesh/utils.hpp>

Calculate the positive modulo of two integer numbers.

Parameters

x	Left-hand side operand \( x \) of the modulo operation.
y	Right-hand side operand \( y \geq 0 \) of the modulo operation.

Returns

\[ \begin{cases} x \mod y & \text{if } x \geq 0 \\ x \mod y + y & \text{if } \text{x < 0} \end{cases} \]

Definition at line 111 of file utils.hpp.

sign()

int triqs::mesh::sign ( statistic_enum s )

inlinenodiscard

#include <triqs/mesh/utils.hpp>

Get the sign associated with the given particle statistics.

Parameters

s	triqs::mesh::statistic_enum value.

Returns

\( 1 \) for bosons and \( -1 \) for fermions.

Definition at line 171 of file utils.hpp.

values()

template<MeshWithValues M>

auto triqs::mesh::values ( M const & m )

nodiscard

#include <triqs/mesh/utils.hpp>

Get the values of all mesh points in a mesh.

Template Parameters

M	A mesh type whose points each carry a value.

Parameters

m	A mesh object.

Returns

Array containing the values of all mesh points.

Definition at line 124 of file utils.hpp.