Struct RegularizedBoseKernel 

pub struct RegularizedBoseKernel { /* private fields */ }

Regularized bosonic analytical continuation kernel

Deprecated: use LogisticKernel, the default kernel for both statistics. RegularizedBoseKernel will be removed in a future release (https://github.com/SpM-lab/sparse-ir-rs/issues/273).

In dimensionless variables x = 2τ/β - 1, y = βω/Λ, the integral kernel is:

K(x, y) = y * exp(-Λ y (x + 1) / 2) / (1 - exp(-Λ y))

This kernel is used for bosonic Green’s functions. The factor y regularizes the singularity at ω = 0, making the kernel well-behaved for numerical work.

The dimensionalized kernel is related by:

K(τ, ω) = ωmax * K(2τ/β - 1, ω/ωmax)

where ωmax = Λ/β.

Properties

• Centrosymmetric: K(x, y) = K(-x, -y)
• ypower = 1: K(x, y) carries one power of y; in physical units K(τ, ω) = ω e^{-τω} / (1 - e^{-βω}) acts on ρ(ω)/ω, i.e. G(τ) = -∫ dω K(τ, ω) ρ(ω)/ω (irbasis paper, Chikano et al., CPC 240, 181 (2019), arXiv:1807.05237, Eqs. (1)-(3))
• Bosonic only: Does not support fermionic statistics
• Regularizer: w(β, ω) = ω for bosonic statistics (see regularizer)

Numerical Stability

The expression v / (exp(v) - 1) is evaluated using expm1 for small |v|.

Implementations

impl RegularizedBoseKernel

pub fn new(lambda: f64) -> Result<RegularizedBoseKernel, Error>

👎Deprecated:

use LogisticKernel, the default kernel for both statistics; RegularizedBoseKernel will be removed in a future release (https://github.com/SpM-lab/sparse-ir-rs/issues/273)

Create a new RegularizedBoseKernel

Arguments

• lambda - Kernel cutoff Λ (must be positive and finite)

Errors

Error::InvalidParameter if lambda is not positive and finite. At Λ = 0 the kernel is infinite at y = 0 (K = 1/Λ there), so its SVE does not exist.

Trait Implementations

impl AbstractKernel for RegularizedBoseKernel

fn compute<T>(&self, x: T, y: T) -> T

where T: CustomNumeric + Copy + Debug,

Compute the kernel value K(x, y) with high precision

fn is_centrosymmetric(&self) -> bool

Check if the kernel is centrosymmetric

impl CentrosymmKernel for RegularizedBoseKernel

fn compute_reduced<T>(&self, x: T, y: T, symmetry: SymmetryType) -> T

where T: CustomNumeric + Copy + Debug,

Compute the reduced kernel value

fn lambda(&self) -> f64

Get the cutoff parameter Λ (lambda)

impl Clone for RegularizedBoseKernel

fn clone(&self) -> RegularizedBoseKernel

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Copy for RegularizedBoseKernel

impl Debug for RegularizedBoseKernel

fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl KernelProperties for RegularizedBoseKernel

type SVEHintsType<T: Copy + Debug + Send + Sync + CustomNumeric + 'static> = RegularizedBoseSVEHints<T>

Associated type for SVE hints

fn ypower(&self) -> i32

Power with which the y coordinate scales.

fn conv_radius(&self) -> f64

Convergence radius of the Matsubara basis asymptotic model

fn xmax(&self) -> f64

Get the upper bound of the x domain

fn ymax(&self) -> f64

Get the upper bound of the y domain

fn regularizer<S>(&self, _beta: f64, omega: f64) -> f64

where S: StatisticsType + 'static,

A regularizer for a bosonic kernel for avoiding a divergence at omega = 0.

fn sve_hints<T>( &self, epsilon: f64, ) -> <RegularizedBoseKernel as KernelProperties>::SVEHintsType<T>

where T: Copy + Debug + Send + Sync + CustomNumeric + 'static,

Create SVE hints for this kernel type.

impl PartialEq for RegularizedBoseKernel

fn eq(&self, other: &RegularizedBoseKernel) -> bool

Equality operator ==.

fn ne(&self, other: &Rhs) -> bool

Inequality operator !=.

impl StructuralPartialEq for RegularizedBoseKernel