Struct DiscreteGaussianIntegerSampler 

pub struct DiscreteGaussianIntegerSampler {
    pub center: Q,
    pub s: Q,
    pub lower_bound: Z,
    pub interval_size: Z,
    pub lookup_table_setting: LookupTableSetting,
    pub table: HashMap<Z, f64>,
}

Enables for discrete Gaussian sampling out of [⌈center - s * tailcut⌉ , ⌊center + s * tailcut⌋ ].

WARNING: If the attributes are not set using DiscreteGaussianIntegerSampler::init, we can’t guarantee sampling from the correct discrete Gaussian distribution. Altering any value will invalidate the HashMap in table and might invalidate other attributes, too.

Attributes:

• center: specifies the position of the center with peak probability
• s: specifies the Gaussian parameter, which is proportional to the standard deviation sigma * sqrt(2 * pi) = s
• lower_bound: specifies the lower bound to sample uniformly from
• interval_size: specifies the interval size to sample uniformly from
• lookup_table_setting: Specifies whether a lookup-table should be used and how it should be filled, i.e. lazily on-the-fly (impacting sampling time slightly) or precomputed
• table: the lookup-table if one is used

Examples

use qfall_math::{integer::Z, rational::Q};
use qfall_math::utils::sample::discrete_gauss::{DiscreteGaussianIntegerSampler, LookupTableSetting};
let n = Z::from(1024);
let center = 0.0;
let gaussian_parameter = 1.0;
let tailcut = 6.0;

let mut dgis = DiscreteGaussianIntegerSampler::init(center, gaussian_parameter, tailcut, LookupTableSetting::NoLookup).unwrap();

let sample = dgis.sample_z();

Fields

center: Q

s: Q

lower_bound: Z

interval_size: Z

lookup_table_setting: LookupTableSetting

table: HashMap<Z, f64>

Implementations

impl DiscreteGaussianIntegerSampler

pub fn init( center: impl Into<Q>, s: impl Into<Q>, tailcut: impl Into<Q>, lookup_table_setting: LookupTableSetting, ) -> Result<Self, MathError>

Initializes the DiscreteGaussianIntegerSampler with

• center as the center of the discrete Gaussian to sample from,
• s defining the Gaussian parameter, which is proportional to the standard deviation sigma * sqrt(2 * pi) = s,
• lower_bound as ⌈center - 6 * s⌉,
• interval_size as ⌊center + 6 * s⌋ - ⌈center - 6 * s⌉ + 1, and
• table as an empty HashMap to store evaluations of the Gaussian function.

Parameters:

• n: specifies the range from which is sampled
• center: as the center of the discrete Gaussian to sample from
• s: specifies the Gaussian parameter, which is proportional to the standard deviation sigma * sqrt(2 * pi) = s

Returns a sample chosen according to the specified discrete Gaussian distribution or a MathError if the specified parameters were not chosen appropriately, i.e. n > 1 or s > 0.

Examples

use qfall_math::{integer::Z, rational::Q};
use qfall_math::utils::sample::discrete_gauss::{DiscreteGaussianIntegerSampler, LookupTableSetting};
let center = 0.0;
let gaussian_parameter = 1.0;
let tailcut = 6.0;

let mut dgis = DiscreteGaussianIntegerSampler::init(center, gaussian_parameter, tailcut, LookupTableSetting::Precompute).unwrap();

Errors and Failures

• Returns a MathError of type InvalidIntegerInput if tailcut < 0 or s < 0.

pub fn sample_z(&mut self) -> Z

Chooses a sample according to the discrete Gaussian distribution out of [lower_bound , lower_bound + interval_size ].

This function implements discrete Gaussian sampling according to the definition of SampleZ as in [1].

Examples

use qfall_math::{integer::Z, rational::Q};
use qfall_math::utils::sample::discrete_gauss::{DiscreteGaussianIntegerSampler, LookupTableSetting};
let center = 0.0;
let gaussian_parameter = 1.0;
let tailcut = 6.0;

let mut dgis = DiscreteGaussianIntegerSampler::init(center, gaussian_parameter, tailcut, LookupTableSetting::Precompute).unwrap();

let sample = dgis.sample_z();

Trait Implementations

impl Clone for DiscreteGaussianIntegerSampler

fn clone(&self) -> DiscreteGaussianIntegerSampler

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for DiscreteGaussianIntegerSampler

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for DiscreteGaussianIntegerSampler

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Serialize for DiscreteGaussianIntegerSampler

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.