Struct Pdf 

pub struct Pdf { /* private fields */ }

Represents a Probability Distribution Function.

PDFs are used to indicate to schedule generators where samples should be taken.

Implementations

impl Pdf

pub fn from_integral( integral: impl Fn(f64) -> f64 + 'static + Send + Sync, len: usize, ) -> Pdf

Create a PDF from a continuous representation.

Expects the integral of the PDF being represented. This is often called the Cumulative Distribution Function or CDF. The function will receive inputs from 0..=len. The len parameter is the length of the PDF in number of samples.

The CDF is expected to be monotonically increasing, and integral(len as f64) - integral(0.) must be one. These are the necessary conditions for a function to be a valid CDF.

It is not assumed that integral(0.) = 0..

Example

// This represents an unweighted PDF because the integral of a constant function is linear.
// You can use the `unweighted` preset instead if you would like
let pdf = Pdf::from_integral(|v| v / 256., 256);

Panics

This function will assert that

• integral(len as f64) - integral(0.) ≈ 1. with some margin for floating point error allowed;
• the CDF is monotonically increasing for particular intervals; and
• len is non-zero.

pub fn from_discrete(discrete: Vec<f64>) -> Pdf

Create a PDF from a discrete representation.

Expects a list of probabilities, one for each sample, that are all non-negative and sum to one.

Example

let pdf = Pdf::from_discrete(vec![0.125, 0.5, 0.375]);

Panics

This function will assert that

• the sum of all of the probabilities is one, with some margin for floating point error allowed;
• all probabilities are non-negative; and
• the length of the PDF is non-zero.

pub fn get_distribution(&self) -> &[f64]

Calculate the discrete representation of the PDF.

This method is memoized.

Example

assert!(
    unweighted(3)
        .get_distribution()
        .iter()
        .zip([1. / 3., 1. / 3., 1. / 3.])
        .all(|(l, r)| (l - r).abs() < 0.00001),
);

pub fn get_integral(&self) -> &[f64]

Calculate the integral of the PDF for whole number values

The output has length self.len() + 1. The value at index 0 is guaranteed to be zero and the output at index self.len() is guaranteed to be one with a small margin for floating point error.

This method is memoized.

Example

assert!(
    Pdf::from_discrete(vec![0.3, 0.6, 0.1])
        .get_integral()
        .iter()
        .zip([0., 0.3, 0.9, 1.])
        .all(|(l, r)| (l - r).abs() < 0.00001),
);

pub fn slice(&self, range: Range<usize>) -> Pdf

Slice a PDF to fit a certain range

The PDF will be automatically rescaled to still sum to one.

Example

assert!(
    exponential(256, 4.)
        .slice(0..128)
        .get_distribution()
        .iter()
        .zip(exponential(128, 2.)
           .get_distribution()
        )
        .all(|(l, r)| (l - r).abs() < 0.00001),
);

pub fn len(&self) -> usize

Returns the length of the PDF in number of samples.

Example

assert_eq!(linear(256).len(), 256);

pub fn probabilities(&self, count: usize) -> &Probabilities

Calculate the probabilities of selecting each sample position under random sampling given the number of samples to select.

Example

// With unweighted sampling and selecting 128 out of 256,
// each sample position has a 1/2 chance of being selected.
assert!(
    unweighted(256)
        .probabilities(128)
        .iter()
        .all(|v| (*v - 0.5).abs() < 0.000001)
);

Note that this only gives a very good approximation because the true value is (as of now) computationally infeasible to find.

This method is memoized.

pub fn sample_pdf<R: Rng + ?Sized>(&self, rng: &mut R) -> usize

Sample the PDF using the given Rng

Returns the zero-based index of the position that was sampled.

pub fn continuous_integral<'a>(&'a self) -> Rc<dyn Fn(f64) -> f64 + 'a>

Return a continuous representation of the integral of the PDF. Applying 0. to the returned function will return 0..

This function is implemented for discretely represented PDFs by interpolating self.get_integral() using Catmull-Rom to give a once-differentiable interpolation.

Example

let pdf = qsin(256, QSinBias::Low, PI);
let integral = pdf.continuous_integral();

assert_eq!(integral(0.), 0.);
assert_eq!(integral(256.), 1.);
let c = FRAC_PI_2 - 1.;
assert_eq!(integral(128.), (FRAC_PI_4 + FRAC_PI_4.cos()) / c - 1. / c);

Panics

The function returned will panic if it is called with values outside of the range of the PDF.

Trait Implementations

impl Debug for Pdf

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

Formats the value using the given formatter.