# gamma.rs.html -- source
Source to the Rust file `C:\Users\zcdziura\.cargo\registry\src\github.com-88ac128001ac3a9a\rand-0.3.14\src\distributions\gamma.rs`.
Keywords: rust, rustlang, rust-lang

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    // Copyright 2013 The Rust Project Developers. See the COPYRIGHT
    // file at the top-level directory of this distribution and at
    // http://rust-lang.org/COPYRIGHT.
    //
    // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
    // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
    // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
    // option. This file may not be copied, modified, or distributed
    // except according to those terms.
    //
    // ignore-lexer-test FIXME #15679

    //! The Gamma and derived distributions.

    use self::GammaRepr::*;
    use self::ChiSquaredRepr::*;

    use {Rng, Open01};
    use super::normal::StandardNormal;
    use super::{IndependentSample, Sample, Exp};

    /// The Gamma distribution `Gamma(shape, scale)` distribution.
    ///
    /// The density function of this distribution is
    ///
    /// ```text
    /// f(x) =  x^(k - 1) * exp(-x / θ) / (Γ(k) * θ^k)
    /// ```
    ///
    /// where `Γ` is the Gamma function, `k` is the shape and `θ` is the
    /// scale and both `k` and `θ` are strictly positive.
    ///
    /// The algorithm used is that described by Marsaglia & Tsang 2000[1],
    /// falling back to directly sampling from an Exponential for `shape
    /// == 1`, and using the boosting technique described in [1] for
    /// `shape < 1`.
    ///
    /// # Example
    ///
    /// ```rust
    /// use rand::distributions::{IndependentSample, Gamma};
    ///
    /// let gamma = Gamma::new(2.0, 5.0);
    /// let v = gamma.ind_sample(&mut rand::thread_rng());
    /// println!("{} is from a Gamma(2, 5) distribution", v);
    /// ```
    ///
    /// [1]: George Marsaglia and Wai Wan Tsang. 2000. "A Simple Method
    /// for Generating Gamma Variables" *ACM Trans. Math. Softw.* 26, 3
    /// (September 2000),
    /// 363-372. DOI:[10.1145/358407.358414](http://doi.acm.org/10.1145/358407.358414)
    #[derive(Clone, Copy)]
    pub struct Gamma {
        repr: GammaRepr,
    }

    #[derive(Clone, Copy)]
    enum GammaRepr {
        Large(GammaLargeShape),
        One(Exp),
        Small(GammaSmallShape)
    }

    // These two helpers could be made public, but saving the
    // match-on-Gamma-enum branch from using them directly (e.g. if one
    // knows that the shape is always > 1) doesn't appear to be much
    // faster.

    /// Gamma distribution where the shape parameter is less than 1.
    ///
    /// Note, samples from this require a compulsory floating-point `pow`
    /// call, which makes it significantly slower than sampling from a
    /// gamma distribution where the shape parameter is greater than or
    /// equal to 1.
    ///
    /// See `Gamma` for sampling from a Gamma distribution with general
    /// shape parameters.
    #[derive(Clone, Copy)]
    struct GammaSmallShape {
        inv_shape: f64,
        large_shape: GammaLargeShape
    }

    /// Gamma distribution where the shape parameter is larger than 1.
    ///
    /// See `Gamma` for sampling from a Gamma distribution with general
    /// shape parameters.
    #[derive(Clone, Copy)]
    struct GammaLargeShape {
        scale: f64,
        c: f64,
        d: f64
    }

    impl Gamma {
        /// Construct an object representing the `Gamma(shape, scale)`
        /// distribution.
        ///
        /// Panics if `shape <= 0` or `scale <= 0`.
        pub fn new(shape: f64, scale: f64) -> Gamma {
            assert!(shape > 0.0, "Gamma::new called with shape <= 0");
            assert!(scale > 0.0, "Gamma::new called with scale <= 0");

            let repr = match shape {
                1.0         => One(Exp::new(1.0 / scale)),
                0.0 ... 1.0 => Small(GammaSmallShape::new_raw(shape, scale)),
                _           => Large(GammaLargeShape::new_raw(shape, scale))
            };
            Gamma { repr: repr }
        }
    }

    impl GammaSmallShape {
        fn new_raw(shape: f64, scale: f64) -> GammaSmallShape {
            GammaSmallShape {
                inv_shape: 1. / shape,
                large_shape: GammaLargeShape::new_raw(shape + 1.0, scale)
            }
        }
    }

    impl GammaLargeShape {
        fn new_raw(shape: f64, scale: f64) -> GammaLargeShape {
            let d = shape - 1. / 3.;
            GammaLargeShape {
                scale: scale,
                c: 1. / (9. * d).sqrt(),
                d: d
            }
        }
    }

    impl Sample<f64> for Gamma {
        fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) }
    }
    impl Sample<f64> for GammaSmallShape {
        fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) }
    }
    impl Sample<f64> for GammaLargeShape {
        fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) }
    }

    impl IndependentSample<f64> for Gamma {
        fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 {
            match self.repr {
                Small(ref g) => g.ind_sample(rng),
                One(ref g) => g.ind_sample(rng),
                Large(ref g) => g.ind_sample(rng),
            }
        }
    }
    impl IndependentSample<f64> for GammaSmallShape {
        fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 {
            let Open01(u) = rng.gen::<Open01<f64>>();

            self.large_shape.ind_sample(rng) * u.powf(self.inv_shape)
        }
    }
    impl IndependentSample<f64> for GammaLargeShape {
        fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 {
            loop {
                let StandardNormal(x) = rng.gen::<StandardNormal>();
                let v_cbrt = 1.0 + self.c * x;
                if v_cbrt <= 0.0 { // a^3 <= 0 iff a <= 0
                    continue
                }

                let v = v_cbrt * v_cbrt * v_cbrt;
                let Open01(u) = rng.gen::<Open01<f64>>();

                let x_sqr = x * x;
                if u < 1.0 - 0.0331 * x_sqr * x_sqr ||
                    u.ln() < 0.5 * x_sqr + self.d * (1.0 - v + v.ln()) {
                    return self.d * v * self.scale
                }
            }
        }
    }

    /// The chi-squared distribution `χ²(k)`, where `k` is the degrees of
    /// freedom.
    ///
    /// For `k > 0` integral, this distribution is the sum of the squares
    /// of `k` independent standard normal random variables. For other
    /// `k`, this uses the equivalent characterisation `χ²(k) = Gamma(k/2,
    /// 2)`.
    ///
    /// # Example
    ///
    /// ```rust
    /// use rand::distributions::{ChiSquared, IndependentSample};
    ///
    /// let chi = ChiSquared::new(11.0);
    /// let v = chi.ind_sample(&mut rand::thread_rng());
    /// println!("{} is from a χ²(11) distribution", v)
    /// ```
    #[derive(Clone, Copy)]
    pub struct ChiSquared {
        repr: ChiSquaredRepr,
    }

    #[derive(Clone, Copy)]
    enum ChiSquaredRepr {
        // k == 1, Gamma(alpha, ..) is particularly slow for alpha < 1,
        // e.g. when alpha = 1/2 as it would be for this case, so special-
        // casing and using the definition of N(0,1)^2 is faster.
        DoFExactlyOne,
        DoFAnythingElse(Gamma),
    }

    impl ChiSquared {
        /// Create a new chi-squared distribution with degrees-of-freedom
        /// `k`. Panics if `k < 0`.
        pub fn new(k: f64) -> ChiSquared {
            let repr = if k == 1.0 {
                DoFExactlyOne
            } else {
                assert!(k > 0.0, "ChiSquared::new called with `k` < 0");
                DoFAnythingElse(Gamma::new(0.5 * k, 2.0))
            };
            ChiSquared { repr: repr }
        }
    }
    impl Sample<f64> for ChiSquared {
        fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) }
    }
    impl IndependentSample<f64> for ChiSquared {
        fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 {
            match self.repr {
                DoFExactlyOne => {
                    // k == 1 => N(0,1)^2
                    let StandardNormal(norm) = rng.gen::<StandardNormal>();
                    norm * norm
                }
                DoFAnythingElse(ref g) => g.ind_sample(rng)
            }
        }
    }

    /// The Fisher F distribution `F(m, n)`.
    ///
    /// This distribution is equivalent to the ratio of two normalised
    /// chi-squared distributions, that is, `F(m,n) = (χ²(m)/m) /
    /// (χ²(n)/n)`.
    ///
    /// # Example
    ///
    /// ```rust
    /// use rand::distributions::{FisherF, IndependentSample};
    ///
    /// let f = FisherF::new(2.0, 32.0);
    /// let v = f.ind_sample(&mut rand::thread_rng());
    /// println!("{} is from an F(2, 32) distribution", v)
    /// ```
    #[derive(Clone, Copy)]
    pub struct FisherF {
        numer: ChiSquared,
        denom: ChiSquared,
        // denom_dof / numer_dof so that this can just be a straight
        // multiplication, rather than a division.
        dof_ratio: f64,
    }

    impl FisherF {
        /// Create a new `FisherF` distribution, with the given
        /// parameter. Panics if either `m` or `n` are not positive.
        pub fn new(m: f64, n: f64) -> FisherF {
            assert!(m > 0.0, "FisherF::new called with `m < 0`");
            assert!(n > 0.0, "FisherF::new called with `n < 0`");

            FisherF {
                numer: ChiSquared::new(m),
                denom: ChiSquared::new(n),
                dof_ratio: n / m
            }
        }
    }
    impl Sample<f64> for FisherF {
        fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) }
    }
    impl IndependentSample<f64> for FisherF {
        fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 {
            self.numer.ind_sample(rng) / self.denom.ind_sample(rng) * self.dof_ratio
        }
    }

    /// The Student t distribution, `t(nu)`, where `nu` is the degrees of
    /// freedom.
    ///
    /// # Example
    ///
    /// ```rust
    /// use rand::distributions::{StudentT, IndependentSample};
    ///
    /// let t = StudentT::new(11.0);
    /// let v = t.ind_sample(&mut rand::thread_rng());
    /// println!("{} is from a t(11) distribution", v)
    /// ```
    #[derive(Clone, Copy)]
    pub struct StudentT {
        chi: ChiSquared,
        dof: f64
    }

    impl StudentT {
        /// Create a new Student t distribution with `n` degrees of
        /// freedom. Panics if `n <= 0`.
        pub fn new(n: f64) -> StudentT {
            assert!(n > 0.0, "StudentT::new called with `n <= 0`");
            StudentT {
                chi: ChiSquared::new(n),
                dof: n
            }
        }
    }
    impl Sample<f64> for StudentT {
        fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) }
    }
    impl IndependentSample<f64> for StudentT {
        fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 {
            let StandardNormal(norm) = rng.gen::<StandardNormal>();
            norm * (self.dof / self.chi.ind_sample(rng)).sqrt()
        }
    }

    #[cfg(test)]
    mod test {
        use distributions::{Sample, IndependentSample};
        use super::{ChiSquared, StudentT, FisherF};

        #[test]
        fn test_chi_squared_one() {
            let mut chi = ChiSquared::new(1.0);
            let mut rng = ::test::rng();
            for _ in 0..1000 {
                chi.sample(&mut rng);
                chi.ind_sample(&mut rng);
            }
        }
        #[test]
        fn test_chi_squared_small() {
            let mut chi = ChiSquared::new(0.5);
            let mut rng = ::test::rng();
            for _ in 0..1000 {
                chi.sample(&mut rng);
                chi.ind_sample(&mut rng);
            }
        }
        #[test]
        fn test_chi_squared_large() {
            let mut chi = ChiSquared::new(30.0);
            let mut rng = ::test::rng();
            for _ in 0..1000 {
                chi.sample(&mut rng);
                chi.ind_sample(&mut rng);
            }
        }
        #[test]
        #[should_panic]
        #[cfg_attr(target_env = "msvc", ignore)]
        fn test_chi_squared_invalid_dof() {
            ChiSquared::new(-1.0);
        }

        #[test]
        fn test_f() {
            let mut f = FisherF::new(2.0, 32.0);
            let mut rng = ::test::rng();
            for _ in 0..1000 {
                f.sample(&mut rng);
                f.ind_sample(&mut rng);
            }
        }

        #[test]
        fn test_t() {
            let mut t = StudentT::new(11.0);
            let mut rng = ::test::rng();
            for _ in 0..1000 {
                t.sample(&mut rng);
                t.ind_sample(&mut rng);
            }
        }
    }

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