legume_numeric/param/

ndarray_gamma.rs

extern crate special;

use crate::param::io::*;
use crate::param::traits::*;
use ndarray::prelude::*;
use rayon::prelude::*;

#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct GammaMatrix {
    num_rows: usize,
    num_columns: usize,
    //////////////////////
    // hyper parameters //
    //////////////////////
    a0: f32,
    b0: f32,
    ///////////////////////////
    // sufficient statistics //
    ///////////////////////////
    a_stat: Array2<f32>,
    b_stat: Array2<f32>,
    //////////////////////////
    // estimated parameters //
    //////////////////////////
    estimated_mean: Array2<f32>,
    estimated_sd: Array2<f32>,
    estimated_log_mean: Array2<f32>,
    estimated_log_sd: Array2<f32>,
}

impl ParamIo for GammaMatrix {
    type Mat = Array2<f32>;
}

impl TwoStatParam for GammaMatrix {
    type Mat = Array2<f32>;
    type Scalar = f32;

    /// New Poisson-Gamma parameter matrix
    ///
    /// ```text
    /// x[i,j] ~ Poisson(lambda[i,j])
    /// lambda[i,j] ~ Gamma(a0, b0)
    /// ```
    ///
    /// #Arguments
    /// * `dims` - dimensions of the matrix (num of rows, num of columns)
    /// * `a` - hyper parameter a0
    /// * `b` - hyper parameter b0
    ///
    fn new(dims: (usize, usize), a: Self::Scalar, b: Self::Scalar) -> Self {
        Self {
            num_rows: dims.0,
            num_columns: dims.1,
            a0: a,
            b0: b,
            a_stat: Self::Mat::zeros(dims).mapv_into(|x| x + a),
            b_stat: Self::Mat::zeros(dims).mapv_into(|x| x + b),
            estimated_mean: Self::Mat::zeros(dims),
            estimated_sd: Self::Mat::zeros(dims),
            estimated_log_mean: Self::Mat::zeros(dims),
            estimated_log_sd: Self::Mat::zeros(dims),
        }
    }

    fn add_stat(&mut self, add_a: &Self::Mat, add_b: &Self::Mat) {
        self.a_stat += add_a;
        self.b_stat += add_b;
    }

    fn update_stat(&mut self, add_a: &Self::Mat, add_b: &Self::Mat) {
        self.reset_stat();
        self.add_stat(add_a, add_b);
    }

    fn update_stat_col(&mut self, add_a: &Self::Mat, add_b: &Self::Mat, k: usize) {
        self.a_stat.column_mut(k).zip_mut_with(add_a, |x, add_x| {
            *x = self.a0 + add_x;
        });
        self.b_stat.column_mut(k).zip_mut_with(add_b, |x, add_x| {
            *x = self.b0 + add_x;
        });
    }

    fn reset_stat(&mut self) {
        self.a_stat.fill(self.a0);
        self.b_stat.fill(self.b0);
    }

    // fn nrows(&self) -> usize {
    //     self.num_rows
    // }

    // fn ncols(&self) -> usize {
    //     self.num_columns
    // }

    // fn len(&self) -> usize {
    //     self.num_rows * self.num_columns
    // }
    fn map_calibrate_mean(&mut self) {
        self.estimated_mean = &self.a_stat / &self.b_stat;
    }
    fn map_calibrate_sd(&mut self) {
        self.estimated_sd = &self.a_stat.mapv(|x| x.sqrt()) / &self.b_stat;
    }
    fn map_calibrate_log_mean(&mut self) {
        use special::Gamma;
        self.estimated_log_mean = &self.a_stat.mapv(Gamma::digamma) - &self.b_stat.mapv(|b| b.ln());
    }
    fn map_calibrate_log_sd(&mut self) {
        // `sd[ln X] = sqrt(trigamma(a))` exactly — see the `dmatrix_gamma`
        // sibling for why the old `1/sqrt(a - 1)` was wrong wherever counts are
        // sparse, and why returning 0 below `a = 1` inverted the truth.
        self.estimated_log_sd = self.a_stat.mapv(|a: f32| {
            use special::Gamma;
            a.trigamma().sqrt()
        });
    }
}

impl Inference for GammaMatrix {
    type Mat = Array2<f32>;
    type Scalar = f32;

    fn posterior_mean(&self) -> &Self::Mat {
        &self.estimated_mean
    }

    fn posterior_sd(&self) -> &Self::Mat {
        &self.estimated_sd
    }

    fn posterior_log_mean(&self) -> &Self::Mat {
        &self.estimated_log_mean
    }

    fn posterior_log_sd(&self) -> &Self::Mat {
        &self.estimated_log_sd
    }

    fn posterior_sample(&self) -> anyhow::Result<Self::Mat> {
        use rand_distr::{Distribution, Gamma};
        let eps = 1e-8;

        let a_slice = self
            .a_stat
            .as_slice()
            .ok_or(anyhow::anyhow!("failed to take slice on a_stat"))?;
        let b_slice = self
            .b_stat
            .as_slice()
            .ok_or(anyhow::anyhow!("failed to take slice on b_stat"))?;

        let sampled = a_slice
            .par_iter()
            .zip(b_slice.par_iter())
            .map_init(rand::rng, |rng, (&a, &b)| -> anyhow::Result<f32> {
                let shape = a + eps;
                let scale = (b + eps).recip();
                let pdf = Gamma::new(shape, scale)?;
                Ok(pdf.sample(rng))
            })
            .collect::<anyhow::Result<Vec<_>>>()?;

        Ok(Self::Mat::from_shape_vec(
            (self.nrows(), self.ncols()),
            sampled,
        )?)
    }

    fn posterior_log_sample(&self, seed: u64) -> anyhow::Result<Self::Mat> {
        use rand::rngs::SmallRng;
        use rand::SeedableRng;
        use rand_distr::{Distribution, StandardNormal};

        // Fixed chunk width, so which elements share an RNG is a property of
        // the data shape and not of the thread pool.
        const CHUNK: usize = 1024;

        let m_slice = self.estimated_log_mean.as_slice().ok_or(anyhow::anyhow!(
            "failed to take slice on estimated_log_mean"
        ))?;
        let s_slice = self
            .estimated_log_sd
            .as_slice()
            .ok_or(anyhow::anyhow!("failed to take slice on estimated_log_sd"))?;

        let mut sampled = vec![0.0f32; m_slice.len()];
        sampled
            .par_chunks_mut(CHUNK)
            .enumerate()
            .for_each(|(ci, out)| {
                let mut rng =
                    SmallRng::seed_from_u64(seed ^ (ci as u64).wrapping_mul(0x9E37_79B9_7F4A_7C15));
                let base = ci * CHUNK;
                for (k, o) in out.iter_mut().enumerate() {
                    let z: f32 = StandardNormal.sample(&mut rng);
                    *o = m_slice[base + k] + s_slice[base + k] * z;
                }
            });

        Ok(Self::Mat::from_shape_vec(
            (self.nrows(), self.ncols()),
            sampled,
        )?)
    }

    fn nrows(&self) -> usize {
        self.num_rows
    }

    fn ncols(&self) -> usize {
        self.num_columns
    }
}