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use nalgebra::{Const, DefaultAllocator, Dim, OMatrix, OVector, RealField, U1};
use nalgebra::allocator::Allocator;
use num_traits::{Pow, ToPrimitive, FromPrimitive};
use num_traits::real::Real;
use rand_core::RngCore;
use rand_distr::{Distribution, StandardNormal, Uniform};
use crate::models::{Estimator, KalmanEstimator, KalmanState};
use crate::noise::{CorrelatedNoise, CoupledNoise};
pub struct SampleState<N: RealField, D: Dim>
where
DefaultAllocator: Allocator<N, D>,
{
pub s: Samples<N, D>,
pub w: Likelihoods,
pub rng: Box<dyn RngCore>
}
pub type Samples<N, D> = Vec<OVector<N, D>>;
pub type Likelihoods = Vec<f32>;
pub type Resamples = Vec<u32>;
pub type Resampler = dyn FnMut(&mut Likelihoods, &mut dyn RngCore) -> Result<(Resamples, u32, f32), &'static str>;
pub type Roughener<N, D> = dyn FnMut(&mut Samples<N, D>, &mut dyn RngCore);
impl<N: RealField, D: Dim> SampleState<N, D>
where
DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
{
pub fn new_equal_likelihood(s: Samples<N, D>, rng: Box<dyn RngCore>) -> SampleState<N, D> {
let samples = s.len();
SampleState {
s,
w: vec![1f32; samples],
rng
}
}
pub fn predict(&mut self, f: fn(&OVector<N, D>) -> OVector<N, D>)
{
self.s.iter_mut().for_each(|el|{
el.copy_from(&f(el))
});
}
pub fn predict_sampled(&mut self, f: impl Fn(&OVector<N, D>, &mut dyn RngCore) -> OVector<N, D>)
{
for si in 0..self.s.len() {
let ps = f(&self.s[si], &mut self.rng);
self.s[si].copy_from(&ps)
}
}
pub fn observe<LikelihoodFn>(&mut self, l: LikelihoodFn)
where
LikelihoodFn: Fn(&OVector<N, D>) -> f32,
{
let mut wi = self.w.iter_mut();
for si in self.s.iter() {
let w = wi.next().unwrap();
*w *= l(si);
}
}
pub fn observe_likelihood(&mut self, l: Likelihoods) {
assert_eq!(self.w.len(), l.len());
let mut li = l.iter();
for wi in self.w.iter_mut() {
*wi *= li.next().unwrap();
}
}
pub fn update_resample(&mut self, resampler: &mut Resampler, roughener: &mut Roughener<N, D>) -> Result<(u32, f32), &'static str>
{
let (resamples, unqiue_samples, lcond) = resampler(&mut self.w, self.rng.as_mut())?;
live_samples(&mut self.s, &resamples);
self.w.fill(1.);
roughener(&mut self.s, self.rng.as_mut());
Ok((unqiue_samples, lcond))
}
}
impl<N: FromPrimitive + RealField, D: Dim> Estimator<N, D> for SampleState<N, D>
where
DefaultAllocator: Allocator<N, D>,
{
fn state(&self) -> Result<OVector<N, D>, &'static str> {
let s_shape = self.s[0].shape_generic();
let mut x = OVector::zeros_generic(s_shape.0, s_shape.1);
for s in self.s.iter() {
x += s;
}
x /= N::from_usize(self.s.len()).unwrap();
Ok(x)
}
}
pub fn standard_resampler(w: &mut Likelihoods, rng: &mut dyn RngCore) -> Result<(Resamples, u32, f32), &'static str>
{
let (lmin, lcum) = cumaltive_likelihood(w)?;
let uniform01: Uniform<f32> = Uniform::new(0f32, 1f32);
let mut ur: Vec<f32> = uniform01.sample_iter(rng).take(w.len()).collect();
ur.sort_by(|a, b| a.partial_cmp(b).unwrap());
assert!(*ur.first().unwrap() >= 0. && *ur.last().unwrap() < 1.);
ur.iter_mut().for_each(|el| *el *= lcum);
let mut uri = ur.iter();
let mut urn = uri.next();
let mut unique : u32 = 0;
let mut resamples = Resamples::with_capacity(w.len());
for wi in w.iter() {
let mut res: u32 = 0;
if (urn.is_some()) && *urn.unwrap() < *wi {
unique += 1;
loop {
res += 1;
urn = uri.next();
if urn.is_none() { break; }
if !(*urn.unwrap() < *wi) { break;}
}
}
resamples.push(res);
}
if uri.peekable().peek().is_some() {
return Err("likelihoods are not numeric and cannot be resampled");
}
return Ok((resamples, unique, lmin / lcum));
}
pub fn systematic_resampler(l: &mut Likelihoods, rng: &mut dyn RngCore) -> Result<(Resamples, u32, f32), &'static str>
{
let (lmin, lcum) = cumaltive_likelihood(l)?;
let uniform01: Uniform<f32> = Uniform::new(0f32, 1f32);
let glen = l.len();
let gstep = lcum / glen as f32;
let goffset = uniform01.sample(rng) * gstep;
let mut resamples = Resamples::with_capacity(glen);
let mut unique: u32 = 0;
let mut gi: u32 = 0;
for li in l.iter() {
let mut res: u32 = 0;
if (goffset + lcum * gi as f32 / glen as f32) < *li {
unique += 1;
loop {
res += 1;
gi += 1;
if !((goffset + lcum * gi as f32 / glen as f32) < *li) {break;}
}
}
resamples.push(res);
}
Ok((resamples, unique, lmin / lcum))
}
fn cumaltive_likelihood(l: &mut Likelihoods) -> Result<(f32, f32), &'static str> {
let mut lmin = f32::max_value();
let mut lcum = 0.;
{
let mut c = 0.;
for li in l.iter_mut() {
if *li < lmin {
lmin = *li;
}
let y = *li - c;
let t = lcum + y;
c = t - lcum - y;
lcum = t;
*li = t;
}
}
if lmin < 0.{
return Err("negative likelihood");
}
if lcum <= 0. {
return Err("zero cumulative likelihood sum");
}
if lcum != lcum {
return Err("NaN cumulative likelihood sum");
}
Ok((lmin, lcum))
}
pub fn live_samples<N: RealField, D:Dim>(s: &mut Samples<N, D>, resamples: &Resamples)
where
DefaultAllocator: Allocator<N, D>,
{
let mut si = s.len();
let mut livei = si;
for pr in resamples.iter().rev() {
si -= 1;
if *pr > 0 {
livei -= 1;
s[livei] = s[si].clone();
}
}
assert_eq!(si, 0);
si = 0;
for pr in resamples {
let mut res = *pr;
if res > 0 {
loop {
s[si] = s[livei].clone();
si += 1;
res -= 1;
if res == 0 { break; }
}
livei += 1;
}
}
assert_eq!(si, s.len());
assert_eq!(livei, s.len());
}
pub fn roughen_minmax<N: Copy + FromPrimitive + RealField, D:Dim>(s: &mut Samples<N, D>, k: f32, rng: &mut dyn RngCore)
where
DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
{
let x_dim = s[0].shape_generic().0;
let x_size = x_dim.value();
let mut xmin = s[0].clone();
let mut xmax = xmin.clone();
for si in s.iter() {
let mut mini = xmin.iter_mut();
let mut maxi = xmax.iter_mut();
for xd in si.iter() {
let minx = mini.next().unwrap();
let maxx = maxi.next().unwrap();
if *xd < *minx {*minx = *xd;}
if *xd > *maxx {*maxx = *xd;}
}
}
let sigma_scale = k * f32::pow(s.len() as f32, -1f32/(x_size as f32));
let sigma = (xmax - xmin) * N::from_f32(sigma_scale).unwrap();
let noise = normal_noise_sampler(sigma);
for si in s.iter_mut() {
*si += noise(&mut *rng);
}
}
pub fn roughen_noise<N: Copy + FromPrimitive + RealField, D: Dim, ND: Dim>(s: &mut Samples<N, D>, noise: &CoupledNoise<N, D, ND>, k: f32, rng: &mut dyn RngCore)
where
DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, ND> + Allocator<N, ND, ND> + Allocator<N, D> + Allocator<N, ND>
{
let sigma_scale = N::from_f32(k * f32::pow(s.len() as f32, -1f32/(noise.G.nrows() as f32))).unwrap();
let mut coupling = noise.G.clone();
for (i, mut c) in coupling.column_iter_mut().enumerate() {
c *= sigma_scale * noise.q[i];
}
let noise = normal_noise_sampler_coupled(coupling);
for si in s.iter_mut() {
*si += noise(&mut *rng);
}
}
impl<N: Copy + FromPrimitive + RealField, D: Dim> KalmanEstimator<N, D> for SampleState<N, D>
where
DefaultAllocator: Allocator<N, D, D> + Allocator<N, U1, D> + Allocator<N, D>,
{
fn init(&mut self, state: &KalmanState<N, D>) -> Result<(), &'static str> {
for s in self.s.iter_mut() {
s.copy_from(&state.x);
}
let coupled_noise = CoupledNoise::from_correlated(&CorrelatedNoise { Q: state.X.clone() })?;
let sampler = normal_noise_sampler_coupled(coupled_noise.G);
self.predict_sampled(move |x: &OVector<N,D>, rng: &mut dyn RngCore| -> OVector<N,D> {
x + sampler(rng)
});
Ok(())
}
fn kalman_state(&self) -> Result<KalmanState<N, D>, &'static str> {
let x = self.state()?;
let s_shape = self.s[0].shape_generic();
let mut xx = OMatrix::zeros_generic(s_shape.0, s_shape.0);
for s in self.s.iter() {
let sx = s - &x;
let sxt = sx.transpose();
xx += sx * sxt;
}
xx /= N::from_usize(self.s.len()).unwrap();
Ok(KalmanState { x, X: xx })
}
}
pub fn normal_noise_sampler<N: Copy + FromPrimitive + RealField, D: Dim>(std_dev: OVector<N, D>) -> impl Fn(&mut dyn RngCore) -> OVector<N,D>
where
DefaultAllocator: Allocator<N, D>,
{
move |rng: &mut dyn RngCore| -> OVector<N,D> {
let rnormal = StandardNormal.sample_iter(rng)
.enumerate()
.map(|(i, n): (usize, f32)| {N::from_f32(n).unwrap() * std_dev[i]}).
take(std_dev.nrows());
OVector::from_iterator_generic(std_dev.shape_generic().0, Const::<1>, rnormal)
}
}
pub fn normal_noise_sampler_coupled<N: FromPrimitive + RealField, D: Dim, ND: Dim>(coupleing: OMatrix<N, D, ND>) -> impl Fn(&mut dyn RngCore) -> OVector<N,D>
where
DefaultAllocator: Allocator<N, D, ND> + Allocator<N, D> + Allocator<N, ND>,
{
move |rng: &mut dyn RngCore| -> OVector<N,D> {
let rnormal = StandardNormal.sample_iter(rng).map(|n: f32| {N::from_f32(n).unwrap()}).take(coupleing.ncols());
let n = OVector::from_iterator_generic(coupleing.shape_generic().1, Const::<1>, rnormal);
&coupleing * n
}
}
pub fn gaussian_observation_likelihood<'r, N: Copy + RealField + ToPrimitive, D: Dim, ZD: Dim>(
z: &'r OVector<N, ZD>, h: fn(&OVector<N, D>) -> OVector<N, ZD>,
noise: &CorrelatedNoise<N, ZD>) -> impl Fn(&OVector<N, D>) -> f32 + 'r
where
DefaultAllocator: Allocator<N, D, D> + Allocator<N, ZD, ZD> + Allocator<N, D> + Allocator<N, ZD>
{
let cholesky = noise.Q.clone().cholesky().unwrap();
let zinv = cholesky.inverse();
let zinv_diagonal = cholesky.l_dirty().iter().step_by(noise.Q.nrows()+1);
let determinate_zinv = zinv_diagonal.fold(N::one(), |prod: N, n: &N| prod * *n).to_f32().unwrap();
move |x: &OVector<N, D>| -> f32 {
let innov = z - h(x);
let logl = innov.dot(&(&zinv * &innov)).to_f32().unwrap();
(-0.5 * (logl + determinate_zinv.ln())).exp()
}
}