diffusionx 0.12.0

//! Brownian excursion simulation

use crate::{
    FloatExt, SimulationError, XResult, check_duration_time_step,
    random::PAR_THRESHOLD,
    simulation::{continuous::BrownianBridge, prelude::*},
    utils::minmax,
};
use rand_distr::{Distribution, StandardNormal};
use rayon::prelude::*;

/// Brownian excursion
#[derive(Debug, Clone)]
pub struct BrownianExcursion<T: FloatExt = f64> {
    _marker: std::marker::PhantomData<T>,
}

impl<T: FloatExt> Default for BrownianExcursion<T> {
    fn default() -> Self {
        Self::new()
    }
}

impl<T: FloatExt> BrownianExcursion<T> {
    /// Create a new `BrownianExcursion`
    ///
    /// # Example
    ///
    /// ```rust
    /// use diffusionx::simulation::continuous::BrownianExcursion;
    ///
    /// let be = BrownianExcursion::new();
    /// ```
    pub fn new() -> Self {
        Self {
            _marker: std::marker::PhantomData,
        }
    }
    /// Get the first passage time of the Brownian excursion simulation
    ///
    /// # Arguments
    ///
    /// * `domain` - The domain of the Brownian excursion simulation.
    /// * `time_step` - The time step of the Brownian excursion simulation.
    ///
    /// # Example
    ///
    /// ```rust
    /// use diffusionx::simulation::continuous::BrownianExcursion;
    ///
    /// let be = BrownianExcursion::new();
    /// let fpt = be.fpt((-1.0, 1.0), 0.1).unwrap();
    /// ```
    pub fn fpt(&self, domain: (T, T), time_step: T) -> XResult<Option<T>>
    where
        StandardNormal: Distribution<T>,
    {
        let (a, b) = domain;
        let (t, x) = self.simulate(T::one(), time_step)?;
        if let Some(index) = x.iter().position(|&x| x <= a || x >= b) {
            Ok(Some(t[index]))
        } else {
            Ok(None)
        }
    }
}

impl<T: FloatExt> ContinuousProcess<T> for BrownianExcursion<T>
where
    StandardNormal: Distribution<T>,
{
    fn start(&self) -> T {
        T::zero()
    }

    fn simulate(&self, duration: T, time_step: T) -> XResult<(Vec<T>, Vec<T>)> {
        simulate_brownian_excursion(duration, time_step)
    }

    fn displacement(&self, _: T, _: T) -> XResult<T> {
        Ok(T::zero())
    }
}

/// Simulate Brownian excursion
///
/// # Arguments
///
/// * `duration` - The duration of the trajectory.
/// * `time_step` - The time step of the simulation.
///
/// # Example
///
/// ```rust
/// use diffusionx::simulation::continuous::brownian_excursion::simulate_brownian_excursion;
///
/// let time_step = 0.1;
/// let duration = 1.0;
/// let (t, x) = simulate_brownian_excursion(duration, time_step).unwrap();
/// ```
pub fn simulate_brownian_excursion<T: FloatExt>(
    duration: T,
    time_step: T,
) -> XResult<(Vec<T>, Vec<T>)>
where
    StandardNormal: Distribution<T>,
{
    if duration > T::one() {
        return Err(SimulationError::InvalidParameters(format!(
            "The `duration` must be in (0.0, 1.0], got {duration:?}."
        ))
        .into());
    }

    check_duration_time_step(duration, time_step)?;

    let bridge: BrownianBridge<T> = BrownianBridge::new();
    let (bridge_t, bridge_traj) = bridge.simulate(T::one(), time_step)?;

    // Find the minimum value and its index within [0, 1]
    let (min_traj, _) = minmax(&bridge_traj); // Assuming minmax returns Result

    let min_traj_index = bridge_traj
        .iter()
        .position(|&x| (x - min_traj).abs() < T::epsilon()) // Use tolerance for float comparison
        .ok_or(SimulationError::Unknown)?;

    let tau_m = bridge_t[min_traj_index];

    let x = if bridge_t.len() < PAR_THRESHOLD {
        bridge_t
            .iter() // Parallelize the mapping
            .map(|&t_i| {
                // Correct modulo calculation for tt
                let tt = (t_i + tau_m) % T::one();

                // Find the index in the original bridge time corresponding to tt
                // Use >= for better accuracy and handle potential errors
                let index = bridge_t.iter().position(|&t| t >= tt).unwrap();

                // Apply the transformation
                bridge_traj[index] - min_traj
            })
            .collect()
    } else {
        bridge_t
            .par_iter() // Parallelize the mapping
            .map(|&t_i| {
                // Correct modulo calculation for tt
                let tt = (t_i + tau_m) % T::one();

                // Find the index in the original bridge time corresponding to tt
                // Use >= for better accuracy and handle potential errors
                let index = bridge_t.iter().position(|&t| t >= tt).unwrap();

                // Apply the transformation
                bridge_traj[index] - min_traj
            })
            .collect()
    }; // Collect results from parallel iterator

    Ok((bridge_t, x))
}

#[cfg(test)]
mod tests {
    use super::*;
    use crate::simulation::prelude::Moment;

    #[test]
    fn test_simulate_be() {
        let be = BrownianExcursion::new();
        let duration = 1.0;
        let time_step = 0.1;
        let (t, x) = be.simulate(duration, time_step).unwrap();
        println!("t: {t:?}");
        println!("x: {x:?}");
    }

    #[test]
    fn test_raw_moment() {
        let be = BrownianExcursion::new();
        let duration = 1.0;
        let time_step = 0.1;
        let traj = be.duration(duration).unwrap();
        let moment = traj.raw_moment(1, 1000, time_step).unwrap();
        println!("moment: {moment:?}");
    }

    #[test]
    fn test_fpt() {
        let be = BrownianExcursion::new();
        let time_step = 0.1;
        let fpt = be.fpt((-1.0, 1.0), time_step).unwrap();
        println!("fpt: {fpt:?}");
    }

    #[test]
    fn test_occupation_time() {
        let be = BrownianExcursion::new();
        let time_step = 0.1;
        let ot = be.occupation_time((-1.0, 1.0), 1.0, time_step).unwrap();
        println!("ot: {ot:?}");
    }

    #[test]
    fn test_send_sync() {
        fn assert_send_sync<T: Send + Sync>() {}
        assert_send_sync::<BrownianExcursion>();
    }
}