russell_ode 1.13.0

use crate::StrError;
use crate::{Method, System};
use crate::{DORMAND_PRINCE_5_D, DORMAND_PRINCE_8_AD, DORMAND_PRINCE_8_CD, DORMAND_PRINCE_8_D};
use russell_lab::Vector;

/// Handles the dense output of explicit Runge-Kutta methods
pub(crate) struct ErkDenseOut {
    /// Holds the method
    method: Method,

    /// System dimension
    ndim: usize,

    /// Dense output values (nstage_dense * ndim)
    d: Vec<Vector>,

    /// k values for dense output
    kd: Vec<Vector>,

    /// y values for dense output
    yd: Vector,
}

impl ErkDenseOut {
    /// Allocates a new instance
    pub(crate) fn new(method: Method, ndim: usize) -> Result<Self, StrError> {
        match method {
            Method::Radau5 => Err("INTERNAL ERROR: cannot use Radau5 with ErkDenseOut"),
            Method::BwEuler => Err("INTERNAL ERROR: cannot use BwEuler with ErkDenseOut"),
            Method::FwEuler => Err("INTERNAL ERROR: cannot use FwEuler with ErkDenseOut"),
            Method::Rk2 => Err("dense output is not available for the Rk2 method"),
            Method::Rk3 => Err("dense output is not available for the Rk3 method"),
            Method::Heun3 => Err("dense output is not available for the Heun3 method"),
            Method::Rk4 => Err("dense output is not available for the Rk4 method"),
            Method::Rk4alt => Err("dense output is not available for the Rk4alt method"),
            Method::MdEuler => Err("dense output is not available for the MdEuler method"),
            Method::Merson4 => Err("dense output is not available for the Merson4 method"),
            Method::Zonneveld4 => Err("dense output is not available for the Zonneveld4 method"),
            Method::Fehlberg4 => Err("dense output is not available for the Fehlberg4 method"),
            Method::DoPri5 => Ok(ErkDenseOut {
                method,
                ndim,
                d: vec![Vector::new(ndim); 5],
                kd: Vec::new(),
                yd: Vector::new(0),
            }),
            Method::Verner6 => Err("dense output is not available for the Verner6 method"),
            Method::Fehlberg7 => Err("dense output is not available for the Fehlberg7 method"),
            Method::DoPri8 => Ok(ErkDenseOut {
                method,
                ndim,
                d: vec![Vector::new(ndim); 8],
                kd: vec![Vector::new(ndim); 3],
                yd: Vector::new(ndim),
            }),
        }
    }

    /// Updates the data and returns the number of function evaluations
    pub(crate) fn update<'a, A>(
        &mut self,
        system: &System<A>,
        x: f64,
        y: &Vector,
        h: f64,
        w: &Vector,
        k: &Vec<Vector>,
        args: &mut A,
    ) -> Result<usize, StrError> {
        let mut n_function_eval = 0;

        if self.method == Method::DoPri5 {
            let dd = &DORMAND_PRINCE_5_D;
            for m in 0..self.ndim {
                let y_diff = w[m] - y[m];
                let b_spl = h * k[0][m] - y_diff;
                self.d[0][m] = y[m];
                self.d[1][m] = y_diff;
                self.d[2][m] = b_spl;
                self.d[3][m] = y_diff - h * k[6][m] - b_spl;
                self.d[4][m] = dd[0][0] * k[0][m]
                    + dd[0][2] * k[2][m]
                    + dd[0][3] * k[3][m]
                    + dd[0][4] * k[4][m]
                    + dd[0][5] * k[5][m]
                    + dd[0][6] * k[6][m];
                self.d[4][m] *= h;
            }
        }

        if self.method == Method::DoPri8 {
            let aad = &DORMAND_PRINCE_8_AD;
            let ccd = &DORMAND_PRINCE_8_CD;
            let dd = &DORMAND_PRINCE_8_D;

            // first function evaluation
            for m in 0..self.ndim {
                self.yd[m] = y[m]
                    + h * (aad[0][0] * k[0][m]
                        + aad[0][6] * k[6][m]
                        + aad[0][7] * k[7][m]
                        + aad[0][8] * k[8][m]
                        + aad[0][9] * k[9][m]
                        + aad[0][10] * k[10][m]
                        + aad[0][11] * k[11][m]
                        + aad[0][12] * k[11][m]);
            }
            let u = x + ccd[0] * h;
            (system.function)(&mut self.kd[0], u, &self.yd, args)?;

            // second function evaluation
            for m in 0..self.ndim {
                self.yd[m] = y[m]
                    + h * (aad[1][0] * k[0][m]
                        + aad[1][5] * k[5][m]
                        + aad[1][6] * k[6][m]
                        + aad[1][7] * k[7][m]
                        + aad[1][10] * k[10][m]
                        + aad[1][11] * k[11][m]
                        + aad[1][12] * k[11][m]
                        + aad[1][13] * self.kd[0][m]);
            }
            let u = x + ccd[1] * h;
            (system.function)(&mut self.kd[1], u, &self.yd, args)?;

            // next third function evaluation
            for m in 0..self.ndim {
                self.yd[m] = y[m]
                    + h * (aad[2][0] * k[0][m]
                        + aad[2][5] * k[5][m]
                        + aad[2][6] * k[6][m]
                        + aad[2][7] * k[7][m]
                        + aad[2][8] * k[8][m]
                        + aad[2][12] * k[11][m]
                        + aad[2][13] * self.kd[0][m]
                        + aad[2][14] * self.kd[1][m]);
            }
            let u = x + ccd[2] * h;
            (system.function)(&mut self.kd[2], u, &self.yd, args)?;

            // final results
            for m in 0..self.ndim {
                let y_diff = w[m] - y[m];
                let b_spl = h * k[0][m] - y_diff;
                self.d[0][m] = y[m];
                self.d[1][m] = y_diff;
                self.d[2][m] = b_spl;
                self.d[3][m] = y_diff - h * k[11][m] - b_spl;
                self.d[4][m] = h
                    * (dd[0][0] * k[0][m]
                        + dd[0][5] * k[5][m]
                        + dd[0][6] * k[6][m]
                        + dd[0][7] * k[7][m]
                        + dd[0][8] * k[8][m]
                        + dd[0][9] * k[9][m]
                        + dd[0][10] * k[10][m]
                        + dd[0][11] * k[11][m]
                        + dd[0][12] * k[11][m]
                        + dd[0][13] * self.kd[0][m]
                        + dd[0][14] * self.kd[1][m]
                        + dd[0][15] * self.kd[2][m]);
                self.d[5][m] = h
                    * (dd[1][0] * k[0][m]
                        + dd[1][5] * k[5][m]
                        + dd[1][6] * k[6][m]
                        + dd[1][7] * k[7][m]
                        + dd[1][8] * k[8][m]
                        + dd[1][9] * k[9][m]
                        + dd[1][10] * k[10][m]
                        + dd[1][11] * k[11][m]
                        + dd[1][12] * k[11][m]
                        + dd[1][13] * self.kd[0][m]
                        + dd[1][14] * self.kd[1][m]
                        + dd[1][15] * self.kd[2][m]);
                self.d[6][m] = h
                    * (dd[2][0] * k[0][m]
                        + dd[2][5] * k[5][m]
                        + dd[2][6] * k[6][m]
                        + dd[2][7] * k[7][m]
                        + dd[2][8] * k[8][m]
                        + dd[2][9] * k[9][m]
                        + dd[2][10] * k[10][m]
                        + dd[2][11] * k[11][m]
                        + dd[2][12] * k[11][m]
                        + dd[2][13] * self.kd[0][m]
                        + dd[2][14] * self.kd[1][m]
                        + dd[2][15] * self.kd[2][m]);
                self.d[7][m] = h
                    * (dd[3][0] * k[0][m]
                        + dd[3][5] * k[5][m]
                        + dd[3][6] * k[6][m]
                        + dd[3][7] * k[7][m]
                        + dd[3][8] * k[8][m]
                        + dd[3][9] * k[9][m]
                        + dd[3][10] * k[10][m]
                        + dd[3][11] * k[11][m]
                        + dd[3][12] * k[11][m]
                        + dd[3][13] * self.kd[0][m]
                        + dd[3][14] * self.kd[1][m]
                        + dd[3][15] * self.kd[2][m]);
            }
            n_function_eval = 3;
        }

        Ok(n_function_eval)
    }

    /// Calculates the dense output
    pub(crate) fn calculate(&self, y_out: &mut Vector, x_out: f64, x: f64, h: f64) {
        if self.method == Method::DoPri5 {
            let x_prev = x - h;
            let theta = (x_out - x_prev) / h;
            let u_theta = 1.0 - theta;
            for m in 0..self.ndim {
                y_out[m] = self.d[0][m]
                    + theta
                        * (self.d[1][m] + u_theta * (self.d[2][m] + theta * (self.d[3][m] + u_theta * self.d[4][m])));
            }
        }
        if self.method == Method::DoPri8 {
            let x_prev = x - h;
            let theta = (x_out - x_prev) / h;
            let u_theta = 1.0 - theta;
            for m in 0..self.ndim {
                let par = self.d[4][m] + theta * (self.d[5][m] + u_theta * (self.d[6][m] + theta * self.d[7][m]));
                y_out[m] = self.d[0][m]
                    + theta * (self.d[1][m] + u_theta * (self.d[2][m] + theta * (self.d[3][m] + u_theta * par)));
            }
        }
    }
}

////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

#[cfg(test)]
mod tests {
    use super::ErkDenseOut;
    use crate::{Method, System};
    use russell_lab::Vector;

    #[test]
    fn new_captures_errors() {
        assert_eq!(
            ErkDenseOut::new(Method::Radau5, 1).err(),
            Some("INTERNAL ERROR: cannot use Radau5 with ErkDenseOut")
        );
        assert_eq!(
            ErkDenseOut::new(Method::BwEuler, 1).err(),
            Some("INTERNAL ERROR: cannot use BwEuler with ErkDenseOut")
        );
        assert_eq!(
            ErkDenseOut::new(Method::FwEuler, 1).err(),
            Some("INTERNAL ERROR: cannot use FwEuler with ErkDenseOut")
        );
        assert_eq!(
            ErkDenseOut::new(Method::Rk2, 1).err(),
            Some("dense output is not available for the Rk2 method")
        );
        assert_eq!(
            ErkDenseOut::new(Method::Rk3, 1).err(),
            Some("dense output is not available for the Rk3 method")
        );
        assert_eq!(
            ErkDenseOut::new(Method::Heun3, 1).err(),
            Some("dense output is not available for the Heun3 method")
        );
        assert_eq!(
            ErkDenseOut::new(Method::Rk4, 1).err(),
            Some("dense output is not available for the Rk4 method")
        );
        assert_eq!(
            ErkDenseOut::new(Method::Rk4alt, 1).err(),
            Some("dense output is not available for the Rk4alt method")
        );
        assert_eq!(
            ErkDenseOut::new(Method::MdEuler, 1).err(),
            Some("dense output is not available for the MdEuler method")
        );
        assert_eq!(
            ErkDenseOut::new(Method::Merson4, 1).err(),
            Some("dense output is not available for the Merson4 method")
        );
        assert_eq!(
            ErkDenseOut::new(Method::Zonneveld4, 1).err(),
            Some("dense output is not available for the Zonneveld4 method")
        );
        assert_eq!(
            ErkDenseOut::new(Method::Fehlberg4, 1).err(),
            Some("dense output is not available for the Fehlberg4 method")
        );
        assert_eq!(
            ErkDenseOut::new(Method::Verner6, 1).err(),
            Some("dense output is not available for the Verner6 method")
        );
        assert_eq!(
            ErkDenseOut::new(Method::Fehlberg7, 1).err(),
            Some("dense output is not available for the Fehlberg7 method")
        );
    }

    #[test]
    fn update_captures_errors() {
        struct Args {
            count: usize,
            fail: usize,
        }
        let mut system = System::new(1, |_f: &mut Vector, _x: f64, _y: &Vector, args: &mut Args| {
            args.count += 1;
            if args.count == args.fail {
                Err("STOP")
            } else {
                Ok(())
            }
        });
        let mut out = ErkDenseOut::new(Method::DoPri8, system.ndim).unwrap();
        let mut args = Args { count: 0, fail: 1 };
        let h = 0.1;
        let y = Vector::new(system.ndim);
        let w = Vector::new(system.ndim);
        let nstage = 12;
        let k = vec![Vector::new(system.ndim); nstage];
        assert_eq!(
            out.update(&mut system, 0.0, &y, h, &w, &k, &mut args).err(),
            Some("STOP")
        );
        args.count = 0;
        args.fail = 2;
        assert_eq!(
            out.update(&mut system, 0.0, &y, h, &w, &k, &mut args).err(),
            Some("STOP")
        );
        args.count = 0;
        args.fail = 3;
        assert_eq!(
            out.update(&mut system, 0.0, &y, h, &w, &k, &mut args).err(),
            Some("STOP")
        );
    }
}