lsode 0.2.7

Solve systems of differntial equations using LSODE subroutine from ODEPACK written in Fortran.
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use libc::{c_double, c_int};
use std::slice;
use libffi::high::Closure4;


#[link(name = "gfortran")]
extern {
    /// Call `DLSODE` subroutine from ODEPACK
    ///
    /// For info on passed arguments look inside ODEPACK.
    pub fn dlsode_(f: extern fn(*const c_int, *const c_double, *mut c_double, *mut c_double),
               neq: &c_int,
               y: *mut c_double,
               t: &mut c_double,
               tout: &c_double,
               itol: &c_int,
               rtol: &c_double,
               atol: &c_double,
               itask: &c_int,
               istate: &mut c_int,
               iopt: &c_int,
               rwork: *mut c_double,
               lrw: &c_int,
               iwork: *mut c_int,
               liw: &c_int,
               jac: extern fn(&c_int, &c_double, *mut c_double, &c_int, &c_int, *const c_double, &c_int),
               mf: &c_int
               );
}

/// A dummy function to pass to `dlsode_` in case the user does not want to specify a Jacobian.
pub extern fn fake_jacobian(
    _neq: &c_int,
    _t:   &c_double,
    _y:   *mut c_double,
    _ml:  &c_int,
    _mu:  &c_int,
    _pd:  *const c_double,
    _nr:  &c_int
    ) { }


/// Solves system of ODEs for times in `t_dense`.
/// First time in `t_dense` has to be the initial time.
///
/// Each equation in the system of ODEs has the form:
/// 
/// > *dy/dt = f(y, t)*
/// 
/// The function expects the function *f* as the first argument `rhs`.
/// Initial state is given in `y0`.
///
/// # Example
///
/// ```
/// let y0 = [1.0];
/// let ts = vec![0.0, 1.0];
/// let f = |y: &[f64], t: &f64| {
///     let mut dy = vec![0.0];
///     dy[0] = *t * y[0]; 
///     dy
///     };
/// let sol = lsode::solve_ode(f, &y0, ts, 1e-6, 1e-6);
/// 
/// assert!((sol[1][0] - y0[0]*0.5_f64.exp()).abs() < 1e-3, "error too large");
/// ```
pub fn solve_ode<F>(
    rhs: F, 
    y0: &[f64],
    t_dense: Vec<f64>,
    atol: f64,
    rtol: f64,
    ) -> Vec<Vec<f64>> 
where F: Fn(&[f64], &f64) -> Vec<f64>
{

    let f = | n: *const c_int, t_ptr: *const c_double, y_ptr: *mut c_double, dy_ptr: *mut c_double | {
        let (dy, y, t) = unsafe {
            (
                slice::from_raw_parts_mut(dy_ptr, n as usize),
                slice::from_raw_parts(y_ptr, n as usize),
                *t_ptr
            )
        };
        let dy_new = rhs(y, &t);
        for (i, deriv) in dy_new.iter().enumerate() {
            dy[i] = *deriv
        }
    };
    let closure = Closure4::new(&f);
    let call = closure.code_ptr();

    let mut y: Vec<f64> = y0.to_vec();
    let n = y0.len();
    let mut t = t_dense[0];

    let itol = 1;
    let itask = 1;
    let iopt = 0;
    let mut istate = 1;
    let mf = 22;

    let lrw = 22 + 9*n + n*n;
    let liw = 20 + n;
    let mut rwork: Vec<f64> = (0..lrw).map(|_i| 0.0 as c_double).collect();
    let mut iwork: Vec<i32> = (0..liw).map(|_i| 0 as c_int).collect();

    let mut result = Vec::new();

    for tout in t_dense {
        unsafe { dlsode_(
                *call,
                &(n as i32),
                y.as_mut_ptr(),
                &mut t,
                &tout,
                &itol,
                &rtol,
                &atol,
                &itask,
                &mut istate,
                &iopt,
                rwork.as_mut_ptr(),
                &(lrw as i32),
                iwork.as_mut_ptr(),
                &(liw as i32),
                fake_jacobian,
                &mf
                ); }

        result.push(y.clone());
    }
    result
}

/// Generates vector from `start` to `stop` with constant  spacing.
///
/// # Example
///
/// ```
/// assert_eq!(lsode::linspace(0.0, 2.0, 3), vec![0.0, 1.0, 2.0]);
/// ```
pub fn linspace(start: f64, stop: f64, n_points: usize) -> Vec<f64> {
    (0..n_points).map(|i| start + i as f64*(stop - start)/(n_points - 1) as f64).collect()
}