optrs 0.1.0

Forcefield molecule optimization
Documentation 
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use std::collections::HashSet;
use crate::coordinates::{angle_value, Point, Vector3D};
use crate::ff::forcefield::EnergyFunction;


trait HarmonicAngle{
    fn i(&self) -> usize;
    fn j(&self) -> usize;
    fn k(&self) -> usize;
}


pub struct HarmonicAngleTypeA{
    pub(crate) i:     usize,
    pub(crate) j:     usize,
    pub(crate) k:     usize,
    pub(crate) k_ijk: f64,
    pub(crate) n:     f64
}


impl EnergyFunction for HarmonicAngleTypeA {
    fn involves_idxs(&self, idxs: Vec<usize>) -> bool { involves_idxs(self, idxs) }

    fn force_constant(&self) -> f64 { self.k_ijk }

    /// Energy: k/n^2 (1-cos(nθ))
    fn energy(&self, coordinates: &Vec<Point>) -> f64 {

        let theta = theta(self, coordinates);

        (self.k_ijk / self.n.powi(2)) * (1.0 - (self.n * theta).cos())
    }

    /// Add the gradient for this term
    fn add_gradient(&self,
                    coordinates: &Vec<Point>,
                    gradient:    &mut Vec<Vector3D>){

        let x_i = coordinates[self.i].x;
        let y_i = coordinates[self.i].y;
        let z_i = coordinates[self.i].z;

        let x_j = coordinates[self.j].x;
        let y_j = coordinates[self.j].y;
        let z_j = coordinates[self.j].z;

        let x_k = coordinates[self.k].x;
        let y_k = coordinates[self.k].y;
        let z_k = coordinates[self.k].z;

        let v0 = -x_j + x_k;
        let v1 = (z_i - z_j).powi(2);
        let v2 = (y_i - y_j).powi(2);
        let v3 = (x_i - x_j).powi(2);
        let v4 = v3 + v2 + v1;
        let v5 = -z_j + z_k;
        let v6 = v5.powi(2);
        let v7 = z_i - z_j;
        let v8 = -y_j + y_k;
        let v9 = v8.powi(2);
        let v10 = v0.powi(2);
        let v11 = y_i - y_j;
        let v12 = x_i - x_j;
        let v13 = v10 + v9 + v6;
        let v14 = v4*v13;
        let v15 = v13.sqrt();
        let v16 = v4.sqrt();
        let v17 = v16*v15;
        let v18 = v12*v0 + v11*v8 + v7*v5;
        let v19 = v18.powi(2);
        let v20 = (-v19/v14 + 1.).sqrt();
        let v21 = (v18/v17).acos();
        let v22 = (self.n*v21).sin();
        gradient[self.i].x += -self.k_ijk*((-x_i + x_j)*v18/(v4.powf(1.5)*v15) + v0/v17)*v22/(self.n*v20);
        gradient[self.i].y += -self.k_ijk*((-y_i + y_j)*v18/(v4.powf(1.5)*v15) + v8/v17)*v22/(self.n*v20);
        gradient[self.i].z += -self.k_ijk*((-z_i + z_j)*v18/(v4.powf(1.5)*v15) + v5/v17)*v22/(self.n*v20);
        gradient[self.j].x += -self.k_ijk*(v12*v18/(v4.powf(1.5)*v15) + v0*v18/(v16*v13.powf(1.5)) + (-x_i + 2.*x_j - x_k)/v17)*v22/(self.n*v20);
        gradient[self.j].y += -self.k_ijk*(v11*v18/(v4.powf(1.5)*v15) + v8*v18/(v16*v13.powf(1.5)) + (-y_i + 2.*y_j - y_k)/v17)*v22/(self.n*v20);
        gradient[self.j].z += -self.k_ijk*(v7*v18/(v4.powf(1.5)*v15) + v5*v18/(v16*v13.powf(1.5)) + (-z_i + 2.*z_j - z_k)/v17)*v22/(self.n*v20);
        gradient[self.k].x += -self.k_ijk*(v12/v17 + (x_j - x_k)*v18/(v16*v13.powf(1.5)))*v22/(self.n*v20);
        gradient[self.k].y += -self.k_ijk*(v11/v17 + (y_j - y_k)*v18/(v16*v13.powf(1.5)))*v22/(self.n*v20);
        gradient[self.k].z += -self.k_ijk*(v7/v17 + (z_j - z_k)*v18/(v16*v13.powf(1.5)))*v22/(self.n*v20);
    }
}
impl HarmonicAngle for HarmonicAngleTypeA {
    fn i(&self) -> usize {self.i}
    fn j(&self) -> usize {self.j}
    fn k(&self) -> usize {self.k}
}

pub struct HarmonicAngleTypeB{
    pub(crate) i:     usize,
    pub(crate) j:     usize,
    pub(crate) k:     usize,
    pub(crate) k_ijk: f64,
    pub(crate) c0:    f64,
    pub(crate) c1:    f64,
    pub(crate) c2:    f64
}

impl EnergyFunction for HarmonicAngleTypeB {

    fn involves_idxs(&self, idxs: Vec<usize>) -> bool { involves_idxs(self, idxs) }

    fn force_constant(&self) -> f64 { self.k_ijk }

    /// Energy: k(c0 + c1 cos(θ) + c2 cos(2θ))
    fn energy(&self, coordinates: &Vec<Point>) -> f64 {

        let theta = theta(self, coordinates);

        self.k_ijk * (self.c0 + self.c1 * theta.cos() + self.c2 * (2. * theta).cos())
    }

    /// Add the gradient for this term
    fn add_gradient(&self,
                    coordinates: &Vec<Point>,
                    gradient:    &mut Vec<Vector3D>){

        let x_i = coordinates[self.i].x;
        let y_i = coordinates[self.i].y;
        let z_i = coordinates[self.i].z;

        let x_j = coordinates[self.j].x;
        let y_j = coordinates[self.j].y;
        let z_j = coordinates[self.j].z;

        let x_k = coordinates[self.k].x;
        let y_k = coordinates[self.k].y;
        let z_k = coordinates[self.k].z;

        let v0 = -x_j + x_k;
        let v1 = (z_i - z_j).powi(2);
        let v2 = (y_i - y_j).powi(2);
        let v3 = (x_i - x_j).powi(2);
        let v4 = v3 + v2 + v1;
        let v5 = -z_j + z_k;
        let v6 = v5.powi(2);
        let v7 = z_i - z_j;
        let v8 = -y_j + y_k;
        let v9 = v8.powi(2);
        let v10 = v0.powi(2);
        let v11 = y_i - y_j;
        let v12 = x_i - x_j;
        let v13 = v10 + v9 + v6;
        let v14 = v4*v13;
        let v15 = v13.sqrt();
        let v16 = v4.sqrt();
        let v17 = v16*v15;
        let v18 = v12*v0 + v11*v8 + v7*v5;
        let v19 = v18.powi(2);
        let v20 = (v18/v17).acos();
        let v21 = (-v19/v14 + 1.).sqrt();
        let v22 = (2.*v20).sin();
        gradient[self.i].x += self.k_ijk*(self.c1*(-x_i + x_j)*v18/(v4.powf(1.5)*v15) + self.c1*v0/v17 + 2.*self.c2*((-x_i + x_j)*v18/(v4.powf(1.5)*v15) + v0/v17)*v22/v21);
        gradient[self.i].y += self.k_ijk*(self.c1*(-y_i + y_j)*v18/(v4.powf(1.5)*v15) + self.c1*v8/v17 + 2.*self.c2*((-y_i + y_j)*v18/(v4.powf(1.5)*v15) + v8/v17)*v22/v21);
        gradient[self.i].z += self.k_ijk*(self.c1*(-z_i + z_j)*v18/(v4.powf(1.5)*v15) + self.c1*v5/v17 + 2.*self.c2*((-z_i + z_j)*v18/(v4.powf(1.5)*v15) + v5/v17)*v22/v21);
        gradient[self.j].x += self.k_ijk*(self.c1*v12*v18/(v4.powf(1.5)*v15) + self.c1*v0*v18/(v16*v13.powf(1.5)) + self.c1*(-x_i + 2.*x_j - x_k)/v17 + 2.*self.c2*(v12*v18/(v4.powf(1.5)*v15) + v0*v18/(v16*v13.powf(1.5)) + (-x_i + 2.*x_j - x_k)/v17)*v22/v21);
        gradient[self.j].y += self.k_ijk*(self.c1*v11*v18/(v4.powf(1.5)*v15) + self.c1*v8*v18/(v16*v13.powf(1.5)) + self.c1*(-y_i + 2.*y_j - y_k)/v17 + 2.*self.c2*(v11*v18/(v4.powf(1.5)*v15) + v8*v18/(v16*v13.powf(1.5)) + (-y_i + 2.*y_j - y_k)/v17)*v22/v21);
        gradient[self.j].z += self.k_ijk*(self.c1*v7*v18/(v4.powf(1.5)*v15) + self.c1*v5*v18/(v16*v13.powf(1.5)) + self.c1*(-z_i + 2.*z_j - z_k)/v17 + 2.*self.c2*(v7*v18/(v4.powf(1.5)*v15) + v5*v18/(v16*v13.powf(1.5)) + (-z_i + 2.*z_j - z_k)/v17)*v22/v21);
        gradient[self.k].x += self.k_ijk*(self.c1*v12/v17 + self.c1*(x_j - x_k)*v18/(v16*v13.powf(1.5)) + 2.*self.c2*(v12/v17 + (x_j - x_k)*v18/(v16*v13.powf(1.5)))*v22/v21);
        gradient[self.k].y += self.k_ijk*(self.c1*v11/v17 + self.c1*(y_j - y_k)*v18/(v16*v13.powf(1.5)) + 2.*self.c2*(v11/v17 + (y_j - y_k)*v18/(v16*v13.powf(1.5)))*v22/v21);
        gradient[self.k].z += self.k_ijk*(self.c1*v7/v17 + self.c1*(z_j - z_k)*v18/(v16*v13.powf(1.5)) + 2.*self.c2*(v7/v17 + (z_j - z_k)*v18/(v16*v13.powf(1.5)))*v22/v21);

    }
}
impl HarmonicAngle for HarmonicAngleTypeB {
    fn i(&self) -> usize {self.i}
    fn j(&self) -> usize {self.j}
    fn k(&self) -> usize {self.k}
}

fn involves_idxs(angle: &dyn HarmonicAngle, idxs: Vec<usize>) -> bool {
    idxs.len() == 3 && HashSet::from([angle.i(), angle.j(), angle.k()]) == HashSet::from_iter(idxs)
}

#[inline(always)]
fn theta(angle:       &dyn HarmonicAngle,
         coordinates: &Vec<Point>) -> f64{

    angle_value(angle.i(), angle.j(), angle.k(), coordinates)
}


/*
   /$$                           /$$
  | $$                          | $$
 /$$$$$$    /$$$$$$   /$$$$$$$ /$$$$$$   /$$$$$$$
|_  $$_/   /$$__  $$ /$$_____/|_  $$_/  /$$_____/
  | $$    | $$$$$$$$|  $$$$$$   | $$   |  $$$$$$
  | $$ /$$| $$_____/ \____  $$  | $$ /$$\____  $$
  |  $$$$/|  $$$$$$$ /$$$$$$$/  |  $$$$//$$$$$$$/
   \___/   \_______/|_______/    \___/ |_______/
 */

#[cfg(test)]
mod tests{

    use super::*;
    use crate::utils::*;

    struct TestHarmonicAngle{i: usize, j: usize, k: usize}

    impl HarmonicAngle for TestHarmonicAngle{
        fn i(&self) -> usize {self.i}
        fn j(&self) -> usize {self.j}
        fn k(&self) -> usize {self.k}
    }

    /// Ensure a bend angle can be calculated correctly. Compared to an Avogadro reference
    #[test]
    fn test_angle_calculation(){

        // Coordinates for a H2O molecule
        let x: Vec<Point> = Vec::from([
            Point{x: -2.17305, y: -1.64172, z: 0.01027},
            Point{x: -1.18373, y: -1.60261, z: -0.00725},
            Point{x: -2.46242, y: -0.77749, z: -0.37700}
        ]);

        let angle = theta(&TestHarmonicAngle{i: 1, j: 0, k: 2}, &x);

        assert!(is_close(angle, 1.8239, 1E-3));
    }

}