use crate::numerical::matrix::Matrix;
use crate::numerical::solve::{solve_linear_system, LinearSolution};
use std::ops::Sub;
#[derive(Clone, Copy, Default)]
pub struct Vector2D {
    x: f64,
    y: f64,
}
impl Vector2D {
    pub fn new(x: f64, y: f64) -> Self {
        Self { x, y }
    }
    pub fn norm(&self) -> f64 {
        (self.x * self.x + self.y * self.y).sqrt()
    }
}
impl Sub for Vector2D {
    type Output = Self;
    fn sub(self, rhs: Self) -> Self {
        Self {
            x: self.x - rhs.x,
            y: self.y - rhs.y,
        }
    }
}
#[derive(Clone, Copy, Default)]
pub struct Vector3D {
    x: f64,
    y: f64,
    z: f64,
}
impl Vector3D {
    #[allow(dead_code)]
    pub fn new(x: f64, y: f64, z: f64) -> Self {
        Self { x, y, z }
    }
    #[allow(dead_code)]
    pub fn norm(&self) -> f64 {
        (self.x * self.x + self.y * self.y + self.z * self.z).sqrt()
    }
}
impl Sub for Vector3D {
    type Output = Self;
    fn sub(self, rhs: Self) -> Self {
        Self {
            x: self.x - rhs.x,
            y: self.y - rhs.y,
            z: self.z - rhs.z,
        }
    }
}
/// Specifies the type of boundary condition on an element.
pub enum BoundaryCondition<T> {
    Potential(T),
    Flux(T),
}
#[allow(dead_code)]
pub struct Element2D {
    p1: Vector2D,
    p2: Vector2D,
    midpoint: Vector2D,
    length: f64,
    normal: Vector2D,
}
impl Element2D {
    pub(crate) fn new(p1: Vector2D, p2: Vector2D) -> Self {
        let diff = p2 - p1;
        let length = diff.norm();
        let normal = Vector2D::new(diff.y / length, -diff.x / length);
        let midpoint = Vector2D::new((p1.x + p2.x) / 2.0, (p1.y + p2.y) / 2.0);
        Self {
            p1,
            p2,
            midpoint,
            length,
            normal,
        }
    }
}
/// Solves a 2D Laplace problem (e.g., potential flow, steady-state heat conduction)
/// using the Boundary Element Method (BEM) with constant elements.
///
/// This function discretizes the boundary of the domain into elements and applies
/// boundary conditions to solve for unknown potentials or fluxes on the boundary.
///
/// # Arguments
/// * `points` - A `Vec` of `(x, y)` tuples defining the vertices of the boundary polygon.
/// * `bcs` - A `Vec` of `BoundaryCondition` for each element, specifying known potential or flux.
///
/// # Returns
/// A `Result` containing a tuple `(u, q)`, where `u` is a `Vec<f64>` of potentials
/// and `q` is a `Vec<f64>` of normal fluxes on each element. Returns an `Err` string
/// if the system is ill-posed or has no unique solution.
pub fn solve_laplace_bem_2d(
    points: &[(f64, f64)],
    bcs: &[BoundaryCondition<f64>],
) -> Result<(Vec<f64>, Vec<f64>), String> {
    let n = points.len();
    if n != bcs.len() {
        return Err("Number of points and boundary conditions must match.".to_string());
    }
    let elements: Vec<_> = (0..n)
        .map(|i| {
            Element2D::new(
                Vector2D::new(points[i].0, points[i].1),
                Vector2D::new(points[(i + 1) % n].0, points[(i + 1) % n].1),
            )
        })
        .collect();
    let mut h_mat = Matrix::zeros(n, n);
    let mut g_mat = Matrix::zeros(n, n);
    for i in 0..n {
        for j in 0..n {
            if i == j {
                *h_mat.get_mut(i, i) = 0.5;
            } else {
                let r = (elements[j].midpoint - elements[i].midpoint).norm();
                let h_ij = -1.0 / (2.0 * std::f64::consts::PI * r);
                let g_ij = -1.0 / (2.0 * std::f64::consts::PI) * elements[j].length * r.ln();
                *h_mat.get_mut(i, j) = h_ij * elements[j].length;
                *g_mat.get_mut(i, j) = g_ij;
            }
        }
    }
    let mut a_mat = Matrix::zeros(n, n);
    let mut b_vec = vec![0.0; n];
    let mut u_unknown_indices = Vec::new();
    let mut q_unknown_indices = Vec::new();
    for i in 0..n {
        match bcs[i] {
            BoundaryCondition::Potential(u_val) => {
                q_unknown_indices.push(i);
                for j in 0..n {
                    *a_mat.get_mut(i, j) -= *g_mat.get(i, j);
                    b_vec[i] -= *h_mat.get(i, j) * u_val;
                }
            }
            BoundaryCondition::Flux(q_val) => {
                u_unknown_indices.push(i);
                for j in 0..n {
                    *a_mat.get_mut(i, j) += *h_mat.get(i, j);
                    b_vec[i] += *g_mat.get(i, j) * q_val;
                }
            }
        }
    }
    let solution = match solve_linear_system(&a_mat, &b_vec)? {
        LinearSolution::Unique(sol) => sol,
        _ => return Err("BEM system has no unique solution.".to_string()),
    };
    let mut u = vec![0.0; n];
    let mut q = vec![0.0; n];
    let mut sol_idx = 0;
    for i in 0..n {
        match bcs[i] {
            BoundaryCondition::Potential(u_val) => {
                u[i] = u_val;
                q[i] = solution[sol_idx];
                sol_idx += 1;
            }
            BoundaryCondition::Flux(q_val) => {
                q[i] = q_val;
                u[i] = solution[sol_idx];
                sol_idx += 1;
            }
        }
    }
    Ok((u, q))
}
/// Scenario for 2D BEM: Simulates potential flow around a cylinder.
///
/// This function sets up a circular boundary and applies boundary conditions
/// corresponding to a uniform flow in the x-direction. It then uses the BEM solver
/// to calculate the potential and flux on the cylinder's surface.
///
/// # Returns
/// A `Result` containing a tuple `(u, q)` of potentials and fluxes on the cylinder surface,
/// or an error string if the BEM system cannot be solved.
pub fn simulate_2d_cylinder_scenario() -> Result<(Vec<f64>, Vec<f64>), String> {
    let n_points = 40;
    let radius = 1.0;
    let mut points = Vec::new();
    let mut bcs = Vec::new();
    for i in 0..n_points {
        let angle = 2.0 * std::f64::consts::PI * (f64::from(i)) / (f64::from(n_points));
        let (x, y) = (radius * angle.cos(), radius * angle.sin());
        points.push((x, y));
        bcs.push(BoundaryCondition::Potential(1.0 * x));
    }
    solve_laplace_bem_2d(&points, &bcs)
}
/// Solves a 3D Laplace problem on a cubic domain using a simplified BEM approach.
///
/// **NOTE**: A full 3D BEM implementation with proper numerical integration over surface
/// elements is extremely complex and beyond the scope of a single file implementation.
/// It requires mesh data structures, multi-point Gaussian quadrature on surfaces,
/// and careful handling of singular integrals. This function serves as a placeholder
/// for a future, more dedicated implementation.
///
/// # Returns
/// A `Result` indicating success or an error string if the implementation is not yet complete.
pub fn solve_laplace_bem_3d() -> Result<(), String> {
    println!("3D BEM is a complex topic requiring a dedicated library. This is a placeholder.");
    Ok(())
}
