trigivs 0.2.0

use crate::solver_error::SolverErrors;
use crate::solver_parts::*;

use num_traits::Float;

/// Holds tridiagonal system precomputed for working with multiple righ hand sides without heap allocation
///
/// # Example
///
/// ```
/// let sup = [-4.];
/// let diag = [3., 2.];
/// let sub = [5.];
///
/// let rhs1 = [-3., 21.];
/// let rhs2 = [-23., 5.];
///
/// let precomputed = trigivs::prelude::precompute_givens(&sup, &diag, &sub).unwrap();
///
/// let x1 = precomputed.solve_givens_rhs(&rhs1).unwrap();
/// let x2 = precomputed.solve_givens_rhs(&rhs2).unwrap();
/// ```
#[derive(Clone, Debug)]
pub struct TridiagSysPrecomp<T: Float, const D: usize, const S: usize> {
    diag: [T; D],
    sup1: Option<[T; S]>,
    sup2: Option<[T; S]>,

    sins_cosins: Option<[(T, T); S]>,
}

/// Holds precomputed tridiagonal system with Ruiz preconditioning for working with multiple righ hand sides without heap allocation
///
/// # Example
///
/// ```
/// let sup = [-4.];
/// let diag = [3., 2.];
/// let sub = [5.];
///
/// let rhs1 = [-3., 21.];
/// let rhs2 = [-23., 5.];
///
/// let precomputed = trigivs::prelude::precompute_givens_ruiz(
///     &sup,
///     &diag,
///     &sub,
///     5,
///     0.001
/// ).unwrap();
///
/// let x1 = precomputed.solve_givens_rhs(&rhs1).unwrap();
/// let x2 = precomputed.solve_givens_rhs(&rhs2).unwrap();
/// ```
#[derive(Clone, Debug)]
pub struct TridiagSysRuizPrecomp<T: Float, const D: usize, const S: usize> {
    sys: TridiagSysPrecomp<T, D, S>,

    row_mul: [T; D],
    col_mul: [T; D],
}

/// Solves a trigiagonal system of linear equations without heap allocation
///
/// # Arguments
///
/// * `sub` - subdiagonal elements, length n-1
/// * `diag` - main diagonal elements, length n
/// * `sup` - superdiagonal elements, length n-1
/// * `rhs` - right-hand side vector, length n
///
/// # Example
///
/// ```
/// let sup = [-4.];
/// let diag = [3., 2.];
/// let sub = [5.];
/// let rhs = [-3., 21.];
///
/// let x = trigivs::prelude::solve_givens(&sup, &diag, &sub, &rhs).unwrap();
/// ```
pub fn solve_givens<T: Float, const D: usize, const S: usize>(
    sup: &[T; S],
    diag: &[T; D],
    sub: &[T; S],
    rhs: &[T; D],
) -> Result<[T; D], SolverErrors> {
    const {
        assert!(
            D == S + 1,
            "Sub and sup diagonals must be exctly 1 element smaller than main diagonal"
        )
    };

    let mut a = sup.clone();
    let mut d = diag.clone();
    let mut rhs = rhs.clone();

    let mut ur = [T::zero(); S];
    let u = if S > 1 { &mut ur[..S - 1] } else { &mut [] };

    let mut x = [T::zero(); D];

    solve_givens_body(sub, &mut d, &mut a, u, &mut rhs, &mut x)?;

    Ok(x)
}

/// Precomputes a system for multiple differenr RHS without heap allocation
///
/// # Arguments
///
/// * `sup` - superdiagonal elements, length n-1
/// * `diag` - main diagonal elements, length n
/// * `sub` - subdiagonal elements, length n-1
///
/// # Example
///
/// ```
/// let sup = [-4.];
/// let diag = [3., 2.];
/// let sub = [5.];
///
/// let rhs = [-3., 21.];
///
/// let precomputed = trigivs::prelude::precompute_givens(&sup, &diag, &sub).unwrap();
///
/// ```
pub fn precompute_givens<T: Float, const D: usize, const S: usize>(
    sup: &[T; S],
    diag: &[T; D],
    sub: &[T; S],
) -> Result<TridiagSysPrecomp<T, D, S>, SolverErrors> {
    const {
        assert!(
            D == S + 1,
            "Sub and sup diagonals must be exctly 1 element smaller than main diagonal"
        )
    };

    let mut a = sup.clone();
    let mut d = diag.clone();

    let mut ur = [T::zero(); S];
    let u = if S > 1 { &mut ur[..S - 1] } else { &mut [] };

    let mut sins_cosins = [(T::zero(), T::zero()); S];

    precompute_givens_body(sub, &mut d, &mut a, u, &mut sins_cosins)?;

    Ok(TridiagSysPrecomp {
        diag: d,
        sup1: if a.len() > 0 { Some(a) } else { None },
        sup2: if u.len() > 0 { Some(ur) } else { None },
        sins_cosins: if sins_cosins.len() > 0 {
            Some(sins_cosins)
        } else {
            None
        },
    })
}

/// Precomputes a system for multiple differenr RHS with Ruiz preconditioning without heap allocation
///
/// # Arguments
///
/// * `sup` - superdiagonal elements, length n-1
/// * `diag` - main diagonal elements, length n
/// * `sub` - subdiagonal elements, length n-1
/// * `r_iter` - maximum amount of iterations for Ruiz preconditioning (impractical over 10)
/// * `r_eps` - finishing criteria for Ruiz preconditioning through maximum column/row inf-norm deviation from 1
///
/// # Example
///
/// ```
/// let sup = [-4.];
/// let diag = [3., 2.];
/// let sub = [5.];
///
/// let rhs = [-3., 21.];
///
/// let precomputed = trigivs::prelude::precompute_givens_ruiz(&sup, &diag, &sub, 5, 0.01).unwrap();
/// ```
pub fn precompute_givens_ruiz<T: Float, const D: usize, const S: usize>(
    sup: &[T; S],
    diag: &[T; D],
    sub: &[T; S],
    r_iter: usize,
    r_eps: T,
) -> Result<TridiagSysRuizPrecomp<T, D, S>, SolverErrors> {
    const {
        assert!(
            D == S + 1,
            "Sub and sup diagonals must be exctly 1 element smaller than main diagonal"
        )
    };

    let mut sub_b = sub.clone();
    let mut sup_b = sup.clone();
    let mut diag_b = diag.clone();

    let mut col_b = [T::one(); D];
    let mut row_b = [T::one(); D];

    get_ruiz_equilibrium_mul(
        &diag_b, &sup_b, &sub_b, &mut row_b, &mut col_b, r_iter, r_eps,
    )?;
    apply_ruiz(&mut diag_b, &mut sup_b, &mut sub_b, &row_b, &col_b);

    let mut sins_cosins = [(T::zero(), T::zero()); S];

    let mut ur = [T::zero(); S];
    let u = if S > 1 { &mut ur[..S - 1] } else { &mut [] };

    precompute_givens_body(&sub_b, &mut diag_b, &mut sup_b, u, &mut sins_cosins)?;

    Ok(TridiagSysRuizPrecomp {
        sys: TridiagSysPrecomp {
            diag: diag_b,
            sup1: if sup_b.len() > 0 { Some(sup_b) } else { None },
            sup2: if u.len() > 0 { Some(ur) } else { None },
            sins_cosins: if sins_cosins.len() > 0 {
                Some(sins_cosins)
            } else {
                None
            },
        },
        row_mul: row_b,
        col_mul: col_b,
    })
}

impl<T: Float, const D: usize, const S: usize> TridiagSysPrecomp<T, D, S> {
    /// Solves precomputed system with a provided right hand side without heap allocation
    ///
    /// # Arguments
    ///
    /// * `rhs` - right-hand side vector, length n
    ///
    /// # Example
    ///
    /// ```
    /// let sup = [-4.];
    /// let diag = [3., 2.];
    /// let sub = [5.];
    ///
    /// let rhs = [-3., 21.];
    ///
    /// let precomputed = trigivs::prelude::precompute_givens(&sup, &diag, &sub).unwrap();
    ///
    /// let x = precomputed.solve_givens_rhs(&rhs).unwrap();
    /// ```
    pub fn solve_givens_rhs(&self, rhs: &[T; D]) -> Result<[T; D], SolverErrors> {
        let mut rhsl = rhs.clone();

        if let Some(sins_cosins) = &self.sins_cosins {
            solve_givens_sc_rhs_body(sins_cosins, &mut rhsl);
        }

        let mut x_buffer = [T::zero(); D];

        compute_x(
            &mut x_buffer,
            &rhsl,
            &self.diag,
            self.sup1.as_ref().map_or(&[], |v| v.as_slice()),
            self.sup2.as_ref().map_or(&[], |v| v.as_slice()),
        )?;

        Ok(x_buffer)
    }
}

impl<T: Float, const D: usize, const S: usize> TridiagSysRuizPrecomp<T, D, S> {
    /// Solves precomputed system with a provided right hand side without heap allocation
    ///
    /// # Arguments
    ///
    /// * `rhs` - right-hand side vector, length n
    ///
    /// # Example
    ///
    /// ```
    /// let sup = [-4.];
    /// let diag = [3., 2.];
    /// let sub = [5.];
    ///
    /// let rhs = [-3., 21.];
    ///
    /// let precomputed = trigivs::prelude::precompute_givens_ruiz(&sup, &diag, &sub, 5, 0.001).unwrap();
    ///
    /// let x = precomputed.solve_givens_rhs(&rhs).unwrap();
    /// ```
    pub fn solve_givens_rhs(&self, rhs: &[T; D]) -> Result<[T; D], SolverErrors> {
        let mut rhsl = rhs.clone();
        rhsl.iter_mut()
            .zip(self.row_mul)
            .for_each(|(r, row)| *r = *r * row);

        let mut x = self.sys.solve_givens_rhs(&rhsl)?;
        x.iter_mut()
            .zip(self.col_mul)
            .for_each(|(x, col)| *x = *x * col);

        Ok(x)
    }
}

/// Refines a tridiagonal system solution using the Kaczmarz iterative method without heap allocation
///
/// # Arguments
///
/// * `sup` - superdiagonal elements, length n-1
/// * `diag` - main diagonal elements, length n
/// * `sub` - subdiagonal elements, length n-1
/// * `rhs` - right-hand side vector, length n
/// * `x_init` - initial solution approximation, length n
/// * `iter` - maximum number of Kaczmarz iterations to perform
/// * `eps` - convergence tolerance
///
/// # Example
///
/// ```
/// let sub = [5.];
/// let diag = [3., 2.];
/// let sup = [-4.];
/// let rhs = [-3., 21.];
///
/// let x_init = [1., 1.];
/// let x_refined = trigivs::prelude::tridiag_iter_kaczmarz(
///     &sub,
///     &diag,
///     &sup,
///     &rhs,
///     &x_init,
///     1000,
///     1e-6
/// ).unwrap();
/// ```
///
pub fn tridiag_iter_kaczmarz<T: Float, const D: usize, const S: usize>(
    sup: &[T; S],
    diag: &[T; D],
    sub: &[T; S],
    rhs: &[T; D],
    x_init: &[T; D],
    iter: usize,
    eps: T,
) -> Result<[T; D], SolverErrors> {
    const {
        assert!(
            D == S + 1,
            "Sub and sup diagonals must be exctly 1 element smaller than main diagonal"
        )
    };

    let mut x = x_init.clone();
    let mut ai_ai_dotproducts = [T::zero(); D];
    if D == 1 {
        ai_ai_dotproducts[0] = diag[0].powi(2);
    } else {
        ai_ai_dotproducts[0] = diag[0].powi(2) + sup[0].powi(2);
        ai_ai_dotproducts
            .iter_mut()
            .enumerate()
            .skip(1)
            .take(D - 2)
            .for_each(|(i, elem)| *elem = diag[i].powi(2) + sup[i].powi(2) + sub[i - 1].powi(2));
        ai_ai_dotproducts[D - 1] = sub[D - 2].powi(2) + diag[D - 1].powi(2)
    }
    kaczmarz_body(
        sub,
        diag,
        sup,
        rhs,
        &ai_ai_dotproducts,
        &mut x,
        D,
        iter,
        eps,
    )?;
    Ok(x)
}

/// Compute row and column scaling parameters using Ruiz preconditioning without heap allocation
///
/// # Arguments
///
/// * `sup` - superdiagonal elements, length n-1
/// * `diag` - main diagonal elements, length n
/// * `sub` - subdiagonal elements, length n-1
/// * `r_iter` - maximum amount of iterations for Ruiz preconditioning (impractical over 10)
/// * `r_eps` - finishing criteria for Ruiz preconditioning through maximum column/row inf-norm deviation from 1
///
/// # Output
///
/// (R, C)
/// * `R` - row scaling parmeters
/// * `C` - column scaling parmeters
///
/// # Example
///
/// ```
/// let sup = [-4.];
/// let diag = [3., 2.];
/// let sub = [5.];
///
/// let (row_s, column_s) = trigivs::prelude::compute_ruiz_scaling(&sup, &diag, &sub, 5, 0.01).unwrap();
/// ```
pub fn compute_ruiz_scaling<T: Float, const D: usize, const S: usize>(
    sup: &[T; S],
    diag: &[T; D],
    sub: &[T; S],
    iter: usize,
    eps: T,
) -> Result<([T; D], [T; D]), SolverErrors> {
    const {
        assert!(
            D == S + 1,
            "Sub and sup diagonals must be exctly 1 element smaller than main diagonal"
        )
    };

    let mut row_b = [T::one(); D];
    let mut col_b = [T::one(); D];
    get_ruiz_equilibrium_mul(diag, sup, sub, &mut row_b, &mut col_b, iter, eps)?;
    Ok((row_b, col_b))
}

/// Solves a tridiagonal system using Givens rotations with Ruiz preconditioning without heap allocation
///
/// # Arguments
///
/// * `sup` - superdiagonal elements, length n-1
/// * `diag` - main diagonal elements, length n
/// * `sub` - subdiagonal elements, length n-1
/// * `r_iter` - maximum amount of iterations for Ruiz preconditioning (impractical over 10)
/// * `r_eps` - finishing criteria for Ruiz preconditioning through maximum column/row inf-norm deviation from 1
///
/// # Example
///
/// ```
/// let sub = [5.];
/// let diag = [3., 2.];
/// let sup = [-4.];
/// let rhs = [-3., 21.];
///
/// let x = trigivs::prelude::solve_givens_ruiz_precond(
///     &sub,
///     &diag,
///     &sup,
///     &rhs,
///     5,
///     0.001
/// ).unwrap();
/// ```
///
pub fn solve_givens_ruiz_precond<T: Float, const D: usize, const S: usize>(
    sup: &[T; S],
    diag: &[T; D],
    sub: &[T; S],
    rhs: &[T; D],
    r_iter: usize,
    r_eps: T,
) -> Result<[T; D], SolverErrors> {
    const {
        assert!(
            D == S + 1,
            "Sub and sup diagonals must be exctly 1 element smaller than main diagonal"
        )
    };

    let mut sub_b = sub.clone();
    let mut sup_b = sup.clone();
    let mut diag_b = diag.clone();
    let mut rhs = rhs.clone();

    let mut col_b = [T::one(); D];

    {
        let mut row_b = [T::one(); D];
        get_ruiz_equilibrium_mul(
            &diag_b, &sup_b, &sub_b, &mut row_b, &mut col_b, r_iter, r_eps,
        )?;
        apply_ruiz(&mut diag_b, &mut sup_b, &mut sub_b, &row_b, &col_b);
        rhs.iter_mut()
            .zip(row_b)
            .for_each(|(rhs, row)| *rhs = *rhs * row);
    }

    let mut ur = [T::zero(); S];
    let u = if S > 1 { &mut ur[..S - 1] } else { &mut [] };

    let mut x = [T::zero(); D];

    solve_givens_body(&sub_b, &mut diag_b, &mut sup_b, u, &mut rhs, &mut x)?;

    x.iter_mut().zip(col_b).for_each(|(x, col)| *x = *x * col);

    Ok(x)
}