//! Solve linear problem using LU decomposition

use lapacke;
use num_traits::Zero;

use crate::error::*;
use crate::layout::MatrixLayout;
use crate::types::*;

use super::NormType;
use super::{into_result, Pivot, Transpose};

/// Wraps `*getrf`, `*getri`, and `*getrs`
pub trait Solve_: Scalar + Sized {
    /// Computes the LU factorization of a general `m x n` matrix `a` using
    /// partial pivoting with row interchanges.
    ///
    /// If the result matches `Err(LinalgError::Lapack(LapackError {
    /// return_code )) if return_code > 0`, then `U[(return_code-1,
    /// return_code-1)]` is exactly zero. The factorization has been completed,
    /// but the factor `U` is exactly singular, and division by zero will occur
    /// if it is used to solve a system of equations.
    unsafe fn lu(l: MatrixLayout, a: &mut [Self]) -> Result<Pivot>;
    unsafe fn inv(l: MatrixLayout, a: &mut [Self], p: &Pivot) -> Result<()>;
    /// Estimates the the reciprocal of the condition number of the matrix in 1-norm.
    ///
    /// `anorm` should be the 1-norm of the matrix `a`.
    unsafe fn rcond(l: MatrixLayout, a: &[Self], anorm: Self::Real) -> Result<Self::Real>;
    unsafe fn solve(l: MatrixLayout, t: Transpose, a: &[Self], p: &Pivot, b: &mut [Self]) -> Result<()>;
}

macro_rules! impl_solve {
    ($scalar:ty, $getrf:path, $getri:path, $gecon:path, $getrs:path) => {
        impl Solve_ for $scalar {
            unsafe fn lu(l: MatrixLayout, a: &mut [Self]) -> Result<Pivot> {
                let (row, col) = l.size();
                let k = ::std::cmp::min(row, col);
                let mut ipiv = vec![0; k as usize];
                let info = $getrf(l.lapacke_layout(), row, col, a, l.lda(), &mut ipiv);
                into_result(info, ipiv)
            }

            unsafe fn inv(l: MatrixLayout, a: &mut [Self], ipiv: &Pivot) -> Result<()> {
                let (n, _) = l.size();
                let info = $getri(l.lapacke_layout(), n, a, l.lda(), ipiv);
                into_result(info, ())
            }

            unsafe fn rcond(l: MatrixLayout, a: &[Self], anorm: Self::Real) -> Result<Self::Real> {
                let (n, _) = l.size();
                let mut rcond = Self::Real::zero();
                let info = $gecon(
                    l.lapacke_layout(),
                    NormType::One as u8,
                    n,
                    a,
                    l.lda(),
                    anorm,
                    &mut rcond,
                );
                into_result(info, rcond)
            }

            unsafe fn solve(l: MatrixLayout, t: Transpose, a: &[Self], ipiv: &Pivot, b: &mut [Self]) -> Result<()> {
                let (n, _) = l.size();
                let nrhs = 1;
                let ldb = 1;
                let info = $getrs(l.lapacke_layout(), t as u8, n, nrhs, a, l.lda(), ipiv, b, ldb);
                into_result(info, ())
            }
        }
    };
} // impl_solve!

impl_solve!(f64, lapacke::dgetrf, lapacke::dgetri, lapacke::dgecon, lapacke::dgetrs);
impl_solve!(f32, lapacke::sgetrf, lapacke::sgetri, lapacke::sgecon, lapacke::sgetrs);
impl_solve!(c64, lapacke::zgetrf, lapacke::zgetri, lapacke::zgecon, lapacke::zgetrs);
impl_solve!(c32, lapacke::cgetrf, lapacke::cgetri, lapacke::cgecon, lapacke::cgetrs);