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//! QR decomposition
//!
//! [Wikipedia article on QR decomposition](https://en.wikipedia.org/wiki/QR_decomposition)

use ndarray::*;
use num_traits::Zero;

use crate::convert::*;
use crate::error::*;
use crate::layout::*;
use crate::triangular::*;
use crate::types::*;

pub use lax::UPLO;

/// QR decomposition for matrix reference
///
/// This creates copy due for reshaping array.
/// To avoid copy and the matrix is square, please use `QRSquare*` traits.
pub trait QR {
    type Q;
    type R;
    fn qr(&self) -> Result<(Self::Q, Self::R)>;
}

/// QR decomposition
///
/// This creates copy due for reshaping array.
/// To avoid copy and the matrix is square, please use `QRSquare*` traits.
pub trait QRInto: Sized {
    type Q;
    type R;
    fn qr_into(self) -> Result<(Self::Q, Self::R)>;
}

/// QR decomposition for square matrix reference
pub trait QRSquare: Sized {
    type Q;
    type R;
    fn qr_square(&self) -> Result<(Self::Q, Self::R)>;
}

/// QR decomposition for square matrix
pub trait QRSquareInto: Sized {
    type R;
    fn qr_square_into(self) -> Result<(Self, Self::R)>;
}

/// QR decomposition for mutable reference of square matrix
pub trait QRSquareInplace: Sized {
    type R;
    fn qr_square_inplace(&mut self) -> Result<(&mut Self, Self::R)>;
}

impl<A, S> QRSquareInplace for ArrayBase<S, Ix2>
where
    A: Scalar + Lapack,
    S: DataMut<Elem = A>,
{
    type R = Array2<A>;

    fn qr_square_inplace(&mut self) -> Result<(&mut Self, Self::R)> {
        let l = self.square_layout()?;
        let r = A::qr(l, self.as_allocated_mut()?)?;
        let r: Array2<_> = into_matrix(l, r)?;
        Ok((self, r.into_triangular(UPLO::Upper)))
    }
}

impl<A, S> QRSquareInto for ArrayBase<S, Ix2>
where
    A: Scalar + Lapack,
    S: DataMut<Elem = A>,
{
    type R = Array2<A>;

    fn qr_square_into(mut self) -> Result<(Self, Self::R)> {
        let (_, r) = self.qr_square_inplace()?;
        Ok((self, r))
    }
}

impl<A, S> QRSquare for ArrayBase<S, Ix2>
where
    A: Scalar + Lapack,
    S: Data<Elem = A>,
{
    type Q = Array2<A>;
    type R = Array2<A>;

    fn qr_square(&self) -> Result<(Self::Q, Self::R)> {
        let a = self.to_owned();
        a.qr_square_into()
    }
}

impl<A, S> QRInto for ArrayBase<S, Ix2>
where
    A: Scalar + Lapack,
    S: DataMut<Elem = A>,
{
    type Q = Array2<A>;
    type R = Array2<A>;

    fn qr_into(mut self) -> Result<(Self::Q, Self::R)> {
        let n = self.nrows();
        let m = self.ncols();
        let k = ::std::cmp::min(n, m);
        let l = self.layout()?;
        let r = A::qr(l, self.as_allocated_mut()?)?;
        let r: Array2<_> = into_matrix(l, r)?;
        let q = self;
        Ok((take_slice(&q, n, k), take_slice_upper(&r, k, m)))
    }
}

impl<A, S> QR for ArrayBase<S, Ix2>
where
    A: Scalar + Lapack,
    S: Data<Elem = A>,
{
    type Q = Array2<A>;
    type R = Array2<A>;

    fn qr(&self) -> Result<(Self::Q, Self::R)> {
        let a = self.to_owned();
        a.qr_into()
    }
}

fn take_slice<A, S1, S2>(a: &ArrayBase<S1, Ix2>, n: usize, m: usize) -> ArrayBase<S2, Ix2>
where
    A: Copy,
    S1: Data<Elem = A>,
    S2: DataMut<Elem = A> + DataOwned,
{
    let av = a.slice(s![..n as isize, ..m as isize]);
    replicate(&av)
}

fn take_slice_upper<A, S1, S2>(a: &ArrayBase<S1, Ix2>, n: usize, m: usize) -> ArrayBase<S2, Ix2>
where
    A: Copy + Zero,
    S1: Data<Elem = A>,
    S2: DataMut<Elem = A> + DataOwned,
{
    let av = a.slice(s![..n, ..m]);
    let mut a = replicate(&av);
    Zip::indexed(&mut a).for_each(|(i, j), elt| {
        if i > j {
            *elt = A::zero()
        }
    });
    a
}