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//! Singular-value decomposition (SVD) by divide-and-conquer (?gesdd)

use super::{convert::*, error::*, layout::*, types::*};
use ndarray::*;

pub use lax::JobSvd;

/// Singular-value decomposition of matrix (copying) by divide-and-conquer
pub trait SVDDC {
    type U;
    type VT;
    type Sigma;
    fn svddc(&self, uvt_flag: JobSvd) -> Result<(Option<Self::U>, Self::Sigma, Option<Self::VT>)>;
}

/// Singular-value decomposition of matrix by divide-and-conquer
pub trait SVDDCInto {
    type U;
    type VT;
    type Sigma;
    fn svddc_into(
        self,
        uvt_flag: JobSvd,
    ) -> Result<(Option<Self::U>, Self::Sigma, Option<Self::VT>)>;
}

/// Singular-value decomposition of matrix reference by divide-and-conquer
pub trait SVDDCInplace {
    type U;
    type VT;
    type Sigma;
    fn svddc_inplace(
        &mut self,
        uvt_flag: JobSvd,
    ) -> Result<(Option<Self::U>, Self::Sigma, Option<Self::VT>)>;
}

impl<A, S> SVDDC for ArrayBase<S, Ix2>
where
    A: Scalar + Lapack,
    S: Data<Elem = A>,
{
    type U = Array2<A>;
    type VT = Array2<A>;
    type Sigma = Array1<A::Real>;

    fn svddc(&self, uvt_flag: JobSvd) -> Result<(Option<Self::U>, Self::Sigma, Option<Self::VT>)> {
        self.to_owned().svddc_into(uvt_flag)
    }
}

impl<A, S> SVDDCInto for ArrayBase<S, Ix2>
where
    A: Scalar + Lapack,
    S: DataMut<Elem = A>,
{
    type U = Array2<A>;
    type VT = Array2<A>;
    type Sigma = Array1<A::Real>;

    fn svddc_into(
        mut self,
        uvt_flag: JobSvd,
    ) -> Result<(Option<Self::U>, Self::Sigma, Option<Self::VT>)> {
        self.svddc_inplace(uvt_flag)
    }
}

impl<A, S> SVDDCInplace for ArrayBase<S, Ix2>
where
    A: Scalar + Lapack,
    S: DataMut<Elem = A>,
{
    type U = Array2<A>;
    type VT = Array2<A>;
    type Sigma = Array1<A::Real>;

    fn svddc_inplace(
        &mut self,
        uvt_flag: JobSvd,
    ) -> Result<(Option<Self::U>, Self::Sigma, Option<Self::VT>)> {
        let l = self.layout()?;
        let svd_res = A::svddc(l, uvt_flag, self.as_allocated_mut()?)?;
        let (m, n) = l.size();
        let k = m.min(n);

        let (u_col, vt_row) = match uvt_flag {
            JobSvd::All => (m, n),
            JobSvd::Some => (k, k),
            JobSvd::None => (0, 0),
        };

        let u = svd_res
            .u
            .map(|u| into_matrix(l.resized(m, u_col), u).unwrap());

        let vt = svd_res
            .vt
            .map(|vt| into_matrix(l.resized(vt_row, n), vt).unwrap());

        let s = ArrayBase::from(svd_res.s);
        Ok((u, s, vt))
    }
}