nalgebra/nalgebra-lapack/src/qr.rs

use num_complex::Complex;
use num::Zero;

use ::ComplexHelper;
use na::{Scalar, DefaultAllocator, Matrix, VectorN, MatrixMN};
use na::dimension::{Dim, DimMin, DimMinimum, U1};
use na::storage::Storage;
use na::allocator::Allocator;

use lapack::fortran as interface;


/// The QR decomposition of a general matrix.
pub struct QR<N: Scalar, R: DimMin<C>, C: Dim>
    where DefaultAllocator: Allocator<N, R, C> +
                            Allocator<N, DimMinimum<R, C>> {
    qr:  MatrixMN<N, R, C>,
    tau: VectorN<N, DimMinimum<R, C>>
}

impl<N: QRScalar + Zero, R: DimMin<C>, C: Dim> QR<N, R, C>
    where DefaultAllocator: Allocator<N, R, C> +
                            Allocator<N, R, DimMinimum<R, C>> +
                            Allocator<N, DimMinimum<R, C>, C> +
                            Allocator<N, DimMinimum<R, C>> {
    /// Computes the QR decomposition of the matrix `m`.
    pub fn new(mut m: MatrixMN<N, R, C>) -> QR<N, R, C> {
        let (nrows, ncols) = m.data.shape();

        let mut info  = 0;
        let mut tau = unsafe { Matrix::new_uninitialized_generic(nrows.min(ncols), U1) };

        if nrows.value() == 0 || ncols.value() == 0 {
            return QR { qr: m, tau: tau };
        }

        let lwork = N::xgeqrf_work_size(nrows.value() as i32, ncols.value() as i32,
                                        m.as_mut_slice(), nrows.value() as i32,
                                        tau.as_mut_slice(), &mut info);

        let mut work = unsafe { ::uninitialized_vec(lwork as usize) };

        N::xgeqrf(nrows.value() as i32, ncols.value() as i32, m.as_mut_slice(),
                  nrows.value() as i32, tau.as_mut_slice(), &mut work, lwork, &mut info);

        QR { qr: m, tau: tau }
    }

    /// Retrieves the upper trapezoidal submatrix `R` of this decomposition.
    #[inline]
    pub fn r(&self) -> MatrixMN<N, DimMinimum<R, C>, C> {
        let (nrows, ncols) = self.qr.data.shape();
        self.qr.rows_generic(0, nrows.min(ncols)).upper_triangle()
    }
}

impl<N: QRReal + Zero, R: DimMin<C>, C: Dim> QR<N, R, C>
    where DefaultAllocator: Allocator<N, R, C> +
                            Allocator<N, R, DimMinimum<R, C>> +
                            Allocator<N, DimMinimum<R, C>, C> +
                            Allocator<N, DimMinimum<R, C>> {
    /// Retrieves the matrices `(Q, R)` of this decompositions.
    pub fn unpack(self) -> (MatrixMN<N, R, DimMinimum<R, C>>, MatrixMN<N, DimMinimum<R, C>, C>) {
        (self.q(), self.r())
    }


    /// Computes the orthogonal matrix `Q` of this decomposition.
    #[inline]
    pub fn q(&self) -> MatrixMN<N, R, DimMinimum<R, C>> {
        let (nrows, ncols)  = self.qr.data.shape();
        let min_nrows_ncols = nrows.min(ncols);

        if min_nrows_ncols.value() == 0 {
            return MatrixMN::from_element_generic(nrows, min_nrows_ncols, N::zero());
        }

        let mut q = self.qr.generic_slice((0, 0), (nrows, min_nrows_ncols)).into_owned();

        let mut info  = 0;
        let nrows = nrows.value() as i32;

        let lwork = N::xorgqr_work_size(nrows, min_nrows_ncols.value() as i32,
                                        self.tau.len() as i32, q.as_mut_slice(), nrows,
                                        self.tau.as_slice(), &mut info);

        let mut work = vec![ N::zero(); lwork as usize ];

        N::xorgqr(nrows, min_nrows_ncols.value() as i32, self.tau.len() as i32, q.as_mut_slice(),
                  nrows, self.tau.as_slice(), &mut work, lwork, &mut info);

        q
    }
}





/*
 *
 * Lapack functions dispatch.
 *
 */
/// Trait implemented by scalar types for which Lapack funtion exist to compute the
/// QR decomposition.
pub trait QRScalar: Scalar {
    fn xgeqrf(m: i32, n: i32, a: &mut [Self], lda: i32, tau: &mut [Self],
              work: &mut [Self], lwork: i32, info: &mut i32);

    fn xgeqrf_work_size(m: i32, n: i32, a: &mut [Self], lda: i32,
                        tau: &mut [Self], info: &mut i32) -> i32;
}

/// Trait implemented by reals for which Lapack funtion exist to compute the
/// QR decomposition.
pub trait QRReal: QRScalar {
    #[allow(missing_docs)]
    fn xorgqr(m: i32, n: i32, k: i32, a: &mut [Self], lda: i32, tau: &[Self], work: &mut [Self],
              lwork: i32, info: &mut i32);

    #[allow(missing_docs)]
    fn xorgqr_work_size(m: i32, n: i32, k: i32, a: &mut [Self], lda: i32,
                        tau: &[Self], info: &mut i32) -> i32;
}

macro_rules! qr_scalar_impl(
    ($N: ty, $xgeqrf: path) => (
        impl QRScalar for $N {
            #[inline]
            fn xgeqrf(m: i32, n: i32, a: &mut [Self], lda: i32, tau: &mut [Self],
                      work: &mut [Self], lwork: i32, info: &mut i32) {
                $xgeqrf(m, n, a, lda, tau, work, lwork, info)
            }

            #[inline]
            fn xgeqrf_work_size(m: i32, n: i32, a: &mut [Self], lda: i32, tau: &mut [Self],
                                info: &mut i32) -> i32 {
                let mut work = [ Zero::zero() ];
                let lwork = -1 as i32;

                $xgeqrf(m, n, a, lda, tau, &mut work, lwork, info);
                ComplexHelper::real_part(work[0]) as i32
            }
        }
    )
);

macro_rules! qr_real_impl(
    ($N: ty, $xorgqr: path) => (
        impl QRReal for $N {
            #[inline]
            fn xorgqr(m: i32, n: i32, k: i32, a: &mut [Self], lda: i32, tau: &[Self],
                      work: &mut [Self], lwork: i32, info: &mut i32) {
                $xorgqr(m, n, k, a, lda, tau, work, lwork, info)
            }

            #[inline]
            fn xorgqr_work_size(m: i32, n: i32, k: i32, a: &mut [Self], lda: i32, tau: &[Self],
                                info: &mut i32) -> i32 {
                let mut work = [ Zero::zero() ];
                let lwork = -1 as i32;

                $xorgqr(m, n, k, a, lda, tau, &mut work, lwork, info);
                ComplexHelper::real_part(work[0]) as i32
            }
        }
    )
);

qr_scalar_impl!(f32, interface::sgeqrf);
qr_scalar_impl!(f64, interface::dgeqrf);
qr_scalar_impl!(Complex<f32>, interface::cgeqrf);
qr_scalar_impl!(Complex<f64>, interface::zgeqrf);

qr_real_impl!(f32, interface::sorgqr);
qr_real_impl!(f64, interface::dorgqr);