nalgebra/nalgebra-lapack/src/lu.rs

use num::{Zero, One};
use num_complex::Complex;

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

use lapack::fortran as interface;

/// LU decomposition with partial pivoting.
///
/// This decomposes a matrix `M` with m rows and n columns into three parts:
/// * `L` which is a `m × min(m, n)` lower-triangular matrix.
/// * `U` which is a `min(m, n) × n` upper-triangular matrix.
/// * `P` which is a `m * m` permutation matrix.
///
/// Those are such that `M == P * L * U`.
pub struct LU<N: Scalar, R: DimMin<C>, C: Dim>
    where DefaultAllocator: Allocator<i32, DimMinimum<R, C>> +
                            Allocator<N, R, C> {
    lu: MatrixMN<N, R, C>,
    p:  VectorN<i32, DimMinimum<R, C>>
}

impl<N: LUScalar, R: Dim, C: Dim> LU<N, R, C>
    where N: Zero + One,
          R: DimMin<C>,
          DefaultAllocator: Allocator<N, R, C> +
                            Allocator<N, R, R> +
                            Allocator<N, R, DimMinimum<R, C>> +
                            Allocator<N, DimMinimum<R, C>, C> +
                            Allocator<i32, DimMinimum<R, C>> {

    pub fn new(mut m: MatrixMN<N, R, C>) -> Self {
        let (nrows, ncols)  = m.data.shape();
        let min_nrows_ncols = nrows.min(ncols);
        let nrows           = nrows.value() as i32;
        let ncols           = ncols.value() as i32;

        let mut ipiv: VectorN<i32, _> = Matrix::zeros_generic(min_nrows_ncols, U1);

        let mut info = 0;

        N::xgetrf(nrows, ncols, m.as_mut_slice(), nrows, ipiv.as_mut_slice(), &mut info);
        lapack_panic!(info);

        LU { lu: m, p: ipiv }
    }

    /// Gets the lower-triangular matrix part of the decomposition.
    #[inline]
    pub fn l(&self) -> MatrixMN<N, R, DimMinimum<R, C>> {
        let (nrows, ncols) = self.lu.data.shape();
        let mut res = self.lu.columns_generic(0, nrows.min(ncols)).into_owned();

        res.fill_upper_triangle(Zero::zero(), 1);
        res.fill_diagonal(One::one());

        res
    }

    /// Gets the upper-triangular matrix part of the decomposition.
    #[inline]
    pub fn u(&self) -> MatrixMN<N, DimMinimum<R, C>, C> {
        let (nrows, ncols) = self.lu.data.shape();
        let mut res = self.lu.rows_generic(0, nrows.min(ncols)).into_owned();

        res.fill_lower_triangle(Zero::zero(), 1);

        res
    }

    /// Gets the row permutation matrix of this decomposition.
    ///
    /// Computing the permutation matrix explicitly is costly and usually not necessary.
    /// To permute rows of a matrix or vector, use the method `self.permute(...)` instead.
    #[inline]
    pub fn p(&self) -> MatrixN<N, R> {
        let (dim, _) = self.lu.data.shape();
        let mut id = Matrix::identity_generic(dim, dim);
        self.permute(&mut id);

        id
    }

    // FIXME: when we support resizing a matrix, we could add unwrap_u/unwrap_l that would
    // re-use the memory from the internal matrix!

    /// Gets the LAPACK permutation indices.
    #[inline]
    pub fn permutation_indices(&self) -> &VectorN<i32, DimMinimum<R, C>> {
        &self.p
    }

    /// Applies the permutation matrix to a given matrix or vector in-place.
    #[inline]
    pub fn permute<C2: Dim>(&self, rhs: &mut MatrixMN<N, R, C2>)
        where DefaultAllocator: Allocator<N, R, C2> {

        let (nrows, ncols) = rhs.shape();

        N::xlaswp(ncols as i32, rhs.as_mut_slice(), nrows as i32,
                  1, self.p.len() as i32, self.p.as_slice(), -1);
    }

    fn generic_solve<R2: Dim, C2: Dim>(&self, trans: u8, mut b: MatrixMN<N, R2, C2>)
        -> Option<MatrixMN<N, R2, C2>>
        where DefaultAllocator: Allocator<N, R2, C2> +
                                Allocator<i32, R2> {

        let dim = self.lu.nrows();

        assert!(self.lu.is_square(), "Unable to solve a set of under/over-determined equations.");
        assert!(b.nrows() == dim, "The number of rows of `b` must be equal to the dimension of the matrix `a`.");

        let nrhs = b.ncols() as i32;
        let lda  = dim as i32;
        let ldb  = dim as i32;
        let mut info = 0;

        N::xgetrs(trans, dim as i32, nrhs, self.lu.as_slice(), lda, self.p.as_slice(),
                      b.as_mut_slice(), ldb, &mut info);
        lapack_check!(info);

        Some(b)
    }

    /// Solves the linear system `self * x = b`, where `x` is the unknown to be determined.
    pub fn solve<R2: Dim, C2: Dim>(&self, b: MatrixMN<N, R2, C2>)
        -> Option<MatrixMN<N, R2, C2>>
        where DefaultAllocator: Allocator<N, R2, C2> +
                                Allocator<i32, R2> {

        self.generic_solve(b'N', b)
    }

    /// Solves the linear system `self.transpose() * x = b`, where `x` is the unknown to be
    /// determined.
    pub fn solve_transpose<R2: Dim, C2: Dim>(&self, b: MatrixMN<N, R2, C2>)
        -> Option<MatrixMN<N, R2, C2>>
        where DefaultAllocator: Allocator<N, R2, C2> +
                                Allocator<i32, R2> {

        self.generic_solve(b'T', b)
    }

    /// Solves the linear system `self.conjugate_transpose() * x = b`, where `x` is the unknown to
    /// be determined.
    pub fn solve_conjugate_transpose<R2: Dim, C2: Dim>(&self, b: MatrixMN<N, R2, C2>)
        -> Option<MatrixMN<N, R2, C2>>
        where DefaultAllocator: Allocator<N, R2, C2> +
                                Allocator<i32, R2> {

        self.generic_solve(b'T', b)
    }
}

impl<N: LUScalar, D: Dim> LU<N, D, D>
    where N: Zero + One,
          D: DimMin<D, Output = D>,
          DefaultAllocator: Allocator<N, D, D> +
                            Allocator<i32, D> {
    /// Computes the inverse of the decomposed matrix.
    pub fn inverse(mut self) -> Option<MatrixN<N, D>> {
        let dim = self.lu.nrows() as i32;
        let mut info = 0;
        let lwork = N::xgetri_work_size(dim, self.lu.as_mut_slice(),
                                        dim, self.p.as_mut_slice(),
                                        &mut info);
        lapack_check!(info);

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

        N::xgetri(dim, self.lu.as_mut_slice(), dim, self.p.as_mut_slice(),
                  &mut work, lwork, &mut info);
        lapack_check!(info);

        Some(self.lu)
    }
}




/*
 *
 * Lapack functions dispatch.
 *
 */
pub trait LUScalar: Scalar {
    fn xgetrf(m: i32, n: i32, a: &mut [Self], lda: i32, ipiv: &mut [i32], info: &mut i32);
    fn xlaswp(n: i32, a: &mut [Self], lda: i32, k1: i32, k2: i32, ipiv: &[i32], incx: i32);
    fn xgetrs(trans: u8, n: i32, nrhs: i32, a: &[Self], lda: i32, ipiv: &[i32],
              b: &mut [Self], ldb: i32, info: &mut i32);
    fn xgetri(n: i32, a: &mut [Self], lda: i32, ipiv: &[i32],
              work: &mut [Self], lwork: i32, info: &mut i32);
    fn xgetri_work_size(n: i32, a: &mut [Self], lda: i32, ipiv: &[i32], info: &mut i32) -> i32;
}


macro_rules! lup_scalar_impl(
    ($N: ty, $xgetrf: path, $xlaswp: path, $xgetrs: path, $xgetri: path) => (
        impl LUScalar for $N {
            #[inline]
            fn xgetrf(m: i32, n: i32, a: &mut [Self], lda: i32, ipiv: &mut [i32], info: &mut i32) {
                $xgetrf(m, n, a, lda, ipiv, info)
            }

            #[inline]
            fn xlaswp(n: i32, a: &mut [Self], lda: i32, k1: i32, k2: i32, ipiv: &[i32], incx: i32) {
                $xlaswp(n, a, lda, k1, k2, ipiv, incx)
            }

            #[inline]
            fn xgetrs(trans: u8, n: i32, nrhs: i32, a: &[Self], lda: i32, ipiv: &[i32],
                      b: &mut [Self], ldb: i32, info: &mut i32) {
                $xgetrs(trans, n, nrhs, a, lda, ipiv, b, ldb, info)
            }

            #[inline]
            fn xgetri(n: i32, a: &mut [Self], lda: i32, ipiv: &[i32],
                      work: &mut [Self], lwork: i32, info: &mut i32) {
                $xgetri(n, a, lda, ipiv, work, lwork, info)
            }

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

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


lup_scalar_impl!(f32, interface::sgetrf, interface::slaswp, interface::sgetrs, interface::sgetri);
lup_scalar_impl!(f64, interface::dgetrf, interface::dlaswp, interface::dgetrs, interface::dgetri);
lup_scalar_impl!(Complex<f32>, interface::cgetrf, interface::claswp, interface::cgetrs, interface::cgetri);
lup_scalar_impl!(Complex<f64>, interface::zgetrf, interface::zlaswp, interface::zgetrs, interface::zgetri);