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#ifndef LU_HPP
#define LU_HPP 1

#include <boost/numeric/ublas/operation.hpp>
#include <boost/numeric/ublas/vector_proxy.hpp>
#include <boost/numeric/ublas/matrix_proxy.hpp>
#include <boost/numeric/ublas/vector.hpp>
#include <boost/numeric/ublas/triangular.hpp>
#include "gemm.hpp"

namespace foo {

template <typename MP, typename MA>
void
swap_rows(const MP &P, MA &A, bool reverse=false)
{
    typedef typename MP::size_type size_type;

    size_type size = P.size();
    if (!reverse) {
        for (size_type i=0; i<size; ++i) {
            if (i!=P(i)) {
                row(A, i).swap(row(A, P(i)));
            }
        }
    } else {
        for (size_type I=size; I>=1; --I) {
            size_type i = I-1;
            if (i!=P(i)) {
                row(A, i).swap(row(A, P(i)));
            }
        }
    }
}

template <typename Alpha, typename MA, typename VX, typename VY>
void
ger(const Alpha &alpha, const VX &x, const VY &y, MA &A)
{
    typedef typename MA::size_type  size_type;

    for (size_type i=0; i<A.size1(); ++i) {
        for (size_type j=0; j<A.size2(); ++j) {
            A(i,j) += alpha*x(i)*y(j);
        }
    }

}

// Unblocked LU factorization with partial pivoting
template <typename MA, typename MP>
typename MA::size_type
lu_unblocked(MA &A, MP &P)
{
    namespace ublas = boost::numeric::ublas;
    using ublas::range;
    using ublas::matrix_column;
    using ublas::matrix_row;

    typedef typename MA::size_type  size_type;
    typedef typename MA::value_type value_type;

    size_type singular = 0;
    size_type m  = A.size1 ();
    size_type n  = A.size2 ();
    size_type mn = std::min(m, n);


    for (size_type i=0; i<mn; ++ i) {
        matrix_column<MA> A_i(column(A,i));
        matrix_row<MA>    Ai_(row(A,i));

        P(i) = i + index_norm_inf(project(A_i, range(i, m)));
        if (A(P(i),i) != value_type()) {
            if (P(i)!=i) {
                row(A, P(i)).swap (Ai_);
            }
        } else {
            singular = i+1;
        }
        value_type alpha = value_type(1)/A(i,i);
        project (A_i, range(i+1, m)) *= alpha;
        /*
        project (A, range(i+1, m), range (i+1, n)).minus_assign (
                outer_prod (project(A_i, range(i+1, m)),
                            project(Ai_, range(i+1, n))));
        */
        auto A_ = project (A, range(i+1, m), range (i+1, n));
        auto x_ = project(A_i, range(i+1, m));
        auto y_ = project(Ai_, range(i+1, n));
        ger(-1, x_, y_, A_);
    }
    return singular;
}

// Blocked LU factorization with partial pivoting
template <typename MA, typename MP>
typename MA::size_type
lu_blocked(MA &A, MP &P)
{
    namespace ublas = boost::numeric::ublas;
    using ublas::range;
    using ublas::matrix_column;
    using ublas::matrix_row;

    typedef typename MA::size_type  size_type;
    typedef typename MA::value_type value_type;

    size_type singular  = 0;
    size_type singular_ = 0;
    size_type m  = A.size1 ();
    size_type n  = A.size2 ();
    size_type mn = std::min(m, n);
    size_type bs = 64;

    if (bs>=mn) {
        singular = lu_unblocked(A, P);
    } else {
        for (size_type j=0; j<mn; j+=bs) {
            auto jb = std::min(mn-j, bs);

            auto A_ = project(A, range(j,m), range(j,j+jb));
            auto P_ = project(P, range(j,m));

            singular_ = lu_unblocked(A_, P_);

            if (singular==0 && singular_>0) {
                singular = singular_ + j;
            }

            auto A_left = project(A, range(j,m), range(0,j));
            foo::swap_rows(project(P, range(j,j+jb)), A_left);

            if (j+jb<=n) {
                auto A_right  = project(A, range(j,m), range(j+jb,n));
                foo::swap_rows(project(P, range(j,j+jb)), A_right);

                const auto L  = project(A, range(j,j+jb), range(j,j+jb));
                auto  U_right = project(A, range(j,j+jb), range(j+jb,n));

                //inplace_solve(L, U_right, ublas::unit_lower_tag());
                trlsm(value_type(1), true, L, U_right);

                if (j+jb<=m) {

                    auto A_ = project(A, range(j+jb,m), range(j+jb,n));
                    gemm(value_type(-1),
                         project(A, range(j+jb,m), range(j,j+jb)),
                         project(A, range(j,j+jb), range(j+jb,n)),
                         value_type(1),
                         A_);
                }
            }

            for (size_type i=j; i<std::min(m, j+jb); ++i) {
                P(i) += j;
            }
        }
    }
    return singular;
}

// Blocked recursive LU factorization with partial pivoting
template <typename MA, typename MP>
typename MA::size_type
lu_blocked_recursive(MA &A, MP &P)
{
    namespace ublas = boost::numeric::ublas;
    using ublas::range;
    using ublas::matrix_column;
    using ublas::matrix_row;

    typedef typename MA::size_type  size_type;
    typedef typename MA::value_type value_type;

    size_type singular  = 0;
    size_type singular_ = 0;
    size_type m  = A.size1();
    size_type n  = A.size2();
    size_type mn = std::min(m, n);
    size_type bs = 8;


    if (bs>=mn) {
        singular = lu_unblocked(A, P);
    } else {
        size_type k;
        for (k=1; k<mn/2; k*=2);

        auto A_left  = project(A, range(0,m), range(0,k));
        singular_ = lu_blocked_recursive(A_left, P);
        if (singular==0 && singular_>0) {
            singular = singular_;
        }

        auto A_right = project(A, range(0,m), range(k,n));
        auto mk      = std::min(m, k);
        foo::swap_rows(project(P, range(0,mk)), A_right);

        const auto L  = project(A, range(0,mk), range(0,mk));
        auto  U_right = project(A, range(0,mk), range(mk,n));

        //inplace_solve(L, U_right, ublas::unit_lower_tag());
        trlsm(value_type(1), true, L, U_right);

        auto A_ = project(A, range(mk,m), range(mk,n));
        auto P_ = project(P, range(mk,m));
        gemm(value_type(-1),
             project(A, range(mk,m), range(0,mk)),
             project(A, range(0,mk), range(mk,n)),
             value_type(1),
             A_);
        //std::cout << std::endl;
        //std::cout << "M = " << m << ", N = " << n << ", K = " << k << std::endl;
        //std::cout << "m = " << (m-mk) << ", n = " << (n-mk) << ", k = " << mk << std::endl;

        singular_ = lu_blocked_recursive(A_, P_);
        if (singular==0 && singular_>0) {
            singular = singular_ + mk;
        }

        auto A_left_bottom = project(A, range(mk,m), range(0,k));
        foo::swap_rows(project(P, range(mk,mn)), A_left_bottom);

        for (size_type i=mk; i<mn; ++i) {
            P(i) += mk;
        }
    }
    return singular;
}

} // namespace foo

#endif // LU_HPP





































































































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