triangular.hpp

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//
//  Copyright (c) 2000-2002
//  Joerg Walter, Mathias Koch
//
//  Distributed under the Boost Software License, Version 1.0. (See
//  accompanying file LICENSE_1_0.txt or copy at
//  http://www.boost.org/LICENSE_1_0.txt)
//
//  The authors gratefully acknowledge the support of
//  GeNeSys mbH & Co. KG in producing this work.
//

#ifndef _BOOST_UBLAS_TRIANGULAR_
#define _BOOST_UBLAS_TRIANGULAR_

#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/detail/temporary.hpp>
#include <boost/type_traits/remove_const.hpp>

// Iterators based on ideas of Jeremy Siek

namespace boost { namespace numeric { namespace ublas {

    namespace detail {
        using namespace boost::numeric::ublas;

        // Matrix resizing algorithm
        template <class L, class T, class M>
        BOOST_UBLAS_INLINE
        void matrix_resize_preserve (M& m, M& temporary) {
            typedef L layout_type;
            typedef T triangular_type;
            typedef typename M::size_type size_type;
            const size_type msize1 (m.size1 ());        // original size
            const size_type msize2 (m.size2 ());
            const size_type size1 (temporary.size1 ());    // new size is specified by temporary
            const size_type size2 (temporary.size2 ());
            // Common elements to preserve
            const size_type size1_min = (std::min) (size1, msize1);
            const size_type size2_min = (std::min) (size2, msize2);
            // Order for major and minor sizes
            const size_type major_size = layout_type::size_M (size1_min, size2_min);
            const size_type minor_size = layout_type::size_m (size1_min, size2_min);
            // Indexing copy over major
            for (size_type major = 0; major != major_size; ++major) {
                for (size_type minor = 0; minor != minor_size; ++minor) {
                        // find indexes - use invertability of element_ functions
                    const size_type i1 = layout_type::index_M(major, minor);
                    const size_type i2 = layout_type::index_m(major, minor);
                    if ( triangular_type::other(i1,i2) ) {
                        temporary.data () [triangular_type::element (layout_type (), i1, size1, i2, size2)] =
                            m.data() [triangular_type::element (layout_type (), i1, msize1, i2, msize2)];
                    }
                }
            }
            m.assign_temporary (temporary);
        }
    }

    // Array based triangular matrix class
    template<class T, class TRI, class L, class A>
    class triangular_matrix:
        public matrix_container<triangular_matrix<T, TRI, L, A> > {

        typedef T *pointer;
        typedef TRI triangular_type;
        typedef L layout_type;
        typedef triangular_matrix<T, TRI, L, A> self_type;
    public:
#ifdef BOOST_UBLAS_ENABLE_PROXY_SHORTCUTS
        using matrix_container<self_type>::operator ();
#endif
        typedef typename A::size_type size_type;
        typedef typename A::difference_type difference_type;
        typedef T value_type;
        typedef const T &const_reference;
        typedef T &reference;
        typedef A array_type;

        typedef const matrix_reference<const self_type> const_closure_type;
        typedef matrix_reference<self_type> closure_type;
        typedef vector<T, A> vector_temporary_type;
        typedef matrix<T, L, A> matrix_temporary_type;  // general sub-matrix
        typedef packed_tag storage_category;
        typedef typename L::orientation_category orientation_category;

        // Construction and destruction
        BOOST_UBLAS_INLINE
        triangular_matrix ():
            matrix_container<self_type> (),
            size1_ (0), size2_ (0), data_ (0) {}
        BOOST_UBLAS_INLINE
        triangular_matrix (size_type size1, size_type size2):
            matrix_container<self_type> (),
            size1_ (size1), size2_ (size2), data_ (triangular_type::packed_size (layout_type (), size1, size2)) {
        }
        BOOST_UBLAS_INLINE
        triangular_matrix (size_type size1, size_type size2, const array_type &data):
            matrix_container<self_type> (),
            size1_ (size1), size2_ (size2), data_ (data) {}
        BOOST_UBLAS_INLINE
        triangular_matrix (const triangular_matrix &m):
            matrix_container<self_type> (),
            size1_ (m.size1_), size2_ (m.size2_), data_ (m.data_) {}
        template<class AE>
        BOOST_UBLAS_INLINE
        triangular_matrix (const matrix_expression<AE> &ae):
            matrix_container<self_type> (),
            size1_ (ae ().size1 ()), size2_ (ae ().size2 ()),
            data_ (triangular_type::packed_size (layout_type (), size1_, size2_)) {
            matrix_assign<scalar_assign> (*this, ae);
        }

        // Accessors
        BOOST_UBLAS_INLINE
        size_type size1 () const {
            return size1_;
        }
        BOOST_UBLAS_INLINE
        size_type size2 () const {
            return size2_;
        }

        // Storage accessors
        BOOST_UBLAS_INLINE
        const array_type &data () const {
            return data_;
        }
        BOOST_UBLAS_INLINE
        array_type &data () {
            return data_;
        }

        // Resizing
        BOOST_UBLAS_INLINE
        void resize (size_type size1, size_type size2, bool preserve = true) {
            if (preserve) {
                self_type temporary (size1, size2);
                detail::matrix_resize_preserve<layout_type, triangular_type> (*this, temporary);
            }
            else {
                data ().resize (triangular_type::packed_size (layout_type (), size1, size2));
                size1_ = size1;
                size2_ = size2;
            }
        }
        BOOST_UBLAS_INLINE
        void resize_packed_preserve (size_type size1, size_type size2) {
            size1_ = size1;
            size2_ = size2;
            data ().resize (triangular_type::packed_size (layout_type (), size1_, size2_), value_type ());
        }

        // Element access
        BOOST_UBLAS_INLINE
        const_reference operator () (size_type i, size_type j) const {
            BOOST_UBLAS_CHECK (i < size1_, bad_index ());
            BOOST_UBLAS_CHECK (j < size2_, bad_index ());
            if (triangular_type::other (i, j))
                return data () [triangular_type::element (layout_type (), i, size1_, j, size2_)];
            else if (triangular_type::one (i, j))
                return one_;
            else
                return zero_;
        }
        BOOST_UBLAS_INLINE
        reference at_element (size_type i, size_type j) {
            BOOST_UBLAS_CHECK (i < size1_, bad_index ());
            BOOST_UBLAS_CHECK (j < size2_, bad_index ());
            return data () [triangular_type::element (layout_type (), i, size1_, j, size2_)];
        }
        BOOST_UBLAS_INLINE
        reference operator () (size_type i, size_type j) {
            BOOST_UBLAS_CHECK (i < size1_, bad_index ());
            BOOST_UBLAS_CHECK (j < size2_, bad_index ());
            if (!triangular_type::other (i, j)) {
                bad_index ().raise ();
                // NEVER reached
            }
            return data () [triangular_type::element (layout_type (), i, size1_, j, size2_)];
        }
        
        // Element assignment
        BOOST_UBLAS_INLINE
        reference insert_element (size_type i, size_type j, const_reference t) {
            return (operator () (i, j) = t);
        }
        BOOST_UBLAS_INLINE
        void erase_element (size_type i, size_type j) {
            operator () (i, j) = value_type/*zero*/();
        }
        
        // Zeroing
        BOOST_UBLAS_INLINE
        void clear () {
            // data ().clear ();
            std::fill (data ().begin (), data ().end (), value_type/*zero*/());
        }

        // Assignment
        BOOST_UBLAS_INLINE
        triangular_matrix &operator = (const triangular_matrix &m) {
            size1_ = m.size1_;
            size2_ = m.size2_;
            data () = m.data ();
            return *this;
        }
        BOOST_UBLAS_INLINE
        triangular_matrix &assign_temporary (triangular_matrix &m) {
            swap (m);
            return *this;
        }
        template<class AE>
        BOOST_UBLAS_INLINE
        triangular_matrix &operator = (const matrix_expression<AE> &ae) {
            self_type temporary (ae);
            return assign_temporary (temporary);
        }
        template<class AE>
        BOOST_UBLAS_INLINE
        triangular_matrix &assign (const matrix_expression<AE> &ae) {
            matrix_assign<scalar_assign> (*this, ae);
            return *this;
        }
        template<class AE>
        BOOST_UBLAS_INLINE
        triangular_matrix& operator += (const matrix_expression<AE> &ae) {
            self_type temporary (*this + ae);
            return assign_temporary (temporary);
        }
        template<class AE>
        BOOST_UBLAS_INLINE
        triangular_matrix &plus_assign (const matrix_expression<AE> &ae) {
            matrix_assign<scalar_plus_assign> (*this, ae);
            return *this;
        }
        template<class AE>
        BOOST_UBLAS_INLINE
        triangular_matrix& operator -= (const matrix_expression<AE> &ae) {
            self_type temporary (*this - ae);
            return assign_temporary (temporary);
        }
        template<class AE>
        BOOST_UBLAS_INLINE
        triangular_matrix &minus_assign (const matrix_expression<AE> &ae) {
            matrix_assign<scalar_minus_assign> (*this, ae);
            return *this;
        }
        template<class AT>
        BOOST_UBLAS_INLINE
        triangular_matrix& operator *= (const AT &at) {
            matrix_assign_scalar<scalar_multiplies_assign> (*this, at);
            return *this;
        }
        template<class AT>
        BOOST_UBLAS_INLINE
        triangular_matrix& operator /= (const AT &at) {
            matrix_assign_scalar<scalar_divides_assign> (*this, at);
            return *this;
        }

        // Swapping
        BOOST_UBLAS_INLINE
        void swap (triangular_matrix &m) {
            if (this != &m) {
                // BOOST_UBLAS_CHECK (size2_ == m.size2_, bad_size ());
                std::swap (size1_, m.size1_);
                std::swap (size2_, m.size2_);
                data ().swap (m.data ());
            }
        }
        BOOST_UBLAS_INLINE
        friend void swap (triangular_matrix &m1, triangular_matrix &m2) {
            m1.swap (m2);
        }

        // Iterator types
#ifdef BOOST_UBLAS_USE_INDEXED_ITERATOR
        typedef indexed_iterator1<self_type, packed_random_access_iterator_tag> iterator1;
        typedef indexed_iterator2<self_type, packed_random_access_iterator_tag> iterator2;
        typedef indexed_const_iterator1<self_type, packed_random_access_iterator_tag> const_iterator1;
        typedef indexed_const_iterator2<self_type, packed_random_access_iterator_tag> const_iterator2;
#else
        class const_iterator1;
        class iterator1;
        class const_iterator2;
        class iterator2;
#endif
        typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
        typedef reverse_iterator_base1<iterator1> reverse_iterator1;
        typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;
        typedef reverse_iterator_base2<iterator2> reverse_iterator2;

        // Element lookup
        BOOST_UBLAS_INLINE
        const_iterator1 find1 (int rank, size_type i, size_type j) const {
            if (rank == 1)
                i = triangular_type::restrict1 (i, j, size1_, size2_);
	    if (rank == 0)
		i = triangular_type::global_restrict1 (i, size1_, j, size2_);
            return const_iterator1 (*this, i, j);
        }
        BOOST_UBLAS_INLINE
        iterator1 find1 (int rank, size_type i, size_type j) {
            if (rank == 1)
                i = triangular_type::mutable_restrict1 (i, j, size1_, size2_);
	    if (rank == 0)
		i = triangular_type::global_mutable_restrict1 (i, size1_, j, size2_);
            return iterator1 (*this, i, j);
        }
        BOOST_UBLAS_INLINE
        const_iterator2 find2 (int rank, size_type i, size_type j) const {
            if (rank == 1)
                j = triangular_type::restrict2 (i, j, size1_, size2_);
	    if (rank == 0)
		j = triangular_type::global_restrict2 (i, size1_, j, size2_);
            return const_iterator2 (*this, i, j);
        }
        BOOST_UBLAS_INLINE
        iterator2 find2 (int rank, size_type i, size_type j) {
            if (rank == 1)
                j = triangular_type::mutable_restrict2 (i, j, size1_, size2_);
	    if (rank == 0)
		j = triangular_type::global_mutable_restrict2 (i, size1_, j, size2_);
            return iterator2 (*this, i, j);
        }

        // Iterators simply are indices.

#ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
        class const_iterator1:
            public container_const_reference<triangular_matrix>,
            public random_access_iterator_base<packed_random_access_iterator_tag,
                                               const_iterator1, value_type> {
        public:
            typedef typename triangular_matrix::value_type value_type;
            typedef typename triangular_matrix::difference_type difference_type;
            typedef typename triangular_matrix::const_reference reference;
            typedef const typename triangular_matrix::pointer pointer;

            typedef const_iterator2 dual_iterator_type;
            typedef const_reverse_iterator2 dual_reverse_iterator_type;

            // Construction and destruction
            BOOST_UBLAS_INLINE
            const_iterator1 ():
                container_const_reference<self_type> (), it1_ (), it2_ () {}
            BOOST_UBLAS_INLINE
            const_iterator1 (const self_type &m, size_type it1, size_type it2):
                container_const_reference<self_type> (m), it1_ (it1), it2_ (it2) {}
            BOOST_UBLAS_INLINE
            const_iterator1 (const iterator1 &it):
                container_const_reference<self_type> (it ()), it1_ (it.it1_), it2_ (it.it2_) {}

            // Arithmetic
            BOOST_UBLAS_INLINE
            const_iterator1 &operator ++ () {
                ++ it1_;
                return *this;
            }
            BOOST_UBLAS_INLINE