banded.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_BANDED_
#define _BOOST_UBLAS_BANDED_

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

// Iterators based on ideas of Jeremy Siek

namespace boost { namespace numeric { namespace ublas {

    // Array based banded matrix class
    template<class T, class L, class A>
    class banded_matrix:
        public matrix_container<banded_matrix<T, L, A> > {

        typedef T *pointer;
        typedef L layout_type;
        typedef banded_matrix<T, 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
        banded_matrix ():
            matrix_container<self_type> (),
            size1_ (0), size2_ (0),
            lower_ (0), upper_ (0), data_ (0) {}
        BOOST_UBLAS_INLINE
        banded_matrix (size_type size1, size_type size2, size_type lower = 0, size_type upper = 0):
            matrix_container<self_type> (),
            size1_ (size1), size2_ (size2),
            lower_ (lower), upper_ (upper), data_ ((std::max) (size1, size2) * (lower + 1 + upper)) {
        }
        BOOST_UBLAS_INLINE
        banded_matrix (size_type size1, size_type size2, size_type lower, size_type upper, const array_type &data):
            matrix_container<self_type> (),
            size1_ (size1), size2_ (size2),
            lower_ (lower), upper_ (upper), data_ (data) {}
        BOOST_UBLAS_INLINE
        banded_matrix (const banded_matrix &m):
            matrix_container<self_type> (),
            size1_ (m.size1_), size2_ (m.size2_),
            lower_ (m.lower_), upper_ (m.upper_), data_ (m.data_) {}
        template<class AE>
        BOOST_UBLAS_INLINE
        banded_matrix (const matrix_expression<AE> &ae, size_type lower = 0, size_type upper = 0):
            matrix_container<self_type> (),
            size1_ (ae ().size1 ()), size2_ (ae ().size2 ()),
            lower_ (lower), upper_ (upper),
            data_ ((std::max) (size1_, size2_) * (lower_ + 1 + upper_)) {
            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_;
        }
        BOOST_UBLAS_INLINE
        size_type lower () const {
            return lower_;
        }
        BOOST_UBLAS_INLINE
        size_type upper () const {
            return upper_;
        }

        // 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, size_type lower = 0, size_type upper = 0, bool preserve = true) {
            if (preserve) {
                self_type temporary (size1, size2, lower, upper);
                detail::matrix_resize_preserve<layout_type> (*this, temporary);
            }
            else {
                data ().resize ((std::max) (size1, size2) * (lower + 1 + upper));
                size1_ = size1;
                size2_ = size2;
                lower_ = lower;
                upper_ = upper;
            }
        }

        BOOST_UBLAS_INLINE
        void resize_packed_preserve (size_type size1, size_type size2, size_type lower = 0, size_type upper = 0) {
            size1_ = size1;
            size2_ = size2;
            lower_ = lower;
            upper_ = upper;
            data ().resize ((std::max) (size1, size2) * (lower + 1 + upper), 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 ());
#ifdef BOOST_UBLAS_OWN_BANDED
            const size_type k = (std::max) (i, j);
            const size_type l = lower_ + j - i;
            if (k < (std::max) (size1_, size2_) &&
                l < lower_ + 1 + upper_)
                return data () [layout_type::element (k, (std::max) (size1_, size2_),
                                                       l, lower_ + 1 + upper_)];
#else
            const size_type k = j;
            const size_type l = upper_ + i - j;
            if (k < size2_ &&
                l < lower_ + 1 + upper_)
                return data () [layout_type::element (k, size2_,
                                                       l, lower_ + 1 + upper_)];
#endif
            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 ());
#ifdef BOOST_UBLAS_OWN_BANDED
            const size_type k = (std::max) (i, j);
            const size_type l = lower_ + j - i;
            return data () [layout_type::element (k, (std::max) (size1_, size2_),
                                                   l, lower_ + 1 + upper_)];
#else
            const size_type k = j;
            const size_type l = upper_ + i - j;
            return data () [layout_type::element (k, size2_,
                                                   l, lower_ + 1 + upper_)];
#endif
        }
        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 ());
#ifdef BOOST_UBLAS_OWN_BANDED
            const size_type k = (std::max) (i, j);
            const size_type l = lower_ + j - i;
            if (! (k < (std::max) (size1_, size2_) &&
                  l < lower_ + 1 + upper_) ) {
                bad_index ().raise ();
                // NEVER reached
            }
            return data () [layout_type::element (k, (std::max) (size1_, size2_),
                                                       l, lower_ + 1 + upper_)];
#else
            const size_type k = j;
            const size_type l = upper_ + i - j;
            if (! (k < size2_ &&
                   l < lower_ + 1 + upper_) ) {
                bad_index ().raise ();
                // NEVER reached
            }
            return data () [layout_type::element (k, size2_,
                                                       l, lower_ + 1 + upper_)];
#endif
        }

        // 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 () {
            std::fill (data ().begin (), data ().end (), value_type/*zero*/());
        }

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

        // Swapping
        BOOST_UBLAS_INLINE
        void swap (banded_matrix &m) {
            if (this != &m) {
                std::swap (size1_, m.size1_);
                std::swap (size2_, m.size2_);
                std::swap (lower_, m.lower_);
                std::swap (upper_, m.upper_);
                data ().swap (m.data ());
            }
        }
        BOOST_UBLAS_INLINE
        friend void swap (banded_matrix &m1, banded_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) {
                size_type lower_i = (std::max) (difference_type (j - upper_), difference_type (0));
                i = (std::max) (i, lower_i);
                size_type upper_i = (std::min) (j + 1 + lower_, size1_);
                i = (std::min) (i, upper_i);
            }
            return const_iterator1 (*this, i, j);
        }
        BOOST_UBLAS_INLINE
        iterator1 find1 (int rank, size_type i, size_type j) {
            if (rank == 1) {
                size_type lower_i = (std::max) (difference_type (j - upper_), difference_type (0));
                i = (std::max) (i, lower_i);
                size_type upper_i = (std::min) (j + 1 + lower_, size1_);
                i = (std::min) (i, upper_i);
            }
            return iterator1 (*this, i, j);
        }
        BOOST_UBLAS_INLINE
        const_iterator2 find2 (int rank, size_type i, size_type j) const {
            if (rank == 1) {
                size_type lower_j = (std::max) (difference_type (i - lower_), difference_type (0));
                j = (std::max) (j, lower_j);
                size_type upper_j = (std::min) (i + 1 + upper_, size2_);
                j = (std::min) (j, upper_j);
            }
            return const_iterator2 (*this, i, j);
        }
        BOOST_UBLAS_INLINE
        iterator2 find2 (int rank, size_type i, size_type j) {
            if (rank == 1) {
                size_type lower_j = (std::max) (difference_type (i - lower_), difference_type (0));
                j = (std::max) (j, lower_j);
                size_type upper_j = (std::min) (i + 1 + upper_, size2_);
                j = (std::min) (j, upper_j);
            }
            return iterator2 (*this, i, j);
        }

        // Iterators simply are indices.

#ifndef BOOST_UBLAS_USE_INDEXED_ITERATOR
        class const_iterator1:
            public container_const_reference<banded_matrix>,