functional.hpp

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            // Guard against size_type overflow
            BOOST_UBLAS_CHECK (size_j == 0 || size_i <= (std::numeric_limits<size_type>::max) () / size_j, bad_size ());
            return size_i * size_j;
        }

        // Indexing conversion to storage element
        static
        BOOST_UBLAS_INLINE
        size_type element (size_type i, size_type size_i, size_type j, size_type size_j) {
            BOOST_UBLAS_CHECK (i < size_i, bad_index ());
            BOOST_UBLAS_CHECK (j < size_j, bad_index ());
            detail::ignore_unused_variable_warning(size_i);
            // Guard against size_type overflow
            BOOST_UBLAS_CHECK (i <= ((std::numeric_limits<size_type>::max) () - j) / size_j, bad_index ());
            return i * size_j + j;
        }
        static
        BOOST_UBLAS_INLINE
        size_type address (size_type i, size_type size_i, size_type j, size_type size_j) {
            BOOST_UBLAS_CHECK (i <= size_i, bad_index ());
            BOOST_UBLAS_CHECK (j <= size_j, bad_index ());
            // Guard against size_type overflow - address may be size_j past end of storage
            BOOST_UBLAS_CHECK (size_j == 0 || i <= ((std::numeric_limits<size_type>::max) () - j) / size_j, bad_index ());
            detail::ignore_unused_variable_warning(size_i);
            return i * size_j + j;
        }

        // Storage element to index conversion
        static
        BOOST_UBLAS_INLINE
        difference_type distance_i (difference_type k, size_type /* size_i */, size_type size_j) {
            return size_j != 0 ? k / size_j : 0;
        }
        static
        BOOST_UBLAS_INLINE
        difference_type distance_j (difference_type k, size_type /* size_i */, size_type /* size_j */) {
            return k;
        }
        static
        BOOST_UBLAS_INLINE
        size_type index_i (difference_type k, size_type /* size_i */, size_type size_j) {
            return size_j != 0 ? k / size_j : 0;
        }
        static
        BOOST_UBLAS_INLINE
        size_type index_j (difference_type k, size_type /* size_i */, size_type size_j) {
            return size_j != 0 ? k % size_j : 0;
        }
        static
        BOOST_UBLAS_INLINE
        bool fast_i () {
            return false;
        }
        static
        BOOST_UBLAS_INLINE
        bool fast_j () {
            return true;
        }

        // Iterating storage elements
        template<class I>
        static
        BOOST_UBLAS_INLINE
        void increment_i (I &it, size_type /* size_i */, size_type size_j) {
            it += size_j;
        }
        template<class I>
        static
        BOOST_UBLAS_INLINE
        void increment_i (I &it, difference_type n, size_type /* size_i */, size_type size_j) {
            it += n * size_j;
        }
        template<class I>
        static
        BOOST_UBLAS_INLINE
        void decrement_i (I &it, size_type /* size_i */, size_type size_j) {
            it -= size_j;
        }
        template<class I>
        static
        BOOST_UBLAS_INLINE
        void decrement_i (I &it, difference_type n, size_type /* size_i */, size_type size_j) {
            it -= n * size_j;
        }
        template<class I>
        static
        BOOST_UBLAS_INLINE
        void increment_j (I &it, size_type /* size_i */, size_type /* size_j */) {
            ++ it;
        }
        template<class I>
        static
        BOOST_UBLAS_INLINE
        void increment_j (I &it, difference_type n, size_type /* size_i */, size_type /* size_j */) {
            it += n;
        }
        template<class I>
        static
        BOOST_UBLAS_INLINE
        void decrement_j (I &it, size_type /* size_i */, size_type /* size_j */) {
            -- it;
        }
        template<class I>
        static
        BOOST_UBLAS_INLINE
        void decrement_j (I &it, difference_type n, size_type /* size_i */, size_type /* size_j */) {
            it -= n;
        }

        // Triangular access
        static
        BOOST_UBLAS_INLINE
        size_type triangular_size (size_type size_i, size_type size_j) {
            size_type size = (std::max) (size_i, size_j);
            // Guard against size_type overflow - simplified
            BOOST_UBLAS_CHECK (size == 0 || size / 2 < (std::numeric_limits<size_type>::max) () / size /* +1/2 */, bad_size ());
            return ((size + 1) * size) / 2;
        }
        static
        BOOST_UBLAS_INLINE
        size_type lower_element (size_type i, size_type size_i, size_type j, size_type size_j) {
            BOOST_UBLAS_CHECK (i < size_i, bad_index ());
            BOOST_UBLAS_CHECK (j < size_j, bad_index ());
            BOOST_UBLAS_CHECK (i >= j, bad_index ());
            detail::ignore_unused_variable_warning(size_i);
            detail::ignore_unused_variable_warning(size_j);
            // FIXME size_type overflow
            // sigma_i (i + 1) = (i + 1) * i / 2
            // i = 0 1 2 3, sigma = 0 1 3 6
            return ((i + 1) * i) / 2 + j;
        }
        static
        BOOST_UBLAS_INLINE
        size_type upper_element (size_type i, size_type size_i, size_type j, size_type size_j) {
            BOOST_UBLAS_CHECK (i < size_i, bad_index ());
            BOOST_UBLAS_CHECK (j < size_j, bad_index ());
            BOOST_UBLAS_CHECK (i <= j, bad_index ());
            // FIXME size_type overflow
            // sigma_i (size - i) = size * i - i * (i - 1) / 2
            // i = 0 1 2 3, sigma = 0 4 7 9
            return (i * (2 * (std::max) (size_i, size_j) - i + 1)) / 2 + j - i;
        }

        // Major and minor indices
        static
        BOOST_UBLAS_INLINE
        size_type index_M (size_type index1, size_type /* index2 */) {
            return index1;
        }
        static
        BOOST_UBLAS_INLINE
        size_type index_m (size_type /* index1 */, size_type index2) {
            return index2;
        }
        static
        BOOST_UBLAS_INLINE
        size_type size_M (size_type size_i, size_type /* size_j */) {
            return size_i;
        }
        static
        BOOST_UBLAS_INLINE
        size_type size_m (size_type /* size_i */, size_type size_j) {
            return size_j;
        }
    };

    // This functor defines storage layout and it's properties
    // matrix (i,j) -> storage [i + j * size_i]
    template <class Z, class D>
    struct basic_column_major {
        typedef Z size_type;
        typedef D difference_type;
        typedef column_major_tag orientation_category;

        static
        BOOST_UBLAS_INLINE
        size_type storage_size (size_type size_i, size_type size_j) {
            // Guard against size_type overflow
            BOOST_UBLAS_CHECK (size_i == 0 || size_j <= (std::numeric_limits<size_type>::max) () / size_i, bad_size ());
            return size_i * size_j;
        }

        // Indexing conversion to storage element
        static
        BOOST_UBLAS_INLINE
        size_type element (size_type i, size_type size_i, size_type j, size_type size_j) {
            BOOST_UBLAS_CHECK (i < size_i, bad_index ());
            BOOST_UBLAS_CHECK (j < size_j, bad_index ());
            detail::ignore_unused_variable_warning(size_j);
            // Guard against size_type overflow
            BOOST_UBLAS_CHECK (j <= ((std::numeric_limits<size_type>::max) () - i) / size_i, bad_index ());
            return i + j * size_i;
        }
        static
        BOOST_UBLAS_INLINE
        size_type address (size_type i, size_type size_i, size_type j, size_type size_j) {
            BOOST_UBLAS_CHECK (i <= size_i, bad_index ());
            BOOST_UBLAS_CHECK (j <= size_j, bad_index ());
            detail::ignore_unused_variable_warning(size_j);
            // Guard against size_type overflow - address may be size_i past end of storage
            BOOST_UBLAS_CHECK (size_i == 0 || j <= ((std::numeric_limits<size_type>::max) () - i) / size_i, bad_index ());
            return i + j * size_i;
        }

        // Storage element to index conversion
        static
        BOOST_UBLAS_INLINE
        difference_type distance_i (difference_type k, size_type /* size_i */, size_type /* size_j */) {
            return k;
        }
        static
        BOOST_UBLAS_INLINE
        difference_type distance_j (difference_type k, size_type size_i, size_type /* size_j */) {
            return size_i != 0 ? k / size_i : 0;
        }
        static
        BOOST_UBLAS_INLINE
        size_type index_i (difference_type k, size_type size_i, size_type /* size_j */) {
            return size_i != 0 ? k % size_i : 0;
        }
        static
        BOOST_UBLAS_INLINE
        size_type index_j (difference_type k, size_type size_i, size_type /* size_j */) {
            return size_i != 0 ? k / size_i : 0;
        }
        static
        BOOST_UBLAS_INLINE
        bool fast_i () {
            return true;
        }
        static
        BOOST_UBLAS_INLINE
        bool fast_j () {
            return false;
        }

        // Iterating
        template<class I>
        static
        BOOST_UBLAS_INLINE
        void increment_i (I &it, size_type /* size_i */, size_type /* size_j */) {
            ++ it;
        }
        template<class I>
        static
        BOOST_UBLAS_INLINE
        void increment_i (I &it, difference_type n, size_type /* size_i */, size_type /* size_j */) {
            it += n;
        }
        template<class I>
        static
        BOOST_UBLAS_INLINE
        void decrement_i (I &it, size_type /* size_i */, size_type /* size_j */) {
            -- it;
        }
        template<class I>
        static
        BOOST_UBLAS_INLINE
        void decrement_i (I &it, difference_type n, size_type /* size_i */, size_type /* size_j */) {
            it -= n;
        }
        template<class I>
        static
        BOOST_UBLAS_INLINE
        void increment_j (I &it, size_type size_i, size_type /* size_j */) {
            it += size_i;
        }
        template<class I>
        static
        BOOST_UBLAS_INLINE
        void increment_j (I &it, difference_type n, size_type size_i, size_type /* size_j */) {
            it += n * size_i;
        }
        template<class I>
        static
        BOOST_UBLAS_INLINE
        void decrement_j (I &it, size_type size_i, size_type /* size_j */) {
            it -= size_i;
        }
        template<class I>
        static
        BOOST_UBLAS_INLINE
        void decrement_j (I &it, difference_type n, size_type size_i, size_type /* size_j */) {
            it -= n* size_i;
        }

        // Triangular access
        static
        BOOST_UBLAS_INLINE
        size_type triangular_size (size_type size_i, size_type size_j) {
            size_type size = (std::max) (size_i, size_j);
            // Guard against size_type overflow - simplified
            BOOST_UBLAS_CHECK (size == 0 || size / 2 < (std::numeric_limits<size_type>::max) () / size /* +1/2 */, bad_size ());
            return ((size + 1) * size) / 2;
        }
        static
        BOOST_UBLAS_INLINE
        size_type lower_element (size_type i, size_type size_i, size_type j, size_type size_j) {
            BOOST_UBLAS_CHECK (i < size_i, bad_index ());
            BOOST_UBLAS_CHECK (j < size_j, bad_index ());
            BOOST_UBLAS_CHECK (i >= j, bad_index ());
            // FIXME size_type overflow
            // sigma_j (size - j) = size * j - j * (j - 1) / 2
            // j = 0 1 2 3, sigma = 0 4 7 9
            return i - j + (j * (2 * (std::max) (size_i, size_j) - j + 1)) / 2;
        }
        static
        BOOST_UBLAS_INLINE
        size_type upper_element (size_type i, size_type size_i, size_type j, size_type size_j) {
            BOOST_UBLAS_CHECK (i < size_i, bad_index ());
            BOOST_UBLAS_CHECK (j < size_j, bad_index ());
            BOOST_UBLAS_CHECK (i <= j, bad_index ());
            // FIXME size_type overflow
            // sigma_j (j + 1) = (j + 1) * j / 2
            // j = 0 1 2 3, sigma = 0 1 3 6
            return i + ((j + 1) * j) / 2;
        }

        // Major and minor indices
        static
        BOOST_UBLAS_INLINE
        size_type index_M (size_type /* index1 */, size_type index2) {
            return index2;
        }
        static
        BOOST_UBLAS_INLINE
        size_type index_m (size_type index1, size_type /* index2 */) {
            return index1;
        }
        static
        BOOST_UBLAS_INLINE
        size_type size_M (size_type /* size_i */, size_type size_j) {
            return size_j;
        }
        static
        BOOST_UBLAS_