1061 lines
33 KiB
C++
1061 lines
33 KiB
C++
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// Boost.Units - A C++ library for zero-overhead dimensional analysis and
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// unit/quantity manipulation and conversion
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//
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// Copyright (C) 2003-2008 Matthias Christian Schabel
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// Copyright (C) 2008 Steven Watanabe
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//
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// Distributed under the Boost Software License, Version 1.0. (See
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// accompanying file LICENSE_1_0.txt or copy at
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// http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_UNITS_DETAIL_LINEAR_ALGEBRA_HPP
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#define BOOST_UNITS_DETAIL_LINEAR_ALGEBRA_HPP
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#include <boost/units/static_rational.hpp>
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#include <boost/mpl/next.hpp>
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#include <boost/mpl/arithmetic.hpp>
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#include <boost/mpl/and.hpp>
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#include <boost/mpl/assert.hpp>
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#include <boost/units/dim.hpp>
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#include <boost/units/dimensionless_type.hpp>
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#include <boost/units/static_rational.hpp>
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#include <boost/units/detail/dimension_list.hpp>
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#include <boost/units/detail/sort.hpp>
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namespace boost {
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namespace units {
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namespace detail {
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// typedef list<rational> equation;
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template<int N>
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struct eliminate_from_pair_of_equations_impl;
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template<class E1, class E2>
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struct eliminate_from_pair_of_equations;
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template<int N>
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struct elimination_impl;
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template<bool is_zero, bool element_is_last>
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struct elimination_skip_leading_zeros_impl;
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template<class Equation, class Vars>
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struct substitute;
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template<int N>
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struct substitute_impl;
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template<bool is_end>
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struct solve_impl;
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template<class T>
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struct solve;
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template<int N>
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struct check_extra_equations_impl;
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template<int N>
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struct normalize_units_impl;
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struct inconsistent {};
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// generally useful utilies.
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template<int N>
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struct divide_equation {
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template<class Begin, class Divisor>
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struct apply {
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typedef list<typename mpl::divides<typename Begin::item, Divisor>::type, typename divide_equation<N - 1>::template apply<typename Begin::next, Divisor>::type> type;
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};
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};
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template<>
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struct divide_equation<0> {
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template<class Begin, class Divisor>
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struct apply {
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typedef dimensionless_type type;
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};
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};
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// eliminate_from_pair_of_equations takes a pair of
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// equations and eliminates the first variable.
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//
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// equation eliminate_from_pair_of_equations(equation l1, equation l2) {
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// rational x1 = l1.front();
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// rational x2 = l2.front();
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// return(transform(pop_front(l1), pop_front(l2), _1 * x2 - _2 * x1));
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// }
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template<int N>
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struct eliminate_from_pair_of_equations_impl {
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template<class Begin1, class Begin2, class X1, class X2>
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struct apply {
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typedef list<
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typename mpl::minus<
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typename mpl::times<typename Begin1::item, X2>::type,
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typename mpl::times<typename Begin2::item, X1>::type
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>::type,
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typename eliminate_from_pair_of_equations_impl<N - 1>::template apply<
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typename Begin1::next,
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typename Begin2::next,
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X1,
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X2
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>::type
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> type;
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};
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};
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template<>
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struct eliminate_from_pair_of_equations_impl<0> {
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template<class Begin1, class Begin2, class X1, class X2>
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struct apply {
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typedef dimensionless_type type;
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};
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};
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template<class E1, class E2>
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struct eliminate_from_pair_of_equations {
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typedef E1 begin1;
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typedef E2 begin2;
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typedef typename eliminate_from_pair_of_equations_impl<(E1::size::value - 1)>::template apply<
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typename begin1::next,
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typename begin2::next,
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typename begin1::item,
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typename begin2::item
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>::type type;
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};
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// Stage 1. Determine which dimensions should
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// have dummy base units. For this purpose
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// row reduce the matrix.
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template<int N>
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struct make_zero_vector {
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typedef list<static_rational<0>, typename make_zero_vector<N - 1>::type> type;
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};
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template<>
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struct make_zero_vector<0> {
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typedef dimensionless_type type;
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};
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template<int Column, int TotalColumns>
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struct create_row_of_identity {
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typedef list<static_rational<0>, typename create_row_of_identity<Column - 1, TotalColumns - 1>::type> type;
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};
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template<int TotalColumns>
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struct create_row_of_identity<0, TotalColumns> {
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typedef list<static_rational<1>, typename make_zero_vector<TotalColumns - 1>::type> type;
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};
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template<int Column>
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struct create_row_of_identity<Column, 0> {
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// error
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};
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template<int RemainingRows>
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struct determine_extra_equations_impl;
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template<bool first_is_zero, bool is_last>
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struct determine_extra_equations_skip_zeros_impl;
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// not the last row and not zero.
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template<>
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struct determine_extra_equations_skip_zeros_impl<false, false> {
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template<class RowsBegin, int RemainingRows, int CurrentColumn, int TotalColumns, class Result>
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struct apply {
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// remove the equation being eliminated against from the set of equations.
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typedef typename determine_extra_equations_impl<RemainingRows - 1>::template apply<typename RowsBegin::next, typename RowsBegin::item>::type next_equations;
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// since this column was present, strip it out.
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typedef Result type;
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};
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};
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// the last row but not zero.
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template<>
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struct determine_extra_equations_skip_zeros_impl<false, true> {
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template<class RowsBegin, int RemainingRows, int CurrentColumn, int TotalColumns, class Result>
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struct apply {
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// remove this equation.
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typedef dimensionless_type next_equations;
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// since this column was present, strip it out.
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typedef Result type;
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};
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};
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// the first columns is zero but it is not the last column.
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// continue with the same loop.
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template<>
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struct determine_extra_equations_skip_zeros_impl<true, false> {
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template<class RowsBegin, int RemainingRows, int CurrentColumn, int TotalColumns, class Result>
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struct apply {
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typedef typename RowsBegin::next::item next_row;
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typedef typename determine_extra_equations_skip_zeros_impl<
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next_row::item::Numerator == 0,
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RemainingRows == 2 // the next one will be the last.
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>::template apply<
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typename RowsBegin::next,
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RemainingRows - 1,
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CurrentColumn,
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TotalColumns,
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Result
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> next;
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typedef list<typename RowsBegin::item::next, typename next::next_equations> next_equations;
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typedef typename next::type type;
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};
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};
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// all the elements in this column are zero.
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template<>
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struct determine_extra_equations_skip_zeros_impl<true, true> {
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template<class RowsBegin, int RemainingRows, int CurrentColumn, int TotalColumns, class Result>
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struct apply {
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typedef list<typename RowsBegin::item::next, dimensionless_type> next_equations;
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typedef list<typename create_row_of_identity<CurrentColumn, TotalColumns>::type, Result> type;
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};
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};
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template<int RemainingRows>
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struct determine_extra_equations_impl {
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template<class RowsBegin, class EliminateAgainst>
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struct apply {
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typedef list<
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typename eliminate_from_pair_of_equations<typename RowsBegin::item, EliminateAgainst>::type,
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typename determine_extra_equations_impl<RemainingRows-1>::template apply<typename RowsBegin::next, EliminateAgainst>::type
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> type;
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};
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};
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template<>
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struct determine_extra_equations_impl<0> {
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template<class RowsBegin, class EliminateAgainst>
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struct apply {
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typedef dimensionless_type type;
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};
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};
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template<int RemainingColumns, bool is_done>
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struct determine_extra_equations {
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template<class RowsBegin, int TotalColumns, class Result>
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struct apply {
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typedef typename RowsBegin::item top_row;
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typedef typename determine_extra_equations_skip_zeros_impl<
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top_row::item::Numerator == 0,
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RowsBegin::size::value == 1
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>::template apply<
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RowsBegin,
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RowsBegin::size::value,
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TotalColumns - RemainingColumns,
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TotalColumns,
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Result
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> column_info;
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typedef typename determine_extra_equations<
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RemainingColumns - 1,
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column_info::next_equations::size::value == 0
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>::template apply<
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typename column_info::next_equations,
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TotalColumns,
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typename column_info::type
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>::type type;
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};
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};
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template<int RemainingColumns>
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struct determine_extra_equations<RemainingColumns, true> {
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template<class RowsBegin, int TotalColumns, class Result>
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struct apply {
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typedef typename determine_extra_equations<RemainingColumns - 1, true>::template apply<
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RowsBegin,
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TotalColumns,
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list<typename create_row_of_identity<TotalColumns - RemainingColumns, TotalColumns>::type, Result>
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>::type type;
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};
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};
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template<>
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struct determine_extra_equations<0, true> {
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template<class RowsBegin, int TotalColumns, class Result>
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struct apply {
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typedef Result type;
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};
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};
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// Stage 2
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// invert the matrix using Gauss-Jordan elimination
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template<bool is_zero, bool is_last>
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struct invert_strip_leading_zeroes;
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template<int N>
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struct invert_handle_after_pivot_row;
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// When processing column N, none of the first N rows
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// can be the pivot column.
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template<int N>
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struct invert_handle_inital_rows {
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template<class RowsBegin, class IdentityBegin>
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struct apply {
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typedef typename invert_handle_inital_rows<N - 1>::template apply<
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typename RowsBegin::next,
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typename IdentityBegin::next
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> next;
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typedef typename RowsBegin::item current_row;
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typedef typename IdentityBegin::item current_identity_row;
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typedef typename next::pivot_row pivot_row;
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typedef typename next::identity_pivot_row identity_pivot_row;
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typedef list<
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typename eliminate_from_pair_of_equations_impl<(current_row::size::value) - 1>::template apply<
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typename current_row::next,
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pivot_row,
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typename current_row::item,
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static_rational<1>
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>::type,
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typename next::new_matrix
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> new_matrix;
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typedef list<
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typename eliminate_from_pair_of_equations_impl<(current_identity_row::size::value)>::template apply<
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current_identity_row,
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identity_pivot_row,
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typename current_row::item,
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static_rational<1>
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>::type,
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typename next::identity_result
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> identity_result;
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};
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};
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// This handles the switch to searching for a pivot column.
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// The pivot row will be propagated up in the typedefs
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// pivot_row and identity_pivot_row. It is inserted here.
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template<>
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struct invert_handle_inital_rows<0> {
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template<class RowsBegin, class IdentityBegin>
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struct apply {
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typedef typename RowsBegin::item current_row;
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typedef typename invert_strip_leading_zeroes<
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(current_row::item::Numerator == 0),
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(RowsBegin::size::value == 1)
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>::template apply<
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RowsBegin,
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IdentityBegin
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> next;
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// results
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typedef list<typename next::pivot_row, typename next::new_matrix> new_matrix;
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typedef list<typename next::identity_pivot_row, typename next::identity_result> identity_result;
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typedef typename next::pivot_row pivot_row;
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typedef typename next::identity_pivot_row identity_pivot_row;
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};
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};
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// The first internal element which is not zero.
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template<>
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struct invert_strip_leading_zeroes<false, false> {
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template<class RowsBegin, class IdentityBegin>
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struct apply {
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typedef typename RowsBegin::item current_row;
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typedef typename current_row::item current_value;
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typedef typename divide_equation<(current_row::size::value - 1)>::template apply<typename current_row::next, current_value>::type new_equation;
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typedef typename divide_equation<(IdentityBegin::item::size::value)>::template apply<typename IdentityBegin::item, current_value>::type transformed_identity_equation;
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typedef typename invert_handle_after_pivot_row<(RowsBegin::size::value - 1)>::template apply<
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typename RowsBegin::next,
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typename IdentityBegin::next,
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new_equation,
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transformed_identity_equation
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> next;
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// results
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// Note that we don't add the pivot row to the
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// results here, because it needs to propagated up
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// to the diagonal.
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typedef typename next::new_matrix new_matrix;
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typedef typename next::identity_result identity_result;
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typedef new_equation pivot_row;
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typedef transformed_identity_equation identity_pivot_row;
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};
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};
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// The one and only non-zero element--at the end
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||
|
|
template<>
|
||
|
|
struct invert_strip_leading_zeroes<false, true> {
|
||
|
|
template<class RowsBegin, class IdentityBegin>
|
||
|
|
struct apply {
|
||
|
|
typedef typename RowsBegin::item current_row;
|
||
|
|
typedef typename current_row::item current_value;
|
||
|
|
typedef typename divide_equation<(current_row::size::value - 1)>::template apply<typename current_row::next, current_value>::type new_equation;
|
||
|
|
typedef typename divide_equation<(IdentityBegin::item::size::value)>::template apply<typename IdentityBegin::item, current_value>::type transformed_identity_equation;
|
||
|
|
|
||
|
|
// results
|
||
|
|
// Note that we don't add the pivot row to the
|
||
|
|
// results here, because it needs to propagated up
|
||
|
|
// to the diagonal.
|
||
|
|
typedef dimensionless_type identity_result;
|
||
|
|
typedef dimensionless_type new_matrix;
|
||
|
|
typedef new_equation pivot_row;
|
||
|
|
typedef transformed_identity_equation identity_pivot_row;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
// One of the initial zeroes
|
||
|
|
template<>
|
||
|
|
struct invert_strip_leading_zeroes<true, false> {
|
||
|
|
template<class RowsBegin, class IdentityBegin>
|
||
|
|
struct apply {
|
||
|
|
typedef typename RowsBegin::item current_row;
|
||
|
|
typedef typename RowsBegin::next::item next_row;
|
||
|
|
typedef typename invert_strip_leading_zeroes<
|
||
|
|
next_row::item::Numerator == 0,
|
||
|
|
RowsBegin::size::value == 2
|
||
|
|
>::template apply<
|
||
|
|
typename RowsBegin::next,
|
||
|
|
typename IdentityBegin::next
|
||
|
|
> next;
|
||
|
|
typedef typename IdentityBegin::item current_identity_row;
|
||
|
|
// these are propagated up.
|
||
|
|
typedef typename next::pivot_row pivot_row;
|
||
|
|
typedef typename next::identity_pivot_row identity_pivot_row;
|
||
|
|
typedef list<
|
||
|
|
typename eliminate_from_pair_of_equations_impl<(current_row::size::value - 1)>::template apply<
|
||
|
|
typename current_row::next,
|
||
|
|
pivot_row,
|
||
|
|
typename current_row::item,
|
||
|
|
static_rational<1>
|
||
|
|
>::type,
|
||
|
|
typename next::new_matrix
|
||
|
|
> new_matrix;
|
||
|
|
typedef list<
|
||
|
|
typename eliminate_from_pair_of_equations_impl<(current_identity_row::size::value)>::template apply<
|
||
|
|
current_identity_row,
|
||
|
|
identity_pivot_row,
|
||
|
|
typename current_row::item,
|
||
|
|
static_rational<1>
|
||
|
|
>::type,
|
||
|
|
typename next::identity_result
|
||
|
|
> identity_result;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
// the last element, and is zero.
|
||
|
|
// Should never happen.
|
||
|
|
template<>
|
||
|
|
struct invert_strip_leading_zeroes<true, true> {
|
||
|
|
};
|
||
|
|
|
||
|
|
template<int N>
|
||
|
|
struct invert_handle_after_pivot_row {
|
||
|
|
template<class RowsBegin, class IdentityBegin, class MatrixPivot, class IdentityPivot>
|
||
|
|
struct apply {
|
||
|
|
typedef typename invert_handle_after_pivot_row<N - 1>::template apply<
|
||
|
|
typename RowsBegin::next,
|
||
|
|
typename IdentityBegin::next,
|
||
|
|
MatrixPivot,
|
||
|
|
IdentityPivot
|
||
|
|
> next;
|
||
|
|
typedef typename RowsBegin::item current_row;
|
||
|
|
typedef typename IdentityBegin::item current_identity_row;
|
||
|
|
typedef MatrixPivot pivot_row;
|
||
|
|
typedef IdentityPivot identity_pivot_row;
|
||
|
|
|
||
|
|
// results
|
||
|
|
typedef list<
|
||
|
|
typename eliminate_from_pair_of_equations_impl<(current_row::size::value - 1)>::template apply<
|
||
|
|
typename current_row::next,
|
||
|
|
pivot_row,
|
||
|
|
typename current_row::item,
|
||
|
|
static_rational<1>
|
||
|
|
>::type,
|
||
|
|
typename next::new_matrix
|
||
|
|
> new_matrix;
|
||
|
|
typedef list<
|
||
|
|
typename eliminate_from_pair_of_equations_impl<(current_identity_row::size::value)>::template apply<
|
||
|
|
current_identity_row,
|
||
|
|
identity_pivot_row,
|
||
|
|
typename current_row::item,
|
||
|
|
static_rational<1>
|
||
|
|
>::type,
|
||
|
|
typename next::identity_result
|
||
|
|
> identity_result;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<>
|
||
|
|
struct invert_handle_after_pivot_row<0> {
|
||
|
|
template<class RowsBegin, class IdentityBegin, class MatrixPivot, class IdentityPivot>
|
||
|
|
struct apply {
|
||
|
|
typedef dimensionless_type new_matrix;
|
||
|
|
typedef dimensionless_type identity_result;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<int N>
|
||
|
|
struct invert_impl {
|
||
|
|
template<class RowsBegin, class IdentityBegin>
|
||
|
|
struct apply {
|
||
|
|
typedef typename invert_handle_inital_rows<RowsBegin::size::value - N>::template apply<RowsBegin, IdentityBegin> process_column;
|
||
|
|
typedef typename invert_impl<N - 1>::template apply<
|
||
|
|
typename process_column::new_matrix,
|
||
|
|
typename process_column::identity_result
|
||
|
|
>::type type;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<>
|
||
|
|
struct invert_impl<0> {
|
||
|
|
template<class RowsBegin, class IdentityBegin>
|
||
|
|
struct apply {
|
||
|
|
typedef IdentityBegin type;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<int N>
|
||
|
|
struct make_identity {
|
||
|
|
template<int Size>
|
||
|
|
struct apply {
|
||
|
|
typedef list<typename create_row_of_identity<Size - N, Size>::type, typename make_identity<N - 1>::template apply<Size>::type> type;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<>
|
||
|
|
struct make_identity<0> {
|
||
|
|
template<int Size>
|
||
|
|
struct apply {
|
||
|
|
typedef dimensionless_type type;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<class Matrix>
|
||
|
|
struct make_square_and_invert {
|
||
|
|
typedef typename Matrix::item top_row;
|
||
|
|
typedef typename determine_extra_equations<(top_row::size::value), false>::template apply<
|
||
|
|
Matrix, // RowsBegin
|
||
|
|
top_row::size::value, // TotalColumns
|
||
|
|
Matrix // Result
|
||
|
|
>::type invertible;
|
||
|
|
typedef typename invert_impl<invertible::size::value>::template apply<
|
||
|
|
invertible,
|
||
|
|
typename make_identity<invertible::size::value>::template apply<invertible::size::value>::type
|
||
|
|
>::type type;
|
||
|
|
};
|
||
|
|
|
||
|
|
|
||
|
|
// find_base_dimensions takes a list of
|
||
|
|
// base_units and returns a sorted list
|
||
|
|
// of all the base_dimensions they use.
|
||
|
|
//
|
||
|
|
// list<base_dimension> find_base_dimensions(list<base_unit> l) {
|
||
|
|
// set<base_dimension> dimensions;
|
||
|
|
// for_each(base_unit unit : l) {
|
||
|
|
// for_each(dim d : unit.dimension_type) {
|
||
|
|
// dimensions = insert(dimensions, d.tag_type);
|
||
|
|
// }
|
||
|
|
// }
|
||
|
|
// return(sort(dimensions, _1 > _2, front_inserter(list<base_dimension>())));
|
||
|
|
// }
|
||
|
|
|
||
|
|
typedef char set_no;
|
||
|
|
struct set_yes { set_no dummy[2]; };
|
||
|
|
|
||
|
|
template<class T>
|
||
|
|
struct wrap {};
|
||
|
|
|
||
|
|
struct set_end {
|
||
|
|
static set_no lookup(...);
|
||
|
|
typedef mpl::long_<0> size;
|
||
|
|
};
|
||
|
|
|
||
|
|
template<class T, class Next>
|
||
|
|
struct set : Next {
|
||
|
|
using Next::lookup;
|
||
|
|
static set_yes lookup(wrap<T>*);
|
||
|
|
typedef T item;
|
||
|
|
typedef Next next;
|
||
|
|
typedef typename mpl::next<typename Next::size>::type size;
|
||
|
|
};
|
||
|
|
|
||
|
|
template<bool has_key>
|
||
|
|
struct set_insert;
|
||
|
|
|
||
|
|
template<>
|
||
|
|
struct set_insert<true> {
|
||
|
|
template<class Set, class T>
|
||
|
|
struct apply {
|
||
|
|
typedef Set type;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<>
|
||
|
|
struct set_insert<false> {
|
||
|
|
template<class Set, class T>
|
||
|
|
struct apply {
|
||
|
|
typedef set<T, Set> type;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<class Set, class T>
|
||
|
|
struct has_key {
|
||
|
|
static const long size = sizeof(Set::lookup((wrap<T>*)0));
|
||
|
|
static const bool value = (size == sizeof(set_yes));
|
||
|
|
};
|
||
|
|
|
||
|
|
template<int N>
|
||
|
|
struct find_base_dimensions_impl_impl {
|
||
|
|
template<class Begin, class S>
|
||
|
|
struct apply {
|
||
|
|
typedef typename find_base_dimensions_impl_impl<N-1>::template apply<
|
||
|
|
typename Begin::next,
|
||
|
|
S
|
||
|
|
>::type next;
|
||
|
|
|
||
|
|
typedef typename set_insert<
|
||
|
|
(has_key<next, typename Begin::item::tag_type>::value)
|
||
|
|
>::template apply<
|
||
|
|
next,
|
||
|
|
typename Begin::item::tag_type
|
||
|
|
>::type type;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<>
|
||
|
|
struct find_base_dimensions_impl_impl<0> {
|
||
|
|
template<class Begin, class S>
|
||
|
|
struct apply {
|
||
|
|
typedef S type;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<int N>
|
||
|
|
struct find_base_dimensions_impl {
|
||
|
|
template<class Begin>
|
||
|
|
struct apply {
|
||
|
|
typedef typename find_base_dimensions_impl_impl<(Begin::item::dimension_type::size::value)>::template apply<
|
||
|
|
typename Begin::item::dimension_type,
|
||
|
|
typename find_base_dimensions_impl<N-1>::template apply<typename Begin::next>::type
|
||
|
|
>::type type;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<>
|
||
|
|
struct find_base_dimensions_impl<0> {
|
||
|
|
template<class Begin>
|
||
|
|
struct apply {
|
||
|
|
typedef set_end type;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<class T>
|
||
|
|
struct find_base_dimensions {
|
||
|
|
typedef typename insertion_sort<
|
||
|
|
typename find_base_dimensions_impl<
|
||
|
|
(T::size::value)
|
||
|
|
>::template apply<T>::type
|
||
|
|
>::type type;
|
||
|
|
};
|
||
|
|
|
||
|
|
// calculate_base_dimension_coefficients finds
|
||
|
|
// the coefficients corresponding to the first
|
||
|
|
// base_dimension in each of the dimension_lists.
|
||
|
|
// It returns two values. The first result
|
||
|
|
// is a list of the coefficients. The second
|
||
|
|
// is a list with all the incremented iterators.
|
||
|
|
// When we encounter a base_dimension that is
|
||
|
|
// missing from a dimension_list, we do not
|
||
|
|
// increment the iterator and we set the
|
||
|
|
// coefficient to zero.
|
||
|
|
|
||
|
|
template<bool has_dimension>
|
||
|
|
struct calculate_base_dimension_coefficients_func;
|
||
|
|
|
||
|
|
template<>
|
||
|
|
struct calculate_base_dimension_coefficients_func<true> {
|
||
|
|
template<class T>
|
||
|
|
struct apply {
|
||
|
|
typedef typename T::item::value_type type;
|
||
|
|
typedef typename T::next next;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<>
|
||
|
|
struct calculate_base_dimension_coefficients_func<false> {
|
||
|
|
template<class T>
|
||
|
|
struct apply {
|
||
|
|
typedef static_rational<0> type;
|
||
|
|
typedef T next;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
// begins_with_dimension returns true iff its first
|
||
|
|
// parameter is a valid iterator which yields its
|
||
|
|
// second parameter when dereferenced.
|
||
|
|
|
||
|
|
template<class Iterator>
|
||
|
|
struct begins_with_dimension {
|
||
|
|
template<class Dim>
|
||
|
|
struct apply :
|
||
|
|
boost::is_same<
|
||
|
|
Dim,
|
||
|
|
typename Iterator::item::tag_type
|
||
|
|
> {};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<>
|
||
|
|
struct begins_with_dimension<dimensionless_type> {
|
||
|
|
template<class Dim>
|
||
|
|
struct apply : mpl::false_ {};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<int N>
|
||
|
|
struct calculate_base_dimension_coefficients_impl {
|
||
|
|
template<class BaseUnitDimensions,class Dim,class T>
|
||
|
|
struct apply {
|
||
|
|
typedef typename calculate_base_dimension_coefficients_func<
|
||
|
|
begins_with_dimension<typename BaseUnitDimensions::item>::template apply<
|
||
|
|
Dim
|
||
|
|
>::value
|
||
|
|
>::template apply<
|
||
|
|
typename BaseUnitDimensions::item
|
||
|
|
> result;
|
||
|
|
typedef typename calculate_base_dimension_coefficients_impl<N-1>::template apply<
|
||
|
|
typename BaseUnitDimensions::next,
|
||
|
|
Dim,
|
||
|
|
list<typename result::type, T>
|
||
|
|
> next_;
|
||
|
|
typedef typename next_::type type;
|
||
|
|
typedef list<typename result::next, typename next_::next> next;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<>
|
||
|
|
struct calculate_base_dimension_coefficients_impl<0> {
|
||
|
|
template<class Begin, class BaseUnitDimensions, class T>
|
||
|
|
struct apply {
|
||
|
|
typedef T type;
|
||
|
|
typedef dimensionless_type next;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
// add_zeroes pushs N zeroes onto the
|
||
|
|
// front of a list.
|
||
|
|
//
|
||
|
|
// list<rational> add_zeroes(list<rational> l, int N) {
|
||
|
|
// if(N == 0) {
|
||
|
|
// return(l);
|
||
|
|
// } else {
|
||
|
|
// return(push_front(add_zeroes(l, N-1), 0));
|
||
|
|
// }
|
||
|
|
// }
|
||
|
|
|
||
|
|
template<int N>
|
||
|
|
struct add_zeroes_impl {
|
||
|
|
// If you get an error here and your base units are
|
||
|
|
// in fact linearly independent, please report it.
|
||
|
|
BOOST_MPL_ASSERT_MSG((N > 0), base_units_are_probably_not_linearly_independent, (void));
|
||
|
|
template<class T>
|
||
|
|
struct apply {
|
||
|
|
typedef list<
|
||
|
|
static_rational<0>,
|
||
|
|
typename add_zeroes_impl<N-1>::template apply<T>::type
|
||
|
|
> type;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<>
|
||
|
|
struct add_zeroes_impl<0> {
|
||
|
|
template<class T>
|
||
|
|
struct apply {
|
||
|
|
typedef T type;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
// expand_dimensions finds the exponents of
|
||
|
|
// a set of dimensions in a dimension_list.
|
||
|
|
// the second parameter is assumed to be
|
||
|
|
// a superset of the base_dimensions of
|
||
|
|
// the first parameter.
|
||
|
|
//
|
||
|
|
// list<rational> expand_dimensions(dimension_list, list<base_dimension>);
|
||
|
|
|
||
|
|
template<int N>
|
||
|
|
struct expand_dimensions {
|
||
|
|
template<class Begin, class DimensionIterator>
|
||
|
|
struct apply {
|
||
|
|
typedef typename calculate_base_dimension_coefficients_func<
|
||
|
|
begins_with_dimension<DimensionIterator>::template apply<typename Begin::item>::value
|
||
|
|
>::template apply<DimensionIterator> result;
|
||
|
|
typedef list<
|
||
|
|
typename result::type,
|
||
|
|
typename expand_dimensions<N-1>::template apply<typename Begin::next, typename result::next>::type
|
||
|
|
> type;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<>
|
||
|
|
struct expand_dimensions<0> {
|
||
|
|
template<class Begin, class DimensionIterator>
|
||
|
|
struct apply {
|
||
|
|
typedef dimensionless_type type;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<int N>
|
||
|
|
struct create_unit_matrix {
|
||
|
|
template<class Begin, class Dimensions>
|
||
|
|
struct apply {
|
||
|
|
typedef typename create_unit_matrix<N - 1>::template apply<typename Begin::next, Dimensions>::type next;
|
||
|
|
typedef list<typename expand_dimensions<Dimensions::size::value>::template apply<Dimensions, typename Begin::item::dimension_type>::type, next> type;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<>
|
||
|
|
struct create_unit_matrix<0> {
|
||
|
|
template<class Begin, class Dimensions>
|
||
|
|
struct apply {
|
||
|
|
typedef dimensionless_type type;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<class T>
|
||
|
|
struct normalize_units {
|
||
|
|
typedef typename find_base_dimensions<T>::type dimensions;
|
||
|
|
typedef typename create_unit_matrix<(T::size::value)>::template apply<
|
||
|
|
T,
|
||
|
|
dimensions
|
||
|
|
>::type matrix;
|
||
|
|
typedef typename make_square_and_invert<matrix>::type type;
|
||
|
|
static const long extra = (type::size::value) - (T::size::value);
|
||
|
|
};
|
||
|
|
|
||
|
|
// multiply_add_units computes M x V
|
||
|
|
// where M is a matrix and V is a horizontal
|
||
|
|
// vector
|
||
|
|
//
|
||
|
|
// list<rational> multiply_add_units(list<list<rational> >, list<rational>);
|
||
|
|
|
||
|
|
template<int N>
|
||
|
|
struct multiply_add_units_impl {
|
||
|
|
template<class Begin1, class Begin2 ,class X>
|
||
|
|
struct apply {
|
||
|
|
typedef list<
|
||
|
|
typename mpl::plus<
|
||
|
|
typename mpl::times<
|
||
|
|
typename Begin2::item,
|
||
|
|
X
|
||
|
|
>::type,
|
||
|
|
typename Begin1::item
|
||
|
|
>::type,
|
||
|
|
typename multiply_add_units_impl<N-1>::template apply<
|
||
|
|
typename Begin1::next,
|
||
|
|
typename Begin2::next,
|
||
|
|
X
|
||
|
|
>::type
|
||
|
|
> type;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<>
|
||
|
|
struct multiply_add_units_impl<0> {
|
||
|
|
template<class Begin1, class Begin2 ,class X>
|
||
|
|
struct apply {
|
||
|
|
typedef dimensionless_type type;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<int N>
|
||
|
|
struct multiply_add_units {
|
||
|
|
template<class Begin1, class Begin2>
|
||
|
|
struct apply {
|
||
|
|
typedef typename multiply_add_units_impl<
|
||
|
|
(Begin2::item::size::value)
|
||
|
|
>::template apply<
|
||
|
|
typename multiply_add_units<N-1>::template apply<
|
||
|
|
typename Begin1::next,
|
||
|
|
typename Begin2::next
|
||
|
|
>::type,
|
||
|
|
typename Begin2::item,
|
||
|
|
typename Begin1::item
|
||
|
|
>::type type;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<>
|
||
|
|
struct multiply_add_units<1> {
|
||
|
|
template<class Begin1, class Begin2>
|
||
|
|
struct apply {
|
||
|
|
typedef typename add_zeroes_impl<
|
||
|
|
(Begin2::item::size::value)
|
||
|
|
>::template apply<dimensionless_type>::type type1;
|
||
|
|
typedef typename multiply_add_units_impl<
|
||
|
|
(Begin2::item::size::value)
|
||
|
|
>::template apply<
|
||
|
|
type1,
|
||
|
|
typename Begin2::item,
|
||
|
|
typename Begin1::item
|
||
|
|
>::type type;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
|
||
|
|
// strip_zeroes erases the first N elements of a list if
|
||
|
|
// they are all zero, otherwise returns inconsistent
|
||
|
|
//
|
||
|
|
// list strip_zeroes(list l, int N) {
|
||
|
|
// if(N == 0) {
|
||
|
|
// return(l);
|
||
|
|
// } else if(l.front == 0) {
|
||
|
|
// return(strip_zeroes(pop_front(l), N-1));
|
||
|
|
// } else {
|
||
|
|
// return(inconsistent);
|
||
|
|
// }
|
||
|
|
// }
|
||
|
|
|
||
|
|
template<int N>
|
||
|
|
struct strip_zeroes_impl;
|
||
|
|
|
||
|
|
template<class T>
|
||
|
|
struct strip_zeroes_func {
|
||
|
|
template<class L, int N>
|
||
|
|
struct apply {
|
||
|
|
typedef inconsistent type;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<>
|
||
|
|
struct strip_zeroes_func<static_rational<0> > {
|
||
|
|
template<class L, int N>
|
||
|
|
struct apply {
|
||
|
|
typedef typename strip_zeroes_impl<N-1>::template apply<typename L::next>::type type;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<int N>
|
||
|
|
struct strip_zeroes_impl {
|
||
|
|
template<class T>
|
||
|
|
struct apply {
|
||
|
|
typedef typename strip_zeroes_func<typename T::item>::template apply<T, N>::type type;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<>
|
||
|
|
struct strip_zeroes_impl<0> {
|
||
|
|
template<class T>
|
||
|
|
struct apply {
|
||
|
|
typedef T type;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
// Given a list of base_units, computes the
|
||
|
|
// exponents of each base unit for a given
|
||
|
|
// dimension.
|
||
|
|
//
|
||
|
|
// list<rational> calculate_base_unit_exponents(list<base_unit> units, dimension_list dimensions);
|
||
|
|
|
||
|
|
template<class T>
|
||
|
|
struct is_base_dimension_unit {
|
||
|
|
typedef mpl::false_ type;
|
||
|
|
typedef void base_dimension_type;
|
||
|
|
};
|
||
|
|
template<class T>
|
||
|
|
struct is_base_dimension_unit<list<dim<T, static_rational<1> >, dimensionless_type> > {
|
||
|
|
typedef mpl::true_ type;
|
||
|
|
typedef T base_dimension_type;
|
||
|
|
};
|
||
|
|
|
||
|
|
template<int N>
|
||
|
|
struct is_simple_system_impl {
|
||
|
|
template<class Begin, class Prev>
|
||
|
|
struct apply {
|
||
|
|
typedef is_base_dimension_unit<typename Begin::item::dimension_type> test;
|
||
|
|
typedef mpl::and_<
|
||
|
|
typename test::type,
|
||
|
|
mpl::less<Prev, typename test::base_dimension_type>,
|
||
|
|
typename is_simple_system_impl<N-1>::template apply<
|
||
|
|
typename Begin::next,
|
||
|
|
typename test::base_dimension_type
|
||
|
|
>
|
||
|
|
> type;
|
||
|
|
static const bool value = (type::value);
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<>
|
||
|
|
struct is_simple_system_impl<0> {
|
||
|
|
template<class Begin, class Prev>
|
||
|
|
struct apply : mpl::true_ {
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<class T>
|
||
|
|
struct is_simple_system {
|
||
|
|
typedef T Begin;
|
||
|
|
typedef is_base_dimension_unit<typename Begin::item::dimension_type> test;
|
||
|
|
typedef typename mpl::and_<
|
||
|
|
typename test::type,
|
||
|
|
typename is_simple_system_impl<
|
||
|
|
T::size::value - 1
|
||
|
|
>::template apply<
|
||
|
|
typename Begin::next::type,
|
||
|
|
typename test::base_dimension_type
|
||
|
|
>
|
||
|
|
>::type type;
|
||
|
|
static const bool value = type::value;
|
||
|
|
};
|
||
|
|
|
||
|
|
template<bool>
|
||
|
|
struct calculate_base_unit_exponents_impl;
|
||
|
|
|
||
|
|
template<>
|
||
|
|
struct calculate_base_unit_exponents_impl<true> {
|
||
|
|
template<class T, class Dimensions>
|
||
|
|
struct apply {
|
||
|
|
typedef typename expand_dimensions<(T::size::value)>::template apply<
|
||
|
|
typename find_base_dimensions<T>::type,
|
||
|
|
Dimensions
|
||
|
|
>::type type;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<>
|
||
|
|
struct calculate_base_unit_exponents_impl<false> {
|
||
|
|
template<class T, class Dimensions>
|
||
|
|
struct apply {
|
||
|
|
// find the units that correspond to each base dimension
|
||
|
|
typedef normalize_units<T> base_solutions;
|
||
|
|
// pad the dimension with zeroes so it can just be a
|
||
|
|
// list of numbers, making the multiplication easy
|
||
|
|
// e.g. if the arguments are list<pound, foot> and
|
||
|
|
// list<mass,time^-2> then this step will
|
||
|
|
// yield list<0,1,-2>
|
||
|
|
typedef typename expand_dimensions<(base_solutions::dimensions::size::value)>::template apply<
|
||
|
|
typename base_solutions::dimensions,
|
||
|
|
Dimensions
|
||
|
|
>::type dimensions;
|
||
|
|
// take the unit corresponding to each base unit
|
||
|
|
// multiply each of its exponents by the exponent
|
||
|
|
// of the base_dimension in the result and sum.
|
||
|
|
typedef typename multiply_add_units<dimensions::size::value>::template apply<
|
||
|
|
dimensions,
|
||
|
|
typename base_solutions::type
|
||
|
|
>::type units;
|
||
|
|
// Now, verify that the dummy units really
|
||
|
|
// cancel out and remove them.
|
||
|
|
typedef typename strip_zeroes_impl<base_solutions::extra>::template apply<units>::type type;
|
||
|
|
};
|
||
|
|
};
|
||
|
|
|
||
|
|
template<class T, class Dimensions>
|
||
|
|
struct calculate_base_unit_exponents {
|
||
|
|
typedef typename calculate_base_unit_exponents_impl<is_simple_system<T>::value>::template apply<T, Dimensions>::type type;
|
||
|
|
};
|
||
|
|
|
||
|
|
} // namespace detail
|
||
|
|
|
||
|
|
} // namespace units
|
||
|
|
|
||
|
|
} // namespace boost
|
||
|
|
|
||
|
|
#endif
|