mirror of https://github.com/CGAL/cgal
added Substitute(_homogeneous)
rm related operators from Evaluate
This commit is contained in:
Michael Hemmer
parent
672daa420b
commit
c788e0182f
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@ -422,61 +422,36 @@ public:
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return typename CT::Cast()(p);
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}
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};
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};
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// Evaluate_homogeneous_func for recursive homogeneous evaluation of a
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// polynomial, used by Polynomial_traits_d_base for polynomials.
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template< class Polynomial, int d = CGAL::Polynomial_traits_d< Polynomial>::d >
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struct Evaluate_homogeneous_func;
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struct Substitute_homogeneous{
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public:
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// this is the end of the recursion
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// begin contains the homogeneous variabel
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// hdegree is the remaining degree
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template <class Input_iterator>
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typename
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CGAL::Coercion_traits<
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typename std::iterator_traits<Input_iterator>::value_type,
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Innermost_coefficient>::Type
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operator()(
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const Innermost_coefficient& p,
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Input_iterator begin,
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Input_iterator end,
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int hdegree){
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typedef typename std::iterator_traits<Input_iterator>::value_type
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value_type;
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typedef CGAL::Coercion_traits<Innermost_coefficient,value_type> CT;
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typename CT::Type result =
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typename CT::Cast()(CGAL::ipower(*begin++,hdegree))
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* typename CT::Cast()(p);
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template< class Polynomial >
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struct Evaluate_homogeneous_func< Polynomial, 1 > {
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typedef typename CGAL::Polynomial_traits_d< Polynomial > PT;
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typedef typename PT::Coefficient Coefficient;
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typedef typename PT::Innermost_coefficient ICoeff;
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typedef typename CGAL::Polynomial_traits_d< Coefficient > PTC;
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template< class Input_iterator >
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ICoeff operator()( const Polynomial& p,
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Input_iterator begin,
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Input_iterator end,
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int total_degree,
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const ICoeff& v ) const {
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// TODO: remove --end in case of Input_iterator
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--end;
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CGAL_precondition( begin == end );
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return p.evaluate_homogeneous( (*end), v, total_degree );
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}
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};
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template< class Polynomial, int d >
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struct Evaluate_homogeneous_func {
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typedef typename CGAL::Polynomial_traits_d< Polynomial > PT;
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typedef typename PT::Coefficient Coefficient;
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typedef typename PT::Innermost_coefficient ICoeff;
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typedef typename CGAL::Polynomial_traits_d< Coefficient > PTC;
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template< class Input_iterator >
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ICoeff operator()( const Polynomial& p,
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Input_iterator begin,
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Input_iterator end,
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int total_degree,
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const ICoeff& v ) const {
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CGAL_precondition( begin != end );
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//typename PT::Evaluate evaluate;
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typename PT::Degree degree;
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Evaluate_homogeneous_func< Coefficient > eval_hom;
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// TODO: remove --end in case of Input_iterator
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--end;
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std::vector< ICoeff > cv;
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for( int i = 0; i <= degree(p); ++i ) {
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cv.push_back( eval_hom( p[i], begin, end, total_degree - i, v ) );
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CGAL_precondition(end == begin);
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CGAL_precondition(hdegree >= 0);
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return result;
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}
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return (CGAL::Polynomial< ICoeff >( cv.begin(), cv.end() )).evaluate((*end));
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}
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};
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};
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// Now the version for the polynomials with all functors provided by all
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@ -862,78 +837,67 @@ public:
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}
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};
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// Evaluate;
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// Evaluate;
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struct Evaluate
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:public Unary_function<Polynomial_d,Innermost_coefficient>{
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:public Unary_function<Polynomial_d,Coefficient>{
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// Evaluate with respect to one variable
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Coefficient
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operator()(const Polynomial_d& p, Innermost_coefficient x, int i = (d-1))
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const {
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if(i == (d-1) )
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return p.evaluate(x);
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else{
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return Move()(p,i).evaluate(x);
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}
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operator()(const Polynomial_d& p, Coefficient x) const {
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return p.evaluate(x);
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}
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template< class Input_iterator >
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Innermost_coefficient
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operator()(
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const Polynomial_d& p,
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Input_iterator begin,
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Input_iterator end ) const
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Coefficient
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operator()(const Polynomial_d& p, Coefficient x, int i ) const {
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return Move()(p,i).evaluate(x);
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}
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#define ICOEFF typename First_if_different<Innermost_coefficient, Coefficient>::Type
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Coefficient operator()
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( const Polynomial_d& p, const ICOEFF& x) const
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{
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CGAL_precondition( begin != end );
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typename PT::Evaluate evaluatePoly;
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typename PTC::Evaluate evaluateCoeff;
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// TODO: remove --end in case of Input_iterator
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--end;
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return evaluateCoeff( evaluatePoly( p, (*end) ), begin, end );
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}
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return p.evaluate(x);
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}
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Coefficient operator()
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(const Polynomial_d& p, const ICOEFF& x, int i) const
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{
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return Move()(p,i,PT::d-1).evaluate(x);
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}
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#undef ICOEFF
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};
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// Evaluate_homogeneous;
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// Evaluate_homogeneous;
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struct Evaluate_homogeneous{
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typedef Coefficient result_type;
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typedef Polynomial_d first_argument_type;
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typedef Innermost_coefficient second_argument_type;
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typedef Innermost_coefficient third_argument_type;
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typedef Arity_tag< 3 > Arity;
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Coefficient
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operator()(
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const Polynomial_d& p,
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Innermost_coefficient a,
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Innermost_coefficient b,
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int i = (PT::d-1) ) const {
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if (i == (d-1) )
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return p.evaluate_homogeneous(a,b);
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else
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return Move()(p,i,PT::d-1).evaluate_homogeneous(a,b);
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typedef Coefficient second_argument_type;
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typedef Coefficient third_argument_type;
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typedef Arity_tag< 3 > Arity;
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Coefficient operator()(
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const Polynomial_d& p, Coefficient a, Coefficient b) const
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{
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return p.evaluate_homogeneous(a,b);
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}
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template< class Input_iterator >
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Innermost_coefficient operator()( const Polynomial_d & p,
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Input_iterator begin,
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Input_iterator end ) const {
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typename PT::Total_degree total_degree;
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typename PT::Evaluate_homogeneous eval_hom;
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return eval_hom( p, begin, end, total_degree(p) );
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Coefficient operator()(
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const Polynomial_d& p, Coefficient a, Coefficient b, int i) const
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{
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return Move()(p,i,PT::d-1).evaluate_homogeneous(a,b);
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}
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template< class Input_iterator >
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Innermost_coefficient operator()( const Polynomial_d& p,
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Input_iterator begin,
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Input_iterator end,
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int total_degree ) const {
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--end;
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Evaluate_homogeneous_func< Polynomial_d > eval_hom;
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return eval_hom( p, begin, end, total_degree, (*end) );
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#define ICOEFF typename First_if_different<Innermost_coefficient, Coefficient>::Type
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Coefficient operator()
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( const Polynomial_d& p, const ICOEFF& a, const ICOEFF& b) const
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{
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return p.evaluate_homogeneous(a,b);
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}
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Coefficient operator()
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(const Polynomial_d& p, const ICOEFF& a, const ICOEFF& b, int i) const
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{
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return Move()(p,i,PT::d-1).evaluate_homogeneous(a,b);
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}
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#undef ICOEFF
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};
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// Is_zero_at;
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// Is_zero_at;
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struct Is_zero_at {
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private:
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typedef Algebraic_structure_traits<Innermost_coefficient> AST;
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@ -946,8 +910,8 @@ public:
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const Polynomial_d& p,
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Input_iterator begin,
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Input_iterator end ) const {
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typename PT::Evaluate evaluate;
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return( CGAL::is_zero( evaluate( p, begin, end ) ) );
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typename PT::Substitute substitute;
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return( CGAL::is_zero( substitute( p, begin, end ) ) );
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}
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};
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@ -960,13 +924,11 @@ public:
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typedef BOOL result_type;
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template< class Input_iterator >
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BOOL operator()(
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const Polynomial_d& p,
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Input_iterator begin,
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Input_iterator end ) const
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BOOL operator()
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( const Polynomial_d& p, Input_iterator begin, Input_iterator end ) const
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{
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typename PT::Evaluate_homogeneous evaluate_homogeneous;
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return( CGAL::is_zero( evaluate_homogeneous( p, begin, end ) ) );
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typename PT::Substitute_homogeneous substitute_homogeneous;
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return( CGAL::is_zero( substitute_homogeneous( p, begin, end ) ) );
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}
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};
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@ -984,13 +946,11 @@ public:
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Input_iterator begin,
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Input_iterator end ) const
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{
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typename PT::Evaluate evaluate;
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return CGAL::sign( evaluate( p, begin, end ) );
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typename PT::Substitute substitute;
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return CGAL::sign( substitute( p, begin, end ) );
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}
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};
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// TODO: Fix error in evaluate homogenous
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// Sign_at_homogeneous;
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struct Sign_at_homogeneous {
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typedef Real_embeddable_traits<Innermost_coefficient> RT;
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typedef typename RT::Sign::result_type SIGN;
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@ -1002,8 +962,8 @@ public:
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const Polynomial_d& p,
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Input_iterator begin,
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Input_iterator end) const {
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typename PT::Evaluate_homogeneous evaluate_homogeneous;
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return CGAL::sign( evaluate_homogeneous( p, begin, end ) );
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typename PT::Substitute_homogeneous substitute_homogeneous;
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return CGAL::sign( substitute_homogeneous( p, begin, end ) );
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}
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};
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@ -1344,8 +1304,7 @@ public:
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Polynomial_d operator()( Polynomial_d p, const Innermost_coefficient& c,
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int i = (PT::d-1) ) {
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typename PT::Scale_homogeneous scale_homogeneous;
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typename PT::Scale_homogeneous scale_homogeneous;
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return scale_homogeneous( p, c, Innermost_coefficient(1), i );
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}
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@ -1553,37 +1512,37 @@ public:
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}
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};
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// substitute every variable by its new value in the iterator range
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// substitute every variable by its new value in the iterator range
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// begin refers to the innermost/first variable
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struct Substitute{
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public:
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template <class Input_iterator>
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typename
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CGAL::Coercion_traits
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<typename std::iterator_traits<Input_iterator>::value_type,
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Innermost_coefficient>::Type
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typename CGAL::Coercion_traits<
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typename std::iterator_traits<Input_iterator>::value_type,
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Innermost_coefficient
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>::Type
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operator()(
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const Polynomial_d& p_,
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const Polynomial_d& p,
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Input_iterator begin,
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Input_iterator end){
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typedef typename std::iterator_traits<Input_iterator> ITT;
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typedef typename ITT::iterator_category Category;
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return (*this)(p_,begin,end,Category());
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return (*this)(p,begin,end,Category());
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}
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template <class Input_iterator>
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typename
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CGAL::Coercion_traits
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<typename std::iterator_traits<Input_iterator>::value_type,
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Innermost_coefficient>::Type
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typename CGAL::Coercion_traits<
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typename std::iterator_traits<Input_iterator>::value_type,
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Innermost_coefficient
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>::Type
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operator()(
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const Polynomial_d& p_,
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const Polynomial_d& p,
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Input_iterator begin,
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Input_iterator end,
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std::forward_iterator_tag){
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typedef typename std::iterator_traits<Input_iterator> ITT;
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std::list<typename ITT::value_type> list(begin,end);
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return (*this)(p_,list.begin(),list.end());
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return (*this)(p,list.begin(),list.end());
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}
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template <class Input_iterator>
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@ -1592,7 +1551,7 @@ public:
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<typename std::iterator_traits<Input_iterator>::value_type,
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Innermost_coefficient>::Type
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operator()(
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const Polynomial_d& p_,
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const Polynomial_d& p,
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Input_iterator begin,
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Input_iterator end,
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std::bidirectional_iterator_tag){
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@ -1602,9 +1561,7 @@ public:
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typedef CGAL::Coercion_traits<Innermost_coefficient,value_type> CT;
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typename PTC::Substitute subs;
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Polynomial_d p = p_;
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end--;
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typename CT::Type x = typename CT::Cast()(*end);
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typename CT::Type x = typename CT::Cast()(*(--end));
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int i = Degree()(p);
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typename CT::Type y =
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@ -1616,7 +1573,72 @@ public:
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}
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return y;
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}
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}; // substitute every variable by its new value in the iterator range
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// begin refers to the innermost/first variable
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struct Substitute_homogeneous{
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template<typename Input_iterator>
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struct Result_type{
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typedef std::iterator_traits<Input_iterator> ITT;
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typedef typename ITT::value_type value_type;
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typedef Coercion_traits<value_type, Innermost_coefficient> CT;
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typedef typename CT::Type Type;
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};
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public:
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template <class Input_iterator>
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typename Result_type<Input_iterator>::Type
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operator()( const Polynomial_d& p, Input_iterator begin, Input_iterator end){
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int hdegree = Total_degree()(p);
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typedef std::iterator_traits<Input_iterator> ITT;
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std::list<typename ITT::value_type> list(begin,end);
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// make the homogeneous variable the first in the list
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list.push_front(list.back());
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list.pop_back();
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// reverse and begin with the outermost variable
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return (*this)(p, list.rbegin(), list.rend(), hdegree);
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}
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// this operator is undcoumented and for internal use:
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// the iterator range starts with the outermost variable
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// and ends with the homogeneous variable
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template <class Input_iterator>
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typename Result_type<Input_iterator>::Type
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operator()(
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const Polynomial_d& p,
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Input_iterator begin,
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Input_iterator end,
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int hdegree){
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typedef std::iterator_traits<Input_iterator> ITT;
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typedef typename ITT::value_type value_type;
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typedef Coercion_traits<value_type, Innermost_coefficient> CT;
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typedef typename CT::Type Type;
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typename PTC::Substitute_homogeneous subsh;
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typename CT::Type x = typename CT::Cast()(*begin++);
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int i = Degree()(p);
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typename CT::Type y = subsh(Get_coefficient()(p,i),begin,end, hdegree-i);
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while (--i >= 0){
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y *= x;
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y += subsh(Get_coefficient()(p,i),begin,end,hdegree-i);
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}
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return y;
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}
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};
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};
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} // namespace CGALi
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@ -926,33 +926,18 @@ void test_evaluate(){
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assert(evaluate(Polynomial_d(1),ICoeff(0)) == Coeff(1));
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assert(evaluate(Polynomial_d(2),ICoeff(5)) == Coeff(2));
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assert(
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evaluate(Polynomial_d(Coeff(3),Coeff(2)),ICoeff(0)) == Coeff(3));
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assert(
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evaluate(Polynomial_d(Coeff(3),Coeff(2)),ICoeff(1)) == Coeff(5));
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assert(
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evaluate(Polynomial_d(Coeff(3),Coeff(2)),ICoeff(2)) == Coeff(7));
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assert( evaluate(Polynomial_d(Coeff(3),Coeff(2)),ICoeff(0)) == Coeff(3));
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assert( evaluate(Polynomial_d(Coeff(3),Coeff(2)),ICoeff(1)) == Coeff(5));
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assert( evaluate(Polynomial_d(Coeff(3),Coeff(2)),ICoeff(2)) == Coeff(7));
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for(int i = 0; i < 5; i++){
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int n = my_rnd.get_int(0,PT::d-1);
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Polynomial_d p,q;
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p = generate_sparse_random_polynomial<Polynomial_d>();
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assert(evaluate(p,ICoeff(3),n) ==
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evaluate(move(p,n,PT::d-1),ICoeff(3)));
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assert(evaluate(p,ICoeff(3),n)
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== evaluate(move(p,n,PT::d-1),ICoeff(3)));
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}
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Polynomial_d p(Coeff(1), Coeff(2), Coeff(3));
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std::vector< ICoeff > ev;
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for(int i = 0; i < PT::d-1; ++i) {
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ev.push_back(ICoeff(0));
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}
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ev.push_back(ICoeff(1));
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assert(evaluate(p, ev.begin(), ev.end()) == ICoeff(1+2+3));
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ev.pop_back();
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ev.push_back(ICoeff(2));
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assert(evaluate(p, ev.begin(), ev.end()) == ICoeff(1+4+12));
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std::cerr << " ok "<< std::endl;
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}
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@ -967,34 +952,13 @@ void test_evaluate_homogeneous(){
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assert(evh(Polynomial_d(1),ICoeff(0),ICoeff(2)) == Coeff(1));
|
||||
assert(evh(Polynomial_d(2),ICoeff(5),ICoeff(3)) == Coeff(2));
|
||||
|
||||
assert(evh(Polynomial_d(Coeff(3),Coeff(2)),ICoeff(0),ICoeff(1)) ==
|
||||
Coeff(3));
|
||||
assert(evh(Polynomial_d(Coeff(3),Coeff(2)),ICoeff(1),ICoeff(1)) ==
|
||||
Coeff(5));
|
||||
assert(evh(Polynomial_d(Coeff(3),Coeff(2)),ICoeff(2),ICoeff(3)) ==
|
||||
Coeff(9+4));
|
||||
assert(evh( Polynomial_d(Coeff(3),Coeff(2)) , ICoeff(0),ICoeff(1))
|
||||
== Coeff(3));
|
||||
assert(evh( Polynomial_d(Coeff(3),Coeff(2)) , ICoeff(1),ICoeff(1))
|
||||
== Coeff(5));
|
||||
assert(evh( Polynomial_d(Coeff(3),Coeff(2)) , ICoeff(2),ICoeff(3))
|
||||
== Coeff(9+4));
|
||||
|
||||
// hdegree parameter no longer available
|
||||
/*assert(evh(Polynomial_d(Coeff(5),Coeff(7)),ICoeff(2),ICoeff(3),2)
|
||||
== Coeff(5*3*3+7*3*2));*/
|
||||
|
||||
Polynomial_d p(Coeff(1), Coeff(2), Coeff(3));
|
||||
std::vector< ICoeff > ev;
|
||||
for(int i = 0; i < PT::d-1; ++i) {
|
||||
ev.push_back(ICoeff(0));
|
||||
}
|
||||
ev.push_back(ICoeff(1));
|
||||
ev.push_back(ICoeff(1));
|
||||
assert(evh(p, ev.begin(), ev.end()) == ICoeff(1+2+3));
|
||||
ev.pop_back();
|
||||
ev.push_back(ICoeff(2));
|
||||
assert(evh(p, ev.begin(), ev.end()) == ICoeff(4+4+3));
|
||||
ev.pop_back();
|
||||
ev.pop_back();
|
||||
ev.push_back(ICoeff(2));
|
||||
ev.push_back(ICoeff(2));
|
||||
assert(evh(p, ev.begin(), ev.end()) == ICoeff(4+8+12));
|
||||
|
||||
std::cerr << " ok "<< std::endl;
|
||||
}
|
||||
|
||||
|
|
@ -1036,31 +1000,25 @@ void test_is_zero_at_homogeneous() {
|
|||
|
||||
typename PT::Is_zero_at_homogeneous is_zero_at_homogeneous;
|
||||
|
||||
Polynomial_d p(Coeff(-1), Coeff(0), Coeff(1));
|
||||
Polynomial_d p(Coeff(-1), Coeff(0), Coeff(4));
|
||||
std::cout << p << std::endl;
|
||||
|
||||
std::vector< ICoeff > cv;
|
||||
for(int i = 0; i < PT::d-1; ++i)
|
||||
cv.push_back(ICoeff(0));
|
||||
|
||||
for(int v = 1; v < 5; ++v) {
|
||||
cv.push_back(ICoeff(0));
|
||||
cv.push_back(ICoeff(v));
|
||||
assert(!is_zero_at_homogeneous(p, cv.begin(), cv.end()));
|
||||
|
||||
cv.pop_back();
|
||||
cv.pop_back();
|
||||
cv.push_back(ICoeff(v));
|
||||
cv.push_back(ICoeff(v));
|
||||
assert(is_zero_at_homogeneous(p, cv.begin(), cv.end()));
|
||||
|
||||
cv.pop_back();
|
||||
cv.pop_back();
|
||||
cv.push_back(ICoeff(-v));
|
||||
cv.push_back(ICoeff(v));
|
||||
assert(is_zero_at_homogeneous(p, cv.begin(), cv.end()));
|
||||
|
||||
cv.pop_back();
|
||||
cv.pop_back();
|
||||
|
||||
for(int v = 2; v < 5; ++v) {
|
||||
cv.push_back(ICoeff(v));
|
||||
cv.push_back(ICoeff(2*v));
|
||||
assert(is_zero_at_homogeneous(p, cv.begin(), cv.end()));
|
||||
cv.pop_back();
|
||||
cv.pop_back();
|
||||
|
||||
cv.push_back(ICoeff(v));
|
||||
cv.push_back(ICoeff(2*-v));
|
||||
assert(is_zero_at_homogeneous(p, cv.begin(), cv.end()));
|
||||
cv.pop_back();
|
||||
cv.pop_back();
|
||||
}
|
||||
|
||||
std::cerr << " ok" << std::endl;
|
||||
|
|
@ -1258,15 +1216,7 @@ void test_substitute(){
|
|||
assert(Innermost_coefficient(2)
|
||||
== substitute(Polynomial_d(2),vec.begin(),vec.end()));
|
||||
assert(Innermost_coefficient(-2)
|
||||
== substitute(Polynomial_d(-2),vec.begin(),vec.end()));
|
||||
|
||||
for(int i = 0; i< 5; i++){
|
||||
Polynomial_d p =
|
||||
generate_sparse_random_polynomial<Polynomial_d>(3);
|
||||
assert(typename PT::Evaluate()(p,vec.begin(),vec.end())
|
||||
== substitute(p,vec.begin(),vec.end()));
|
||||
}
|
||||
|
||||
== substitute(Polynomial_d(-2),vec.begin(),vec.end()));
|
||||
|
||||
for(int i = 0; i< 5; i++){
|
||||
typedef typename PT
|
||||
|
|
@ -1289,6 +1239,50 @@ void test_substitute(){
|
|||
std::cerr << " ok "<< std::endl;
|
||||
}
|
||||
|
||||
// // Substitute;
|
||||
template <class Polynomial_traits_d>
|
||||
void test_substitute_homogeneous(){
|
||||
std::cerr << "start test_substitute_homogeneous "; std::cerr.flush();
|
||||
CGAL_SNAP_CGALi_TRAITS_D(Polynomial_traits_d);
|
||||
typename PT::Substitute_homogeneous substitute_homogeneous;
|
||||
typedef typename PT::Innermost_coefficient Innermost_coefficient;
|
||||
|
||||
|
||||
std::vector<Innermost_coefficient> vec;
|
||||
for(int i = 0; i < PT::d; i++){
|
||||
vec.push_back(Innermost_coefficient(i));
|
||||
}
|
||||
vec.push_back(Innermost_coefficient(3));
|
||||
assert(Innermost_coefficient(0)
|
||||
== substitute_homogeneous(Polynomial_d(0),vec.begin(),vec.end()));
|
||||
assert(Innermost_coefficient(1)
|
||||
== substitute_homogeneous(Polynomial_d(1),vec.begin(),vec.end()));
|
||||
assert(Innermost_coefficient(2)
|
||||
== substitute_homogeneous(Polynomial_d(2),vec.begin(),vec.end()));
|
||||
assert(Innermost_coefficient(-2)
|
||||
== substitute_homogeneous(Polynomial_d(-2),vec.begin(),vec.end()));
|
||||
|
||||
for(int i = 0; i< 5; i++){
|
||||
typedef typename PT
|
||||
:: template Rebind<Innermost_coefficient,5>::Other PT_5;
|
||||
typedef typename PT_5::Polynomial_d Polynomial_5;
|
||||
std::vector<Polynomial_5> vec1,vec2;
|
||||
for(int j = 0; j < PT::d+1; j++){
|
||||
vec1.push_back(
|
||||
generate_sparse_random_polynomial<Polynomial_5>(3));
|
||||
}
|
||||
vec2=vec1;
|
||||
std::swap(vec2[0],vec2[PT::d-1]);
|
||||
Polynomial_d p
|
||||
= generate_sparse_random_polynomial<Polynomial_d>(3);
|
||||
assert( substitute_homogeneous(p,vec1.begin(),vec1.end()) ==
|
||||
substitute_homogeneous(typename PT::Swap()(p,0,PT::d-1),
|
||||
vec2.begin(),vec2.end()));
|
||||
}
|
||||
|
||||
std::cerr << " ok "<< std::endl;
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
|
|
@ -1373,6 +1367,8 @@ struct Test_polynomial_traits_d<Polynomial_traits_d, CGAL::Null_tag > {
|
|||
test_canonicalize<Polynomial_traits_d>();
|
||||
// Substitute;
|
||||
test_substitute<Polynomial_traits_d>();
|
||||
// Substitute_homogeneous;
|
||||
test_substitute_homogeneous<Polynomial_traits_d>();
|
||||
// private:
|
||||
// Innermost_leading_coefficient;
|
||||
}
|
||||
|
|
|
|||
Loading…
Reference in New Issue