concepts.hpp

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#else
            pointer p;
#endif
            // Element assigment
            value_type r = m.insert_element (i, j, t);
            m.insert_element (i, j, t) = r;
            // Zeroing
            m.clear ();
            // Resize
            m.resize (n, n);
            m.resize (n, n, false);

            ignore_unused_variable_warning (p);
            ignore_unused_variable_warning (r);
        }
    };

    template<class M>
    struct SparseMatrixConcept {
        typedef M matrix_type;
        typedef typename M::size_type size_type;

        void constraints () {
            function_requires< MatrixConcept<matrix_type> >();
        }
    };

    template<class M>
    struct Mutable_SparseMatrixConcept {
        typedef M matrix_type;
        typedef typename M::size_type size_type;
        typedef typename M::value_type value_type;

        void constraints () {
            function_requires< SparseMatrixConcept<matrix_type> >();
            function_requires< Mutable_MatrixConcept<matrix_type> >();
            size_type i (0), j (0);
            matrix_type m;
            // Elemnent erasure
            m.erase_element (i, j);
        }
    };

    template<class T>
    T
    ZeroElement (T);
    template<>
    float
    ZeroElement (float) {
        return 0.f;
    }
    template<>
    double
    ZeroElement (double) {
        return 0.;
    }
    template<>
    vector<float>
    ZeroElement (vector<float>) {
        return zero_vector<float> ();
    }
    template<>
    vector<double>
    ZeroElement (vector<double>) {
        return zero_vector<double> ();
    }
    template<>
    matrix<float>
    ZeroElement (matrix<float>) {
        return zero_matrix<float> ();
    }
    template<>
    matrix<double>
    ZeroElement (matrix<double>) {
        return zero_matrix<double> ();
    }
    template<>
    std::complex<float>
    ZeroElement (std::complex<float>) {
        return std::complex<float> (0.f);
    }
    template<>
    std::complex<double>
    ZeroElement (std::complex<double>) {
        return std::complex<double> (0.);
    }
    template<>
    vector<std::complex<float> >
    ZeroElement (vector<std::complex<float> >) {
        return zero_vector<std::complex<float> > ();
    }
    template<>
    vector<std::complex<double> >
    ZeroElement (vector<std::complex<double> >) {
        return zero_vector<std::complex<double> > ();
    }
    template<>
    matrix<std::complex<float> >
    ZeroElement (matrix<std::complex<float> >) {
        return zero_matrix<std::complex<float> > ();
    }
    template<>
    matrix<std::complex<double> >
    ZeroElement (matrix<std::complex<double> >) {
        return zero_matrix<std::complex<double> > ();
    }

    template<class T>
    T
    OneElement (T);
    template<>
    float
    OneElement (float) {
        return 1.f;
    }
    template<>
    double
    OneElement (double) {
        return 1.;
    }
    template<>
    matrix<float>
    OneElement (matrix<float>) {
        return identity_matrix<float> ();
    }
    template<>
    matrix<double>
    OneElement (matrix<double>) {
        return identity_matrix<double> ();
    }
    template<>
    std::complex<float>
    OneElement (std::complex<float>) {
        return std::complex<float> (1.f);
    }
    template<>
    std::complex<double>
    OneElement (std::complex<double>) {
        return std::complex<double> (1.);
    }
    template<>
    matrix<std::complex<float> >
    OneElement (matrix<std::complex<float> >) {
        return identity_matrix<std::complex<float> > ();
    }
    template<>
    matrix<std::complex<double> >
    OneElement (matrix<std::complex<double> >) {
        return identity_matrix<std::complex<double> > ();
    }

    template<class E1, class E2>
    bool
    operator == (const vector_expression<E1> &e1, const vector_expression<E2> &e2) {
        typedef typename promote_traits<typename E1::value_type,
                                                    typename E2::value_type>::promote_type value_type;
        typedef typename type_traits<value_type>::real_type real_type;
        return norm_inf (e1 - e2) == real_type/*zero*/();
    }
    template<class E1, class E2>
    bool
    operator == (const matrix_expression<E1> &e1, const matrix_expression<E2> &e2) {
        typedef typename promote_traits<typename E1::value_type,
                                                    typename E2::value_type>::promote_type value_type;
        typedef typename type_traits<value_type>::real_type real_type;
        return norm_inf (e1 - e2) == real_type/*zero*/();
    }

    template<class T>
    struct AdditiveAbelianGroupConcept {
        typedef T value_type;

        void constraints () {
            bool r;
            value_type a = value_type (), b = value_type (), c = value_type ();
            r = (a + b) + c == a + (b + c);
            r = ZeroElement (value_type ()) + a == a;
            r = a + ZeroElement (value_type ()) == a;
            r = a + (- a) == ZeroElement (value_type ());
            r = (- a) + a == ZeroElement (value_type ());
            r = a + b == b + a;
            ignore_unused_variable_warning (r);
        }
    };

    template<class T>
    struct MultiplicativeAbelianGroupConcept {
        typedef T value_type;

        void constraints () {
            bool r;
            value_type a = value_type (), b = value_type (), c = value_type ();
            r = (a * b) * c == a * (b * c);
            r = OneElement (value_type ()) * a == a;
            r = a * OneElement (value_type ()) == a;
            r = a * (OneElement (value_type ()) / a) == a;
            r = (OneElement (value_type ()) / a) * a == a;
            r = a * b == b * a;
            ignore_unused_variable_warning (r);
        }
    };

    template<class T>
    struct RingWithIdentityConcept {
        typedef T value_type;

        void constraints () {
            function_requires< AdditiveAbelianGroupConcept<value_type> >();
            bool r;
            value_type a = value_type (), b = value_type (), c = value_type ();
            r = (a * b) * c == a * (b * c);
            r = (a + b) * c == a * c + b * c;
            r = OneElement (value_type ()) * a == a;
            r = a * OneElement (value_type ()) == a;
            ignore_unused_variable_warning (r);
        }
    };

    template<class T>
    struct Prod_RingWithIdentityConcept {
        typedef T value_type;

        void constraints () {
            function_requires< AdditiveAbelianGroupConcept<value_type> >();
            bool r;
            value_type a = value_type (), b = value_type (), c = value_type ();
            r = prod (T (prod (a, b)), c) == prod (a, T (prod (b, c)));
            r = prod (a + b, c) == prod (a, c) + prod (b, c);
            r = prod (OneElement (value_type ()), a) == a;
            r = prod (a, OneElement (value_type ())) == a;
            ignore_unused_variable_warning (r);
        }
    };

    template<class T>
    struct CommutativeRingWithIdentityConcept {
        typedef T value_type;

        void constraints () {
            function_requires< RingWithIdentityConcept<value_type> >();
            bool r;
            value_type a = value_type (), b = value_type ();
            r = a * b == b * a;
            ignore_unused_variable_warning (r);
        }
    };

    template<class T>
    struct FieldConcept {
        typedef T value_type;

        void constraints () {
            function_requires< CommutativeRingWithIdentityConcept<value_type> >();
            bool r;
            value_type a = value_type ();
            r = a == ZeroElement (value_type ()) || a * (OneElement (value_type ()) / a) == a;
            r = a == ZeroElement (value_type ()) || (OneElement (value_type ()) / a) * a == a;
            ignore_unused_variable_warning (r);
        }
    };

    template<class T, class V>
    struct VectorSpaceConcept {
        typedef T value_type;
        typedef V vector_type;

        void constraints () {
            function_requires< FieldConcept<value_type> >();
            function_requires< AdditiveAbelianGroupConcept<vector_type> >();
            bool r;
            value_type alpha = value_type (), beta = value_type ();
            vector_type a = vector_type (), b = vector_type ();
            r = alpha * (a + b) == alpha * a + alpha * b;
            r = (alpha + beta) * a == alpha * a + beta * a;
            r = (alpha * beta) * a == alpha * (beta * a);
            r = OneElement (value_type ()) * a == a;
            ignore_unused_variable_warning (r);
        }
    };

    template<class T, class V, class M>
    struct LinearOperatorConcept {