traits.hpp

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        static
        BOOST_UBLAS_INLINE
        real_type norm_inf (const_reference t) {
            return (std::max) (type_traits<real_type>::abs (self_type::real (t)),
                             type_traits<real_type>::abs (self_type::imag (t)));
        }

        static
        BOOST_UBLAS_INLINE
        bool equals (const_reference t1, const_reference t2) {
            return self_type::norm_inf (t1 - t2) < BOOST_UBLAS_TYPE_CHECK_EPSILON *
                   (std::max) ((std::max) (self_type::norm_inf (t1),
                                       self_type::norm_inf (t2)),
                             BOOST_UBLAS_TYPE_CHECK_MIN);
        }
    };
    template<>
    struct type_traits<std::complex<double> > {
        typedef type_traits<std::complex<double> > self_type;
        typedef std::complex<double> value_type;
        typedef const value_type &const_reference;
        typedef value_type &reference;
        typedef double real_type;
#ifndef BOOST_UBLAS_NO_LONG_DOUBLE
        typedef std::complex<long double> precision_type;
#else
        typedef value_type precision_type;
#endif

        BOOST_STATIC_CONSTANT (unsigned, plus_complexity = 2);
        BOOST_STATIC_CONSTANT (unsigned, multiplies_complexity = 6);

        static
        BOOST_UBLAS_INLINE
        real_type real (const_reference t) {
                return std::real (t);
        }
        static
        BOOST_UBLAS_INLINE
        real_type imag (const_reference t) {
                return std::imag (t);
        }
        static
        BOOST_UBLAS_INLINE
        value_type conj (const_reference t) {
                return std::conj (t);
        }

        static
        BOOST_UBLAS_INLINE
        real_type abs (const_reference t) {
                return std::abs (t);
        }
        static
        BOOST_UBLAS_INLINE
        value_type sqrt (const_reference t) {
                return std::sqrt (t);
        }

        static
        BOOST_UBLAS_INLINE
        real_type norm_1 (const_reference t) {
            return type_traits<real_type>::abs (self_type::real (t)) +
                   type_traits<real_type>::abs (self_type::imag (t));
        }
        static
        BOOST_UBLAS_INLINE
        real_type norm_2 (const_reference t) {
            return self_type::abs (t);
        }
        static
        BOOST_UBLAS_INLINE
        real_type norm_inf (const_reference t) {
            return (std::max) (type_traits<real_type>::abs (self_type::real (t)),
                             type_traits<real_type>::abs (self_type::imag (t)));
        }

        static
        BOOST_UBLAS_INLINE
        bool equals (const_reference t1, const_reference t2) {
            return self_type::norm_inf (t1 - t2) < BOOST_UBLAS_TYPE_CHECK_EPSILON *
                   (std::max) ((std::max) (self_type::norm_inf (t1),
                                       self_type::norm_inf (t2)),
                             BOOST_UBLAS_TYPE_CHECK_MIN);
        }
    };
#ifndef BOOST_UBLAS_NO_LONG_DOUBLE
    template<>
    struct type_traits<std::complex<long double> > {
        typedef type_traits<std::complex<long double> > self_type;
        typedef std::complex<long double> value_type;
        typedef const value_type &const_reference;
        typedef value_type &reference;
        typedef long double real_type;
        typedef value_type precision_type;

        BOOST_STATIC_CONSTANT (unsigned, plus_complexity = 2);
        BOOST_STATIC_CONSTANT (unsigned, multiplies_complexity = 6);

        static
        BOOST_UBLAS_INLINE
        real_type real (const_reference t) {
                return std::real (t);
        }
        static
        BOOST_UBLAS_INLINE
        real_type imag (const_reference t) {
                return std::imag (t);
        }
        static
        BOOST_UBLAS_INLINE
        value_type conj (const_reference t) {
                return std::conj (t);
        }

        static
        BOOST_UBLAS_INLINE
        real_type abs (const_reference t) {
                return std::abs (t);
        }
        static
        BOOST_UBLAS_INLINE
        value_type sqrt (const_reference t) {
                return std::sqrt (t);
        }

        static
        BOOST_UBLAS_INLINE
        real_type norm_1 (const_reference t) {
            return type_traits<real_type>::abs (self_type::real (t)) +
                   type_traits<real_type>::abs (self_type::imag (t));
        }
        static
        BOOST_UBLAS_INLINE
        real_type norm_2 (const_reference t) {
            return self_type::abs (t);
        }
        static
        BOOST_UBLAS_INLINE
        real_type norm_inf (const_reference t) {
            return (std::max) (type_traits<real_type>::abs (self_type::real (t)),
                             type_traits<real_type>::abs (self_type::imag (t)));
        }

        static
        BOOST_UBLAS_INLINE
        bool equals (const_reference t1, const_reference t2) {
            return self_type::norm_inf (t1 - t2) < BOOST_UBLAS_TYPE_CHECK_EPSILON *
                   (std::max) ((std::max) (self_type::norm_inf (t1),
                                       self_type::norm_inf (t2)),
                             BOOST_UBLAS_TYPE_CHECK_MIN);
        }
    };
#endif

#ifdef BOOST_UBLAS_USE_INTERVAL
    template<>
    struct type_traits<boost::numeric::interval<float> > {
        typedef type_traits<boost::numeric::interval<float> > self_type;
        typedef boost::numeric::interval<float> value_type;
        typedef const value_type &const_reference;
        typedef value_type &reference;
        typedef value_type real_type;
        typedef boost::numeric::interval<double> precision_type;

        BOOST_STATIC_CONSTANT (unsigned, plus_complexity = 1);
        BOOST_STATIC_CONSTANT (unsigned, multiplies_complexity = 1);

        static
        BOOST_UBLAS_INLINE
        real_type real (const_reference t) {
                return t;
        }
        static
        BOOST_UBLAS_INLINE
        real_type imag (const_reference t) {
                return 0;
        }
        static
        BOOST_UBLAS_INLINE
        value_type conj (const_reference t) {
                return t;
        }

        static
        BOOST_UBLAS_INLINE
        real_type abs (const_reference t) {
            return boost::numeric::abs (t);
        }
        static
        BOOST_UBLAS_INLINE
        value_type sqrt (const_reference t) {
            return boost::numeric::sqrt (t);
        }

        static
        BOOST_UBLAS_INLINE
        real_type norm_1 (const_reference t) {
            return self_type::abs (t);
        }
        static
        BOOST_UBLAS_INLINE
        real_type norm_2 (const_reference t) {
            return self_type::abs (t);
        }
        static
        BOOST_UBLAS_INLINE
        real_type norm_inf (const_reference t) {
            return self_type::abs (t);
        }

        static
        BOOST_UBLAS_INLINE
        bool equals (const_reference t1, const_reference t2) {
            return self_type::norm_inf (t1 - t2) < BOOST_UBLAS_TYPE_CHECK_EPSILON *
                   (std::max) ((std::max) (self_type::norm_inf (t1),
                                       self_type::norm_inf (t2)),
                             BOOST_UBLAS_TYPE_CHECK_MIN);
        }
    };
    template<>
    struct type_traits<boost::numeric::interval<double> > {
        typedef type_traits<boost::numeric::interval<double> > self_type;
        typedef boost::numeric::interval<double> value_type;
        typedef const value_type &const_reference;
        typedef value_type &reference;
        typedef value_type real_type;
#ifndef BOOST_UBLAS_NO_LONG_DOUBLE
        typedef boost::numeric::interval<long double> precision_type;
#else
        typedef value_type precision_type;
#endif

        BOOST_STATIC_CONSTANT (unsigned, plus_complexity = 1);
        BOOST_STATIC_CONSTANT (unsigned, multiplies_complexity = 1);

        static
        BOOST_UBLAS_INLINE
        real_type real (const_reference t) {
                return t;
        }
        static
        BOOST_UBLAS_INLINE
        real_type imag (const_reference t) {
                return 0;
        }
        static
        BOOST_UBLAS_INLINE
        value_type conj (const_reference t) {
                return t;
        }

        static
        BOOST_UBLAS_INLINE
        real_type abs (const_reference t) {
            return boost::numeric::abs (t);
        }
        static
        BOOST_UBLAS_INLINE
        value_type sqrt (const_reference t) {
            return boost::numeric::sqrt (t);
        }

        static
        BOOST_UBLAS_INLINE
        real_type norm_1 (const_reference t) {
            return self_type::abs (t);
        }
        static
        BOOST_UBLAS_INLINE
        real_type norm_2 (const_reference t) {
            return self_type::abs (t);
        }
        static
        BOOST_UBLAS_INLINE
        real_type norm_inf (const_reference t) {
            return self_type::abs (t);
        }

        static
        BOOST_UBLAS_INLINE
        bool equals (const_reference t1, const_reference t2) {
            return self_type::norm_inf (t1 - t2) < BOOST_UBLAS_TYPE_CHECK_EPSILON *
                   (std::max) ((std::max) (self_type::norm_inf (t1),
                                       self_type::norm_inf (t2)),
                             BOOST_UBLAS_TYPE_CHECK_MIN);
        }
    };
#ifndef BOOST_UBLAS_NO_LONG_DOUBLE
    template<>
    struct type_traits<boost::numeric::interval<long double> > {
        typedef type_traits<boost::numeric::interval<long double> > self_type;
        typedef boost::numeric::interval<long double> value_type;
        typedef const value_type &const_reference;
        typedef value_type &reference;
        typedef value_type real_type;
        typedef value_type precision_type;

        BOOST_STATIC_CONSTANT (unsigned, plus_complexity = 1);
        BOOST_STATIC_CONSTANT (unsigned, multiplies_complexity = 1);

        static
        BOOST_UBLAS_INLINE
        real_type real (const_reference t) {
                return t;
        }
        static
        BOOST_UBLAS_INLINE
        real_type imag (const_reference t) {
                return 0;
        }
        static
        BOOST_UBLAS_INLINE
        value_type conj (const_reference t) {
                return t;
        }

        static
        BOOST_UBLAS_INLINE
        real_type abs (const_reference t) {
            return boost::numeric::abs (t);
        }
        static
        BOOST_UBLAS_INLINE
        value_type sqrt (const_reference t) {
            return boost::numeric::sqrt (t);
        }

        static
        BOOST_UBLAS_INLINE
        real_type norm_1 (const_reference t) {
            return self_type::abs (t);
        }
        static
        BOOST_UBLAS_INLINE
        real_type norm_2 (const_reference t) {
            return self_type::abs (t);
        }
        static
        BOOST_UBLAS_INLINE
        real_type norm_inf (const_reference t) {
            return self_type::abs (t);
        }

        static
        BOOST_UBLAS_INLINE
        bool equals (const_reference t1, const_reference t2) {
            return self_type::norm_inf (t1 - t2) < BOOST_UBLAS_TYPE_CHECK_EPSILON *
                   (std::max) ((std::max) (self_type::norm_inf (t1),
                                       self_type::norm_inf (t2)),
                             BOOST_UBLAS_TYPE_CHECK_MIN);
        }
    };
#endif

#ifdef BOOST_UBLAS_USE_BOOST_COMPLEX
    template<>
    struct type_traits<boost::complex<boost::numeric::interval<float> > > {
        typedef type_traits<boost::complex<boost::numeric::interval<float> > > self_type;
        typedef boost::complex<boost::numeric::interval<float> > value_type;
        typedef const value_type &const_reference;
        typedef value_type &reference;
        typedef boost::numeric::interval<float> real_type;
        typedef boost::complex<boost::numeric::interval<double> > precision_type;

        BOOST_STATIC_CONSTANT (unsigned, plus_complexity = 2);
        BOOST_STATIC_CONSTANT (unsigned, multiplies_complexity = 6);