hermitian.hpp

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//
//  Copyright (c) 2000-2002
//  Joerg Walter, Mathias Koch
//
//  Permission to use, copy, modify, distribute and sell this software
//  and its documentation for any purpose is hereby granted without fee,
//  provided that the above copyright notice appear in all copies and
//  that both that copyright notice and this permission notice appear
//  in supporting documentation.  The authors make no representations
//  about the suitability of this software for any purpose.
//  It is provided "as is" without express or implied warranty.
//
//  The authors gratefully acknowledge the support of
//  GeNeSys mbH & Co. KG in producing this work.
//

#ifndef BOOST_UBLAS_HERMITIAN_H
#define BOOST_UBLAS_HERMITIAN_H

#include <boost/numeric/ublas/config.hpp>
#include <boost/numeric/ublas/storage.hpp>
#include <boost/numeric/ublas/matrix.hpp>

// Iterators based on ideas of Jeremy Siek
// Hermitian matrices are square. Thanks to Peter Schmitteckert for spotting this.

namespace boost { namespace numeric { namespace ublas {

    template<class M>
    bool is_hermitian (const M &m) {
        typedef typename M::size_type size_type;

        if (m.size1 () != m.size2 ())
            return false;
        size_type size = BOOST_UBLAS_SAME (m.size1 (), m.size2 ());
        for (size_type i = 0; i < size; ++ i) {
            for (size_type j = i; j < size; ++ j) {
                if (m (i, j) != conj (m (j, i)))
                    return false;
            }
        }
        return true;
    }

#ifdef BOOST_UBLAS_STRICT_HERMITIAN

    template<class M>
    class hermitian_matrix_element:
       public container_reference<M> {
    public:
        typedef M matrix_type;
        typedef typename M::size_type size_type;
        typedef typename M::value_type value_type;
        typedef const value_type &const_reference;
        typedef value_type &reference;
        typedef value_type *pointer;

        // Construction and destruction
        BOOST_UBLAS_INLINE
        hermitian_matrix_element (matrix_type &m, size_type i, size_type j, value_type d):
            container_reference<matrix_type> (m), i_ (i), j_ (j), d_ (d), dirty_ (false) {}
        BOOST_UBLAS_INLINE
        hermitian_matrix_element (const hermitian_matrix_element &p):
            container_reference<matrix_type> (p), i_ (p.i_), d_ (p.d_), dirty_ (p.dirty_) {}
        BOOST_UBLAS_INLINE
        ~hermitian_matrix_element () {
            if (dirty_)
                ((*this) ()).at (i_, j_, d_);
        }

        // Assignment
        BOOST_UBLAS_INLINE
        hermitian_matrix_element &operator = (const hermitian_matrix_element &p) {
            // Overide the implict copy assignment
            d_ = p.d_;
            dirty_ = true;
            return *this;
        }
        template<class D>
        BOOST_UBLAS_INLINE
        hermitian_matrix_element &operator = (const D &d) {
            d_ = d;
            dirty_ = true;
            return *this;
        }
        template<class D>
        BOOST_UBLAS_INLINE
        hermitian_matrix_element &operator += (const D &d) {
            d_ += d;
            dirty_ = true;
            return *this;
        }
        template<class D>
        BOOST_UBLAS_INLINE
        hermitian_matrix_element &operator -= (const D &d) {
            d_ -= d;
            dirty_ = true;
            return *this;
        }
        template<class D>
        BOOST_UBLAS_INLINE
        hermitian_matrix_element &operator *= (const D &d) {
            d_ *= d;
            dirty_ = true;
            return *this;
        }
        template<class D>
        BOOST_UBLAS_INLINE
        hermitian_matrix_element &operator /= (const D &d) {
            d_ /= d;
            dirty_ = true;
            return *this;
        }
        
        // Comparison
        template<class D>
        BOOST_UBLAS_INLINE
        bool operator == (const D &d) const {
            return d_ == d;
        }
        template<class D>
        BOOST_UBLAS_INLINE
        bool operator != (const D &d) const {
            return d_ != d;
        }

        // Conversion
        BOOST_UBLAS_INLINE
        operator const_reference () const {
            return d_;
        }

        // Swapping
        BOOST_UBLAS_INLINE
        void swap (hermitian_matrix_element p) {
            if (this != &p) {
                dirty_ = true;
                p.dirty_ = true;
                std::swap (d_, p.d_);
            }
        }
#ifndef BOOST_UBLAS_NO_MEMBER_FRIENDS
        BOOST_UBLAS_INLINE
        friend void swap (hermitian_matrix_element p1, hermitian_matrix_element p2) {
            p1.swap (p2);
        }
#endif

    private:
        size_type i_;
        size_type j_;
        value_type d_;
        bool dirty_;
    };

    template<class M>
    struct type_traits<hermitian_matrix_element<M> > {
        typedef typename M::value_type element_type;
        typedef type_traits<hermitian_matrix_element<M> > self_type;
        typedef typename type_traits<element_type>::value_type value_type;
        typedef typename type_traits<element_type>::const_reference const_reference;
        typedef hermitian_matrix_element<M> reference;
        typedef typename type_traits<element_type>::real_type real_type;
        typedef typename type_traits<element_type>::precision_type precision_type;

        BOOST_STATIC_CONSTANT (unsigned, plus_complexity = type_traits<element_type>::plus_complexity);
        BOOST_STATIC_CONSTANT (unsigned, multiplies_complexity = type_traits<element_type>::multiplies_complexity);

        static
        BOOST_UBLAS_INLINE
        real_type real (const_reference t) {
            return type_traits<element_type>::real (t);
        }
        static
        BOOST_UBLAS_INLINE
        real_type imag (const_reference t) {
            return type_traits<element_type>::imag (t);
        }
        static
        BOOST_UBLAS_INLINE
        value_type conj (const_reference t) {
            return type_traits<element_type>::conj (t);
        }

        static
        BOOST_UBLAS_INLINE
        real_type abs (const_reference t) {
            return type_traits<element_type>::abs (t);
        }
        static
        BOOST_UBLAS_INLINE
        value_type sqrt (const_reference t) {
            return type_traits<element_type>::sqrt (t);
        }

        static
        BOOST_UBLAS_INLINE
        real_type norm_1 (const_reference t) {
            return type_traits<element_type>::norm_1 (t);
        }
        static
        BOOST_UBLAS_INLINE
        real_type norm_2 (const_reference t) {
            return type_traits<element_type>::norm_2 (t);
        }
        static
        BOOST_UBLAS_INLINE
        real_type norm_inf (const_reference t) {
            return type_traits<element_type>::norm_inf (t);
        }

        static
        BOOST_UBLAS_INLINE
        bool equals (const_reference t1, const_reference t2) {
            return type_traits<element_type>::equals (t1, t2);
        }
    };

    template<class M1, class T2>
    struct promote_traits<hermitian_matrix_element<M1>, T2> {
        typedef typename promote_traits<typename hermitian_matrix_element<M1>::value_type, T2>::promote_type promote_type;
    };
    template<class T1, class M2>
    struct promote_traits<T1, hermitian_matrix_element<M2> > {
        typedef typename promote_traits<T1, typename hermitian_matrix_element<M2>::value_type>::promote_type promote_type;
    };
    template<class M1, class M2>
    struct promote_traits<hermitian_matrix_element<M1>, hermitian_matrix_element<M2> > {
        typedef typename promote_traits<typename hermitian_matrix_element<M1>::value_type,
                                        typename hermitian_matrix_element<M2>::value_type>::promote_type promote_type;
    };

#endif

    // Array based hermitian matrix class
    template<class T, class F1, class F2, class A>
    class hermitian_matrix:
        public matrix_expression<hermitian_matrix<T, F1, F2, A> > {
    public:
#ifndef BOOST_UBLAS_NO_PROXY_SHORTCUTS
        BOOST_UBLAS_USING matrix_expression<hermitian_matrix<T, F1, F2, A> >::operator ();
#endif
        typedef typename A::size_type size_type;
        typedef typename A::difference_type difference_type;
        typedef T value_type;
        // FIXME: no better way to not return the address of a temporary?
        // typedef const T &const_reference;
        typedef const T const_reference;
#ifndef BOOST_UBLAS_STRICT_HERMITIAN
        typedef T &reference;
#else
        typedef hermitian_matrix_element<hermitian_matrix<T, F1, F2, A> > reference;
#endif
        typedef A array_type;
    private:
        typedef T &true_reference;
        typedef T *pointer;
        typedef F1 functor1_type;
        typedef F2 functor2_type;
        typedef hermitian_matrix<T, F1, F2, A> self_type;
    public:
#ifndef BOOST_UBLAS_CT_REFERENCE_BASE_TYPEDEFS
        typedef const matrix_const_reference<const self_type> const_closure_type;
#else
        typedef const matrix_reference<const self_type> const_closure_type;
#endif
        typedef matrix_reference<self_type> closure_type;
        typedef vector<T, A> vector_temporary_type;
        typedef matrix<T, F2, A> matrix_temporary_type;  // general sub-matrix
        typedef packed_tag storage_category;
        typedef typename F1::packed_category packed_category;
        typedef typename F2::orientation_category orientation_category;

        // Construction and destruction
        BOOST_UBLAS_INLINE
        hermitian_matrix ():
            matrix_expression<self_type> (),
            size_ (0), data_ (0) {}
        BOOST_UBLAS_INLINE
        hermitian_matrix (size_type size):
            matrix_expression<self_type> (),
            size_ (BOOST_UBLAS_SAME (size, size)), data_ (functor1_type::packed_size (size, size)) {
        }
        BOOST_UBLAS_INLINE
        hermitian_matrix (size_type size1, size_type size2):
            matrix_expression<self_type> (),
            size_ (BOOST_UBLAS_SAME (size1, size2)), data_ (functor1_type::packed_size (size1, size2)) {
        }
        BOOST_UBLAS_INLINE
        hermitian_matrix (size_type size, const array_type &data):
            matrix_expression<self_type> (),
            size_ (size), data_ (data) {}
        BOOST_UBLAS_INLINE
        hermitian_matrix (const hermitian_matrix &m):
            matrix_expression<self_type> (),
            size_ (m.size_), data_ (m.data_) {}
        template<class AE>
        BOOST_UBLAS_INLINE
        hermitian_matrix (const matrix_expression<AE> &ae):
            matrix_expression<self_type> (),
            size_ (BOOST_UBLAS_SAME (ae ().size1 (), ae ().size2 ())),
            data_ (functor1_type::packed_size (size_, size_)) {
            matrix_assign (scalar_assign<true_reference, BOOST_UBLAS_TYPENAME AE::value_type> (), *this, ae);
        }

        // Accessors
        BOOST_UBLAS_INLINE
        size_type size1 () const {
            return size_;
        }
        BOOST_UBLAS_INLINE
        size_type size2 () const {
            return size_;
        }
        BOOST_UBLAS_INLINE
        const array_type &data () const {
            return data_;
        }
        BOOST_UBLAS_INLINE
        array_type &data () {
            return data_;
        }

        // Resizing
        BOOST_UBLAS_INLINE
        void resize (size_type size, bool preserve = true) {
            size_ = size;
            if (preserve) {
                self_type temporary (size_, size_);