dft_tools/triqs/gfs/local/tail.hpp

/*******************************************************************************
 *
 * TRIQS: a Toolbox for Research in Interacting Quantum Systems
 *
 * Copyright (C) 2012 by M. Ferrero, O. Parcollet
 *
 * TRIQS is free software: you can redistribute it and/or modify it under the
 * terms of the GNU General Public License as published by the Free Software
 * Foundation, either version 3 of the License, or (at your option) any later
 * version.
 *
 * TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
 * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
 * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
 * details.
 *
 * You should have received a copy of the GNU General Public License along with
 * TRIQS. If not, see <http://www.gnu.org/licenses/>.
 *
 ******************************************************************************/
#ifndef TRIQS_GF_LOCAL_TAIL_H
#define TRIQS_GF_LOCAL_TAIL_H
#include <triqs/arrays.hpp>
#include <triqs/arrays/algorithms.hpp>
#include <triqs/gfs/tools.hpp>
#include <triqs/python_tools/cython_proxy.hpp>

namespace triqs { namespace gfs { namespace local {

  namespace details {
    static constexpr double small = 1.e-10;
  }

  namespace tqa= triqs::arrays; namespace tql= triqs::clef;  namespace mpl= boost::mpl;
  typedef std::complex<double> dcomplex;

  class tail;                            // the value class
  class tail_view;                       // the view class

  template<typename G> struct LocalTail  : mpl::false_{};  // a boolean trait to identify the objects modelling the concept LocalTail
  template<> struct LocalTail<tail >     : mpl::true_{};
  template<> struct LocalTail<tail_view >: mpl::true_{};
  template<> struct LocalTail<python_tools::cython_proxy<tail_view>>: mpl::true_{};

  // a trait to find the scalar of the algebra i.e. the true scalar and the matrix ...
  template <typename T> struct is_scalar_or_element : mpl::or_< tqa::ImmutableMatrix<T>, utility::is_in_ZRC<T> > {};

  // ---------------------- implementation --------------------------------

  /// A common implementation class. Idiom: ValueView
  template<bool IsView> class tail_impl  {
    public:
      typedef tail_view view_type;
      typedef tail      regular_type;

      typedef arrays::array      <dcomplex,3>                         data_regular_type;
      typedef arrays::array_view <dcomplex,3>                         data_view_type;
      typedef typename mpl::if_c<IsView, data_view_type, data_regular_type>::type  data_type;

      typedef arrays::array<long,2>                                   mask_regular_type;
      typedef arrays::array_view<long,2>                              mask_view_type;
      typedef typename mpl::if_c<IsView, mask_view_type, mask_regular_type>::type  mask_type;

      typedef arrays::matrix_view<dcomplex>  mv_type;
      typedef arrays::matrix_view<dcomplex>  const_mv_type;

      data_view_type data()             { return _data;}
      const data_view_type data() const { return _data;}
      mask_view_type mask_view()             { return mask;}
      const mask_view_type mask_view() const { return mask;}

      long order_min() const {return omin;}
      long order_max() const {return min_element(mask);}
      size_t size() const {return _data.shape()[0];}
      long smallest_nonzero() const {
        long om = omin;
        while ((om < this->order_max()) && (max_element(abs(_data(om-omin,tqa::range(),tqa::range()))) < details::small)) om++;
        return om;
      }

      typedef tqa::mini_vector<size_t,2> shape_type;
      shape_type shape() const { return shape_type(_data.shape()[1], _data.shape()[2]);}
      size_t shape(int i) const { return _data.shape()[i];}

      bool is_decreasing_at_infinity() const { return (smallest_nonzero() >=1);}

    protected:

      long omin;
      mask_type mask;
      data_type _data;

      // All constructors
      tail_impl(): omin(0), mask(), _data() {} // all arrays of zero size (empty)
      tail_impl(size_t N1, size_t N2, size_t size_, long order_min):
        omin(order_min), mask(tqa::make_shape(N1,N2)), _data(tqa::make_shape(size_,N1,N2)) {
          mask() = order_min+size_-1;
          _data() = 0;
      }
      tail_impl(data_type const &d, mask_type const &m, long omin_): mask(m), _data(d), omin(omin_) {}
      tail_impl(tail_impl<!IsView> const & x): omin(x.omin), mask(x.mask), _data(x._data) {}
      tail_impl(tail_impl const &) = default;
      tail_impl(tail_impl &&) = default;

      friend class tail_impl<!IsView>;

    public:

      mv_type operator() (int n) {
        if (n>this->order_max()) TRIQS_RUNTIME_ERROR<<" n > Max Order. n= "<<n <<", Max Order = "<<order_max() ;
        if (n<this->order_min()) TRIQS_RUNTIME_ERROR<<" n < Min Order. n= "<<n <<", Min Order = "<<order_min() ;
        return this->_data(n-omin, tqa::range(), tqa::range());
      }

      const_mv_type operator() (int n) const {
        if (n>this->order_max()) TRIQS_RUNTIME_ERROR<<" n > Max Order. n= "<<n <<", Max Order = "<<order_max() ;
        if (n<this->order_min())  { mv_type::regular_type r(this->shape()); r()=0; return r;}
        return this->_data(n-omin, tqa::range(), tqa::range());
      }

      /// same as (), but if n is too large, then returns 0 instead of raising an exception
      const_mv_type get_or_zero (int n) const {
        if ( (n>this->order_max()) || (n<this->order_min()) ) { mv_type::regular_type r(this->shape()); r()=0; return r; }
        return this->_data(n-omin, tqa::range(), tqa::range());
      }

      operator freq_infty() const { return freq_infty(); }

      /// Evaluate the tail to  sum_{n=order_min}^ordermax M_n/omega^n 
      arrays::matrix<dcomplex> evaluate(dcomplex const &omega) const {
       auto r = arrays::matrix<dcomplex>{this->shape()};
       r() = 0;
       auto omin = this->order_min();
       auto omax = this->order_max(); // precompute since long to do...
       auto _ = arrays::range{};
       for (int u = omax; u >= omin; --u)
        r = r / omega +
            const_mv_type{this->_data(u - omin, _, _)}; // need to make a matrix view because otherwise + is not defined
       r /= pow(omega, omin);
       return r;
      }

      /// Save in txt file: doc the format  ? ---> prefer serialization or hdf5 !
      void save(std::string file, bool accumulate=false) const {}

      /// Load from txt file: doc the format ?
      //void load(std::string file){}

      friend std::string get_triqs_hdf5_data_scheme(tail_impl const & g) { return "TailGf"; }

      ///
      friend void h5_write (h5::group fg, std::string subgroup_name, tail_impl const & t) {
        auto  gr = fg.create_group(subgroup_name);
        h5_write(gr,"omin",t.omin);
        h5_write(gr,"mask",t.mask);
        h5_write(gr,"data",t._data);
      }

      friend void h5_read  (h5::group fg, std::string subgroup_name, tail_impl & t){
        auto gr = fg.open_group(subgroup_name);
        h5_read(gr,"omin",t.omin);
        h5_read(gr,"mask",t.mask);
        h5_read(gr,"data",t._data);
      }

      //  BOOST Serialization
      friend class boost::serialization::access;
      template<class Archive>
        void serialize(Archive & ar, const unsigned int version) {
          ar & boost::serialization::make_nvp("omin",omin);
          ar & boost::serialization::make_nvp("mask",mask);
          ar & boost::serialization::make_nvp("data",_data);
        }

      friend std::ostream & operator << (std::ostream & out, tail_impl const & x) {
        out <<"tail/tail_view: min/smallest/max = "<< x.order_min() << " " << x.smallest_nonzero() << " "<< x.order_max();
        for (long u = x.order_min(); u <= x.order_max(); ++u) out <<"\n ...  Order "<<u << " = " << x(u);
        return out;
      }

  };

  // -----------------------------
  // the view class
  class tail_view: public tail_impl <true> {
    typedef tail_impl <true>  B;
    friend class tail;

    public:
    template<bool V> tail_view(tail_impl<V> const & t): B(t){}
    tail_view(B::data_type const &d, B::mask_type const &m, long order_min): B(d, m, order_min) {}
    tail_view(tail_view const &) = default;
    tail_view(tail_view &&) = default;

    void rebind(tail_view const &X) {
      omin = X.omin;
      mask.rebind(X.mask);
      _data.rebind(X._data);
    }
    inline void rebind(tail const &X);

    // operator = for views
    tail_view & operator = (const tail_view & rhs) {
      if ((_data.shape()[1] != rhs._data.shape()[1]) || (_data.shape()[2] != rhs._data.shape()[2]) || (omin != rhs.omin))
        TRIQS_RUNTIME_ERROR<<"tails are incompatible";
      mask = rhs.mask;
      _data = rhs._data;
      return *this;
    }
    inline tail_view & operator=(const tail & rhs);

    tail_view & operator = (std::complex<double> const & x) {
      _data() = 0.0;
      mv_type(_data(-omin, tqa::range(), tqa::range())) = x;
      mask() = omin+size()-1;
      return *this;
    }

    using B::operator(); // import all previously defined operator() for overloading
    friend std::ostream & triqs_nvl_formal_print(std::ostream & out, tail_view const & x) { return out<<"tail_view"; }

  };

  // -----------------------------
  // the regular class
  class tail: public tail_impl <false> {
    typedef tail_impl <false>  B;
    friend class tail_view;
    public:
    tail():B() {}
    typedef tqa::mini_vector<size_t,2> shape_type;
    tail(size_t N1, size_t N2, size_t size_=10, long order_min=-1): B(N1,N2,size_,order_min) {}
    tail(shape_type const & sh, size_t size_=10, long order_min=-1): B(sh[0],sh[1],size_,order_min) {}
    tail(tail const & g): B(g) {}
    tail(tail_view const & g): B(g) {}
    tail(tail &&) = default;

    // operator = for values
    tail & operator = (tail_view const & rhs) {
      omin = rhs.omin;
      mask = rhs.mask;
      _data = rhs._data;
      return *this;
    }
    tail & operator = (tail const & rhs) {
      omin = rhs.omin;
      mask = rhs.mask;
      _data = rhs._data;
      return *this;
    }

    using B::operator();

    /// The simplest tail corresponding to omega
    static tail_view omega(size_t N1, size_t N2, size_t size_, long order_min) {
      tail t(N1, N2, size_, order_min);
      t(-1) = 1;
      return t;
    }

    /// The simplest tail corresponding to omega, constructed from a shape for convenience
    static tail_view omega(tail::shape_type const & sh, size_t size_, long order_min) { return omega(sh[0],sh[1],size_,order_min); }

  };

  template<typename RHS> void assign_from_expression(tail_view t,RHS const & rhs) { t = rhs( tail::omega(t.shape(),t.size(),t.order_min()) ); }

  inline void tail_view::rebind(tail const &X) {
    omin = X.omin;
    mask.rebind(X.mask);
    _data.rebind(X._data);
  }

  inline tail_view & tail_view::operator = (const tail & rhs) {
    if ((_data.shape()[1] != rhs._data.shape()[1]) || (_data.shape()[2] != rhs._data.shape()[2]) || (omin != rhs.omin))
      TRIQS_RUNTIME_ERROR<<"tails are incompatible";
    mask = rhs.mask;
    _data = rhs._data;
    return *this;
  }

  /// Slice in orbital space
  //template<bool V> tail_view slice_target(tail_impl<V> const & t, tqa::range R1, tqa::range R2) {
  inline tail_view slice_target(tail_view t, tqa::range R1, tqa::range R2) {
    return tail_view(t.data()(tqa::range(),R1,R2), t.mask_view()(R1,R2), t.order_min());
  }

  inline tail inverse(tail_view const & t) {
    long omin1 = - t.smallest_nonzero();
    long omax1 = std::min(t.order_max() + 2*omin1, t.order_min()+long(t.size())-1);
    size_t si = omax1-omin1+1;

    tail res(t.shape(), t.size(), t.order_min());
    res.mask_view() = omax1;

    res(omin1) = inverse(t(-omin1));

    for (size_t n=1; n<si; n++) {
      for (size_t p=0; p<n; p++) {
        res(omin1 + n) -= t(n-omin1-p) * res(omin1+p);
      }
      res(omin1 + n) = res(omin1) * make_clone(res(omin1 + n));
    }
    return res;
  }
  
  inline tail inverse(tail const & t) { return inverse(tail_view(t));}

  inline tail mult_impl(tail_view const & l, tail_view const& r) {
    if (l.shape()[1] != r.shape()[0] || l.order_min() != r.order_min() || l.size() != r.size())
      TRIQS_RUNTIME_ERROR<< "tail multiplication: shape mismatch";
    long omin1 = l.smallest_nonzero() + r.smallest_nonzero();
    long omax1 = std::min(std::min(r.order_max()+l.smallest_nonzero(), l.order_max()+r.smallest_nonzero()), r.order_min()+long(r.size())-1);
    size_t si = omax1-omin1+1;

    tail res(l.shape(), l.size(), l.order_min());
    res.mask_view() = omax1;

    for (long n=res.order_min(); n<=res.order_max(); ++n) {
      // sum_{p}^n a_p b_{n-p}. p <= a.n_max, p >= a.n_min and n-p <=b.n_max and n-p >= b.n_min
      // hence p <= min ( a.n_max, n-b.n_min ) and p >= max ( a.n_min, n- b.n_max)
      const long pmin = std::max(l.smallest_nonzero(), n - r.order_max() );
      const long pmax = std::min(l.order_max(), n - r.smallest_nonzero() );
      for (long p = pmin; p <= pmax; ++p)  { res(n) += l(p) * r(n-p);}
    }
    return res;
  }

  template<typename T1, typename T2>
    TYPE_ENABLE_IF(tail,mpl::and_<LocalTail<T1>, LocalTail<T2>>)
    operator* (T1 const & a, T2 const & b) { return mult_impl(a,b); }

  template<typename T1, typename T2> TYPE_ENABLE_IF(tail,mpl::and_<tqa::ImmutableMatrix<T1>, LocalTail<T2>>)
    operator* (T1 const & a, T2 const & b) {
      tail res(b); for (long n=res.order_min(); n<=res.order_max(); ++n) res(n)=a*res(n); return res;
    }

  template<typename T1, typename T2> TYPE_ENABLE_IF(tail,mpl::and_<LocalTail<T1>, tqa::ImmutableMatrix<T2>>)
    operator* (T1 const & a, T2 const & b) {
      tail res(a); for (long n=res.order_min(); n<=res.order_max(); ++n) res(n)=res(n)*b; return res;
    }

  inline tail operator * (dcomplex a, tail_view const & r) { tail res(r); res.data()*=a; return res;}
  inline tail operator * (tail_view const & r, dcomplex a) { return a*r; }

  template<typename T1, typename T2> TYPE_ENABLE_IF(tail,mpl::and_<LocalTail<T1>, LocalTail<T2>>)
    operator/ (T1 const & a, T2 const & b) { return a * inverse(b); }

  inline tail operator / (tail_view const & r, dcomplex a) { tail res(r); res.data() /=a; return res;}
  inline tail operator / (dcomplex a, tail_view const & r) { return a * inverse(r); }

  template<typename T1, typename T2> TYPE_ENABLE_IF(tail,mpl::and_<LocalTail<T1>, LocalTail<T2>>)
    operator + (T1 const & l, T2 const& r) {
      if (l.shape() != r.shape() || l.order_min() != r.order_min() || (l.size() != r.size()))
        TRIQS_RUNTIME_ERROR<< "tail addition: shape mismatch";
      tail res(l.shape(), l.size(), l.order_min());
      res.mask_view() = std::min(l.order_max(), r.order_max());
      for (long i = res.order_min(); i<=res.order_max(); ++i) res(i) = l(i) + r(i);
      return res;
    }

  template<typename T1, typename T2> TYPE_ENABLE_IF(tail,mpl::and_<LocalTail<T1>, LocalTail<T2>>)
    operator - (T1 const & l, T2 const& r) {
      if (l.shape() != r.shape() || l.order_min() != r.order_min() || (l.size() != r.size()))
        TRIQS_RUNTIME_ERROR<< "tail addition: shape mismatch";
      tail res(l.shape(), l.size(), l.order_min());
      res.mask_view() = std::min(l.order_max(), r.order_max());
      for (long i = res.order_min(); i<=res.order_max(); ++i) res(i) = l(i) - r(i);
      return res;
    }

  template<typename T1, typename T2> TYPE_ENABLE_IF(tail,mpl::and_<is_scalar_or_element<T1>, LocalTail<T2>>)
    operator + (T1 const & a, T2 const & t) {
      tail res(t);
      res(0) += a;
      return res;
    }

  template<typename T1, typename T2> TYPE_ENABLE_IF(tail,mpl::and_<LocalTail<T1>, is_scalar_or_element<T2>>)
    operator + (T1 const & t, T2 const & a) { return a+t;}

  template<typename T1, typename T2> TYPE_ENABLE_IF(tail,mpl::and_<is_scalar_or_element<T1>, LocalTail<T2>>)
    operator - (T1 const & a, T2 const & t) { return (-a) + t;}

  template<typename T1, typename T2> TYPE_ENABLE_IF(tail,mpl::and_<LocalTail<T1>, is_scalar_or_element<T2>>)
    operator - (T1 const & t, T2 const & a) { return (-a) + t;}

}}}
#endif