mirror of
https://github.com/triqs/dft_tools
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346 lines
12 KiB
C++
346 lines
12 KiB
C++
/*******************************************************************************
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*
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* TRIQS: a Toolbox for Research in Interacting Quantum Systems
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*
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* Copyright (C) 2014 by I. Krivenko, O. Parcollet, M. Ferrero
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*
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* TRIQS is free software: you can redistribute it and/or modify it under the
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* terms of the GNU General Public License as published by the Free Software
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* Foundation, either version 3 of the License, or (at your option) any later
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* version.
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*
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* TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
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* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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* FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
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* details.
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*
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* You should have received a copy of the GNU General Public License along with
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* TRIQS. If not, see <http://www.gnu.org/licenses/>.
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*
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******************************************************************************/
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#pragma once
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#include <triqs/utility/dressed_iterator.hpp>
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#include <ostream>
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#include <limits>
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#include <cmath>
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#include <complex>
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#include <boost/variant.hpp>
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#include <boost/operators.hpp>
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#include <boost/serialization/vector.hpp>
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#include <boost/serialization/map.hpp>
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#include <boost/serialization/variant.hpp>
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namespace triqs {
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namespace utility {
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/**
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* many_body_operator is a general operator in second quantification
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*/
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template <typename scalar_t>
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class many_body_operator :
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// implements vector space over scalar_t operators
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boost::additive<many_body_operator<scalar_t>>,
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boost::multipliable<many_body_operator<scalar_t>>,
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boost::additive<many_body_operator<scalar_t>, scalar_t>, // op+a a+op op-a
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//boost::subtractable2_left<many_body_operator<scalar_t>, scalar_t>, // a-op
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boost::multipliable<many_body_operator<scalar_t>, scalar_t>, // op*a a*op op/a
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boost::dividable<many_body_operator<scalar_t>, scalar_t> {
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static constexpr scalar_t threshold = std::numeric_limits<scalar_t>::epsilon();
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public:
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/// The indices of the C, C^+ operators are a vector of int/string
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using indices_t = std::vector<boost::variant<int, std::string>>;
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private:
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// The canonical operator: a dagger and some indices
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struct canonical_ops_t {
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bool dagger;
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indices_t indices;
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// Order: dagger < non dagger, and then indices
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// Example: c+_1 < c+_2 < c+_3 < c_3 < c_2 < c_1
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friend bool operator<(canonical_ops_t const& a, canonical_ops_t const& b) {
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if (a.dagger != b.dagger) return (a.dagger > b.dagger);
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if (a.dagger) // a.indices < b.indices
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return std::lexicographical_compare(a.indices.begin(), a.indices.end(), b.indices.begin(), b.indices.end());
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else // b.indices < a.indices
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return std::lexicographical_compare(b.indices.begin(), b.indices.end(), a.indices.begin(), a.indices.end());
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}
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friend bool operator>(canonical_ops_t const& a, canonical_ops_t const& b) { return b < a; }
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friend bool operator==(canonical_ops_t const& a, canonical_ops_t const& b) {
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return (a.dagger == b.dagger && a.indices.size() == b.indices.size() &&
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std::equal(a.indices.begin(), a.indices.end(), b.indices.begin()));
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}
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template <class Archive> void serialize(Archive& ar, const unsigned int version) { ar& dagger& indices; }
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};
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// Monomial: an ordered set of creation/annihilation operators and comparison
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using monomial_t = std::vector<canonical_ops_t>;
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friend bool operator<(monomial_t const& m1, monomial_t const& m2) {
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return m1.size() != m2.size() ? m1.size() < m2.size()
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: std::lexicographical_compare(m1.begin(), m1.end(), m2.begin(), m2.end());
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}
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// Map of all monomials with coefficients
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using monomials_map_t = std::map<monomial_t, scalar_t>;
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monomials_map_t monomials;
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public:
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many_body_operator() = default;
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many_body_operator(many_body_operator const&) = default;
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many_body_operator(many_body_operator&&) = default;
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many_body_operator& operator=(many_body_operator const&) = default;
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many_body_operator& operator=(many_body_operator&&) = default;
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template <typename S> many_body_operator(many_body_operator<S> const& x) { *this = x; }
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template <typename S> many_body_operator& operator=(many_body_operator<S> const& x) {
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monomials.clear();
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for (auto const& y : x.monomials) monomials.insert({y.first, y.second});
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}
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// factory for c, cdag
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static many_body_operator make_canonical(bool is_dag, indices_t indices) {
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many_body_operator res;
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auto m = monomial_t{canonical_ops_t{is_dag, indices}};
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res.monomials.insert({m, 1.0});
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return res;
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}
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// We use utility::dressed_iterator to dress iterators
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// _cdress is a simple struct of refs to dress the iterators (Cf doc)
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struct _cdress {
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monomial_t const& monomial;
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scalar_t coef;
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_cdress(typename monomials_map_t::const_iterator _it) : monomial(_it->first), coef(_it->second) {}
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};
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using const_iterator = utility::dressed_iterator<typename monomials_map_t::const_iterator, _cdress>;
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public:
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// Iterators (only const!)
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const_iterator begin() const noexcept { return monomials.begin(); }
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const_iterator end() const noexcept { return monomials.end(); }
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const_iterator cbegin() const noexcept { return monomials.cbegin(); }
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const_iterator cend() const noexcept { return monomials.cend(); }
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// Is zero operator ?
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bool is_zero() const { return monomials.empty(); }
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// Algebraic operations involving scalar_t constants
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many_body_operator operator-() const {
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auto res = *this;
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for (auto& m : res.monomials) m.second = -m.second;
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return res;
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}
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many_body_operator& operator+=(scalar_t alpha) {
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bool is_new_monomial;
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typename monomials_map_t::iterator it;
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std::tie(it, is_new_monomial) = monomials.insert(std::make_pair(monomial_t(0), alpha));
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if (!is_new_monomial) {
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it->second += alpha;
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erase_zero_monomial(monomials, it);
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}
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return *this;
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}
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many_body_operator& operator-=(scalar_t alpha) { return operator+=(-alpha); }
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friend many_body_operator operator-(scalar_t alpha, many_body_operator const& op) { return -op + alpha; }
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//friend many_body_operator operator/ (many_body_operator const & op, scalar_t alpha) { return op/alpha; }
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many_body_operator& operator*=(scalar_t alpha) {
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if (std::abs(alpha) < 100*std::abs(threshold)) {
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monomials.clear();
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} else {
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for (auto& m : monomials) m.second *= alpha;
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}
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return *this;
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}
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many_body_operator& operator/=(scalar_t alpha) { return operator*=(1.0/alpha); }
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// Algebraic operations
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many_body_operator& operator+=(many_body_operator const& op) {
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bool is_new_monomial;
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typename monomials_map_t::iterator it;
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for (auto const& m : op.monomials) {
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std::tie(it, is_new_monomial) = monomials.insert(m);
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if (!is_new_monomial) {
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it->second += m.second;
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erase_zero_monomial(monomials, it);
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}
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}
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return *this;
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}
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many_body_operator& operator-=(many_body_operator const& op) {
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bool is_new_monomial;
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typename monomials_map_t::iterator it;
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for (auto const& m : op.monomials) {
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std::tie(it, is_new_monomial) = monomials.insert(std::make_pair(m.first, -m.second));
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if (!is_new_monomial) {
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it->second -= m.second;
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erase_zero_monomial(monomials, it);
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}
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}
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return *this;
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}
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many_body_operator& operator*=(many_body_operator const& op) {
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monomials_map_t tmp_map; // product will be stored here
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for (auto const& m : monomials)
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for (auto const& op_m : op.monomials) {
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// prepare an unnormalized product
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monomial_t product_m;
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product_m.reserve(m.first.size() + op_m.first.size());
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for (auto const& op : m.first) product_m.push_back(op);
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for (auto const& op : op_m.first) product_m.push_back(op);
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// std::copy(m.first.begin(), m.first.end(), std::back_inserter(product_m));
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// std::copy(op_m.first.begin(), op_m.first.end(), std::back_inserter(product_m));
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normalize_and_insert(product_m, m.second * op_m.second, tmp_map);
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}
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std::swap(monomials, tmp_map);
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return *this;
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}
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// implementation details of dagger
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//
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private:
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static double _dagger(double x) { return x; }
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static std::complex<double> _dagger(std::complex<double> x) { return conj(x); }
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static canonical_ops_t _dagger(canonical_ops_t const& cop) {
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return {!cop.dagger, cop.indices};
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}
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static monomial_t _dagger(monomial_t const& m) {
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monomial_t res;
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for (auto it = m.rbegin(); it != m.rend(); ++it) res.push_back(_dagger(*it));
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return res;
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}
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public:
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// dagger
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friend many_body_operator dagger(many_body_operator const& op) {
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many_body_operator res;
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for (auto const& x : op) res.monomials.insert({_dagger(x.monomial), _dagger(x.coef)});
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return res;
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}
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// Boost.Serialization
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friend class boost::serialization::access;
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template <class Archive> void serialize(Archive& ar, const unsigned int version) { ar& monomials; }
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private:
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// Normalize a monomial and insert into a map
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static void normalize_and_insert(monomial_t& m, scalar_t coeff, monomials_map_t& target) {
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// The normalization is done by employing a simple bubble sort algorithms.
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// Apart from sorting elements this function keeps track of the sign and
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// recursively calls itself if a permutation of two operators produces a new
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// monomial
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if (m.size() >= 2) {
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bool is_swapped;
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do {
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is_swapped = false;
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for (std::size_t n = 1; n < m.size(); ++n) {
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canonical_ops_t& prev_index = m[n - 1];
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canonical_ops_t& cur_index = m[n];
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if (prev_index == cur_index) return; // The monomial is effectively zero
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if (prev_index > cur_index) {
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// Are we swapping C and C^+ with the same indices?
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// A bit ugly ...
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canonical_ops_t cur_index_flipped_type(cur_index);
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cur_index_flipped_type.dagger = !cur_index_flipped_type.dagger;
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if (prev_index == cur_index_flipped_type) {
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monomial_t new_m;
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new_m.reserve(m.size() - 2);
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std::copy(m.begin(), m.begin() + n - 1, std::back_inserter(new_m));
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std::copy(m.begin() + n + 1, m.end(), std::back_inserter(new_m));
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normalize_and_insert(new_m, coeff, target);
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}
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coeff = -coeff;
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std::swap(prev_index, cur_index);
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is_swapped = true;
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}
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}
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} while (is_swapped);
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}
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// Insert the result
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bool is_new_monomial;
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typename monomials_map_t::iterator it;
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std::tie(it, is_new_monomial) = target.insert(std::make_pair(m, coeff));
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if (!is_new_monomial) {
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it->second += coeff;
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erase_zero_monomial(target, it);
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}
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}
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// Erase a monomial with a close-to-zero coefficient.
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static void erase_zero_monomial(monomials_map_t& m, typename monomials_map_t::iterator& it) {
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if (std::abs(it->second) < 100*std::abs(threshold)) m.erase(it);
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}
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struct print_visitor : public boost::static_visitor<> {
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std::ostream& os;
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print_visitor(std::ostream& os_) : os(os_) {}
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template <typename T> void operator()(T const& x) const { os << x; }
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};
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friend std::ostream& operator<<(std::ostream& os, canonical_ops_t const& op) {
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if (op.dagger) os << "^+";
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os << "(";
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int u = 0;
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for (auto const& i : op.indices) {
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if (u++) os << ",";
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boost::apply_visitor(print_visitor{os}, i);
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}
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return os << ")";
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}
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friend std::ostream& operator<<(std::ostream& os, monomial_t const& m) {
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for (auto const& c : m) {
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os << "C" << c;
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}
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return os;
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}
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// Print many_body_operator itself
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friend std::ostream& operator<<(std::ostream& os, many_body_operator const& op) {
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if (op.monomials.size() != 0) {
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bool print_plus = false;
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for (auto const& m : op.monomials) {
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os << (print_plus ? " + " : "") << m.second;
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if (m.first.size()) os << "*";
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os << m.first;
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print_plus = true;
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}
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} else
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os << "0";
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return os;
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}
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};
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// ---- factories --------------
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// Free functions to make creation/annihilation operators
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template <typename... IndexTypes> many_body_operator<double> c(IndexTypes... indices) {
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return many_body_operator<double>::make_canonical(false, many_body_operator<double>::indices_t{indices...});
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// need to put many_body_operator<double>::indices_t because {} constructor is explicit !?
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}
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template <typename... IndexTypes> many_body_operator<double> c_dag(IndexTypes... indices) {
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return many_body_operator<double>::make_canonical(true, many_body_operator<double>::indices_t{indices...});
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}
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template <typename... IndexTypes> many_body_operator<double> n(IndexTypes... indices) {
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return c_dag(indices...) * c(indices...);
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}
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}
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}
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