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150 lines
4.7 KiB
150 lines
4.7 KiB
// This file is part of Bertini 2.
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//
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// total_degree.hpp is free software: you can redistribute it and/or modify
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// it under the terms of the GNU General Public License as published by
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// the Free Software Foundation, either version 3 of the License, or
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//(at your option) any later version.
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//
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// total_degree.hpp is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU General Public License
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// along with total_degree.hpp. If not, see <http://www.gnu.org/licenses/>.
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//
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// Copyright(C) 2015 - 2021 by Bertini2 Development Team
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//
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// See <http://www.gnu.org/licenses/> for a copy of the license,
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// as well as COPYING. Bertini2 is provided with permitted
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// additional terms in the b2/licenses/ directory.
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// individual authors of this file include:
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// silviana amethyst, university of wisconsin eau claire
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/**
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\file total_degree.hpp
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\brief Defines the TotalDegree start system type.
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*/
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#pragma once
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#include "system/start/utility.hpp"
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#include "system/start_base.hpp"
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namespace bertini {
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namespace start_system {
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/**
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\brief Total degree start system for 1-homogeneous polynomial systems.
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The most basic and easy-to-construct start system in Numerical Algebraic
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Geometry.
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The total degree start system uses functions of the form \f$x_i^{d_i} - r_i\f$,
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where \f$i\f$ is the index of the function relative to the system, \f$d_i\f$ is
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the degree of that function, and \f$r_i\f$ is a random complex number. This is
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very similar to the roots of unity, except that they are moved away from being
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centered around the origin, to being centered around a random complex number.
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Note that the corresponding target system MUST be square -- have the same number
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of functions and variables. The start system cannot be constructed otherwise,
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particularly because it is written to throw at the moment if not square.
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The start points are accesses by index (unsigned long long), instead of being
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generated all at once.
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*/
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class TotalDegree : public StartSystem {
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public:
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TotalDegree() = default;
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virtual ~TotalDegree() = default;
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/**
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Constructor for making a total degree start system from a polynomial system
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\throws std::runtime_error, if the input target system is not square, is not
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polynomial, has a path variable already, has more than one variable group, or
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has any homogeneous variable groups.
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*/
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TotalDegree(System const& s);
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/**
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Get the random value for start function with index
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\param index The index of the start function for which you want the
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corresponding random value.
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*/
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template <typename NumT>
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NumT RandomValue(size_t index) const {
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return random_values_[index]->Eval<NumT>();
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}
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/**
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Get all the random values, in their Node form.
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*/
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std::vector<std::shared_ptr<node::Rational> > const& RandomValues() {
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return random_values_;
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}
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/**
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Get the number of start points for this total degree start system. This is
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the Bezout bound for the target system. Provided here for your convenience.
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*/
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unsigned long long NumStartPoints() const override;
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TotalDegree& operator*=(Nd const& n);
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TotalDegree& operator+=(System const& sys) = delete;
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void SanityChecks(System const& s);
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private:
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/**
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Copy the degrees from another system into this one
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*/
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void CopyDegrees(System const& s);
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/**
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Populate the random values of this system.
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*/
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void SeedRandomValues(int num_functions);
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/**
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Generate the functions for this total degree start system. Assumes the random
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values, degrees, and variables are already g2g.
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*/
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void GenerateFunctions();
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/**
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Get the ith start point, in double precision.
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Called by the base StartSystem's StartPoint(index) method.
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*/
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Vec<dbl> GenerateStartPoint(dbl, unsigned long long index) const override;
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/**
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Get the ith start point, in current default precision.
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Called by the base StartSystem's StartPoint(index) method.
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*/
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Vec<mpfr_complex> GenerateStartPoint(mpfr_complex,
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unsigned long long index) const override;
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std::vector<std::shared_ptr<node::Rational> >
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random_values_; ///< stores the random values for the start functions.
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///< x^d-r, where r is stored in this vector.
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std::vector<unsigned long long>
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degrees_; ///< stores the degrees of the functions.
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friend class boost::serialization::access;
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template <typename Archive>
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void serialize(Archive& ar, const unsigned version) {
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ar& boost::serialization::base_object<StartSystem>(*this);
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ar & random_values_;
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ar & degrees_;
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}
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};
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} // namespace start_system
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} // namespace bertini
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