342 lines
9.6 KiB
C++
342 lines
9.6 KiB
C++
//This file is part of Bertini 2.
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//
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//slice.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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//slice.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 slice.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 bertini2/system/slice.hpp
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\brief Provides the bertini::LinearSlice class.
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*/
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#ifndef BERTINI_SLICE_HPP
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#define BERTINI_SLICE_HPP
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#include "bertini2/function_tree.hpp"
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#include "bertini2/num_traits.hpp"
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#include "bertini2/eigen_extensions.hpp"
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namespace bertini {
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/**
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\brief Base class for other Slices.
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\see LinearSlice
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*/
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class Slice
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{
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};
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/**
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\brief Slice an affine or projective space with a LinearSlice today!
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*/
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class LinearSlice : public Slice
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{
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mutable std::tuple<Mat<dbl>, Mat<mpfr_complex> > coefficients_working_;
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Mat< mpfr_complex > coefficients_highest_precision_; ///< the highest-precision coefficients for the patch
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mutable std::tuple<Vec<dbl>, Vec<mpfr_complex> > constants_working_;
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Vec< mpfr_complex > constants_highest_precision_; ///< the highest-precision coefficients for the patch
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VariableGroup sliced_vars_;
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unsigned num_dims_sliced_;
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mutable unsigned precision_; ///< the current working precision of the patch.
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bool is_homogeneous_;
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public:
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/**
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Produce a random real slice on a variable group, slicing a given number of dimensions.
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*/
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static LinearSlice RandomReal(VariableGroup const& v, unsigned dim, bool homogeneous = false, bool orthogonal = true)
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{
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typedef void (*funtype) (mpfr_complex&, unsigned); // the type for number generation
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funtype gen = bertini::multiprecision::RandomRealAssign;
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return Make(v, dim, homogeneous, orthogonal, gen);
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}
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/**
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\brief Generate a random complex slice.
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*/
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static LinearSlice RandomComplex(VariableGroup const& v, unsigned dim, bool homogeneous = false, bool orthogonal = true)
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{
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typedef void (*funtype) (mpfr_complex&, unsigned); // the type for number generation
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funtype gen = bertini::multiprecision::RandomComplexAssign;
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return Make(v, dim, homogeneous, orthogonal, gen);
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}
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/**
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\brief Evaluate the function values of the LinearSlice, in-place
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*/
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template<typename NumT>
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void Eval(Vec<NumT> & result, Vec<NumT> const& x) const
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{
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result = std::get<Mat<NumT> >(coefficients_working_) * x;
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if (!is_homogeneous_)
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result += std::get<Vec<NumT> >(constants_working_);
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}
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/**
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\brief Evaluate the function values of the LinearSlice
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*/
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template<typename NumT>
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Vec<NumT> Eval(Vec<NumT> const& x) const
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{
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if (!is_homogeneous_)
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return std::get<Mat<NumT> >(coefficients_working_) * x + std::get<Vec<NumT> >(constants_working_);
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else
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return std::get<Mat<NumT> >(coefficients_working_) * x;
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}
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/**
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\brief Evaluate the Jacobian of the LinearSlice, in-place
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*/
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template<typename NumT>
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void Jacobian(Mat<NumT> & result, Mat<NumT> const& x) const
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{
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result = std::get<Mat<NumT> >(coefficients_working_);
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}
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/**
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\brief Evaluate the Jacobian of the LinearSlice
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*/
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template<typename NumT>
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Mat<NumT> Jacobian(Mat<NumT> const& x) const
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{
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return std::get<Mat<NumT> >(coefficients_working_);
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}
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/**
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\brief Get the current precision of the slice.
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\return The current precision, in digits.
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*/
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unsigned Precision() const
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{
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return precision_;
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}
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/**
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\brief Set the precision of the slice.
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Copies the slice coefficients into correct precision for subsequent precision.
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\param new_precision The precision to change to.
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*/
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void Precision(unsigned new_precision) const
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{
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if (new_precision > DoublePrecision())
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{
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Mat<mpfr_complex>& coefficients_mpfr = std::get<Mat<mpfr_complex> >(coefficients_working_);
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Vec<mpfr_complex>& constants_mpfr = std::get<Vec<mpfr_complex> >(constants_working_);
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for (unsigned ii = 0; ii < Dimension(); ++ii)
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{
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for (unsigned jj=0; jj<NumVariables(); ++jj)
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{
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coefficients_mpfr(ii,jj).precision(new_precision);
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if (new_precision>precision_)
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coefficients_mpfr(ii,jj) = coefficients_highest_precision_(ii,jj);
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}
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if (!is_homogeneous_)
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{
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constants_mpfr(ii).precision(new_precision);
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if (new_precision>precision_)
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constants_mpfr(ii) = constants_highest_precision_(ii);
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}
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}
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}
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precision_ = new_precision;
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}
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/**
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\brief Get the dimension of the slice
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*/
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unsigned Dimension() const
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{
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return num_dims_sliced_;
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}
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/**
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\brief Get the number of variables sliced.
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*/
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unsigned NumVariables() const
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{
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return sliced_vars_.size();
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}
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/**
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\brief the default constructor for linear slices.
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Make an empty linear slice.
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*/
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LinearSlice() :
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sliced_vars_(),
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precision_(DefaultPrecision()),
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num_dims_sliced_(0),
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coefficients_highest_precision_(0, 0),
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is_homogeneous_(false),
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constants_highest_precision_(static_cast<unsigned>(0))
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{
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std::get<Mat<dbl> > (coefficients_working_).resize(Dimension(), NumVariables());
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std::get<Mat<mpfr_complex> >(coefficients_working_).resize(Dimension(), NumVariables());
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std::get<Vec<dbl> > (constants_working_).resize(Dimension());
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std::get<Vec<mpfr_complex> >(constants_working_).resize(Dimension());
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}
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/**
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\brief the constructor for linear slices.
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*/
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LinearSlice(VariableGroup const& v, unsigned dim, bool homogeneous) : sliced_vars_(v), precision_(DefaultPrecision()), num_dims_sliced_(dim), coefficients_highest_precision_(dim, v.size()), is_homogeneous_(homogeneous), constants_highest_precision_(dim)
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{
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std::get<Mat<dbl> > (coefficients_working_).resize(Dimension(), NumVariables());
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std::get<Mat<mpfr_complex> >(coefficients_working_).resize(Dimension(), NumVariables());
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if (!homogeneous)
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{
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std::get<Vec<dbl> > (constants_working_).resize(Dimension());
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std::get<Vec<mpfr_complex> >(constants_working_).resize(Dimension());
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}
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}
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/**
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\brief factory function for generating slices
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*/
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static
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LinearSlice Make(VariableGroup const& v, unsigned dim, bool homogeneous, bool orthogonal, std::function<void(mpfr_complex&, unsigned)> gen)
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{
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LinearSlice s(v, dim, homogeneous);
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if (orthogonal)
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{
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using std::min;
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using std::max;
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auto mindim = min(s.Dimension(),s.NumVariables());
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auto maxdim = max(s.Dimension(),s.NumVariables());
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bool need_transpose = s.Dimension() < s.NumVariables();
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s.coefficients_highest_precision_.resize(maxdim,mindim);
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for (unsigned ii(0); ii<maxdim; ++ii)
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for (unsigned jj(0); jj<mindim; ++jj)
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gen(s.coefficients_highest_precision_(ii,jj), MaxPrecisionAllowed());
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auto prev_precision = DefaultPrecision();
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DefaultPrecision(MaxPrecisionAllowed());
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auto QR_factorization = Eigen::HouseholderQR<Mat<mpfr_complex> >(s.coefficients_highest_precision_);
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s.coefficients_highest_precision_ = QR_factorization.householderQ()*Mat<mpfr_complex>::Identity(maxdim, mindim);
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if (need_transpose)
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s.coefficients_highest_precision_.transposeInPlace();
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DefaultPrecision(prev_precision);
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}
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else
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{
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for (unsigned ii(0); ii<s.Dimension(); ++ii)
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for (unsigned jj(0); jj<s.NumVariables(); ++jj)
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gen(s.coefficients_highest_precision_(ii,jj), MaxPrecisionAllowed());
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}
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for (unsigned ii(0); ii<s.Dimension(); ++ii)
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for (unsigned jj(0); jj<s.NumVariables(); ++jj)
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{
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std::get<Mat<dbl> >(s.coefficients_working_)(ii,jj) = dbl(s.coefficients_highest_precision_(ii,jj));
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std::get<Mat<mpfr_complex> >(s.coefficients_working_)(ii,jj) = s.coefficients_highest_precision_(ii,jj);
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}
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if (!homogeneous)
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{
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s.constants_highest_precision_.resize(s.Dimension());
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std::get<Vec<dbl> >(s.constants_working_).resize(s.Dimension());
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std::get<Vec<mpfr_complex> >(s.constants_working_).resize(s.Dimension());
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for (unsigned ii(0); ii<s.Dimension(); ++ii)
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{
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gen(s.constants_highest_precision_(ii), MaxPrecisionAllowed());
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std::get<Vec<dbl> >(s.constants_working_)(ii) = dbl(s.constants_highest_precision_(ii));
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std::get<Vec<mpfr_complex> >(s.constants_working_)(ii) = s.constants_highest_precision_(ii);
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}
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}
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assert(s.coefficients_highest_precision_.rows()==s.Dimension());
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assert(s.coefficients_highest_precision_.cols()==s.NumVariables());
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if (!homogeneous)
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assert(s.constants_highest_precision_.size()==s.Dimension());
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else
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assert(s.constants_highest_precision_.size()==0);
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return s;
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}
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private:
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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 & precision_;
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ar & coefficients_highest_precision_;
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ar & std::get<0>(coefficients_working_);
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ar & std::get<1>(coefficients_working_);
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ar & sliced_vars_;
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}
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friend std::ostream& operator<<(std::ostream&, LinearSlice const&);
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};
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/**
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\brief Provides output streaming for LinearSlice
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*/
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std::ostream& operator<<(std::ostream& out, LinearSlice const& s);
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} // re: namespace bertini
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#endif
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