150 lines
4.6 KiB
C++
150 lines
4.6 KiB
C++
/*
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* Copyright © 2005 Ondra Kamenik
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* Copyright © 2019 Dynare Team
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*
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* This file is part of Dynare.
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*
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* Dynare 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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* Dynare 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 Dynare. If not, see <https://www.gnu.org/licenses/>.
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*/
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// Smolyak quadrature.
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/* This file defines Smolyak (sparse grid) multidimensional quadrature for
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non-nested underlying one dimensional quadrature. Let Q¹ₗ denote the one
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dimensional quadrature of l level. Let nₗ denote a number of points in the l
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level. Than the Smolyak quadrature can be defined as
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⎛ d−1 ⎞
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Qᵈf = ∑ (−1)^{l+d−|k|−1} ⎢ ⎥ (Q¹_k₁⊗…⊗Q¹_{k_d})f
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l≤|k|≤l+d−1 ⎝|k|−l⎠
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where d is the dimension, k is d-dimensional sequence of integers, and |k|
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denotes the sum of the sequence.
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Here we define smolpit as Smolyak iterator and SmolyakQuadrature. */
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#ifndef SMOLYAK_H
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#define SMOLYAK_H
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#include "int_sequence.hh"
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#include "tl_static.hh"
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#include "vector_function.hh"
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#include "quadrature.hh"
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#include "pascal_triangle.hh"
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/* Here we define the Smolyak point iterator. The Smolyak formula can be broken
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to a sum of product quadratures with various combinations of levels. The
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iterator follows this pattern. It maintains an index to a summand and then a
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point coordinates within the summand (product quadrature). The array of
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summands to which the ‘isummand’ points is maintained by the
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SmolyakQuadrature class to which the object knows the pointer ‘smolq’.
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We provide a constructor which points to the beginning of the given summand.
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This constructor is used in SmolyakQuadrature::begin() method which
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approximately divideds all the iterators to subsets of equal size. */
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class SmolyakQuadrature;
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class smolpit
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{
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protected:
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const SmolyakQuadrature &smolq;
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unsigned int isummand{0};
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IntSequence jseq;
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ParameterSignal sig;
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Vector p;
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double w;
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public:
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smolpit(const SmolyakQuadrature &q, unsigned int isum);
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smolpit(const smolpit &spit) = default;
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~smolpit() = default;
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bool operator==(const smolpit &spit) const;
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bool
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operator!=(const smolpit &spit) const
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{
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return !operator==(spit);
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}
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smolpit &operator=(const smolpit &spit) = delete;
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smolpit &operator++();
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const ParameterSignal &
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signal() const
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{
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return sig;
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}
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const Vector &
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point() const
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{
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return p;
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}
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double
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weight() const
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{
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return w;
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}
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void print() const;
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protected:
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void setPointAndWeight();
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};
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/* Here we define the class SmolyakQuadrature. It maintains an array of
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summands of the Smolyak quadrature formula:
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⎛ d−1 ⎞
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∑ (−1)^{l+d−|k|−1} ⎢ ⎥ (Q¹_k₁⊗…⊗Q¹_{k_d})f
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l≤|k|≤l+d−1 ⎝|k|−l⎠
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Each summand is fully specified by sequence k. The summands are here
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represented (besides k) also by sequence of number of points in each level
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selected by k, and also by a cummulative number of evaluations. The latter
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two are added only for conveniency.
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The summands in the code are given by ‘levels’, which is a vector of
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k sequences, further by ‘levpoints’ which is a vector of sequences
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of nuber of points in each level, and by ‘cumevals’ which is the
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cumulative number of points, this is:
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d
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∑ ∏ n_kᵢ
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ᵏ ⁱ⁼¹
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where the sum is done through all k before the current.
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The ‘levels’ and ‘levpoints’ vectors are used by smolpit. */
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class SmolyakQuadrature : public QuadratureImpl<smolpit>
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{
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friend class smolpit;
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int level;
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const OneDQuadrature &uquad;
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std::vector<IntSequence> levels;
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std::vector<IntSequence> levpoints;
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std::vector<int> cumevals;
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public:
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SmolyakQuadrature(int d, int l, const OneDQuadrature &uq);
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~SmolyakQuadrature() override = default;
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int numEvals(int level) const override;
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void designLevelForEvals(int max_eval, int &lev, int &evals) const;
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protected:
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smolpit begin(int ti, int tn, int level) const override;
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unsigned int
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numSummands() const
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{
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return levels.size();
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}
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private:
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int calcNumEvaluations(int level) const;
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};
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#endif
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