551 lines
15 KiB
C++
551 lines
15 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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#include "GeneralMatrix.hh"
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#include <dynlapack.h>
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#include "SylvException.hh"
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#include "rfs_tensor.hh"
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#include "normal_moments.hh"
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#include "vector_function.hh"
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#include "quadrature.hh"
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#include "smolyak.hh"
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#include "product.hh"
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#include "quasi_mcarlo.hh"
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#include <iomanip>
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#include <chrono>
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#include <cmath>
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#include <iostream>
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#include <utility>
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#include <array>
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#include <memory>
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#include <cstdlib>
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/* Evaluates unfolded (Dx)ᵏ power, where x is a vector, D is a Cholesky factor
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(lower triangular) */
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class MomentFunction : public VectorFunction
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{
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GeneralMatrix D;
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int k;
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public:
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MomentFunction(const GeneralMatrix &inD, int kk)
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: VectorFunction(inD.nrows(), UFSTensor::calcMaxOffset(inD.nrows(), kk)),
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D(inD), k(kk)
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{
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}
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MomentFunction(const MomentFunction &func) = default;
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std::unique_ptr<VectorFunction>
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clone() const override
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{
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return std::make_unique<MomentFunction>(*this);
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}
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void eval(const Vector &point, const ParameterSignal &sig, Vector &out) override;
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};
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void
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MomentFunction::eval(const Vector &point, const ParameterSignal &sig, Vector &out)
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{
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if (point.length() != indim() || out.length() != outdim())
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{
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std::cerr << "Wrong length of vectors in MomentFunction::eval" << std::endl;
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std::exit(EXIT_FAILURE);
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}
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Vector y(point);
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y.zeros();
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D.multaVec(y, point);
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URSingleTensor ypow(y, k);
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out.zeros();
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out.add(1.0, ypow.getData());
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}
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class TensorPower : public VectorFunction
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{
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int k;
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public:
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TensorPower(int nvar, int kk)
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: VectorFunction(nvar, UFSTensor::calcMaxOffset(nvar, kk)), k(kk)
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{
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}
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TensorPower(const TensorPower &func) = default;
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std::unique_ptr<VectorFunction>
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clone() const override
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{
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return std::make_unique<TensorPower>(*this);
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}
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void eval(const Vector &point, const ParameterSignal &sig, Vector &out) override;
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};
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void
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TensorPower::eval(const Vector &point, const ParameterSignal &sig, Vector &out)
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{
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if (point.length() != indim() || out.length() != outdim())
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{
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std::cerr << "Wrong length of vectors in TensorPower::eval" << std::endl;
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std::exit(EXIT_FAILURE);
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}
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URSingleTensor ypow(point, k);
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out.zeros();
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out.add(1.0, ypow.getData());
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}
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/* Evaluates (1+1/d)ᵈ(x₁·…·x_d)^(1/d), its integral over [0,1]ᵈ
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is 1.0, and its variation grows exponentially */
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class Function1 : public VectorFunction
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{
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int dim;
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public:
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Function1(int d)
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: VectorFunction(d, 1), dim(d)
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{
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}
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Function1(const Function1 &f)
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: VectorFunction(f.indim(), f.outdim()), dim(f.dim)
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{
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}
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std::unique_ptr<VectorFunction>
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clone() const override
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{
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return std::make_unique<Function1>(*this);
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}
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void eval(const Vector &point, const ParameterSignal &sig, Vector &out) override;
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};
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void
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Function1::eval(const Vector &point, const ParameterSignal &sig, Vector &out)
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{
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if (point.length() != dim || out.length() != 1)
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{
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std::cerr << "Wrong length of vectors in Function1::eval" << std::endl;
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std::exit(EXIT_FAILURE);
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}
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double r = 1;
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for (int i = 0; i < dim; i++)
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r *= point[i];
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r = pow(r, 1.0/dim);
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r *= pow(1.0 + 1.0/dim, static_cast<double>(dim));
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out[0] = r;
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}
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// Evaluates Function1 but with transformation xᵢ=0.5(yᵢ+1)
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// This makes the new function integrate over [−1,1]ᵈ to 1.0
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class Function1Trans : public Function1
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{
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public:
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Function1Trans(int d)
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: Function1(d)
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{
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}
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Function1Trans(const Function1Trans &func) = default;
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std::unique_ptr<VectorFunction>
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clone() const override
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{
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return std::make_unique<Function1Trans>(*this);
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}
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void eval(const Vector &point, const ParameterSignal &sig, Vector &out) override;
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};
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void
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Function1Trans::eval(const Vector &point, const ParameterSignal &sig, Vector &out)
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{
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Vector p(point.length());
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for (int i = 0; i < p.length(); i++)
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p[i] = 0.5*(point[i]+1);
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Function1::eval(p, sig, out);
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out.mult(pow(0.5, indim()));
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}
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/* WallTimer class. Constructor saves the wall time, destructor cancels the
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current time from the saved, and prints the message with time information */
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class WallTimer
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{
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std::string mes;
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std::chrono::time_point<std::chrono::high_resolution_clock> start;
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bool new_line;
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public:
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WallTimer(std::string m, bool nl = true)
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: mes{m}, start{std::chrono::high_resolution_clock::now()}, new_line{nl}
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{
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}
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~WallTimer()
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{
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auto end = std::chrono::high_resolution_clock::now();
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std::chrono::duration<double> duration = end - start;
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std::cout << mes << std::setw(8) << std::setprecision(4) << duration.count();
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if (new_line)
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std::cout << std::endl;
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}
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};
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/****************************************************/
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/* declaration of TestRunnable class */
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/****************************************************/
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class TestRunnable
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{
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public:
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const std::string name;
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int dim; // dimension of the solved problem
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int nvar; // number of variables of the solved problem
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TestRunnable(std::string name_arg, int d, int nv)
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: name{move(name_arg)}, dim(d), nvar(nv)
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{
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}
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virtual ~TestRunnable() = default;
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bool test() const;
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virtual bool run() const = 0;
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protected:
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static bool smolyak_normal_moments(const GeneralMatrix &m, int imom, int level);
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static bool product_normal_moments(const GeneralMatrix &m, int imom, int level);
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static bool qmc_normal_moments(const GeneralMatrix &m, int imom, int level);
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static bool smolyak_product_cube(const VectorFunction &func, const Vector &res,
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double tol, int level);
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static bool qmc_cube(const VectorFunction &func, double res, double tol, int level);
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};
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bool
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TestRunnable::test() const
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{
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std::cout << "Running test <" << name << ">" << std::endl;
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bool passed;
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{
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WallTimer tim("Wall clock time ", false);
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passed = run();
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}
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if (passed)
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{
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std::cout << "............................ passed" << std::endl << std::endl;
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return passed;
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}
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else
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{
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std::cout << "............................ FAILED" << std::endl << std::endl;
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return passed;
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}
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}
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/****************************************************/
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/* definition of TestRunnable static methods */
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/****************************************************/
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bool
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TestRunnable::smolyak_normal_moments(const GeneralMatrix &m, int imom, int level)
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{
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// First make m·mᵀ and then Cholesky factor
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GeneralMatrix msq(m * transpose(m));
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// Make vector function
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int dim = m.nrows();
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TensorPower tp(dim, imom);
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GaussConverterFunction func(tp, msq);
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// Smolyak quadrature
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Vector smol_out(UFSTensor::calcMaxOffset(dim, imom));
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{
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WallTimer tim("\tSmolyak quadrature time: ");
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GaussHermite gs;
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SmolyakQuadrature quad(dim, level, gs);
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quad.integrate(func, level, sthread::detach_thread_group::max_parallel_threads, smol_out);
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std::cout << "\tNumber of Smolyak evaluations: " << quad.numEvals(level) << std::endl;
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}
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// Check against theoretical moments
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UNormalMoments moments(imom, msq);
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smol_out.add(-1.0, moments.get(Symmetry{imom}).getData());
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std::cout << "\tError: " << std::setw(16) << std::setprecision(12) << smol_out.getMax() << std::endl;
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return smol_out.getMax() < 1.e-7;
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}
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bool
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TestRunnable::product_normal_moments(const GeneralMatrix &m, int imom, int level)
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{
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// First make m·mᵀ and then Cholesky factor
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GeneralMatrix msq(m * transpose(m));
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// Make vector function
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int dim = m.nrows();
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TensorPower tp(dim, imom);
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GaussConverterFunction func(tp, msq);
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// Product quadrature
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Vector prod_out(UFSTensor::calcMaxOffset(dim, imom));
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{
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WallTimer tim("\tProduct quadrature time: ");
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GaussHermite gs;
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ProductQuadrature quad(dim, gs);
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quad.integrate(func, level, sthread::detach_thread_group::max_parallel_threads, prod_out);
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std::cout << "\tNumber of product evaluations: " << quad.numEvals(level) << std::endl;
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}
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// Check against theoretical moments
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UNormalMoments moments(imom, msq);
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prod_out.add(-1.0, moments.get(Symmetry{imom}).getData());
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std::cout << "\tError: " << std::setw(16) << std::setprecision(12) << prod_out.getMax() << std::endl;
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return prod_out.getMax() < 1.e-7;
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}
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bool
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TestRunnable::smolyak_product_cube(const VectorFunction &func, const Vector &res,
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double tol, int level)
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{
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if (res.length() != func.outdim())
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{
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std::cerr << "Incompatible dimensions of check value and function." << std::endl;
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std::exit(EXIT_FAILURE);
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}
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GaussLegendre glq;
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Vector out(func.outdim());
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double smol_error;
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double prod_error;
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{
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WallTimer tim("\tSmolyak quadrature time: ");
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SmolyakQuadrature quad(func.indim(), level, glq);
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quad.integrate(func, level, sthread::detach_thread_group::max_parallel_threads, out);
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out.add(-1.0, res);
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smol_error = out.getMax();
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std::cout << "\tNumber of Smolyak evaluations: " << quad.numEvals(level) << std::endl;
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std::cout << "\tError: " << std::setw(16) << std::setprecision(12) << smol_error << std::endl;
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}
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{
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WallTimer tim("\tProduct quadrature time: ");
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ProductQuadrature quad(func.indim(), glq);
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quad.integrate(func, level, sthread::detach_thread_group::max_parallel_threads, out);
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out.add(-1.0, res);
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prod_error = out.getMax();
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std::cout << "\tNumber of product evaluations: " << quad.numEvals(level) << std::endl;
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std::cout << "\tError: " << std::setw(16) << std::setprecision(12) << prod_error << std::endl;
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}
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return smol_error < tol && prod_error < tol;
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}
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bool
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TestRunnable::qmc_cube(const VectorFunction &func, double res, double tol, int level)
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{
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Vector r(1);
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double error1;
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{
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WallTimer tim("\tQuasi-Monte Carlo (Warnock scrambling) time: ");
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WarnockPerScheme wps;
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QMCarloCubeQuadrature qmc(func.indim(), level, wps);
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qmc.integrate(func, level, sthread::detach_thread_group::max_parallel_threads, r);
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error1 = std::max(res - r[0], r[0] - res);
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std::cout << "\tQuasi-Monte Carlo (Warnock scrambling) error: " << std::setw(16) << std::setprecision(12) << error1 << std::endl;
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}
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double error2;
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{
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WallTimer tim("\tQuasi-Monte Carlo (reverse scrambling) time: ");
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ReversePerScheme rps;
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QMCarloCubeQuadrature qmc(func.indim(), level, rps);
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qmc.integrate(func, level, sthread::detach_thread_group::max_parallel_threads, r);
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error2 = std::max(res - r[0], r[0] - res);
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std::cout << "\tQuasi-Monte Carlo (reverse scrambling) error: " << std::setw(16) << std::setprecision(12) << error2 << std::endl;
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}
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double error3;
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{
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WallTimer tim("\tQuasi-Monte Carlo (no scrambling) time: ");
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IdentityPerScheme ips;
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QMCarloCubeQuadrature qmc(func.indim(), level, ips);
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qmc.integrate(func, level, sthread::detach_thread_group::max_parallel_threads, r);
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error3 = std::max(res - r[0], r[0] - res);
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std::cout << "\tQuasi-Monte Carlo (no scrambling) error: " << std::setw(16) << std::setprecision(12) << error3 << std::endl;
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}
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return error1 < tol && error2 < tol && error3 < tol;
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}
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/****************************************************/
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/* definition of TestRunnable subclasses */
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/****************************************************/
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class SmolyakNormalMom1 : public TestRunnable
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{
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public:
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SmolyakNormalMom1()
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: TestRunnable("Smolyak normal moments (dim=2, level=4, order=4)", 4, 2)
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{
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}
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bool
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run() const override
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{
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GeneralMatrix m(2, 2);
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m.zeros();
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m.get(0, 0) = 1;
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m.get(1, 1) = 1;
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return smolyak_normal_moments(m, 4, 4);
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}
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};
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class SmolyakNormalMom2 : public TestRunnable
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{
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public:
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SmolyakNormalMom2()
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: TestRunnable("Smolyak normal moments (dim=3, level=8, order=8)", 8, 3)
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{
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}
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bool
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run() const override
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{
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GeneralMatrix m(3, 3);
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m.zeros();
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m.get(0, 0) = 1;
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m.get(0, 2) = 0.5;
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m.get(1, 1) = 1;
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m.get(1, 0) = 0.5;
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m.get(2, 2) = 2;
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m.get(2, 1) = 4;
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return smolyak_normal_moments(m, 8, 8);
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}
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};
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class ProductNormalMom1 : public TestRunnable
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{
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public:
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ProductNormalMom1()
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: TestRunnable("Product normal moments (dim=2, level=4, order=4)", 4, 2)
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{
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}
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bool
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run() const override
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{
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GeneralMatrix m(2, 2);
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m.zeros();
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m.get(0, 0) = 1;
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m.get(1, 1) = 1;
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return product_normal_moments(m, 4, 4);
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}
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};
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class ProductNormalMom2 : public TestRunnable
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{
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public:
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ProductNormalMom2()
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: TestRunnable("Product normal moments (dim=3, level=8, order=8)", 8, 3)
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{
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}
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bool
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run() const override
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{
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GeneralMatrix m(3, 3);
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m.zeros();
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m.get(0, 0) = 1;
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m.get(0, 2) = 0.5;
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m.get(1, 1) = 1;
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m.get(1, 0) = 0.5;
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m.get(2, 2) = 2;
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m.get(2, 1) = 4;
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return product_normal_moments(m, 8, 8);
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}
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};
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// Note that here we pass 1,1 to tls since smolyak has its own PascalTriangle
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class F1GaussLegendre : public TestRunnable
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{
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public:
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F1GaussLegendre()
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: TestRunnable("Function1 Gauss-Legendre (dim=6, level=13", 1, 1)
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{
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}
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bool
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run() const override
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{
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Function1Trans f1(6);
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Vector res(1);
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res[0] = 1.0;
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return smolyak_product_cube(f1, res, 1e-2, 13);
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}
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};
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class F1QuasiMCarlo : public TestRunnable
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{
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public:
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F1QuasiMCarlo()
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: TestRunnable("Function1 Quasi-Monte Carlo (dim=6, level=1000000)", 1, 1)
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{
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}
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bool
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run() const override
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{
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Function1 f1(6);
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return qmc_cube(f1, 1.0, 1.e-4, 1000000);
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}
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};
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int
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main()
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{
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std::vector<std::unique_ptr<TestRunnable>> all_tests;
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// Fill in vector of all tests
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all_tests.push_back(std::make_unique<SmolyakNormalMom1>());
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all_tests.push_back(std::make_unique<SmolyakNormalMom2>());
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all_tests.push_back(std::make_unique<ProductNormalMom1>());
|
||
all_tests.push_back(std::make_unique<ProductNormalMom2>());
|
||
all_tests.push_back(std::make_unique<F1GaussLegendre>());
|
||
all_tests.push_back(std::make_unique<F1QuasiMCarlo>());
|
||
|
||
// Find maximum dimension and maximum nvar
|
||
int dmax = 0;
|
||
int nvmax = 0;
|
||
for (const auto &test : all_tests)
|
||
{
|
||
dmax = std::max(dmax, test->dim);
|
||
nvmax = std::max(nvmax, test->nvar);
|
||
}
|
||
TLStatic::init(dmax, nvmax); // initialize library
|
||
|
||
// Launch the tests
|
||
int success = 0;
|
||
for (const auto &test : all_tests)
|
||
{
|
||
try
|
||
{
|
||
if (test->test())
|
||
success++;
|
||
}
|
||
catch (const TLException &e)
|
||
{
|
||
std::cout << "Caught TL exception in <" << test->name << ">:" << std::endl;
|
||
e.print();
|
||
}
|
||
catch (SylvException &e)
|
||
{
|
||
std::cout << "Caught Sylv exception in <" << test->name << ">:" << std::endl;
|
||
e.printMessage();
|
||
}
|
||
}
|
||
|
||
int nfailed = all_tests.size() - success;
|
||
std::cout << "There were " << nfailed << " tests that failed out of "
|
||
<< all_tests.size() << " tests run." << std::endl;
|
||
|
||
if (nfailed)
|
||
return EXIT_FAILURE;
|
||
else
|
||
return EXIT_SUCCESS;
|
||
}
|