stieltjes_example.cpp

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// @HEADER
// *****************************************************************************
//                           Stokhos Package
//
// Copyright 2009 NTESS and the Stokhos contributors.
// SPDX-License-Identifier: BSD-3-Clause
// *****************************************************************************
// @HEADER

#include <iostream>
#include <iomanip>

#include "Stokhos.hpp"
#include "Stokhos_StieltjesPCEBasis.hpp"
#include "Stokhos_LanczosProjPCEBasis.hpp"
#include "Stokhos_LanczosPCEBasis.hpp"
#include "Stokhos_UserDefinedQuadrature.hpp"

typedef Stokhos::LegendreBasis<int,double> basis_type;

struct pce_quad_func {
  pce_quad_func(
   const Stokhos::OrthogPolyApprox<int,double>& pce_,
   const Stokhos::OrthogPolyBasis<int,double>& basis_) :
    pce(pce_), basis(basis_), vec(2) {}
  
  double operator() (const double& a, const double& b) const {
    vec[0] = a;
    vec[1] = b;
    return pce.evaluate(vec);
  }
  const Stokhos::OrthogPolyApprox<int,double>& pce;
  const Stokhos::OrthogPolyBasis<int,double>& basis;
  mutable Teuchos::Array<double> vec;
};

double rel_err(double a, double b) {
  return std::abs(a-b)/std::abs(b);
}

int main(int argc, char **argv)
{
  try {

    const unsigned int d = 2;
    const unsigned int pmin = 1;
    const unsigned int pmax = 15;
    const unsigned int np = pmax-pmin+1;
    bool use_pce_quad_points = false;
    bool normalize = false;
    bool project_integrals = false;
    bool lanczos = false;
    bool sparse_grid = true;
#ifndef HAVE_STOKHOS_DAKOTA
    sparse_grid = false;
#endif
    Teuchos::Array<double> mean(np), mean_st(np), std_dev(np), std_dev_st(np);
    Teuchos::Array<double> pt(np), pt_st(np);

    Teuchos::Array< Teuchos::RCP<const Stokhos::OneDOrthogPolyBasis<int,double> > > bases(d); 
    Teuchos::Array<double> eval_pt(d, 0.5);
    double pt_true;
    
    // Loop over orders
    unsigned int n = 0;
    for (unsigned int p=pmin; p<=pmax; p++) {

      std::cout << "p = " << p << std::endl;
      
      // Create product basis
      for (unsigned int i=0; i<d; i++)
  bases[i] = Teuchos::rcp(new basis_type(p));
      Teuchos::RCP<const Stokhos::CompletePolynomialBasis<int,double> > basis = 
  Teuchos::rcp(new Stokhos::CompletePolynomialBasis<int,double>(bases));
      
      // Create approximation
      Stokhos::OrthogPolyApprox<int,double> x(basis), u(basis), v(basis), 
  w(basis), w2(basis);
      for (unsigned int i=0; i<d; i++) {
  x.term(i, 1) = 1.0;
      }

      double x_pt = x.evaluate(eval_pt);
      pt_true = std::sin(x_pt)/(1.0 + exp(x_pt));
      
      // Quadrature
      Teuchos::RCP<const Stokhos::Quadrature<int,double> > quad;
#ifdef HAVE_STOKHOS_DAKOTA
      if (sparse_grid)
        quad = 
    Teuchos::rcp(new Stokhos::SparseGridQuadrature<int,double>(basis, p));
#endif
      if (!sparse_grid)
  quad = 
    Teuchos::rcp(new Stokhos::TensorProductQuadrature<int,double>(basis));

      // Triple product tensor
      Teuchos::RCP<Stokhos::Sparse3Tensor<int,double> > Cijk =
  basis->computeTripleProductTensor();
      
      // Quadrature expansion
      Stokhos::QuadOrthogPolyExpansion<int,double> quad_exp(basis, Cijk, quad);
      
      // Compute PCE via quadrature expansion
      quad_exp.sin(u,x);
      quad_exp.exp(v,x);
      quad_exp.plusEqual(v, 1.0);
      quad_exp.divide(w,u,v);
  
      // Compute Stieltjes basis
      Teuchos::Array< Teuchos::RCP<const Stokhos::OneDOrthogPolyBasis<int,double> > > st_bases(2);
      Teuchos::RCP< Stokhos::LanczosProjPCEBasis<int,double> > stp_basis_u, stp_basis_v;
      Teuchos::RCP< Stokhos::LanczosPCEBasis<int,double> > st_basis_u, st_basis_v;
      if (lanczos) {
        if (project_integrals) {
    stp_basis_u = 
      Teuchos::rcp(new Stokhos::LanczosProjPCEBasis<int,double>(
         p, Teuchos::rcp(&u,false), Cijk, normalize, true));
    stp_basis_v = 
      Teuchos::rcp(new Stokhos::LanczosProjPCEBasis<int,double>(
         p, Teuchos::rcp(&v,false), Cijk, normalize, true));
    st_bases[0] = stp_basis_u;
    st_bases[1] = stp_basis_v;
        }
        else {
      st_basis_u = 
      Teuchos::rcp(new Stokhos::LanczosPCEBasis<int,double>(
       p, Teuchos::rcp(&u,false), quad, normalize, true));
    st_basis_v = 
      Teuchos::rcp(new Stokhos::LanczosPCEBasis<int,double>(
         p, Teuchos::rcp(&v,false), quad, normalize, true));
    st_bases[0] = st_basis_u;
    st_bases[1] = st_basis_v;
        }
      }
      else {
        st_bases[0] =
          Teuchos::rcp(new Stokhos::StieltjesPCEBasis<int,double>(
                       p, Teuchos::rcp(&u,false), quad, use_pce_quad_points,
                       normalize, project_integrals, Cijk));
        st_bases[1] =
          Teuchos::rcp(new Stokhos::StieltjesPCEBasis<int,double>(
                       p, Teuchos::rcp(&v,false), quad, use_pce_quad_points,
                       normalize, project_integrals, Cijk));
      }
      
      Teuchos::RCP<const Stokhos::CompletePolynomialBasis<int,double> > 
  st_basis = 
  Teuchos::rcp(new Stokhos::CompletePolynomialBasis<int,double>(st_bases));
      //std::cout << *st_basis << std::endl;

      Stokhos::OrthogPolyApprox<int,double>  u_st(st_basis), v_st(st_basis),
  w_st(st_basis);
      if (lanczos) {
        if (project_integrals) {
    u_st.term(0, 0) = stp_basis_u->getNewCoeffs(0);
    u_st.term(0, 1) = stp_basis_u->getNewCoeffs(1);
    v_st.term(0, 0) = stp_basis_v->getNewCoeffs(0);
    v_st.term(1, 1) = stp_basis_v->getNewCoeffs(1);
        }
        else {
    u_st.term(0, 0) = st_basis_u->getNewCoeffs(0);
    u_st.term(0, 1) = st_basis_u->getNewCoeffs(1);
    v_st.term(0, 0) = st_basis_v->getNewCoeffs(0);
    v_st.term(1, 1) = st_basis_v->getNewCoeffs(1);
        }
      }
      else {
        u_st.term(0, 0) = u.mean();
        u_st.term(0, 1) = 1.0;
        v_st.term(0, 0) = v.mean();
        v_st.term(1, 1) = 1.0;
      }

      // Triple product tensor
      Teuchos::RCP<Stokhos::Sparse3Tensor<int,double> > st_Cijk =
  st_basis->computeTripleProductTensor();
  
      // Tensor product quadrature
      Teuchos::RCP<const Stokhos::Quadrature<int,double> > st_quad;
      if (!use_pce_quad_points) {
#ifdef HAVE_STOKHOS_DAKOTA
  if (sparse_grid)
    st_quad = Teuchos::rcp(new Stokhos::SparseGridQuadrature<int,double>(st_basis, p));
#endif
  if (!sparse_grid)
    st_quad = Teuchos::rcp(new Stokhos::TensorProductQuadrature<int,double>(st_basis));
      }
      else {
  Teuchos::Array<double> st_points_0;
  Teuchos::Array<double> st_weights_0;
  Teuchos::Array< Teuchos::Array<double> > st_values_0;
  st_bases[0]->getQuadPoints(p+1, st_points_0, st_weights_0, st_values_0);
  Teuchos::Array<double> st_points_1;
  Teuchos::Array<double> st_weights_1;
  Teuchos::Array< Teuchos::Array<double> > st_values_1;
  st_bases[1]->getQuadPoints(p+1, st_points_1, st_weights_1, st_values_1);
  Teuchos::RCP< Teuchos::Array< Teuchos::Array<double> > > st_points =
    Teuchos::rcp(new Teuchos::Array< Teuchos::Array<double> >(st_points_0.size()));
  for (int i=0; i<st_points_0.size(); i++) {
    (*st_points)[i].resize(2);
    (*st_points)[i][0] = st_points_0[i];
    (*st_points)[i][1] = st_points_1[i];
  }
  Teuchos::RCP< Teuchos::Array<double> > st_weights = 
    Teuchos::rcp(new Teuchos::Array<double>(st_weights_0));
  Teuchos::RCP< const Stokhos::OrthogPolyBasis<int,double> > st_b = 
    st_basis;
  st_quad = 
    Teuchos::rcp(new Stokhos::UserDefinedQuadrature<int,double>(st_b,
                      st_points,
                      st_weights));
      }
      
      // Quadrature expansion
      Stokhos::QuadOrthogPolyExpansion<int,double> st_quad_exp(st_basis, 
                     st_Cijk,
                     st_quad);
      
      // Compute w_st = u_st*v_st in Stieltjes basis
      st_quad_exp.divide(w_st, u_st, v_st);
      
      // Project w_st back to original basis
      pce_quad_func st_func(w_st, *st_basis);
      quad_exp.binary_op(st_func, w2, u, v);

      // std::cout.precision(12);
      // std::cout << w;
      // std::cout << w2;
      // std::cout << w_st;
      mean[n] = w.mean();
      mean_st[n] = w2.mean();
      std_dev[n] = w.standard_deviation();
      std_dev_st[n] = w2.standard_deviation();
      pt[n] = w.evaluate(eval_pt);
      pt_st[n] = w2.evaluate(eval_pt);
      n++;
    }

    n = 0;
    int wi=10;
    std::cout << "Statistical error:" << std::endl;
    std::cout << "p  " 
        << std::setw(wi) << "mean" << "  " 
        << std::setw(wi) << "mean_st" << "  "
        << std::setw(wi) << "std_dev" << "  "
        << std::setw(wi) << "std_dev_st" << "  "
        << std::setw(wi) << "point" << "  "
        << std::setw(wi) << "point_st" << std::endl;
    for (unsigned int p=pmin; p<pmax; p++) {
      std::cout.precision(3);
      std::cout.setf(std::ios::scientific);
      std::cout << p << "  " 
    << std::setw(wi) << rel_err(mean[n], mean[np-1]) << "  "
    << std::setw(wi) << rel_err(mean_st[n], mean[np-1]) << "  "
    << std::setw(wi) << rel_err(std_dev[n], std_dev[np-1]) << "  "
    << std::setw(wi) << rel_err(std_dev_st[n], std_dev[np-1]) 
    << "  "
    << std::setw(wi) << rel_err(pt[n], pt_true) << "  "
    << std::setw(wi) << rel_err(pt_st[n], pt_true) 
    << std::endl;
      n++;
    }
      
  }
  catch (std::exception& e) {
    std::cout << e.what() << std::endl;
  }
}