Stokhos_CGDivisionExpansionStrategy.hpp

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

#ifndef STOKHOS_CG_DIVISION_EXPANSION_STRATEGY_HPP
#define STOKHOS_CG_DIVISION_EXPANSION_STRATEGY_HPP

#include "Stokhos_DivisionExpansionStrategy.hpp"
#include "Stokhos_OrthogPolyBasis.hpp"
#include "Stokhos_Sparse3Tensor.hpp"
#include "Stokhos_DiagPreconditioner.hpp"
#include "Stokhos_JacobiPreconditioner.hpp"
#include "Stokhos_GSPreconditioner.hpp"
#include "Stokhos_SchurPreconditioner.hpp"
#include "Stokhos_InversePreconditioner.hpp"
#include "Stokhos_BlockPreconditioner.hpp"

#include "Teuchos_TimeMonitor.hpp"
#include "Teuchos_RCP.hpp"
#include "Teuchos_SerialDenseMatrix.hpp"
#include "Teuchos_BLAS.hpp"
#include "Teuchos_LAPACK.hpp"

#include <iostream>

namespace Stokhos {


  template <typename ordinal_type, typename value_type, typename node_type> 
  class CGDivisionExpansionStrategy :
    public DivisionExpansionStrategy<ordinal_type,value_type,node_type> {
  public:

    CGDivisionExpansionStrategy(
      const Teuchos::RCP<const Stokhos::OrthogPolyBasis<ordinal_type, value_type> >& basis_,
      const Teuchos::RCP<const Stokhos::Sparse3Tensor<ordinal_type, value_type> >& Cijk_, 
      const ordinal_type prec_iter_, 
      const value_type tol_, 
      const ordinal_type PrecNum_, 
      const ordinal_type max_it_, 
      const ordinal_type linear_, 
      const ordinal_type diag_, 
      const ordinal_type equil_);

    virtual ~CGDivisionExpansionStrategy() {}
 
    // Division operation:  c = \alpha*(a/b) + beta*c
    virtual void divide(
      Stokhos::OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
      const value_type& alpha,
      const Stokhos::OrthogPolyApprox<ordinal_type, value_type, node_type>& a, 
      const Stokhos::OrthogPolyApprox<ordinal_type, value_type, node_type>& b,
      const value_type& beta);

  private:

    // Prohibit copying
    CGDivisionExpansionStrategy(
      const CGDivisionExpansionStrategy&);

    // Prohibit Assignment
    CGDivisionExpansionStrategy& operator=(
      const CGDivisionExpansionStrategy& b);

    ordinal_type CG(
      const Teuchos::SerialDenseMatrix<ordinal_type, value_type> &  A, 
      Teuchos::SerialDenseMatrix<ordinal_type,value_type> & X, 
      const Teuchos::SerialDenseMatrix<ordinal_type,value_type> & B, 
      ordinal_type max_iter, 
      value_type tolerance, 
      ordinal_type prec_iter, 
      ordinal_type order, 
      ordinal_type dim, 
      ordinal_type PrecNum, 
      const Teuchos::SerialDenseMatrix<ordinal_type, value_type> & M, 
      ordinal_type diag);

  protected:

    Teuchos::RCP<const Stokhos::OrthogPolyBasis<ordinal_type, value_type> > basis;

    typedef Stokhos::Sparse3Tensor<ordinal_type, value_type> Cijk_type;

    Teuchos::RCP<const Cijk_type> Cijk;

    Teuchos::RCP< Teuchos::SerialDenseMatrix<ordinal_type,value_type> > A, X, B, M;
    
    ordinal_type prec_iter;

    value_type tol;
 
    ordinal_type PrecNum;

    ordinal_type max_it;

    ordinal_type linear;

    ordinal_type diag;

    ordinal_type equil;
       
  }; // class CGDivisionExpansionStrategy

} // namespace Stokhos

template <typename ordinal_type, typename value_type, typename node_type> 
Stokhos::CGDivisionExpansionStrategy<ordinal_type,value_type,node_type>::
CGDivisionExpansionStrategy(
  const Teuchos::RCP<const Stokhos::OrthogPolyBasis<ordinal_type, value_type> >& basis_,
  const Teuchos::RCP<const Stokhos::Sparse3Tensor<ordinal_type, value_type> >& Cijk_,
  const ordinal_type prec_iter_, 
  const value_type tol_, 
  const ordinal_type PrecNum_, 
  const ordinal_type max_it_, 
  const ordinal_type linear_, 
  const ordinal_type diag_, 
  const ordinal_type equil_): 
  basis(basis_),
  Cijk(Cijk_),
  prec_iter(prec_iter_),
  tol(tol_),
  PrecNum(PrecNum_),
  max_it(max_it_),
  linear(linear_),
  diag(diag_),
  equil(equil_)
  
{
  ordinal_type sz = basis->size();
  A = Teuchos::rcp(new Teuchos::SerialDenseMatrix<ordinal_type,value_type>(
         sz, sz));
  B = Teuchos::rcp(new Teuchos::SerialDenseMatrix<ordinal_type,value_type>(
         sz, 1));
  X = Teuchos::rcp(new Teuchos::SerialDenseMatrix<ordinal_type,value_type>(
         sz, 1));
  M = Teuchos::rcp(new Teuchos::SerialDenseMatrix<ordinal_type,value_type>(
                     sz, sz));

}


template <typename ordinal_type, typename value_type, typename node_type> 
void
Stokhos::CGDivisionExpansionStrategy<ordinal_type,value_type,node_type>::
divide(Stokhos::OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
       const value_type& alpha,
       const Stokhos::OrthogPolyApprox<ordinal_type, value_type, node_type>& a, 
       const Stokhos::OrthogPolyApprox<ordinal_type, value_type, node_type>& b,
       const value_type& beta)
{
#ifdef STOKHOS_TEUCHOS_TIME_MONITOR
  TEUCHOS_FUNC_TIME_MONITOR("Stokhos::CGDivisionStrategy::divide()");
#endif

  
  ordinal_type sz = basis->size();
  ordinal_type pa = a.size();
  ordinal_type pb = b.size();
  
  ordinal_type pc;
  if (pb > 1)
    pc = sz;
  else
    pc = pa;
  if (c.size() != pc)
    c.resize(pc);
 
  const value_type* ca = a.coeff();
  const value_type* cb = b.coeff();


  value_type* cc = c.coeff();

  if (pb > 1) {
    // Compute A
    A->putScalar(0.0);
    typename Cijk_type::k_iterator k_begin = Cijk->k_begin();
    typename Cijk_type::k_iterator k_end = Cijk->k_end();
    
    if (pb < Cijk->num_k())
      k_end = Cijk->find_k(pb);
    value_type cijk;
    ordinal_type i,j,k;
    for (typename Cijk_type::k_iterator k_it=k_begin; k_it!=k_end; ++k_it) {
      k = index(k_it);
      for (typename Cijk_type::kj_iterator j_it = Cijk->j_begin(k_it); 
     j_it != Cijk->j_end(k_it); ++j_it) {
  j = index(j_it);
  for (typename Cijk_type::kji_iterator i_it = Cijk->i_begin(j_it);
       i_it  != Cijk->i_end(j_it); ++i_it) {       
    i = index(i_it);
    cijk = value(i_it);
    (*A)(i,j) += cijk*cb[k];
  }
      }
    }

    // Compute B
    B->putScalar(0.0);
    for (ordinal_type i=0; i<pa; i++)
      (*B)(i,0) = ca[i]*basis->norm_squared(i);

    Teuchos::SerialDenseMatrix<ordinal_type,value_type> D(sz, 1);
    //Equilibrate the linear system
    if (equil == 1){
      //Create diag mtx of max row entries
      for (ordinal_type i=0; i<sz; i++){
  Teuchos::SerialDenseMatrix<ordinal_type, value_type> r(Teuchos::View, *A, 1, sz, i, 0);
  D(i,0)=sqrt(r.normOne());
      }


      //Compute inv(D)*A*inv(D)
      for (ordinal_type i=0; i<sz; i++){
  for (ordinal_type j=0; j<sz; j++){
    (*A)(i,j)=(*A)(i,j)/(D(i,0)*D(j,0));
  }
      }

      //Scale b by inv(D)
      for (ordinal_type i=0; i<sz; i++){
  (*B)(i,0)=(*B)(i,0)/D(i,0);
      }

    }

    if (linear == 1){
      //Compute M, the linear matrix to be used in the preconditioner

      pb = basis->dimension()+1;

      M->putScalar(0.0);
      if (pb < Cijk->num_k())
  k_end = Cijk->find_k(pb);
      for (typename Cijk_type::k_iterator k_it=k_begin; k_it!=k_end; ++k_it) {
  k = index(k_it);
  for ( typename Cijk_type::kj_iterator j_it = Cijk->j_begin(k_it);
        j_it != Cijk->j_end(k_it); ++j_it) {
    j = index(j_it);
    for ( typename Cijk_type::kji_iterator i_it = Cijk->i_begin(j_it);
    i_it  != Cijk->i_end(j_it); ++i_it) {
      i = index(i_it);
      cijk = value(i_it);
      (*M)(i,j) += cijk*cb[k];
    }
  }
      }
      
      //Scale M
      if (equil == 1){
  //Compute inv(D)*M*inv(D)
  for (ordinal_type i=0; i<sz; i++){
    for (ordinal_type j=0; j<sz; j++){
      (*M)(i,j)=(*M)(i,j)/(D(i,0)*D(j,0));
    }
  }
      }
      CG(*A,*X,*B, max_it, tol, prec_iter, basis->order(), basis->dimension(), PrecNum, *M, diag);
    }
    
    else{
      
      CG(*A,*X,*B, max_it, tol, prec_iter, basis->order(), basis->dimension(), PrecNum, *A, diag);
    }
    
    if (equil == 1 ) {
      //Rescale X 
      for (ordinal_type i=0; i<sz; i++){
  (*X)(i,0)=(*X)(i,0)/D(i,0);
      }
    }
   
    // Compute c
    for (ordinal_type i=0; i<pc; i++)
      cc[i] = alpha*(*X)(i,0) + beta*cc[i];
  }
  else {
    for (ordinal_type i=0; i<pc; i++)
      cc[i] = alpha*ca[i]/cb[0] + beta*cc[i];
  }
}
 

template <typename ordinal_type, typename value_type, typename node_type>
ordinal_type
Stokhos::CGDivisionExpansionStrategy<ordinal_type,value_type,node_type>::
CG(const Teuchos::SerialDenseMatrix<ordinal_type, value_type> & A, 
   Teuchos::SerialDenseMatrix<ordinal_type,value_type> & X, 
   const Teuchos::SerialDenseMatrix<ordinal_type,value_type> & B, 
   ordinal_type max_iter, 
   value_type tolerance, 
   ordinal_type prec_iter, 
   ordinal_type order , 
   ordinal_type m, 
   ordinal_type PrecNum, 
   const Teuchos::SerialDenseMatrix<ordinal_type, value_type> & M, 
   ordinal_type diag)

{
  ordinal_type n = A.numRows();
  ordinal_type k=0;
  value_type resid;
  Teuchos::SerialDenseMatrix<ordinal_type, value_type> Ax(n,1);
  Ax.multiply(Teuchos::NO_TRANS,Teuchos::NO_TRANS,1.0, A, X, 0.0);
  Teuchos::SerialDenseMatrix<ordinal_type, value_type> r(Teuchos::Copy,B);
  r-=Ax;
  resid=r.normFrobenius();
  Teuchos::SerialDenseMatrix<ordinal_type, value_type> p(r);
  Teuchos::SerialDenseMatrix<ordinal_type, value_type> rho(1,1);
  Teuchos::SerialDenseMatrix<ordinal_type, value_type> oldrho(1,1);
  Teuchos::SerialDenseMatrix<ordinal_type, value_type> pAp(1,1);
  Teuchos::SerialDenseMatrix<ordinal_type, value_type> Ap(n,1);
  value_type b;
  value_type a;
  while (resid > tolerance && k < max_iter){
    Teuchos::SerialDenseMatrix<ordinal_type, value_type> z(r);
    //Solve Mz=r
    if (PrecNum != 0){
      if (PrecNum == 1){
  Stokhos::DiagPreconditioner<ordinal_type, value_type> precond(M);
  precond.ApplyInverse(r,z,prec_iter);
      }
      else if (PrecNum == 2){
  Stokhos::JacobiPreconditioner<ordinal_type, value_type> precond(M);
  precond.ApplyInverse(r,z,2);
      }
      else if (PrecNum == 3){
  Stokhos::GSPreconditioner<ordinal_type, value_type> precond(M,0);
  precond.ApplyInverse(r,z,1);
      }
      else if (PrecNum == 4){
  Stokhos::SchurPreconditioner<ordinal_type, value_type> precond(M, order, m, diag);
  precond.ApplyInverse(r,z,prec_iter);            
      }
    }
    rho.multiply(Teuchos::TRANS,Teuchos::NO_TRANS,1.0, r, z, 0.0);
    

    if (k==0){
      p.assign(z);
      rho.multiply(Teuchos::TRANS, Teuchos::NO_TRANS, 1.0, r, z, 0.0);  
    }
    else {
      b=rho(0,0)/oldrho(0,0);
      p.scale(b);
      p+=z; 
    }
    Ap.multiply(Teuchos::NO_TRANS,Teuchos::NO_TRANS,1.0, A, p, 0.0);
    pAp.multiply(Teuchos::TRANS,Teuchos::NO_TRANS,1.0, p, Ap, 0.0);
    a=rho(0,0)/pAp(0,0);
    Teuchos::SerialDenseMatrix<ordinal_type, value_type> scalep(p);
    scalep.scale(a);
    X+=scalep;
    Ap.scale(a);
    r-=Ap;
    oldrho.assign(rho);
    resid=r.normFrobenius();
    k++;
  }                      
 
  //std::cout << "iteration count  " << k << std::endl;
  return 0; 
}

 #endif // STOKHOS_DIVISION_EXPANSION_STRATEGY_HPP