Stokhos_GMRESDivisionExpansionStrategy.hpp

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

#ifndef STOKHOS_GMRES_DIVISION_EXPANSION_STRATEGY_HPP
#define STOKHOS_GMRES_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_BlockPreconditioner.hpp"

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

namespace Stokhos {


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

    GMRESDivisionExpansionStrategy(
      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 ~GMRESDivisionExpansionStrategy() {}
 
    // 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
    GMRESDivisionExpansionStrategy(
      const GMRESDivisionExpansionStrategy&);

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

      ordinal_type GMRES(
  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 GMRESDivisionExpansionStrategy

} // namespace Stokhos

template <typename ordinal_type, typename value_type, typename node_type> 
Stokhos::GMRESDivisionExpansionStrategy<ordinal_type,value_type,node_type>::
GMRESDivisionExpansionStrategy(
  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::GMRESDivisionExpansionStrategy<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::GMRESDivisionStrategy::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));
  }
      }
    }
    
    
    // Compute X = A^{-1}*B  
    GMRES(*A,*X,*B, max_it, tol, prec_iter, basis->order(), basis->dimension(), PrecNum, *M, diag);
  }
  
  else{
    GMRES(*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::GMRESDivisionExpansionStrategy<ordinal_type,value_type,node_type>::
GMRES(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)
{
  ordinal_type n = A.numRows();
  ordinal_type k = 1;
  value_type resid;
  Teuchos::SerialDenseMatrix<ordinal_type, value_type> P(n,n);
  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> r0(Teuchos::Copy,B);
  r0-=Ax;
  resid=r0.normFrobenius();
  //define vector v=r/norm(r) where r=b-Ax
  Teuchos::SerialDenseMatrix<ordinal_type, value_type> v(n,1);
  r0.scale(1/resid);
  Teuchos::SerialDenseMatrix<ordinal_type, value_type> h(1,1);
  //Matrix of orthog basis vectors V
  Teuchos::SerialDenseMatrix<ordinal_type, value_type> V(n,1);
  //Set v=r0/norm(r0) to be 1st col of V
  for (ordinal_type i=0; i<n; i++){
    V(i,0)=r0(i,0);
  }
  //right hand side
  Teuchos::SerialDenseMatrix<ordinal_type, value_type> bb(1,1);
  bb(0,0)=resid;
  Teuchos::SerialDenseMatrix<ordinal_type, value_type> w(n,1);
  Teuchos::SerialDenseMatrix<ordinal_type, value_type> c;
  Teuchos::SerialDenseMatrix<ordinal_type, value_type> s;
  while (resid > tolerance && k < max_iter){
    h.reshape(k+1,k);
    //Arnoldi iteration(Gram-Schmidt )
    V.reshape(n,k+1);
    //set vk to be kth col of V
    Teuchos::SerialDenseMatrix<ordinal_type, value_type> vk(Teuchos::Copy, V, n,1,0,k-1);
    //Preconditioning step: solve Mz=vk
    Teuchos::SerialDenseMatrix<ordinal_type, value_type> z(vk);
    if (PrecNum == 1){
      Stokhos::DiagPreconditioner<ordinal_type, value_type> precond(M);
      precond.ApplyInverse(vk,z,prec_iter);
    }
    else if (PrecNum == 2){
      Stokhos::JacobiPreconditioner<ordinal_type, value_type> precond(M);
      precond.ApplyInverse(vk,z,2);
    }
    else if (PrecNum == 3){
      Stokhos::GSPreconditioner<ordinal_type, value_type> precond(M,1);
      precond.ApplyInverse(vk,z,1);
    }
    else if (PrecNum == 4){
      Stokhos::SchurPreconditioner<ordinal_type, value_type> precond(M, order, dim, diag);
      precond.ApplyInverse(vk,z,prec_iter);
    }

    w.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, 1, A, z, 0.0);
    Teuchos::SerialDenseMatrix<ordinal_type, value_type> vi(n,1);
    Teuchos::SerialDenseMatrix<ordinal_type, value_type> ip(1,1);
    for (ordinal_type i=0; i<k; i++){
      //set vi to be ith col of V
      Teuchos::SerialDenseMatrix<ordinal_type, value_type> vi(Teuchos::Copy, V, n,1,0,i);
      //Calculate inner product
      ip.multiply(Teuchos::TRANS, Teuchos::NO_TRANS, 1.0, vi, w, 0.0);
      h(i,k-1)= ip(0,0);
      //scale vi by h(i,k-1)
      vi.scale(ip(0,0));
      w-=vi;
    }
    h(k,k-1)=w.normFrobenius(); 
    w.scale(1.0/h(k,k-1));
    //add column vk+1=w to V
    for (ordinal_type i=0; i<n; i++){
      V(i,k)=w(i,0);
    }
    //Solve upper hessenberg least squares problem via Givens rotations
    //Compute previous Givens rotations
    for (ordinal_type i=0; i<k-1; i++){
      value_type q=c(i,0)*h(i,k-1)+s(i,0)*h(i+1,k-1);
      h(i+1,k-1)=-1*s(i,0)*h(i,k-1)+c(i,0)*h(i+1,k-1);
      h(i,k-1)=q;
      
    }
    //Compute next Givens rotations
    c.reshape(k,1);
    s.reshape(k,1);
    bb.reshape(k+1,1);
    value_type l = sqrt(h(k-1,k-1)*h(k-1,k-1)+h(k,k-1)*h(k,k-1));
    c(k-1,0)=h(k-1,k-1)/l;
    s(k-1,0)=h(k,k-1)/l;
    
    // Givens rotation on h and bb
    h(k-1,k-1)=l;
    h(k,k-1)=0;
    
    bb(k,0)=-s(k-1,0)*bb(k-1,0);
    bb(k-1,0)=c(k-1,0)*bb(k-1,0);
    
    //Determine residual    
    resid = fabs(bb(k,0));
    k++;
  }
  //Extract upper triangular square matrix
  bb.reshape(h.numRows()-1 ,1);
  //Solve linear system
  ordinal_type info;
  Teuchos::LAPACK<ordinal_type, value_type> lapack;
  lapack.TRTRS('U', 'N', 'N', h.numRows()-1, 1, h.values(), h.stride(), bb.values(), bb.stride(),&info);
  Teuchos::SerialDenseMatrix<ordinal_type, value_type> ans(X);
  V.reshape(n,k-1);
  ans.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, 1.0, V, bb, 0.0);
  if (PrecNum == 1){
    Stokhos::DiagPreconditioner<ordinal_type, value_type> precond(M);
    precond.ApplyInverse(ans,ans,prec_iter);
  }
  else if (PrecNum == 2){
    Stokhos::JacobiPreconditioner<ordinal_type, value_type> precond(M);
    precond.ApplyInverse(ans,ans,2);
  }
  else if (PrecNum == 3){
    Stokhos::GSPreconditioner<ordinal_type, value_type> precond(M,1);
    precond.ApplyInverse(ans,ans,1);
  }
  else if (PrecNum == 4){
    Stokhos::SchurPreconditioner<ordinal_type, value_type> precond(M, order, dim, diag);
    precond.ApplyInverse(ans,ans,prec_iter);}
  X+=ans;
  
  //std::cout << "iteration count=  " << k-1 << std::endl;        
  
  return 0;
}

#endif // STOKHOS_DIVISION_EXPANSION_STRATEGY_HPP