Stokhos_OrthogonalizationFactory.hpp

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

#ifndef STOKHOS_ORTHOGONALIZATION_FACTORY_HPP
#define STOKHOS_ORTHOGONALIZATION_FACTORY_HPP

#include <string>
#include "Teuchos_Array.hpp"
#include "Teuchos_SerialDenseMatrix.hpp"
#include "Stokhos_SDMUtils.hpp"

namespace Stokhos {

  template <typename ordinal_type, typename value_type>
  class OrthogonalizationFactory {
  public:


    OrthogonalizationFactory() {}

    virtual ~OrthogonalizationFactory() {}

    typedef Teuchos::SerialDenseMatrix<ordinal_type,value_type> SDM;

    static ordinal_type
    createOrthogonalBasis(const std::string& method, value_type threshold,
        bool verbose, const SDM& A,
        const Teuchos::Array<value_type>& w,
        SDM& Q, SDM& R,
        Teuchos::Array<ordinal_type>& piv) {

      ordinal_type m = A.numRows();
      ordinal_type n = A.numCols();
      ordinal_type rank = std::min(m,n);

      if (method == "SVD") { // A = U*diag(sigma)*V^T, Q = U, R = sigma*V^T
  Teuchos::Array<value_type> sigma;
  SDM Vt;
  rank = svd_threshold(threshold, A, sigma, Q, Vt);
  R.reshape(rank, Vt.numCols());
  for (ordinal_type j=0; j<Vt.numCols(); j++)
    for (ordinal_type i=0; i<rank; i++)
      R(i,j) = sigma[i]*Vt(i,j);
  piv.resize(n);
  for (int i=0; i<n; i++)
    piv[i] = i;

  if (verbose) {
    // std::cout << "diag(sigma) = [ ";
    // for (ordinal_type i=0; i<rank; i++)
    //   std::cout << sigma[i] << " ";
    // std::cout << "]" << std::endl;
    
    std::cout << "rank = " << rank << std::endl;
  }
      }

      else { // All QR-based methods

  if (method == "Householder")
    rank = CPQR_Householder_threshold(threshold, A, w, Q, R, piv);

  else if (method == "Householder without Pivoting") {
    QR_Householder(rank, A, w, Q, R);
    piv.resize(n);
    for (int i=0; i<n; i++)
      piv[i] = i;
  }

  else if (method == "Modified Gram-Schmidt")
    rank = CPQR_MGS_threshold(threshold, A, w, Q, R, piv);

  else if (method == "Modified Gram-Schmidt with Reorthogonalization")
    rank = CPQR_MGS_reorthog_threshold(threshold, A, w, Q, R, piv);

  else if (method == "Modified Gram-Schmidt without Pivoting") {
    QR_MGS(rank, A, w, Q, R);
    piv.resize(n);
    for (int i=0; i<n; i++)
      piv[i] = i;
  }

  else if (method == "Modified Gram-Schmidt without Pivoting with Reorthogonalization") {
    QR_MGS2(rank, A, w, Q, R);
    piv.resize(n);
    for (int i=0; i<n; i++)
      piv[i] = i;
  }

  else
    TEUCHOS_TEST_FOR_EXCEPTION(
    true, std::logic_error, 
    "Invalid orthogonalization method " << method);

  if (verbose) {
    // std::cout << "piv = [";
    // for (ordinal_type i=0; i<rank; i++)
    //   std::cout << piv[i] << " ";
    // std::cout << "]" << std::endl;
    
    // std::cout << "diag(R) = [ ";
    // for (ordinal_type i=0; i<rank; i++)
    //   std::cout << R(i,i) << " ";
    // std::cout << "]" << std::endl;
    
    std::cout << "rank = " << rank << std::endl;

    // Check A*P = Q*R
    std::cout << "||A*P-Q*R||_infty = " 
        << Stokhos::residualCPQRError(A,Q,R,piv) << std::endl;
      
    // Check Q^T*diag(w)*Q = I
    std::cout << "||I - Q^T*diag(w)**Q||_infty = " 
        << weightedQROrthogonalizationError(Q,w) << std::endl;
  }
      }

      return rank;
    }

  private:

    // Prohibit copying
    OrthogonalizationFactory(const OrthogonalizationFactory&);

    // Prohibit Assignment
    OrthogonalizationFactory& operator=(const OrthogonalizationFactory&);

  }; // class OrthogonalizationFactory

} // Namespace Stokhos

#endif