sillyPowerMethod.hpp

// @HEADER
// *****************************************************************************
//    Thyra: Interfaces and Support for Abstract Numerical Algorithms
//
// Copyright 2004 NTESS and the Thyra contributors.
// SPDX-License-Identifier: BSD-3-Clause
// *****************************************************************************
// @HEADER

#ifndef THYRA_SILLY_POWER_METHOD_HPP
#define THYRA_SILLY_POWER_METHOD_HPP

#include "Thyra_LinearOpBase.hpp"
#include "Thyra_VectorStdOps.hpp"


template<class Scalar>
bool sillyPowerMethod(
  const Thyra::LinearOpBase<Scalar> &A,
  const int maxNumIters,
  const typename Teuchos::ScalarTraits<Scalar>::magnitudeType tolerance,
  const Teuchos::Ptr<Scalar> &lambda,
  std::ostream &out
  )
{

  // Create some typedefs and some other stuff to make the code cleaner
  typedef Teuchos::ScalarTraits<Scalar> ST; typedef typename ST::magnitudeType ScalarMag;
  using Thyra::apply;
  const Scalar one = ST::one(); using Thyra::NOTRANS;
  //typedef Teuchos::RCP<const Thyra::VectorSpaceBase<Scalar> > VectorSpacePtr; // unused
  typedef Teuchos::RCP<Thyra::VectorBase<Scalar> > VectorPtr;

  // Initialize
  out << "\nStarting power method (target tolerance = "<<tolerance<<") ...\n\n";
  VectorPtr q = createMember(A.domain()), z = createMember(A.range()), r = createMember(A.range());
  Thyra::seed_randomize<Scalar>(0);
  Thyra::randomize( Scalar(-one), Scalar(+one), z.ptr() );

  // Perform iterations
  for( int iter = 0; iter < maxNumIters; ++iter ) {
    const ScalarMag z_nrm = norm(*z);           // Compute natural norm of z
    V_StV( q.ptr(), Scalar(one/z_nrm), *z );    // q = (1/||z||)*z
    apply<Scalar>( A, NOTRANS , *q, z.ptr() );  // z = A*q
    *lambda = scalarProd(*q,*z);                // lambda = <q,z>
    if( iter%(maxNumIters/10) == 0 || iter+1 == maxNumIters ) {
      V_StVpV(r.ptr(),Scalar(-*lambda),*q,*z);  // r = -lambda*q + z
      const ScalarMag r_nrm = norm(*r);         // Compute natural norm of r
      out << "Iter = " << iter << ", lambda = " << (*lambda)
          << ", ||A*q-lambda*q|| = " << r_nrm << std::endl;
      if( r_nrm < tolerance )
        return true;  // Success!
    }
  }

  out << "\nMaximum number of iterations exceeded with ||-lambda*q + z||"
    " > tolerence = " << tolerance << "\n";
  return false; // Failure

} // end sillyPowerMethod


#endif // THYRA_SILLY_POWER_METHOD_HPP