sillyPowerMethod.hpp

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//    Thyra: Interfaces and Support for Abstract Numerical Algorithms
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#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
  ,Scalar                                                        *lambda
  ,std::ostream                                                  *out          = NULL
  )
{
  // Create some typedefs and some other stuff to make the code cleaner
  typedef Teuchos::ScalarTraits<Scalar> ST; typedef typename ST::magnitudeType ScalarMag;
  const Scalar one = ST::one(); using Thyra::NOTRANS;
  typedef Teuchos::RefCountPtr<const Thyra::VectorSpaceBase<Scalar> > VectorSpacePtr;
  typedef Teuchos::RefCountPtr<Thyra::VectorBase<Scalar> > VectorPtr;
  // Initialize
  if(out) *out << "\nStarting power method (target tolerrance = "<<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 );
  // Perform iterations
  for( int iter = 0; iter < maxNumIters; ++iter ) {
    const ScalarMag z_nrm = norm(*z);       // Compute natural norm of z
    V_StV( &*q, Scalar(one/z_nrm), *z );    // q = (1/||z}*z 
    apply( A, NOTRANS , *q, &*z );          // z = A*q
    *lambda = scalarProd(*q,*z);            // lambda = <q,z>    : Approximate maximum absolute eigenvalue
    if( iter%(maxNumIters/10) == 0 || iter+1 == maxNumIters ) {
      V_StVpV(&*r,Scalar(-*lambda),*q,*z);  // r = -lambda*q + z : Compute residual of eigenvalue equation
      const ScalarMag r_nrm = norm(*r);     // Compute natural norm of r
      if(out) *out << "Iter = " << iter << ", lambda = " << (*lambda) << ", ||A*q-lambda*q|| = " << r_nrm << std::endl;
      if( r_nrm < tolerance ) return true;  // Success!
    }
  }
  if(out) *out << "\nMaximum number of iterations exceeded with ||-lambda*q + z|| > tolerence = " << tolerance << "\n";
  return false; // Failure
} // end sillyPowerMethod

#endif // THYRA_SILLY_POWER_METHOD_HPP

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