sillyPowerMethod.hpp

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00001 // @HEADER
00002 // ***********************************************************************
00003 // 
00004 //    Thyra: Interfaces and Support for Abstract Numerical Algorithms
00005 //                 Copyright (2004) Sandia Corporation
00006 // 
00007 // Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
00008 // license for use of this work by or on behalf of the U.S. Government.
00009 // 
00010 // This library is free software; you can redistribute it and/or modify
00011 // it under the terms of the GNU Lesser General Public License as
00012 // published by the Free Software Foundation; either version 2.1 of the
00013 // License, or (at your option) any later version.
00014 //  
00015 // This library is distributed in the hope that it will be useful, but
00016 // WITHOUT ANY WARRANTY; without even the implied warranty of
00017 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
00018 // Lesser General Public License for more details.
00019 //  
00020 // You should have received a copy of the GNU Lesser General Public
00021 // License along with this library; if not, write to the Free Software
00022 // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
00023 // USA
00024 // Questions? Contact Michael A. Heroux (maherou@sandia.gov) 
00025 // 
00026 // ***********************************************************************
00027 // @HEADER
00028 
00029 #ifndef THYRA_SILLY_POWER_METHOD_HPP
00030 #define THYRA_SILLY_POWER_METHOD_HPP
00031 
00032 #include "Thyra_LinearOpBase.hpp"
00033 #include "Thyra_VectorStdOps.hpp"
00034 
00035 
00047 template<class Scalar>
00048 bool sillyPowerMethod(
00049   const Thyra::LinearOpBase<Scalar> &A,
00050   const int maxNumIters,
00051   const typename Teuchos::ScalarTraits<Scalar>::magnitudeType tolerance,
00052   const Teuchos::Ptr<Scalar> &lambda,
00053   std::ostream &out
00054   )
00055 {
00056 
00057   // Create some typedefs and some other stuff to make the code cleaner
00058   typedef Teuchos::ScalarTraits<Scalar> ST; typedef typename ST::magnitudeType ScalarMag;
00059   const Scalar one = ST::one(); using Thyra::NOTRANS;
00060   typedef Teuchos::RCP<const Thyra::VectorSpaceBase<Scalar> > VectorSpacePtr;
00061   typedef Teuchos::RCP<Thyra::VectorBase<Scalar> > VectorPtr;
00062 
00063   // Initialize
00064   out << "\nStarting power method (target tolerrance = "<<tolerance<<") ...\n\n";
00065   VectorPtr q = createMember(A.domain()), z = createMember(A.range()), r = createMember(A.range());
00066   Thyra::seed_randomize<Scalar>(0);
00067   Thyra::randomize( Scalar(-one), Scalar(+one), &*z );
00068 
00069   // Perform iterations
00070   for( int iter = 0; iter < maxNumIters; ++iter ) {
00071     const ScalarMag z_nrm = norm(*z);       // Compute natural norm of z
00072     V_StV( &*q, Scalar(one/z_nrm), *z );    // q = (1/||z}*z 
00073     apply( A, NOTRANS , *q, &*z );          // z = A*q
00074     *lambda = scalarProd(*q,*z);            // lambda = <q,z>    : Approximate maximum absolute eigenvalue
00075     if( iter%(maxNumIters/10) == 0 || iter+1 == maxNumIters ) {
00076       V_StVpV(&*r,Scalar(-*lambda),*q,*z);  // r = -lambda*q + z : Compute residual of eigenvalue equation
00077       const ScalarMag r_nrm = norm(*r);     // Compute natural norm of r
00078       out << "Iter = " << iter << ", lambda = " << (*lambda) << ", ||A*q-lambda*q|| = " << r_nrm << std::endl;
00079       if( r_nrm < tolerance )
00080         return true;  // Success!
00081     }
00082   }
00083 
00084   out << "\nMaximum number of iterations exceeded with ||-lambda*q + z||"
00085     " > tolerence = " << tolerance << "\n";
00086   return false; // Failure
00087 
00088 } // end sillyPowerMethod
00089 
00090 
00091 #endif // THYRA_SILLY_POWER_METHOD_HPP

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