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 
00046 template<class Scalar>
00047 bool sillyPowerMethod(
00048   const Thyra::LinearOpBase<Scalar>                              &A
00049   ,const int                                                     maxNumIters
00050   ,const typename Teuchos::ScalarTraits<Scalar>::magnitudeType   tolerance
00051   ,Scalar                                                        *lambda
00052   ,std::ostream                                                  *out          = NULL
00053   )
00054 {
00055   // Create some typedefs and some other stuff to make the code cleaner
00056   typedef Teuchos::ScalarTraits<Scalar> ST; typedef typename ST::magnitudeType ScalarMag;
00057   const Scalar one = ST::one(); using Thyra::NOTRANS;
00058   typedef Teuchos::RCP<const Thyra::VectorSpaceBase<Scalar> > VectorSpacePtr;
00059   typedef Teuchos::RCP<Thyra::VectorBase<Scalar> > VectorPtr;
00060   // Initialize
00061   if(out) *out << "\nStarting power method (target tolerrance = "<<tolerance<<") ...\n\n";
00062   VectorPtr q = createMember(A.domain()), z = createMember(A.range()), r = createMember(A.range());
00063   Thyra::seed_randomize<Scalar>(0);
00064   Thyra::randomize( Scalar(-one), Scalar(+one), &*z );
00065   // Perform iterations
00066   for( int iter = 0; iter < maxNumIters; ++iter ) {
00067     const ScalarMag z_nrm = norm(*z);       // Compute natural norm of z
00068     V_StV( &*q, Scalar(one/z_nrm), *z );    // q = (1/||z}*z 
00069     apply( A, NOTRANS , *q, &*z );          // z = A*q
00070     *lambda = scalarProd(*q,*z);            // lambda = <q,z>    : Approximate maximum absolute eigenvalue
00071     if( iter%(maxNumIters/10) == 0 || iter+1 == maxNumIters ) {
00072       V_StVpV(&*r,Scalar(-*lambda),*q,*z);  // r = -lambda*q + z : Compute residual of eigenvalue equation
00073       const ScalarMag r_nrm = norm(*r);     // Compute natural norm of r
00074       if(out) *out << "Iter = " << iter << ", lambda = " << (*lambda) << ", ||A*q-lambda*q|| = " << r_nrm << std::endl;
00075       if( r_nrm < tolerance ) return true;  // Success!
00076     }
00077   }
00078   if(out) *out << "\nMaximum number of iterations exceeded with ||-lambda*q + z|| > tolerence = " << tolerance << "\n";
00079   return false; // Failure
00080 } // end sillyPowerMethod
00081 
00082 #endif // THYRA_SILLY_POWER_METHOD_HPP

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