Tpetra Matrix/Vector Services Version of the Day
Tpetra_Power_Method.hpp
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00005 //          Tpetra: Templated Linear Algebra Services Package
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00043 
00044 #ifndef TPETRA_POWER_METHOD_HPP
00045 #define TPETRA_POWER_METHOD_HPP
00046 
00047 #include <Tpetra_Operator.hpp>
00048 #include <Tpetra_Vector.hpp>
00049 #include <Teuchos_ScalarTraits.hpp>
00050 
00051 namespace TpetraExamples {
00052 
00055   template <class Scalar, class Ordinal>
00056   Scalar powerMethod(const Teuchos::RCP<const Tpetra::Operator<Scalar,Ordinal> > &A, int niters, typename Teuchos::ScalarTraits<Scalar>::magnitudeType tolerance, bool verbose) 
00057   {
00058     typedef typename Teuchos::ScalarTraits<Scalar>::magnitudeType Magnitude;
00059     typedef Tpetra::Vector<Scalar,Ordinal> Vector;
00060 
00061     if ( A->getRangeMap() != A->getDomainMap() ) {
00062       throw std::runtime_error("TpetraExamples::powerMethod(): operator must have domain and range maps that are equivalent.");
00063     }
00064     // create three vectors, fill z with random numbers
00065     Teuchos::RCP<Vector> z, q, r;
00066     q = Tpetra::createVector<Scalar>(A->getRangeMap());
00067     r = Tpetra::createVector<Scalar>(A->getRangeMap());
00068     z = Tpetra::createVector<Scalar>(A->getRangeMap());
00069     z->randomize();
00070     // 
00071     Scalar lambda = 0.0;
00072     Magnitude normz, residual = 0.0;
00073     // power iteration
00074     for (int iter = 0; iter < niters; ++iter) {
00075       normz = z->norm2();                             // Compute 2-norm of z
00076       q->scale(1.0/normz, *z);                        // Set q = z / normz
00077       A->apply(*q, *z);                               // Compute z = A*q
00078       lambda = q->dot(*z);                            // Approximate maximum eigenvalue: lamba = dot(q,z)
00079       if ( iter % 100 == 0 || iter + 1 == niters ) {
00080         r->update(1.0, *z, -lambda, *q, 0.0);         // Compute A*q - lambda*q
00081         residual = Teuchos::ScalarTraits<Scalar>::magnitude(r->norm2() / lambda);
00082         if (verbose) {
00083           std::cout << "Iter = " << iter 
00084                     << "  Lambda = " << lambda 
00085                     << "  Residual of A*q - lambda*q = " << residual 
00086                     << std::endl;
00087         }
00088       } 
00089       if (residual < tolerance) {
00090         break;
00091       }
00092     }
00093     return lambda;
00094   }
00095 
00096 } // end of namespace TpetraExamples
00097 
00106 #endif
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