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power_method.cpp
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4// Epetra: Linear Algebra Services Package
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41
42
43#include <stdio.h>
44#include <stdlib.h>
45#include "Epetra_Comm.h"
46#include "Epetra_Map.h"
47#include "Epetra_Vector.h"
48#include "Epetra_CrsMatrix.h"
49// Simple Power method algorithm
51 // variable needed for iteration
52 double lambda = 0.0;
53 int niters = A.RowMap().NumGlobalElements()*10;
54 double tolerance = 1.0e-10;
55 // Create vectors
56 Epetra_Vector q(A.RowMap());
57 Epetra_Vector z(A.RowMap());
58 Epetra_Vector resid(A.RowMap());
59 // Fill z with random Numbers
60 z.Random();
61 // variable needed for iteration
62 double normz;
63 double residual = 0;
64 int iter = 0;
65 while (iter==0 || (iter < niters && residual > tolerance)) {
66 z.Norm2(&normz); // Compute 2-norm of z
67 q.Scale(1.0/normz, z);
68 A.Multiply(false, q, z); // Compute z = A*q
69 q.Dot(z, &lambda); // Approximate maximum eigenvalue
70 if (iter%10==0 || iter+1==niters) {
71 // Compute A*q - lambda*q every 10 iterations
72 resid.Update(1.0, z, -lambda, q, 0.0);
73 resid.Norm2(&residual);
74 if (q.Map().Comm().MyPID()==0)
75 std::cout << "Iter = " << iter << " Lambda = " << lambda
76 << " Two-norm of A*q - lambda*q = "
77 << residual << std::endl;
78 }
79 iter++;
80 }
81 return(lambda);
82}
int NumGlobalElements() const
Number of elements across all processors.
const Epetra_Comm & Comm() const
Access function for Epetra_Comm communicator.
virtual int MyPID() const =0
Return my process ID.
Epetra_CrsMatrix: A class for constructing and using real-valued double-precision sparse compressed r...
const Epetra_Map & RowMap() const
Returns the Epetra_Map object associated with the rows of this matrix.
int Multiply(bool TransA, const Epetra_Vector &x, Epetra_Vector &y) const
Returns the result of a Epetra_CrsMatrix multiplied by a Epetra_Vector x in y.
const Epetra_BlockMap & Map() const
Returns the address of the Epetra_BlockMap for this multi-vector.
int Scale(double ScalarValue)
Scale the current values of a multi-vector, this = ScalarValue*this.
int Dot(const Epetra_MultiVector &A, double *Result) const
Computes dot product of each corresponding pair of vectors.
int Update(double ScalarA, const Epetra_MultiVector &A, double ScalarThis)
Update multi-vector values with scaled values of A, this = ScalarThis*this + ScalarA*A.
int Random()
Set multi-vector values to random numbers.
int Norm2(double *Result) const
Compute 2-norm of each vector in multi-vector.
Epetra_Vector: A class for constructing and using dense vectors on a parallel computer.
double power_method(const Epetra_CrsMatrix &A)