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/*
ARPACK++ v1.2 2/18/2000
c++ interface to ARPACK code.
MODULE RSymShf.cc.
Example program that illustrates how to solve a real symmetric
standard eigenvalue problem in shift and invert mode using the
ARrcSymStdEig class.
1) Problem description:
In this example we try to solve A*x = x*lambda in shift and
invert mode, where A is derived from the central difference
discretization of the 1-dimensional Laplacian on [0,1] with
zero Dirichlet boundary conditions.
2) Data structure used to represent matrix A:
class ARrcSymStdEig requires the user to provide a way to
perform the matrix-vector product w = OPv, where OP =
inv[A - sigma*I]. In this example a class called SymMatrixB was
created with this purpose. SymMatrixB contains a member function,
MultOPv, that takes a vector v and returns the product OPv in w.
3) The reverse communication interface:
This example uses the reverse communication interface, which
means that the desired eigenvalues cannot be obtained directly
from an ARPACK++ class.
Here, the overall process of finding eigenvalues by using the
Arnoldi method is splitted into two parts. In the first, a
sequence of calls to a function called TakeStep is combined
with matrix-vector products in order to find an Arnoldi basis.
In the second part, an ARPACK++ function like FindEigenvectors
(or EigenValVectors) is used to extract eigenvalues and
eigenvectors.
4) Included header files:
File Contents
----------- -------------------------------------------
smatrixb.h The SymMatrixB class definition.
arrssym.h The ARrcSymStdEig class definition.
rsymsol.h The Solution function.
5) ARPACK Authors:
Richard Lehoucq
Kristyn Maschhoff
Danny Sorensen
Chao Yang
Dept. of Computational & Applied Mathematics
Rice University
Houston, Texas
*/
#include "arrssym.h"
#include "smatrixb.h"
#include "rsymsol.h"
template<class T>
void Test(T type)
{
// Creating a symmetric matrix.
SymMatrixB<T> B(100,0.0); // n = 100, shift = 0.0.
// Creating a symmetric eigenvalue problem and defining what we need:
// the four eigenvectors of B nearest to 0.0.
ARrcSymStdEig<T> prob(B.ncols(), 4, (T)0.0);
// Finding an Arnoldi basis.
while (!prob.ArnoldiBasisFound()) {
// Calling ARPACK FORTRAN code. Almost all work needed to
// find an Arnoldi basis is performed by TakeStep.
prob.TakeStep();
if ((prob.GetIdo() == 1)||(prob.GetIdo() == -1)) {
// Performing matrix-vector multiplication.
// In shift and invert mode, w = OPv must be performed
// whenever GetIdo is equal to 1 or -1. GetVector supplies
// a pointer to the input vector, v, and PutVector a pointer
// to the output vector, w.
B.MultOPv(prob.GetVector(), prob.PutVector());
}
}
// Finding eigenvalues and eigenvectors.
prob.FindEigenvectors();
// Printing solution.
Solution(prob);
} // Test.
int main()
{
// Solving a double precision problem with n = 100.
Test((double)0.0);
// Solving a single precision problem with n = 100.
Test((float)0.0);
} // main
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