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/*
ARPACK++ v1.2 2/18/2000
c++ interface to ARPACK code.
MODULE RCompGSh.cc.
Example program that illustrates how to solve a complex
generalized eigenvalue problem in shift and invert mode
using the ARrcCompGenEig class.
1) Problem description:
In this example we try to solve A*x = B*x*lambda in shift and
invert mode, where A and B are derived from a finite element
discretization of a 1-dimensional convection-diffusion operator
(d^2u/dx^2) + rho*(du/dx)
on the interval [0,1] with zero boundary conditions using
piecewise linear elements.
2) Data structure used to represent matrix A:
ARrcCompGenEig is a class thar requires the user to provide a
way to perform the matrix-vector products w = OP*Bv =
inv(A-sigma*B)*B*v and w = B*v, where sigma is the adopted shift.
In this example a class called ComplexGenProblemB was created
with this purpose. ComplexGenProblemB contains a member function,
MultOPv(v,w), that takes a vector v and returns the product OPv
in w. It also contains an object, B, that stores matrix B data.
The product Bv is performed by MultMv, a member function of B.
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
----------- -------------------------------------------
cgenprbb.h The ComplexGenProblemB class definition.
arrgcomp.h The ARrcCompGenEig class definition.
rcompgsl.h The Solution function.
arcomp.h The "arcomplex" (complex) type definition.
5) ARPACK Authors:
Richard Lehoucq
Kristyn Maschhoff
Danny Sorensen
Chao Yang
Dept. of Computational & Applied Mathematics
Rice University
Houston, Texas
*/
#include "arcomp.h"
#include "cgenprbb.h"
#include "rcompgsl.h"
#include "arrgcomp.h"
template<class T>
void Test(T type)
{
// Defining a temporary vector.
arcomplex<T> temp[101];
// Defining a complex pencil with n = 100, rho = 10, sigma = 1.
ComplexGenProblemB<T> P(100, arcomplex<T>(10.0,0.0), arcomplex<T>(1.0,0.0));
// Creating a complex eigenvalue problem and defining what we need:
// the four eigenvectors nearest to 1.0.
ARrcCompGenEig<T> prob(P.A.ncols(), 4L, arcomplex<T>(1.0,0.0));
// 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();
switch (prob.GetIdo()) {
case -1:
// Performing w <- OP*B*v for the first time.
// This product must be performed only if GetIdo is equal to
// -1. GetVector supplies a pointer to the input vector, v,
// and PutVector a pointer to the output vector, w.
P.B.MultMv(prob.GetVector(), temp);
P.MultOPv(temp, prob.PutVector());
break;
case 1:
// Performing w <- OP*B*v when Bv is available.
// This product must be performed whenever GetIdo is equal to
// 1. GetProd supplies a pointer to the previously calculated
// product Bv and PutVector a pointer to the output vector w.
P.MultOPv(prob.GetProd(), prob.PutVector());
break;
case 2:
// Performing w <- B*v.
P.B.MultMv(prob.GetVector(), prob.PutVector());
}
}
// Finding eigenvalues and eigenvectors.
prob.FindEigenvectors();
// Printing solution.
Solution(prob);
} // Test.
int main()
{
// Solving a single precision problem with n = 100.
#ifndef __SUNPRO_CC
Test((float)0.0);
#endif
// Solving a double precision problem with n = 100.
Test((double)0.0);
} // main
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