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/*
ARPACK++ v1.0 8/1/1997
c++ interface to ARPACK code.
MODULE CMatrixA.h
Class template for the nx*nx by nx*nx block tridiagonal matrix
| T -I |
|-I T -I |
OP = | -I T |
| ... -I|
| -I T|
derived from the standard central difference discretization
of the 2 dimensional convection-diffusion operator
(Laplacian u) + rho*(du/dx)
on a unit square with zero boundary condition.
T is a nx by nx tridiagonal matrix with DD on the diagonal,
DL on the subdiagonal, and DU on the superdiagonal.
ARPACK Authors
Richard Lehoucq
Danny Sorensen
Chao Yang
Dept. of Computational & Applied Mathematics
Rice University
Houston, Texas
*/
#ifndef CMATRIXA_H
#define CMATRIXA_H
#include "arcomp.h"
#include "blas1c.h"
#include "arcomp.h"
#include "matprod.h"
template<class T>
class CompMatrixA: public MatrixWithProduct<arcomplex<T> > {
private:
int nx;
void MultTv(arcomplex<T>* x, arcomplex<T>* y);
public:
void MultMv(arcomplex<T>* v, arcomplex<T>* w);
CompMatrixA(int nxval);
}; // CompMatrixA.
template<class T>
void CompMatrixA<T>::MultTv(arcomplex<T>* x, arcomplex<T>* y)
/*
Computes the matrix vector multiplication y <- T*x
where T is a nx by nx tridiagonal matrix with DD on the
diagonal, DL on the subdiagonal, and DU on the superdiagonal.
*/
{
int j;
arcomplex<T> h, h2, dd, dl, du;
const arcomplex<T> half(0.5,0.0);
const arcomplex<T> one(1.0,0.0);
const arcomplex<T> four(4.0,0.0);
const arcomplex<T> rho(1.0e2,0.0);
h = one/arcomplex<T>(nx+1,0);
h2 = h*h;
dd = four/h2;
dl = -one/h2 - half*rho/h;
du = -one/h2 + half*rho/h;
y[0] = dd*x[0] + du*x[1];
for (j = 1; j<nx-1; j++) {
y[j] = dl*x[j-1] + dd*x[j] + du*x[j+1];
}
y[nx-1] = dl*x[nx-2] + dd*x[nx-1];
return;
} // MultTv
template<class T>
void CompMatrixA<T>::MultMv(arcomplex<T>* v, arcomplex<T>* w)
/*
Matrix-vector subroutine. Computes w <- M*v.
*/
{
int j, lo;
arcomplex<T> h2;
const arcomplex<T> one(1.0,0.0);
h2 = one/arcomplex<T>((nx+1)*(nx+1),0.0);
MultTv(v,w);
axpy(nx, -one/h2, &v[nx], 1, w, 1);
for (j = 2; j<=nx-1; j++) {
lo = (j-1)*nx;
MultTv(&v[lo], &w[lo]);
axpy(nx, -one/h2, &v[lo-nx], 1, &w[lo], 1);
axpy(nx, -one/h2, &v[lo+nx], 1, &w[lo], 1);
}
lo = (nx-1)*nx;
MultTv(&v[lo], &w[lo]);
axpy(nx, -one/h2, &v[lo-nx], 1, &w[lo], 1);
return;
} // MultMv
template<class T>
CompMatrixA<T>::CompMatrixA(int nxval):
MatrixWithProduct<arcomplex<T> >(nxval*nxval)
/*
Constructor.
*/
{
nx = nxval;
} // constructor.
#endif // CMATRIXA_H
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