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/*
ARPACK++ v1.2 2/20/2000
c++ interface to ARPACK code.
MODULE DNMatrxA.h
Function template for the matrix
| T -I |
|-I T -I |
A = | -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 Dirichlet boundary conditions.
When rho*h/2 <= 1, the discrete convection-diffusion operator has real
eigenvalues. When rho*h/2 > 1, it has COMPLEX eigenvalues.
ARPACK Authors
Richard Lehoucq
Danny Sorensen
Chao Yang
Dept. of Computational & Applied Mathematics
Rice University
Houston, Texas
*/
#ifndef DNMATRXA_H
#define DNMATRXA_H
#include <math.h>
template<class ARFLOAT, class ARINT>
void DenseMatrixA(ARINT nx, ARFLOAT rho, ARINT& n, ARFLOAT* &A)
{
// Defining internal variables.
ARINT i, j;
ARFLOAT h, h2, df;
ARFLOAT dd, dl, du;
// Defining constants.
h = 1.0/ARFLOAT(nx+1);
h2 = h*h;
dd = 4.0/h2;
df = -1.0/h2;
dl = df - 5.0e-1*rho/h;
du = df + 5.0e-1*rho/h;
// Defining the dimension of A.
n = nx*nx;
// Creating matrix A.
A = new ARFLOAT[n*n];
for (i=0; i<n*n; i++) A[i]=0.0;
for (i=0, j=0; i<n; i++, j+=n+1) {
if (i>=nx) A[j-nx] = df;
if (i%nx) A[j-1] = du;
A[j] = dd;
if ((i+1)%nx) A[j+1] = dl;
if (i<(n-nx)) A[j+nx] = df;
}
} // DenseMatrixA.
#endif // DNMATRXA_H
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