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/*
ARPACK++ v1.2 2/20/2000
c++ interface to ARPACK code.
MODULE LNMatrxB.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 LNMATRXB_H
#define LNMATRXB_H
#include <math.h>
template<class ARFLOAT, class ARINT>
void BlockTridMatrix(ARINT nx, ARINT& n, ARINT& nnz,
ARFLOAT* &A, ARINT* &irow, ARINT* &pcol)
{
// Defining internal variables.
ARINT i, j;
ARFLOAT h, h2, df;
ARFLOAT dd, dl, du;
// Defining constants.
const ARFLOAT rho = 0.0;
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 number of columns and nonzero elements of matrix.
n = nx*nx;
nnz = 5*n-4*nx;
// Creating output vectors.
A = new ARFLOAT[nnz];
irow = new ARINT[nnz];
pcol = new ARINT[n+1];
// Creating matrix.
pcol[0] = 0;
i = 0;
for (j = 0; j < n; j++) {
if (j >= nx) {
A[i] = df; irow[i++] = j-nx;
}
if ((j%nx) != 0) {
A[i] = du; irow[i++] = j-1;
}
A[i] = dd; irow[i++] = j;
if (((j+1)%nx) != 0) {
A[i] = dl; irow[i++] = j+1;
}
if (j < n-nx) {
A[i] = df; irow[i++] = j+nx;
}
pcol[j+1] = i;
}
} // BlockTridMatrix.
#endif // LNMATRXB_H
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