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/*
ARPACK++ v1.2 2/20/2000
c++ interface to ARPACK code.
MODULE LCMatrxA.h
Function 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 conditions.
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 LCMATRXA_H
#define LCMATRXA_H
#include "arcomp.h"
#include "blas1c.h"
template<class ARFLOAT, class ARINT>
void CompMatrixA(ARINT nx, ARINT& nnz, arcomplex<ARFLOAT>* &A,
ARINT* &irow, ARINT* &pcol)
{
ARINT i, j, k, id;
arcomplex<ARFLOAT> h, h2, dd, dl, du, f;
// Defining constants.
const arcomplex<ARFLOAT> half(0.5,0.0);
const arcomplex<ARFLOAT> one(1.0,0.0);
const arcomplex<ARFLOAT> four(4.0,0.0);
const arcomplex<ARFLOAT> rho(1.0e2,0.0);
h = one/arcomplex<ARFLOAT>((ARFLOAT)(nx+1),0);
h2 = h*h;
f = -(one/h2);
dd = four/h2;
dl = f - half*rho/h;
du = f + half*rho/h;
// Defining the number of nonzero matrix elements.
nnz = (5*nx-4)*nx;
// Creating output vectors.
A = new arcomplex<ARFLOAT>[nnz];
irow = new ARINT[nnz];
pcol = new ARINT[nx*nx+1];
// Filling A, irow and pcol.
pcol[0] = 0;
j = 0;
id = 0;
for (k=0; k!=nx; k++) {
for (i=0; i!=nx; i++) {
if (k) {
irow[j] = id-nx;
A[j++] = f;
}
if (i) {
irow[j] = id-1;
A[j++] = du;
}
irow[j] = id;
A[j++] = dd;
if (i!=(nx-1)) {
irow[j] = id+1;
A[j++] = dl;
}
if (k!=(nx-1)) {
irow[j] = id+nx;
A[j++] = f;
}
pcol[++id]= j;
}
}
} // CompMatrixA.
#endif // LCMATRXA_H
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