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/*
ARPACK++ v1.2 2/20/2000
c++ interface to ARPACK code.
MODULE LNMatrxA.h
Function template for the 2-D Brusselator Wave model.
*/
#ifndef LNMATRXA_H
#define LNMATRXA_H
#include <math.h>
template<class ARFLOAT, class ARINT>
void BrusselatorMatrix(ARFLOAT L, ARFLOAT delta1, ARFLOAT delta2,
ARFLOAT alpha, ARFLOAT beta, ARINT n, ARINT& nnz,
ARFLOAT* &A, ARINT* &irow, ARINT* &pcol)
{
// Defining internal variables.
ARINT i, j, icount;
ARINT m, m2;
ARFLOAT h, tau1, tau2;
ARFLOAT d1, d2, alpha2;
// Defining constants.
const ARFLOAT one = 1.0;
const ARFLOAT four = 4.0;
m = ARINT(sqrt(n/2));
m2 = 2*m;
h = one / ARFLOAT(m+1);
tau1 = delta1/(h*h*L*L);
tau2 = delta2/(h*h*L*L);
alpha2 = alpha*alpha;
d1 = -tau1*four + beta - one;
d2 = -tau2*four - alpha2;
// Defining the number of nonzero elements of matrix.
nnz = 6*n-8*m;
// Creating output vectors.
A = new ARFLOAT[nnz];
irow = new ARINT[nnz];
pcol = new ARINT[n+1];
// Creating brusselator matrix.
pcol[0] = 0;
// First two columns.
A[0] = d1; irow[0] = 0;
A[1] = -beta; irow[1] = 1;
A[2] = tau1; irow[2] = 2;
A[3] = tau1; irow[3] = m2;
pcol[1] = 4;
A[4] = alpha2; irow[4] = 0;
A[5] = d2; irow[5] = 1;
A[6] = tau2; irow[6] = 3;
A[7] = tau2; irow[7] = m2+1;
pcol[2] = 8;
// Next 2m-2 columns.
i = pcol[2];
for (j = 2; j < m2; j += 2) {
A[i] = tau1; irow[i++] = j-2;
A[i] = d1; irow[i++] = j;
A[i] = -beta; irow[i++] = j+1;
if (j != m2-2) {
A[i] = tau1; irow[i++] = j+2;
}
A[i] = tau1; irow[i++] = m2+j;
pcol[j+1] = i;
A[i] = tau2; irow[i++] = j-1;
A[i] = alpha2; irow[i++] = j;
A[i] = d2; irow[i++] = j+1;
if (j != m2-2) {
A[i] = tau2; irow[i++] = j+3;
}
A[i] = tau2; irow[i++] = m2+j+1;
pcol[j+2] = i;
}
// Next n-4m columns.
icount = 0;
for (j = m2; j < n-m2; j += 2) {
A[i] = tau1; irow[i++] = j-m2;
if (icount != 0) {
A[i] = tau1; irow[i++] = j-2;
}
A[i] = d1; irow[i++] = j;
A[i] = -beta; irow[i++] = j+1;
if (icount != m2-2) {
A[i] = tau1; irow[i++] = j+2;
}
A[i] = tau1; irow[i++] = j+m2;
pcol[j+1] = i;
A[i] = tau2; irow[i++] = j-m2+1;
if (icount != 0) {
A[i] = tau2; irow[i++] = j-1;
}
A[i] = alpha2; irow[i++] = j;
A[i] = d2; irow[i++] = j+1;
if (icount != m2-2) {
A[i] = tau2; irow[i++] = j+3;
}
A[i] = tau2; irow[i++] = j+m2+1;
pcol[j+2] = i;
icount = (icount+2)%(m2);
}
// Next 2m-2 columns.
for (j = n-m2; j < n-2; j += 2) {
A[i] = tau1; irow[i++] = j-m2;
if (j != n-m2) {
A[i] = tau1; irow[i++] = j-2;
}
A[i] = d1; irow[i++] = j;
A[i] = -beta; irow[i++] = j+1;
A[i] = tau1; irow[i++] = j+2;
pcol[j+1] = i;
A[i] = tau2; irow[i++] = j-m2+1;
if (j != n-m2) {
A[i] = tau2; irow[i++] = j-1;
}
A[i] = alpha2; irow[i++] = j;
A[i] = d2; irow[i++] = j+1;
A[i] = tau2; irow[i++] = j+3;
pcol[j+2] = i;
}
// Last two columns.
A[i] = tau1; irow[i++] = n-m2-2;
A[i] = tau1; irow[i++] = n-4;
A[i] = d1; irow[i++] = n-2;
A[i] = -beta; irow[i++] = n-1;
pcol[n-1] = i;
A[i] = tau2; irow[i++] = n-m2-1;
A[i] = tau2; irow[i++] = n-3;
A[i] = alpha2; irow[i++] = n-2;
A[i] = d2; irow[i++] = n-1;
pcol[n] = i;
} // BrusselatorMatrix.
#endif // LNMATRXA_H
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