// Calculate matrix element of a coulomb potential given the charges
// of the elements
public double coulombPotentialEnergy(matrix A, matrix B)
{
double epsilon_0 = 1; // Unit is set to 1 maight want to make static units
/* int N = problem.getNumberOfParticles() - 1; // For easier readability */
int N = problem.getNumberOfParticles();
double result = 0;
matrix inverse = new QRdecomposition(A + B).inverse();
// For every particle pair (only counting once) calculate interaction
List <Particle> particles = problem.getParticles();
matrix Uinv = problem.getUInverse();
for (int j = 0; j < N; j++)
{
for (int i = 0; i < j; i++)
{
double p_ij = 0;
for (int k = 0; k < N - 1; k++)
{
for (int l = 0; l < N - 1; l++)
{
double b_ijk = Uinv[i, k] - Uinv[j, k];
double b_ijl = Uinv[i, l] - Uinv[j, l];
p_ij += b_ijk * inverse[k, l] * b_ijl;
}
}
/* result += particles[i].getCharge() * particles[j].getCharge() / (4 * Math.PI * epsilon_0) * Math.Sqrt(2 / (p_ij * Math.PI)) * overlapElement(A,B); */
result += particles[i].getCharge() * particles[j].getCharge() * 2.0 / epsilon_0 * Math.Sqrt(1 / (p_ij * Math.PI * 2)) * overlapElement(A, B);
}
}
return(result);
}
public matrix permute(matrix M, Permutation p)
{
matrix Ci = generateC(p.ToArray());
/* matrix tmp = problem.getU().transpose() * Ci * problem.getU(); */
matrix tmp = problem.getU() * Ci * problem.getUInverse();
matrix T = new matrix(M.rows, M.cols);
for (int i = 0; i < M.rows; i++)
{
for (int j = 0; j < M.cols; j++)
{
T[i, j] = tmp[i, j];
}
}
matrix result = T * M * T.transpose();
return(result);
}