public static void Main()
{
// First part of A
int n = 5; // Size of quadratic matrix M.
var rnd = new Random(1);
Console.WriteLine("Part A1");
matrix M = new matrix(n, n);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
M[i, j] = 4 * rnd.NextDouble() - 1.5;
M[j, i] = M[i, j];
}
}
matrix M2 = M.copy();
M.print("We choose an arbitrary matrix M = ");
vector D = new vector(n);
matrix V = new matrix(n, n);
int sweeps = Jacobi_diagonalization.cyclic_sweep(M, V, D);
matrix temp2 = V.T * M2 * V;
Console.WriteLine($"Total number of sweeps done is = {sweeps}");
temp2.print("V.T*M*V = ");
D.print("Eigenvalues = ");
}
public static void Main()
{
//Second part of A
StreamWriter eigenenergies = new StreamWriter("eigenenergiesA2.data", append: false);
StreamWriter outData = new StreamWriter("outA2.data", append: false);
int m = 99;
double s = 1.0 / (m + 1);
matrix H = new matrix(m, m);
for (int i = 0; i < m - 1; i++)
{
matrix.set(H, i, i, -2);
matrix.set(H, i, i + 1, 1);
matrix.set(H, i + 1, i, 1);
}
matrix.set(H, m - 1, m - 1, -2);
matrix.scale(H, -1 / s / s);
vector D2 = new vector(m);
matrix V2 = new matrix(m, m);
int sweeps2 = Jacobi_diagonalization.cyclic_sweep(H, V2, D2);
for (int k = 0; k < m / 3; k++)
{
double exact = PI * PI * (k + 1) * (k + 1);
double calculated = D2[k];
eigenenergies.WriteLine($"{k} {calculated} {exact}");
}
for (int k = 0; k < 4; k++)
{
outData.WriteLine($"{0} {0}");
for (int i = 0; i < m; i++)
{
double factor = Sign(V2[0, k]);
outData.WriteLine($"{(i+1.0)/(m+1.0)} {V2[i,k]*factor/Sqrt(s)}");
}
outData.WriteLine($"{1} {0}");
outData.WriteLine("");
}
outData.Close();
eigenenergies.Close();
}
