static void Main(string[] args)
{
/* Compare the time it takes to diagonalize a matrix
* of size n by different methods:
* Cyclic jacobi, value-by-value and v-b-v
* for both highest and lowest eig val.
*/
Stopwatch sw = new Stopwatch();
foreach (string arg in args)
{
int n = Int32.Parse(arg);
// Generate symmetric nxn matrix A
matrix A = randomMatrix(n, n);
restoreUpperTriang(A);
// Cyclic jacobi
matrix V = new matrix(n, n);
vector e = new vector(n);
sw.Start();
int sweeps = Jacobi.cyclic(A, V, e);
sw.Stop();
double cyclic = sw.Elapsed.Ticks / 10000.0;
sw.Reset();
// Value-by-value full
V = new matrix(n, n);
e = new vector(n);
sw.Start();
vector eigVals = Jacobi.lowestK(A, V, e, n);
sw.Stop();
double VBVfull = sw.Elapsed.Ticks / 10000.0;
sw.Reset();
// Value-by-value 1
V = new matrix(n, n);
e = new vector(n);
sw.Start();
eigVals = Jacobi.lowestK(A, V, e, 1);
sw.Stop();
double VBVlow = sw.Elapsed.Ticks / 10000.0;
sw.Reset();
// Value-by-value 1, highest first
V = new matrix(n, n);
e = new vector(n);
sw.Start();
eigVals = Jacobi.highestK(A, V, e, 1);
sw.Stop();
double VBVhigh = sw.Elapsed.Ticks / 10000.0;
sw.Reset();
// size of matrix and time in ms
WriteLine($"{n} {cyclic} {VBVfull} {VBVlow} {VBVhigh}");
}
}
static void Main()
{
int n = 6;
WriteLine($"Generate symmetric {n}x{n} matrix A");
matrix A = randomMatrix(n, n);
restoreUpperTriang(A);
A.print("A: ");
matrix V = new matrix(n, n);
vector e = new vector(n);
int sweeps;
// Cyclic
sweeps = Jacobi.cyclic(A, V, e);
WriteLine($"Cyclic Jacobi done in {sweeps} sweeps");
e.print("Cyclic eigenvalues: ");
// Lowest k
restoreUpperTriang(A);
V = new matrix(n, n);
e = new vector(n);
int k = n / 3;
vector v = Jacobi.lowestK(A, V, e, k);
v.print($"Lowest {k} values:");
A.print($"Test that {k} rows are cleared");
// Highest k
restoreUpperTriang(A);
V = new matrix(n, n);
e = new vector(n);
k = n / 3;
v = Jacobi.highestK(A, V, e, k);
v.print($"Highest {k} values:");
A.print($"Test that {k} rows are cleared");
restoreUpperTriang(A);
V = new matrix(n, n);
e = new vector(n);
int rots = Jacobi.classic(A, V, e);
e.print($"Classical done! rotations: {rots}");
A.print($"Test that all rows are cleared");
}
static int Main()
{
// Generate matrix A
int n = 12;
WriteLine("Creating random 7x7 matrix, A...");
matrix A = randomMatrix(n, n);
// Make A symmetric
restoreUpperTriang(A);
matrix V = new matrix(n, n);
vector e = new vector(n); // Vector of eigenvalues
A.print("A:");
WriteLine("Calculating eigenvalues...");
(int sweeps, int rots) = Jacobi.cyclic(A, V, e);
WriteLine($"Calculation done! Number of sweeps: {sweeps}");
V.print("Eigenvectors");
matrix D = new matrix(n, n);
for (int i = 0; i < n; i++)
{
D[i, i] = e[i];
}
D.print("Diagonal composition, D:");
restoreUpperTriang(A); // Restore A
matrix test = V.transpose() * A * V;
test.print("Test that V^T * A * V = D");
matrix test2 = V * D * V.transpose();
test2.print("Test that V * D * V^T = A");
WriteLine("Test first eigenvalue and vector:");
vector eigvec = A * V[0];
vector eigval = D[0, 0] * V[0];
eigvec.print("A * V[0] : ");
eigval.print("D[0,0] * V[0] : ");
// Calculate numerically Quantum particle in a box
WriteLine("--- Calculate numerically QM particle in a box ---");
// Generate H
int N = 23; // Number of numerical steps
double s = 1.0 / (N + 1);
matrix H = new matrix(N, N);
for (int i = 0; i < N - 1; i++)
{
H[i, i] = -2;
H[i, i + 1] = 1;
H[i + 1, i] = 1;
}
H[N - 1, N - 1] = -2;
H.print("H, before scaling");
H = -1 / s / s * H;
// Diagonalize H using jacobi
matrix boxV = new matrix(N, N);
vector boxE = new vector(N);
(int hsweeps, int hrots) = Jacobi.cyclic(H, boxV, boxE);
// Test that
WriteLine("Calculation done: Checking that energies are correct");
WriteLine("E_n \t Calculation \t Exact");
for (int k = 0; k < N / 3; k++)
{
double exact = PI * PI * (k + 1) * (k + 1);
double calc = boxE[k];
WriteLine($"E_{k} \t {calc.ToString("N5")} \t {exact.ToString("N5")}");
}
// Scaling factor a
double a = Sqrt(2) / boxV[N / 2, 0];
WriteLine($"a: {a}");
// Generate plotting data to plot with
using (StreamWriter sw = new StreamWriter("data-A.txt")){
// Plot the first 3 wave funcs
// Format: x \t psi0 \t psi_n ...
sw.WriteLine($"0 \t 0 \t 0 \t 0 \t 0 \t 0");
for (int i = 0; i < N; i++)
{
sw.Write($"{(i+1.0)/(N+1)} ");
for (int k = 0; k < 5; k++)
{
sw.Write($"\t {a*boxV[i,k]} ");
}
sw.Write("\n");
}
sw.WriteLine($"1 \t 0 \t 0 \t 0 \t 0 \t 0");
}
return(0);
}