public static int Main()
{
// Loading raw data and converting to logarithmic values
List <double[]> data = misc.load_data("../data.txt");
double[] x = data[0]; double[] y = data[1];
for (int i = 0; i < y.Length; i++)
{
y[i] = Log(y[i]);
} // Logarithmic value
double[] dy = new double[y.Length]; // Allocate array for y errors
for (int i = 0; i < dy.Length; i++)
{
dy[i] = (Exp(y[i]) / 20) / Exp(y[i]);
} // Logarithmic y errors
Func <double, double>[] F = new Func <double, double>[] { s => 1, s => s }; // Array of fitting functions
var res = new lsq_qr(x, y, dy, F); // Variable storing instance of least square class
vector c = res.get_c(); // Retrieve expansion coefficients of fitting functions
double a = Exp(c[0]);
double l = c[1];
var outfile = new System.IO.StreamWriter("../out_A.txt", append: false);
outfile.WriteLine($"---------------------------------------");
outfile.WriteLine($"ThX decay fit using least square method");
outfile.WriteLine($"---------------------------------------");
outfile.WriteLine("Fitting parameters:");
outfile.WriteLine($"a: {a}");
outfile.WriteLine($"lambda: {l}");
outfile.WriteLine($"Fitting t_1/2: {-Log(2)/l} days");
outfile.WriteLine($"Modern t_1/2: 3.66 days");
outfile.Close();
var expout = new System.IO.StreamWriter("expout.txt", append: false);
var logout = new System.IO.StreamWriter("logout.txt", append: false);
for (double i = 0; i < 20; i += 0.25)
{
expout.WriteLine($"{i} {exp(a,l)(i)}");
}
expout.Close();
for (int i = 0; i < x.Length; i++)
{
logout.WriteLine($"{x[i]} {y[i]} {c[0] + c[1]*x[i]}");
}
logout.Close();
return(0);
}
public static int Main()
{
// 1) Amount of operations scaling
matrix A;
int nmax = 100;
Stopwatch time = new Stopwatch();
var diag_scale = new System.IO.StreamWriter("./plot_files/diag_scale.txt", append: false);
for (int n = 20; n < nmax; n += 1)
{
A = misc.gen_matrix(n);
time.Reset();
time.Start();
var res = new jacobi_diagonalization(A);
time.Stop();
diag_scale.WriteLine($"{Log(n)} {Log(time.ElapsedMilliseconds)}");
}
diag_scale.Close();
// Linear fit to logarithmic data to verify n^3 dependence
List <double[]> data = misc.load_data("./plot_files/diag_scale.txt");
double[] x = data[0]; double[] y = data[1];
double[] dy = new double[y.Length]; // Allocate array for y errors
for (int i = 0; i < dy.Length; i++)
{
dy[i] = 1e-3;
} // Logarithmic y errors
Func <double, double>[] F = new Func <double, double>[] { s => 1, s => s }; // Array of fitting functions
var fit = new lsq_qr(x, y, dy, F); // Variable storing instance of least square class
vector c = fit.get_c(); // Retrieve expansion coefficients of fitting functions
double a = c[0];
double b = c[1];
var fit_data = new System.IO.StreamWriter("./plot_files/fit_data.txt", append: false);
for (double n = x[0]; n < x[x.Length - 1]; n += 0.1)
{
fit_data.WriteLine($"{n} {a + b*n}");
}
fit_data.Close();
// 2) Demonstration of value-by-value method
int dim = 10; int eigenvalues = 5;
A = misc.gen_matrix(dim);
matrix Ac = A.copy();
matrix Acc = A.copy();
var A_res = new jacobi_diagonalization(A, "cyclic");
var Ac_res = new jacobi_diagonalization(Ac, "value", "min", eigenvalues);
var Acc_res = new jacobi_diagonalization(Acc, "value", "max", eigenvalues);
var outfile = new System.IO.StreamWriter("../out_B.txt", append: false);
outfile.WriteLine($"---------------------------------");
outfile.WriteLine($"Scaling of matrix diagonalization");
outfile.WriteLine($"---------------------------------");
outfile.WriteLine($"To demonstrate the O(n^3) scaling of the matrix diagonalization procedure, a linear fit is applied to the logaritmic (n,t) data.");
outfile.WriteLine($"Fit result:");
outfile.WriteLine($"log(t) = {a} + {b}*log(n)");
outfile.WriteLine($"Thus, the scaling must be O(n^3) since the slope is approximately equal to 3.\n");
outfile.WriteLine($"-----------------------------------------------");
outfile.WriteLine($"Jacobi diagonalization eigenvalue-by-eigenvalue");
outfile.WriteLine($"-----------------------------------------------");
outfile.WriteLine($"Test of eigenvalue-by-eigenvalue routine:");
outfile.WriteLine($"A random symmetric matrix A of dimension {dim}x{dim} is generated. Rotation angle should be changed into 0.5*arctan2(-2*Apq, App-Aqq) to achieve largest eigenvalue.\n");
outfile.WriteLine($"{eigenvalues} lowest eigenvalues of A:");
vector lowest_eigenvalues = Ac_res.get_eigenvalues();
for (int ir = 0; ir < lowest_eigenvalues.size; ir++)
{
outfile.Write("{0,10:g3} ", lowest_eigenvalues[ir]);
}
outfile.WriteLine("\n");
outfile.WriteLine($"{eigenvalues} highest eigenvalues of A:");
vector highest_eigenvalues = Acc_res.get_eigenvalues();
for (int ir = 0; ir < highest_eigenvalues.size; ir++)
{
outfile.Write("{0,10:g3} ", highest_eigenvalues[ir]);
}
outfile.WriteLine("\n");
outfile.WriteLine($"Eigenvalues of A for comparison:");
vector all_eigenvalues = A_res.get_eigenvalues();
for (int ir = 0; ir < all_eigenvalues.size; ir++)
{
outfile.Write("{0,10:g3} ", all_eigenvalues[ir]);
}
outfile.WriteLine("\n");
outfile.WriteLine($"Comparison of the two diagonalization routines in terms of number of rotations:");
dim = 50;
A = misc.gen_matrix(dim);
Ac = A.copy();
Acc = A.copy();
A_res = new jacobi_diagonalization(A, "cyclic");
Ac_res = new jacobi_diagonalization(Ac, "value", "min", 1);
Acc_res = new jacobi_diagonalization(Acc, "value", "min", dim);
outfile.WriteLine($"Another random symmetric matrix A of dimension {dim}x{dim} is generated.\n");
outfile.WriteLine($"Cyclic method:");
outfile.WriteLine($"Lowest eigenvalue: {A_res.get_eigenvalues()[0]}");
outfile.WriteLine($"Amount of rotations (full diagonalization): {A_res.get_rotations()}\n");
outfile.WriteLine($"Eigenvalue-by-eigenvalue method:");
outfile.WriteLine($"Lowest eigenvalue: {Ac_res.get_eigenvalues()[0]}");
outfile.WriteLine($"Amount of rotations (lowest eigenvalue): {Ac_res.get_rotations()}");
outfile.WriteLine($"Amount of rotations (full diagonalization): {Acc_res.get_rotations()}\n");
outfile.WriteLine($"Thus, the eigenvalue-by-eigenvalue method is suitable for calculuating only the lowest eigenvalues of a matrix whereas the cyclic sweep method is faster for full diagonalization.\n");
outfile.Close();
return(0);
}
public static int Main()
{
// Loading raw data and converting to logarithmic values
List <double[]> data = misc.load_data("../data.txt");
double[] x = data[0]; double[] y = data[1];
for (int i = 0; i < y.Length; i++)
{
y[i] = Log(y[i]);
} // Logarithmic value
double[] dy = new double[y.Length]; // Allocate array for y errors
for (int i = 0; i < dy.Length; i++)
{
dy[i] = (Exp(y[i]) / 20) / Exp(y[i]);
} // Logarithmic y errors
Func <double, double>[] F = new Func <double, double>[] { s => 1, s => s }; // Array of fitting functions
var res = new lsq_qr(x, y, dy, F); // Variable storing instance of least square class
vector c = res.get_c(); // Retrieve expansion coefficients of fitting functions
double a = Exp(c[0]);
double l = c[1];
double[] dc = res.get_dc();
double dl = Log(2) / (l * l) * dc[1]; // Uncertainty in t 1/2 obtained using error of propagation
matrix cov = res.get_cov();
var outfile = new System.IO.StreamWriter("../out_B.txt", append: false);
outfile.WriteLine($"---------------------------------------");
outfile.WriteLine($"ThX decay fit using least square method");
outfile.WriteLine($"---------------------------------------");
outfile.WriteLine("Fitting parameters:");
outfile.WriteLine($"a: {a}");
outfile.WriteLine($"lambda: {l}");
outfile.WriteLine($"Fitting t_1/2: {-Log(2)/l}({dl}) days");
outfile.WriteLine($"Modern t_1/2: 3.66 days");
outfile.WriteLine("The modern value of t_1/2 seems to be within the uncertainty of the fitting t_1/2\n");
outfile.WriteLine($"Covariance matrix:");
for (int ir = 0; ir < cov.size1; ir++)
{
for (int ic = 0; ic < cov.size2; ic++)
{
outfile.Write("{0,10:g3} ", cov[ir, ic]);
}
outfile.WriteLine("");
}
outfile.WriteLine("");
outfile.Close();
var expout = new System.IO.StreamWriter("expout.txt", append: false);
var logout = new System.IO.StreamWriter("logout.txt", append: false);
for (double i = 0; i < 20; i += 0.25)
{
expout.WriteLine($"{i} {exp(a,l)(i)}");
}
expout.Close();
for (int i = 0; i < x.Length; i++)
{
logout.WriteLine($"{x[i]} {y[i]} {c[0] + c[1]*x[i]}");
}
logout.Close();
return(0);
}
