static void Main()
{
Console.WriteLine("Lab4: Tridiagonal algorithm \n-----------------------------------");
try
{
var system = new LSystem(STUDENT_NUMBER, GROUP_NUMBER, 4);
system.GenerateTridiagonalSystem();
Console.WriteLine("Our system:");
system.Print();
var solution = Tridiagonal.Calculate(system);
Console.WriteLine("Solutions via Tridiagonal algorithm:");
solution.Print();
Console.WriteLine("Residuals: ");
system.CalcResiduals(solution)
.Print(15);
}
catch (Exception e)
{
Console.WriteLine(e.Message);
Console.Read();
}
Console.Read();
}
private static void test03()
//****************************************************************************80
//
// Purpose:
//
// TEST03 uses POWER_METHOD2 on the TRIS matrix.
//
// Discussion:
//
// This matrix, despite having a single dominant eigenvalue, will generally
// converge only very slowly under the power method. This has to do with
// the fact that the matrix has only 3 eigenvectors.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 30 August 2008
//
// Author:
//
// John Burkardt
//
{
int i;
int it_num = 0;
Complex lambda = new();
const int n = 50;
double[] x = new double[n];
const double alpha = -1.0;
const double beta = 10.0;
const double gamma = 8.0;
double[] a = Tridiagonal.tris(n, n, alpha, beta, gamma);
Complex[] v = new Complex[n];
int seed = 123456789;
UniformRNG.r8vec_uniform_01(n, ref seed, ref x);
const int it_max = 4000;
const double tol = 0.000001;
Console.WriteLine("");
Console.WriteLine("TEST03");
Console.WriteLine(" Use POWER_METHOD2 on the TRIS (tridiagonal scalar) matrix.");
Console.WriteLine("");
Console.WriteLine(" Matrix order N = " + n + "");
Console.WriteLine(" Maximum iterations = " + it_max + "");
Console.WriteLine(" Error tolerance = " + tol + "");
DateTime ctime1 = DateTime.Now;
PowerMethod.power_method2(n, a, x, it_max, tol, ref lambda, v, ref it_num);
DateTime ctime2 = DateTime.Now;
double ctime = (ctime2 - ctime1).Seconds;
Console.WriteLine("");
Console.WriteLine(" Number of iterations = " + it_num + "");
Console.WriteLine(" CPU time = " + ctime + "");
Console.WriteLine(" Estimated eigenvalue = "
+ lambda.Real.ToString("0.##############")
+ " " + lambda.Imaginary.ToString("0.##############") + "");
Complex[] lambda_vec = Tridiagonal.tris_eigenvalues(n, alpha, beta, gamma);
Complex lambda_max = lambda_vec[0];
for (i = 1; i < n; i++)
{
if (Complex.Abs(lambda_max) < Complex.Abs(lambda_vec[i]))
{
lambda_max = lambda_vec[i];
}
}
Console.WriteLine(" Correct max eigenvalue = "
+ lambda_max.Real.ToString("0.##############")
+ " " + lambda_max.Imaginary.ToString("0.##############") + "");
Console.WriteLine(" Error = " + Complex.Abs(lambda - lambda_max) + "");
}
