private static void Main()
//****************************************************************************80
//
// Purpose:
//
// MAIN is the main program for LORENZ_ODE.
//
// Discussion:
//
// Thanks to Ben Whitney for pointing out an error in specifying a loop,
// 24 May 2016.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 24 May 2016
//
// Author:
//
// John Burkardt
//
{
const string command_filename = "lorenz_ode_commands.txt";
List <string> command_unit = new();
const string data_filename = "lorenz_ode_data.txt";
List <string> data_unit = new();
int j;
const int m = 3;
const int n = 200000;
Console.WriteLine("");
Console.WriteLine("LORENZ_ODE");
Console.WriteLine(" Compute solutions of the Lorenz system.");
Console.WriteLine(" Write data to a file for use by gnuplot.");
//
// Data
//
double t_final = 40.0;
double dt = t_final / n;
//
// Store the initial conditions in entry 0.
//
double[] t = typeMethods.r8vec_linspace_new(n + 1, 0.0, t_final);
double[] x = new double[m * (n + 1)];
x[0 + 0 * m] = 8.0;
x[0 + 1 * m] = 1.0;
x[0 + 2 * m] = 1.0;
//
// Compute the approximate solution at equally spaced times.
//
for (j = 0; j < n; j++)
{
double[] xnew = RungeKutta.rk4vec(t[j], m, x, dt, Lorenz.lorenz_rhs, index: +j * m);
int i;
for (i = 0; i < m; i++)
{
x[i + (j + 1) * m] = xnew[i];
}
}
//
// Create the plot data file.
//
for (j = 0; j <= n; j += 50)
{
data_unit.Add(" " + t[j].ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + x[0 + j * m].ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + x[1 + j * m].ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + x[2 + j * m].ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
File.WriteAllLines(data_filename, data_unit);
Console.WriteLine(" Created data file \"" + data_filename + "\".");
/*
* Create the plot command file.
*/
command_unit.Add("# " + command_filename + "");
command_unit.Add("#");
command_unit.Add("# Usage:");
command_unit.Add("# gnuplot < " + command_filename + "");
command_unit.Add("#");
command_unit.Add("set term png");
command_unit.Add("set output 'xyz_time.png'");
command_unit.Add("set xlabel '<--- T --->'");
command_unit.Add("set ylabel '<--- X(T), Y(T), Z(T) --->'");
command_unit.Add("set title 'X, Y and Z versus Time'");
command_unit.Add("set grid");
command_unit.Add("set style data lines");
command_unit.Add("plot '" + data_filename
+ "' using 1:2 lw 3 linecolor rgb 'blue',"
+ "'' using 1:3 lw 3 linecolor rgb 'red',"
+ "'' using 1:4 lw 3 linecolor rgb 'green'");
command_unit.Add("set output 'xyz_3d.png'");
command_unit.Add("set xlabel '<--- X(T) --->'");
command_unit.Add("set ylabel '<--- Y(T) --->'");
command_unit.Add("set zlabel '<--- Z(T) --->'");
command_unit.Add("set title '(X(T),Y(T),Z(T)) trajectory'");
command_unit.Add("set grid");
command_unit.Add("set style data lines");
command_unit.Add("splot '" + data_filename
+ "' using 2:3:4 lw 1 linecolor rgb 'blue'");
command_unit.Add("quit");
File.WriteAllLines(command_filename, command_unit);
Console.WriteLine(" Created command file '" + command_filename + "'");
Console.WriteLine("");
Console.WriteLine("LORENZ_ODE:");
Console.WriteLine(" Normal end of execution.");
Console.WriteLine("");
}
