lorenz.xmds

XMDS is a code generator that integrates equations. You write them down in human readable form in a

<?xml version="1.0"?>
<!-- Example simulation: lorenz -->

<!-- $Id: lorenz.xmds,v 1.8 2004/07/14 06:37:05 joehope Exp $ -->

<!--  Copyright (C) 2000-2004                                           -->
<!--                                                                    -->
<!--  Code contributed by Greg Collecutt, Joseph Hope and Paul Cochrane -->
<!--                                                                    -->
<!--  This file is part of xmds.                                        -->
<!--                                                                    -->
<!--  This program is free software; you can redistribute it and/or     -->
<!--  modify it under the terms of the GNU General Public License       -->
<!--  as published by the Free Software Foundation; either version 2    -->
<!--  of the License, or (at your option) any later version.            -->
<!--                                                                    -->
<!--  This program is distributed in the hope that it will be useful,   -->
<!--  but WITHOUT ANY WARRANTY; without even the implied warranty of    -->
<!--  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the     -->
<!--  GNU General Public License for more details.                      -->
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<!--  You should have received a copy of the GNU General Public License -->
<!--  along with this program; if not, write to the Free Software       -->
<!--  Foundation, Inc., 59 Temple Place - Suite 330, Boston,            -->
<!--  MA  02111-1307, USA.                                              -->

<!-- Adapted from the example in "Numerical methods for physics"-->
<!-- by Alejandro L. Garcia, pg 78-->

<!-- Try the simulation for different values of xo, yo and zo -->
<!-- e.g.: xo = 1, yo = 1, zo = 20 -->

<!-- Note: this simulation can be run as a shell/Perl/Python script by -->
<!-- changing the values of xo, yo and zo using the command line arguments -->

<simulation>

  <name>lorenz</name>

  <author>Paul Cochrane</author>
  <description>
    Lorenz attractor example simulation.  Adapted from the example in
    "Numerical methods for physics" by Alejandro L. Garcia, page 78.
  </description>

  <!-- Global system parameters and functionality -->
  <prop_dim>t</prop_dim>
  <stochastic>no</stochastic>

  <!-- Global variables for the simulation -->
  <globals>
    <![CDATA[
    const double sigma = 10.0;
    const double b = 8.0/3.0;
    const double r = 28.0;
    ]]>
  </globals>

  <!-- Command line arguments -->
  <argv>
    <arg>
      <name>xo</name>
      <type>double</type>
      <default_value>1.0</default_value>
    </arg>
    <arg>
      <name>yo</name>
      <type>double</type>
      <default_value>1.0</default_value>
    </arg>
    <arg>
      <name>zo</name>
      <type>double</type>
      <default_value>1.0</default_value>
    </arg>
  </argv>

  <!-- Field to be integrated over -->
  <field>
    <samples>1</samples>
    <vector>
      <name>main</name>
      <type>double</type>
      <components>x y z</components>
      <filename> lorenzInput.dat </filename>
      <!-- <![CDATA[
        x = xo;
        y = yo;
	z = zo;
      ]]> -->
    </vector>
  </field>

  <!-- The sequence of integrations to perform -->
  <sequence>
    <integrate>
      <algorithm>RK4EX</algorithm>
      <interval>15.0</interval>
      <lattice>5000</lattice>
      <samples>50</samples>
      <![CDATA[
        dx_dt = sigma*(y - x);
        dy_dt = r*x - y - x*z;
	dz_dt = x*y - b*z;
      ]]>
    </integrate>
  </sequence>

  <!-- The output to generate -->
  <output format="ascii" precision="double">
    <group>
      <sampling>
        <moments>xOut yOut zOut</moments>
          xOut = x;
	  yOut = y;
	  zOut = z;
      </sampling>
    </group>
  </output>

</simulation>