<?xml version="1.0" encoding="UTF-8"?>
<simulation xmds-version="2">
  <name>vibstring3</name>
  <author>Joe Hope</author>
  <description>
    Vibrating string
  </description>
  
  <features>
    <benchmark />
    <error_check />
    <bing />
    <fftw />

    <globals>
      <![CDATA[
      const real T = 10.0;
      const real mass = 1e-3;
      const real length = 1.0;
      const real mu = mass/length;
      ]]>
    </globals>
  </features>
  
  <geometry>
    <propagation_dimension> t </propagation_dimension>
    <transverse_dimensions>
      <dimension name="q" type="integer" lattice="2"  domain="(0, 1)" />
      <dimension name="x" lattice="100"  domain="(0, 1)" />
      <dimension name="y" lattice="100"  domain="(0, 1)" />
      <dimension name="z" lattice="100"  domain="(0, 1)" />
      <dimension name="w" type="integer" domain="(-3, 3)" />
    </transverse_dimensions>
  </geometry>
  
  <vector name="main" dimensions="x y" initial_basis="x y" type="complex">
    <components>
      u uDot
    </components>
    <initialisation>
      <![CDATA[
        u = exp(-100.0*(x-0.5)*(x-0.5));
        uDot = 0.0;
      ]]>
    </initialisation>
  </vector>
  
  <vector name="integrated_u" dimensions="" type="complex">
    <components>
      mom
    </components>
  </vector>
  <computed_vector name="filter1" dimensions="" type="complex">
    <components>moment</components>
    <!-- If the moments are of type 'real', then all dimensions that aren't integrated
         must be evaluated in 'x' space. -->
    <evaluation>
      <dependencies basis="kx ky">integrated_u main</dependencies>
      <![CDATA[
        moment = mod2(u);
      ]]>
    </evaluation>
  </computed_vector>
  
  <sequence>
    <integrate algorithm="RK9" interval="2e-3" steps="100">
      <samples>50 50</samples>
      
      <computed_vector name="filter2" dimensions="" type="complex">
        <components>sparemoment</components>
        <!-- If the moments are of type 'real', then all dimensions that aren't integrated
             must be evaluated in 'x' space. -->
        <evaluation>
          <dependencies basis="kx ky">integrated_u main</dependencies>
          <![CDATA[
            sparemoment = mod2(u);
          ]]>
        </evaluation>
      </computed_vector>
      
      <operators>  <!-- For the x y dimensions -->
        <operator kind="ex">
          <operator_names>L</operator_names>
          <![CDATA[
            L = -T*kx*kx/mu;
          ]]>
        </operator>
        <integration_vectors>main</integration_vectors>
        <![CDATA[
          du_dt = uDot;
          duDot_dt = L[u /**/];
        ]]>
      </operators>
      
      <operators>  <!-- For the zero-dimensional field -->
        <integration_vectors>integrated_u</integration_vectors>
        <dependencies>filter1</dependencies>
        <![CDATA[
          dmom_dt = moment;
        ]]>
      </operators>
      
      <filters>
        <filter>
          <dependencies>filter1 main</dependencies>
          <![CDATA[
            u = 1.0 * u;
          ]]>
        </filter>
      </filters>
    </integrate>
  </sequence>
  
  <output>
      <sampling_group basis="x y" initial_sample="yes">
        <computed_vector name="filter3" dimensions="" type="complex">
          <components>sparemomentagain</components>
          <!-- If the moments are of type 'real', then all dimensions that aren't integrated
               must be evaluated in 'x' space. -->
          <evaluation>
            <dependencies basis="kx ky">integrated_u main</dependencies>
            <![CDATA[
              sparemomentagain = mod2(u);
            ]]>
          </evaluation>
        </computed_vector>
        <operator kind="ex">
          <operator_names>L</operator_names>
          <![CDATA[
            L = -T*kx*kx/mu;
          ]]>
        </operator>
        <moments>amp ke</moments>
        <dependencies>main filter1</dependencies>
        <![CDATA[
          amp = mod2(u + moment);
          ke = mod2(L[u]);
        ]]>
      </sampling_group>
      <sampling_group initial_sample="no">
        <moments>momR momentR</moments>
        <dependencies>integrated_u filter1</dependencies>
        <![CDATA[
          momR = mom.Re();
          momentR = moment.Re();
        ]]>
      </sampling_group>
  </output>
</simulation>