<?xml version="1.0" encoding="UTF-8"?>
<simulation xmds-version="2">
  <name>sine_cross</name>
  <author>Graham Dennis</author>
  <description>
    Sine cross-propagation validity tests.
    
    The 'u' variable checks for errors caused by poorly interpolating
    dependencies. The 'v' variable checks for errors just in the
    cross-propagation algorithm. The 'w' variable checks for errors due
    to IP cross-propagation (should be the smallest). The 'x' variable checks
    for errors due to EX cross-propagation, they should be the same as 'v'.
    You can choose the cross-propagation algorithm to be either 'SI' or 'RK4'.
  </description>
  
  <features>
    <benchmark />
    <bing />
    <!-- That's right, this script breaks the shackles with FFTW! -->
  </features>
  
  <geometry>
    <propagation_dimension> z </propagation_dimension>
    <transverse_dimensions>
      <dimension name="t" lattice="128"  domain="(0, 10)" transform="none" />
    </transverse_dimensions>
  </geometry>
  
  <vector name="main" type="complex">
    <components>
      foo
    </components>
    <initialisation>
      <![CDATA[
      foo = 0.0;
      ]]>
    </initialisation>
  </vector>
  
  <vector name="constants" type="real">
    <components>cosine</components>
    <initialisation>
      <![CDATA[
        cosine = cos(t);
      ]]>
    </initialisation>
  </vector>
  
  <vector name="cross" type="complex">
    <components>u v w x</components>
    <initialisation>
      <![CDATA[
        u = 0.0;
        v = 1.0;
        w = 1.0;
        x = 1.0;
      ]]>
    </initialisation>
  </vector>
  
  <sequence>
    <integrate algorithm="RK9" interval="1" steps="2">
      <samples>1</samples>
      <operators>
        <operator kind="cross_propagation" algorithm="SI" propagation_dimension="t">
          <integration_vectors>cross</integration_vectors>
          <dependencies>constants</dependencies>
          <boundary_condition kind="left">
            <![CDATA[
              u = 0.0;
              v = 1.0;
              w = 1.0;
              x = 1.0;
            ]]>
          </boundary_condition>
          
          <operator kind="ip">
            <operator_names>L</operator_names>
            <![CDATA[
              L = i;
            ]]>
          </operator>
          
          <operator kind="ex">
            <operator_names>M</operator_names>
            <![CDATA[
              M = i;
            ]]>
          </operator>
          
          <![CDATA[
            du_dt = cosine;
            dv_dt = i*v;
            dw_dt = L[w]; // this one is pretty much exact
            dx_dt = M[x];
          ]]>
        </operator>
        <integration_vectors>main</integration_vectors>
        <![CDATA[
        dfoo_dz = 0.0;
        ]]>
      </operators>
    </integrate>
  </sequence>
  
  <output format="ascii">
      <sampling_group basis="t" initial_sample="no">
        <moments>error_u error_v error_w error_x</moments>
        <dependencies>cross</dependencies>
        <![CDATA[
          error_u = abs(u - sin(t));
          error_v = abs(v - polar(1.0, t));
          error_w = abs(w - polar(1.0, t));
          error_x = abs(x - polar(1.0, t));
        ]]>
      </sampling_group>
  </output>
</simulation>