<?xml version="1.0" encoding="UTF-8"?>
<simulation xmds-version="2">
  <testing>
    <xsil_file name="cross_propagation_sic.xsil" expected="cross_propagation_sic_expected.xsil" absolute_tolerance="1e-7" relative_tolerance="1e-5" />
  </testing>
  <name>cross_propagation_sic</name>
  <author>Graham Dennis</author>
  <description>
    Sine cross-propagation validity tests, using the SIC integrator.
    
    The 'u' variable checks for errors caused by poorly interpolating
    dependencies. The 'v' variable checks for errors just in the
    cross-propagation algorithm.
  </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="zerodConstants" type="real" dimensions="">
    <components>bar</components>
    <initialisation>
      <![CDATA[
        bar = M_PI;
      ]]>
    </initialisation>
  </vector>
  
  <vector name="cross" type="complex">
    <components>u v</components>
    <initialisation>
      <![CDATA[
        u = 0.0;
        v = 1.0;
      ]]>
    </initialisation>
  </vector>
  
  <sequence>
    <integrate algorithm="SIC" interval="1" steps="2">
      <samples>1</samples>
      <operators>
        <operator kind="cross_propagation" algorithm="SI" propagation_dimension="t">
          <integration_vectors>cross</integration_vectors>
          <dependencies>constants zerodConstants</dependencies>
          <boundary_condition kind="left">
            <![CDATA[
              // These are shifted back half a step because the interpretation
              // of the boundary conditions for SIC is slightly different for normal
              // cross-propagators. For normal cross-propagators, they start at the left edge
              // for SIC, they start half a step to the left (or right).
              u = sin(-0.5*_dt);
              v = polar(1.0, -0.5*_dt);
            ]]>
          </boundary_condition>
          
          <![CDATA[
            du_dt = cosine;
            dv_dt = i*v;
          ]]>
        </operator>
        <integration_vectors>main</integration_vectors>
        <![CDATA[
        dfoo_dz = 0.0;
        ]]>
      </operators>
    </integrate>
  </sequence>
  
  <output format="binary">
      <sampling_group basis="t" initial_sample="no">
        <moments>error_u error_v</moments>
        <dependencies>cross</dependencies>
        <![CDATA[
          error_u = abs(u - sin(t));
          error_v = abs(v - polar(1.0, t));
        ]]>
      </sampling_group>
  </output>
</simulation>
