<?xml version="1.0" ?><simulation xmds-version="2">
  
  <testing>
    <xsil_file absolute_tolerance="1e-7" expected="vibstring_re_expected.xsil" name="vibstring_re.xsil" relative_tolerance="1e-5">
      <moment_group absolute_tolerance="1e-7" number="1" relative_tolerance="1e-6"/>
      <moment_group absolute_tolerance="1e-3" number="2" relative_tolerance="1e-6"/>
    </xsil_file>
  </testing>
  
  <name>vibstring_re</name>
  <author>Emily McAlister and Graham Dennis</author>
  <description>
    Vibrating string - Test for Richardson Extrapolation
  </description>
  
  <features>
    <benchmark/>
    <bing/>
    <fftw plan="estimate"/>
    <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 domain="(0, 1)" lattice="100" name="x"/>
    </transverse_dimensions>
  </geometry>
  
  <vector initial_basis="x" name="main" type="complex">
    <components>
      u uDot
    </components>
    <initialisation>
      <![CDATA[
        u = exp(-100.0*(x-0.5)*(x-0.5));
        uDot = 0.0;
      ]]>
    </initialisation>
  </vector>
  
  <sequence>
    <integrate algorithm="REMM" interval="2e-3" steps="100">
      <samples>50 50</samples>
      <operators>
        <operator constant="yes" 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>
    </integrate>
  </sequence>
  <output format="binary">
      <sampling_group basis="x" initial_sample="yes">
        <moments>amp</moments>
        <dependencies>main</dependencies>
        <![CDATA[
          amp = u.Re();
        ]]>
      </sampling_group>
      <sampling_group basis="kx(50)" initial_sample="no">
        <moments>amp</moments>
        <dependencies>main</dependencies>
        <![CDATA[
          amp = u.Re();

        ]]>
      </sampling_group>
  </output>

<info>
Script compiled with XMDS2 version VERSION_PLACEHOLDER (SUBVERSION_REVISION_PLACEHOLDER)
See http://www.xmds.org for more information.
</info>

<XSIL Name="moment_group_1">
  <Param Name="n_independent">2</Param>
  <Array Name="variables" Type="Text">
    <Dim>3</Dim>
    <Stream><Metalink Format="Text" Delimiter=" \n"/>
t x amp 
    </Stream>
  </Array>
  <Array Name="data" Type="double">
    <Dim>51</Dim>
    <Dim>100</Dim>
    <Dim>3</Dim>
    <Stream><Metalink Format="Binary" UnsignedLong="uint64" precision="double" Type="Remote" Encoding="LittleEndian"/>
vibstring_re_expected_mg0.dat
    </Stream>
  </Array>
</XSIL>

<XSIL Name="moment_group_2">
  <Param Name="n_independent">2</Param>
  <Array Name="variables" Type="Text">
    <Dim>3</Dim>
    <Stream><Metalink Format="Text" Delimiter=" \n"/>
t kx amp 
    </Stream>
  </Array>
  <Array Name="data" Type="double">
    <Dim>50</Dim>
    <Dim>50</Dim>
    <Dim>3</Dim>
    <Stream><Metalink Format="Binary" UnsignedLong="uint64" precision="double" Type="Remote" Encoding="LittleEndian"/>
vibstring_re_expected_mg1.dat
    </Stream>
  </Array>
</XSIL>
</simulation>
