<?xml version="1.0" encoding="UTF-8"?>
<simulation xmds-version="2">
  <name>nlprojection</name>
  <author>Graham Dennis</author>
  <description>
    Project |psi|^2 psi where psi is the harmonic oscillator groundstate
    onto the harmonic oscillator basis for a three-dimensional trap.
  </description>
  
  <!-- 'features' describes various optional extras that can be plugged into the simulation -->
  <features>
    <auto_vectorise />
    <benchmark />
  </features>
  
  <!-- This is where the geometry of the simulation is defined -->
  <geometry>
    <propagation_dimension> t </propagation_dimension>
    <transverse_dimensions>
      <dimension name="x" lattice="7" spectral_lattice="3" length_scale="1.0" transform="hermite-gauss" />
      <dimension name="y" lattice="7" spectral_lattice="3" length_scale="1.0" transform="hermite-gauss" />
      <dimension name="z" lattice="7" spectral_lattice="3" length_scale="1.0" transform="hermite-gauss" />
    </transverse_dimensions>
  </geometry>
  
  <!-- A vector is a set of variables that can be evolved. -->
  <vector name="wavefunction" initial_basis="nx ny nz" type="real">
    <components>
      phi
    </components>
    <initialisation>
      <![CDATA[
      if (nx == 0 && ny == 0 && nz == 0)
        phi = 1.0;
      else
        phi = 0.0;
      ]]>
    </initialisation>
  </vector>
  
  <!-- This is a dodgy method of evaluating the nonlinear term. 
       It uses the two-field quadrature, and so the result isn't quite right.
  -->
  <computed_vector name="nlterm" dimensions="x y z" type="real">
    <components>
      nl
    </components>
    <evaluation>
      <dependencies basis="x y z">wavefunction</dependencies>
      <![CDATA[
        // Calculate the nonlinear term.
        nl = mod2(phi)*phi;
      ]]>
    </evaluation>
  </computed_vector>
  
  <!-- 
    This is the correct method to evaluate the nonlinear term.
    This uses the four-field quadrature, and so is evaluated to high precision
    even with comparatively few points. The correct result for
    nl(nx => 0,ny => 0, nz => 0) is 6.34936359e-2
   -->
  <computed_vector name="nlterm_4f" dimensions="x y z" type="real">
    <components>
      nl_4f
    </components>
    <evaluation>
      <dependencies basis="x_4f y_4f z_4f">wavefunction</dependencies>
      <![CDATA[
        // Compute nonlinear term
        nl_4f = mod2(phi) * phi;
      ]]>
    </evaluation>
  </computed_vector>
  
  <sequence>
    <!-- This is where the evolution of the simulation would go.
         An 'integrate' block here would describe how to evolve some of the vectors
         defined previously. -->
    <!-- In this case, we have no evolution, all we need to do is save the nonlinear term
         in the harmonic oscillator basis to a file. -->
    <breakpoint filename="nlbreak.xsil" format="hdf5">
      <dependencies basis="nx ny nz">nlterm nlterm_4f</dependencies>
    </breakpoint>
  </sequence>
  <output />
</simulation>
