<?xml version="1.0" encoding="UTF-8"?>
<simulation xmds-version="2">
  <testing>
    <xsil_file name="eigenvalues_break.xsil" expected="eigenvalues_break_expected.xsil" absolute_tolerance="1e-6" relative_tolerance="1e-5" />
    <xsil_file name="eigenvalues.xsil" expected="eigenvalues_expected.xsil" absolute_tolerance="1e-6" relative_tolerance="1e-5" />
  </testing>
  
  <name>eigenvalues</name>
  <author>Graham Dennis</author>
  <description>
    1D TW model of the uniform Peaks system.
  </description>
  
  <features>
    <auto_vectorise />
    <benchmark />
    <fftw plan="exhaustive" />
    <globals>
      <![CDATA[
      /* physical constants  */
       const double omegaz = 2*M_PI*55.0;
       const double omegarho = 2*M_PI*1020.0;
       const double hbar = 1.05457148e-34;
       const double M = 4.0026032*1.66053886e-27;
       const double scatteringLength = 7.51e-9;
       const double Uint3 = 4.0*M_PI*hbar*hbar*scatteringLength/M;
       const double Nparticles = 2.0e6;
       const double mu = pow(15*Nparticles*Uint3*omegarho*omegarho*omegaz/(8.0*M_PI)*pow(M/2,3.0/2.0),2.0/5.0);
       const double Uint = Uint3*5.0*omegarho*omegarho*M/(4.0*M_PI*mu);
       const double Uint_hbar = Uint/hbar;
       const complex miUint_hbar = -i*Uint_hbar;
       const double otherScatteringLength = 5.56e-9;
       const double kappa = otherScatteringLength/scatteringLength;
       double Delta;
       const double hbar_M = hbar/M;
       const double Omega = 2.0*M_PI*3e3;
       
       double mu0 = hbar*1.7786e3*2.0*M_PI;
       double nu = 6.649299328e3;//4.4046e4; // Hertz
       
      ]]>
    </globals>
    <validation kind="run-time" />
  </features>
  
  <geometry>
    <propagation_dimension> t </propagation_dimension>
    <transverse_dimensions>
      <dimension name="kz" lattice="32"  domain="(0, 3e6)" />
      <!-- <dimension name="kz" lattice="1024"  domain="(1.3220e6, 1.3221e6)" /> -->
      <dimension name="p" domain="(1, 4)" type="integer" aliases="q" />
    </transverse_dimensions>
  </geometry>
  
  <vector name="wavefunction" dimensions="" type="complex">
    <components>
      phi1 phi0
    </components>
    <initialisation>
      <![CDATA[
        phi1 = sqrt(mu/Uint);
        phi0 = 0.0;
      ]]>
    </initialisation>
  </vector>
  
  <vector name="matrixterms" dimensions="kz p q" initial_basis="kz" type="complex">
    <components>matrix</components>
    <initialisation>
      <![CDATA[
        if (p == q) {
          matrix = 1.0;
        } else {
          matrix = 0.0;
        }
      ]]>
    </initialisation>
  </vector>
  
  <computed_vector name="hamiltonian_matrix" dimensions="kz p q" type="complex">
    <components>h_matrix</components>
    <evaluation>
      <dependencies>wavefunction</dependencies>
      <![CDATA[
        const double kineticEnergy = 0.5*hbar*hbar*kz*kz/M;
        if (p == 1 && q == 1) h_matrix = Uint*mod2(phi1)+kineticEnergy-mu0;
        if (p == 1 && q == 2) h_matrix = Uint*phi1*phi1;
        if (p == 1 && q == 3) h_matrix = Uint*phi1*conj(phi0)+hbar*Omega;
        if (p == 1 && q == 4) h_matrix = Uint*phi1*phi0;
        
        if (p == 2 && q == 1) h_matrix = -Uint*conj(phi1*phi1);
        if (p == 2 && q == 2) h_matrix = -Uint*mod2(phi1)-kineticEnergy+mu0;
        if (p == 2 && q == 3) h_matrix = -Uint*conj(phi1 * phi0);
        if (p == 2 && q == 4) h_matrix = -Uint*conj(phi1)*phi0 - hbar*Omega;
        
        if (p == 3 && q == 1) h_matrix = Uint*conj(phi1)*phi0 + hbar*Omega;
        if (p == 3 && q == 2) h_matrix = Uint*phi0*phi1;
        if (p == 3 && q == 3) h_matrix = Uint*(2.0*kappa-1.0)*mod2(phi0)-mu0+kineticEnergy;
        if (p == 3 && q == 4) h_matrix = Uint*kappa*phi0*phi0;
        
        if (p == 4 && q == 1) h_matrix = -Uint*conj(phi0*phi1);
        if (p == 4 && q == 2) h_matrix = -Uint*phi1*conj(phi0)-hbar*Omega;
        if (p == 4 && q == 3) h_matrix = -Uint*kappa*conj(phi0*phi0);
        if (p == 4 && q == 4) h_matrix = -Uint*(2.0*kappa-1.0)*mod2(phi0)-kineticEnergy+mu0;
        
        h_matrix *= -i/hbar;
      ]]>
    </evaluation>
  </computed_vector>
  
  <sequence>
    <integrate algorithm="ARK89" interval="1.0/nu" tolerance="1e-8">
      <samples>20 20</samples>
      <operators dimensions="">
        <integration_vectors>wavefunction</integration_vectors>
        <![CDATA[
          dphi1_dt = - i/hbar*( - mu0)*phi1 -i*Omega*phi0;
          dphi0_dt = - i/hbar*( - Uint*(1.0-kappa)*mod2(phi0) - mu0)*phi0 -i*Omega*phi1;
        ]]>
      </operators>
      <operators dimensions="kz p q">
        <integration_vectors>matrixterms</integration_vectors>
        <dependencies>wavefunction hamiltonian_matrix</dependencies>
        <![CDATA[
          dmatrix_dt = 0.0;
          for (long pp = 1; pp <= 4; pp++) {
            dmatrix_dt += h_matrix(q=> pp)*matrix(p=> pp);
          }
        ]]>
      </operators>
    </integrate>
    <breakpoint filename="eigenvalues_break.xsil" format="hdf5">
      <dependencies>matrixterms</dependencies>
    </breakpoint>
  </sequence>
  <output format="hdf5">
      <sampling_group initial_sample="yes">
        <moments>phi1R phi1I phi0R phi0I</moments>
        <dependencies>wavefunction</dependencies>
        <![CDATA[
          _SAMPLE_COMPLEX(phi1); _SAMPLE_COMPLEX(phi0);
        ]]>
      </sampling_group>
      <sampling_group initial_sample="yes" basis="kz p q">
        <moments>matrixR matrixI</moments>
        <dependencies>matrixterms</dependencies>
        <![CDATA[
          _SAMPLE_COMPLEX(matrix);
        ]]>
      </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">1</Param>
  <Array Name="variables" Type="Text">
    <Dim>5</Dim>
    <Stream><Metalink Format="Text" Delimiter=" \n"/>
t phi1R phi1I phi0R phi0I 
    </Stream>
  </Array>
  <Array Name="data" Type="double">
    <Dim>21</Dim>
    <Dim>5</Dim>
    <Stream><Metalink Format="HDF5" Type="Remote" Group="/1"/>
eigenvalues_expected.h5
    </Stream>
  </Array>
</XSIL>

<XSIL Name="moment_group_2">
  <Param Name="n_independent">4</Param>
  <Array Name="variables" Type="Text">
    <Dim>6</Dim>
    <Stream><Metalink Format="Text" Delimiter=" \n"/>
t kz p q matrixR matrixI 
    </Stream>
  </Array>
  <Array Name="data" Type="double">
    <Dim>21</Dim>
    <Dim>32</Dim>
    <Dim>4</Dim>
    <Dim>4</Dim>
    <Dim>6</Dim>
    <Stream><Metalink Format="HDF5" Type="Remote" Group="/2"/>
eigenvalues_expected.h5
    </Stream>
  </Array>
</XSIL>
</simulation>
