def spickle_node_list(nl,filename=None,silent=False):
    """Pack physical field variables from a node list in a dict and pickle.

    (Note: This is not a true pickler class.)

    spickle_node_list(nl,filename) extracts field variables from all nodes of nl,
    which must be a valid node list, and packs them in a dict that is returned
    to the caller. If the optional argument filename is a string then dict will
    also be pickled to a file of that name. The file will be overwritten if it
    exists.

    The s in spickle is for 'serial', a reminder that this method collects all
    nodes of the node list (from all ranks) in a single process. Thus this method
    is mainly useful for interactive work with small node lists. It is the user's
    responsibility to make sure her process has enough memory to hold the returned
    dict.

    See also: pflatten_node_list
    """

    # Make sure we are not wasting our time.
    assert isinstance(nl,(sph.Spheral.NodeSpace.FluidNodeList3d,
                          sph.Spheral.SolidMaterial.SolidNodeList3d)
                      ), "argument 1 must be a node list"
    assert isinstance(silent, bool), "true or false"
    
    # Start collecting data.
    if not silent:
        sys.stdout.write('Pickling ' +  nl.label() + ' ' + nl.name + '........')

    # Get values of field variables stored in internal nodes.
    xloc = nl.positions().internalValues()
    vloc = nl.velocity().internalValues()
    mloc = nl.mass().internalValues()
    rloc = nl.massDensity().internalValues()
    uloc = nl.specificThermalEnergy().internalValues()
    Hloc = nl.Hfield().internalValues()
    #(pressure and temperature are stored in the eos object.)
    eos = nl.equationOfState()
    ploc = sph.ScalarField('ploc',nl)
    Tloc = sph.ScalarField('loc',nl)
    rref = nl.massDensity()
    uref = nl.specificThermalEnergy()
    eos.setPressure(ploc,rref,uref)
    eos.setTemperature(Tloc,rref,uref)

    # Zip fields so that we have all fields for each node in the same tuple.
    #  We do this so we can concatenate everything in a single reduction operation,
    #  to ensure that all fields in one record in the final list belong to the 
    #  same node.
    localFields = zip(xloc, vloc, mloc, rloc, uloc, ploc, Tloc, Hloc)

    # Do a SUM reduction on all ranks.
    #  This works because the + operator for python lists is a concatenation!
    globalFields = mpi.allreduce(localFields, mpi.SUM)

    # Create a dictionary to hold field variables.
    nlFieldDict = dict(name=nl.name,
                       x=[],   # position vector
                       v=[],   # velocity vector
                       m=[],   # mass
                       rho=[], # mass density
                       p=[],   # pressure
                       h=[],   # smoothing ellipsoid axes
                       T=[],   # temperature
                       U=[],   # specific thermal energy
                      )

    # Loop over nodes to fill field values.
    nbGlobalNodes = mpi.allreduce(nl.numInternalNodes, mpi.SUM)
    for k in range(nbGlobalNodes):
        nlFieldDict[  'x'].append((globalFields[k][0].x, globalFields[k][0].y, globalFields[k][0].z))
        nlFieldDict[  'v'].append((globalFields[k][1].x, globalFields[k][1].y, globalFields[k][1].z))
        nlFieldDict[  'm'].append( globalFields[k][2])
        nlFieldDict['rho'].append( globalFields[k][3])
        nlFieldDict[  'U'].append( globalFields[k][4])
        nlFieldDict[  'p'].append( globalFields[k][5])
        nlFieldDict[  'T'].append( globalFields[k][6])
        nlFieldDict[  'h'].append((globalFields[k][7].Inverse().eigenValues().x,
                                   globalFields[k][7].Inverse().eigenValues().y,
                                   globalFields[k][7].Inverse().eigenValues().z,
                                   ))

    # Optionally, pickle the dict to a file.
    if mpi.rank == 0:
        if filename is not None:
            if isinstance(filename, str):
                with open(filename, 'wb') as fid:
                    pickle.dump(nlFieldDict, fid)
                    pass
                pass
            else:
                msg = "Dict NOT pickled to file because " + \
                      "argument 2 is {} instead of {}".format(type(filename), type('x'))
                sys.stderr.write(msg+'\n')
                pass
            pass
        pass
        
    # And Bob's our uncle.
    if not silent:
        print "Done."
    return nlFieldDict
def pflatten_node_list(nl,filename,do_header=True,nl_id=0,silent=False):
    """Flatten physical field values from a node list to a rectangular ascii file.

    pflatten_node_list(nl,filename) extracts field variables from all nodes of nl,
    which must be a valid node list, and writes them as a rectangular table into
    the text file filename. (A short header is also written, using the # comment
    character so the resulting file can be easily read with numpy.loadtext.) The
    file will be overwritten if it exists. If filename has the .gz extension it
    will be compressed using gzip.

    pflatten_node_list(...,do_header=False) omits the header and appends the 
    flattened nl to the end of the file if one exists.

    pflatten_node_list(...,nl_id=id) places the integer id in the first column
    of every node (row) in the node list. This can be used when appending multiple
    lists to the same file, providing a convenient way to distinguish nodes from
    different lists when the file is later read. The default id (for single node
    list files) is 0.

    The format of the output table is (one line per node):
      id eos_id x y z vx vy vz m rho p T U hmin hmax

    The p in pflatten is for 'parallel', a reminder that all nodes will be
    processed in their local rank, without ever being communicated or collected
    in a single process. Each mpi rank will wait its turn to access the output 
    file, so the writing is in fact serial, but avoids bandwidth and memory waste
    and is thus suitable for large node lists from high-res runs.

    See also: spickle_node_list
    """

    # Make sure we are not wasting our time.
    assert isinstance(nl,(sph.Spheral.NodeSpace.FluidNodeList3d,
                          sph.Spheral.SolidMaterial.SolidNodeList3d)
                      ), "argument 1 must be a node list"
    assert isinstance(filename, str), "argument 2 must be a simple string"
    assert isinstance(do_header, bool), "true or false"
    assert isinstance(silent, bool), "true or false"
    assert isinstance(nl_id, int), "int only idents"
    assert not isinstance(nl_id, bool), "int only idents"

    # Determine if file should be compressed.
    if os.path.splitext(filename)[1] == '.gz':
        import gzip
        open = gzip.open
    else:
        import __builtin__
        open = __builtin__.open

    # Write the header.
    if do_header:
        nbGlobalNodes = mpi.allreduce(nl.numInternalNodes, mpi.SUM)
        header = header_template.format(nbGlobalNodes)
        if mpi.rank == 0:
            fid = open(filename,'w')
            fid.write(header)
            fid.close()
            pass
        pass
     
    # Start collecting data.
    if not silent:
        sys.stdout.write('Flattening ' + nl.label() + ' ' + nl.name + '........')
    
    # Get values of field variables stored in internal nodes.
    xloc = nl.positions().internalValues()
    vloc = nl.velocity().internalValues()
    mloc = nl.mass().internalValues()
    rloc = nl.massDensity().internalValues()
    uloc = nl.specificThermalEnergy().internalValues()
    Hloc = nl.Hfield().internalValues()
    #(pressure and temperature are stored in the eos object.)
    eos = nl.equationOfState()
    ploc = sph.ScalarField('ploc',nl)
    Tloc = sph.ScalarField('loc',nl)
    rref = nl.massDensity()
    uref = nl.specificThermalEnergy()
    eos.setPressure(ploc,rref,uref)
    eos.setTemperature(Tloc,rref,uref)

    # Procs take turns writing internal node values to file.
    for proc in range(mpi.procs):
        if proc == mpi.rank:
            fid = open(filename,'a')
            for nk in range(nl.numInternalNodes):
                line  = "{:2d}  ".format(nl_id)
                line += "{:2d}  ".format(getattr(nl,'eos_id',-1))
                line += "{0.x:+12.5e}  {0.y:+12.5e}  {0.z:+12.5e}  ".format(xloc[nk])
                line += "{0.x:+12.5e}  {0.y:+12.5e}  {0.z:+12.5e}  ".format(vloc[nk])
                line += "{0:+12.5e}  ".format(mloc[nk])
                line += "{0:+12.5e}  ".format(rloc[nk])
                line += "{0:+12.5e}  ".format(ploc[nk])
                line += "{0:+12.5e}  ".format(Tloc[nk])
                line += "{0:+12.5e}  ".format(uloc[nk])
                line += "{0:+12.5e}  ".format(Hloc[nk].Inverse().eigenValues().minElement())
                line += "{0:+12.5e}  ".format(Hloc[nk].Inverse().eigenValues().maxElement())
                line += "\n"
                fid.write(line)
                pass
            fid.close()
            pass
        mpi.barrier()
        pass
     
    # And Bob's our uncle.
    if not silent:
        print "Done."
    #assert np.isscalar(rho)
    #assert np.isscalar(eps)
    #assert np.isreal(rho)
    #assert np.isreal(eps)

    # Assign thermo values to fields and calculate pressure
    pressure.rhof[0] = rho
    pressure.epsf[0] = eps
    eos.setPressure(pressure.peef, pressure.rhof, pressure.epsf)

    # Extract pressure from field and return
    return pressure.peef[0]
    # End function pressure
# Static fake node list and thermo fields for function pressure
pressure.nodes = sph.makeVoidNodeList('fakenodes',1)
pressure.rhof = sph.ScalarField('rho',pressure.nodes)
pressure.epsf = sph.ScalarField('eps',pressure.nodes)
pressure.peef = sph.ScalarField('pee',pressure.nodes)

class HydrostaticQIC1LayerDensityProfile():
    """Callable hydrostatic quasi-incompressible density profile."""

    #---------------------------------------------------------------------------
    # The constructor
    #---------------------------------------------------------------------------
    def __init__(self, R, eos, rho0=None, rmin=0, units=None, nbins=100):
        """Class constructor for quasi-incompressible density profile.

        Assuming a barely compressible, one-layer planet, a pressure profile in
        hydrostatic equilibrium can be found by integrating the hydrostatic
        equation with constant density. The equation of state can then be inverted