old_contents: ''' pyflation.analysis.deltaprel - Module to calculate relative pressure
  perturbations.
  
  Author: Ian Huston
  For license and copyright information see LICENSE.txt which was distributed with this file.
  
  '''
  
new_contents: ''' pyflation.analysis.deltaprel - Module to calculate relative pressure
  perturbations.
  
  Author: Ian Huston
  For license and copyright information see LICENSE.txt which was distributed with this file.
  
  '''
  
  def soundspeeds(Vphi, phidot, H):
      """Sound speeds of the background fields
      
      Arguments
      ---------
      Vphi: array_like
            First derivative of the potential with respect to the fields
            
      phidot: array_like
              First derivative of the field values with respect to efold number N.
              
      H: array_like
         The Hubble parameter
         
      All the arguments should have the same number of dimensions. Vphi and phidot
      should be arrays of the same size, but H should have a dimension of size 1 
      corresponding to the "field" dimension of the other variables.
      """
      try:
          calphasq = 1 + 2*Vphi/(3*H**2*phidot)
      except ValueError:
          raise ValueError("""Arrays need to have the correct shape.
                              Vphi and phidot should have exactly the same shape,
                              and H should have a dimension of size 1 corresponding
                              to the "field" dimension of the others.""")
      return calphasq
  
  def rhodots():
      """Derivative in e-fold time of the energy densities of the individual fields."""
      pass
  
  def fullrhodot():
      """Combined derivative in e-fold time of the energy density of the field"""
      pass
  
  def deltarhosmatrix():
      """Matrix of the first order perturbed energy densities of the field components."""
      pass
  
  def deltaprel():
      """Perturbed relative pressure of the fields given as quantum mode functions."""
      pass
  
  def deltaprelspectrum():
      """Power spectrum of the full perturbed relative pressure."""
      pass
subject: Add outlines of functions and code for soundspeeds.