text: """
  .. module:: mcmc
     :synopsis: Monte Carlo procedure
  .. moduleauthor:: Benjamin Audren <benjamin.audren@epfl.ch>
  
  This module defines one key function, :func:`chain`, that handles the Markov
  chain. So far, the code uses only one chain, as no parallelization is done.
  
  The following routine is also defined in this module, which is called at
  every step:
  
  * :func:`get_new_position` returns a new point in the parameter space,
    depending on the proposal density.
  
  The :func:`chain` in turn calls several helper routines, defined in
  :mod:`sampler`. These are called just once:
  
  * :func:`compute_lkl() <sampler.compute_lkl>` is called at every step in the Markov chain, returning
    the likelihood at the current point in the parameter space.
  * :func:`get_covariance_matrix() <sampler.get_covariance_matrix>`
  * :func:`read_args_from_chain() <sampler.read_args_from_chain>`
  * :func:`read_args_from_bestfit() <sampler.read_args_from_bestfit>`
  * :func:`accept_step() <sampler.accept_step>`
  
  Their usage is described in :mod:`sampler`. On the contrary, the following
  routines are called at every step:
  
  The arguments of these functions will often contain **data** and/or **cosmo**.
  They are both initialized instances of respectively :class:`data` and the
  cosmological class. They will thus not be described for every function.
  """
  
  import os
  import sys
  import math
  import random as rd
  import numpy as np
  import warnings
  import scipy.linalg as la
  from pprint import pprint
  
  import io_mp
  import sampler
  
  
  def get_new_position(data, eigv, U, k, Cholesky, Rotation):
      """
      Obtain a new position in the parameter space from the eigen values of the
      inverse covariance matrix, or from the Cholesky decomposition (original
      idea by Anthony Lewis, in `Efficient sampling of fast and slow
      cosmological parameters <http://arxiv.org/abs/1304.4473>`_ )
  
      The three different jumping options, decided when starting a run with the
      flag **-j**  are **global**, **sequential** and **fast** (by default) (see
      :mod:`parser_mp` for reference).
  
      .. warning::
  
          For running Planck data, the option **fast** is highly recommended, as
          it speeds up the convergence. Note that when using this option, the
          list of your likelihoods in your parameter file **must match** the
          ordering of your nuisance parameters (as always, they must come after
          the cosmological parameters, but they also must be ordered between
          likelihood, with, preferentially, the slowest likelihood to compute
          coming first).
  
  
      - **global**: varies all the parameters at the same time. Depending on the
        input covariance matrix, some degeneracy direction will be followed,
        otherwise every parameter will jump independently of each other.
      - **sequential**: varies every parameter sequentially. Works best when
        having no clue about the covariance matrix, or to understand which
        estimated sigma is wrong and slowing down the whole process.
      - **fast**: privileged method when running the Planck likelihood. Described
        in the aforementioned article, it separates slow (cosmological) and fast
        (nuisance) parameters.
  
      Parameters
      ----------
      eigv : numpy array
          Eigenvalues previously computed
      U : numpy_array
          Covariance matrix.
      k : int
          Number of points so far in the chain, is used to rotate through
          parameters
      Cholesky : numpy array
          Cholesky decomposition of the covariance matrix, and its inverse
      Rotation : numpy_array
          Not used yet
  
      """
  
      parameter_names = data.get_mcmc_parameters(['varying'])
      vector_new = np.zeros(len(parameter_names), 'float64')
      sigmas = np.zeros(len(parameter_names), 'float64')
  
      # Write the vector of last accepted points, or if it does not exist
      # (initialization routine), take the mean value
      vector = np.zeros(len(parameter_names), 'float64')
      try:
          for elem in parameter_names:
              vector[parameter_names.index(elem)] = \
                  data.mcmc_parameters[elem]['last_accepted']
      except KeyError:
          for elem in parameter_names:
              vector[parameter_names.index(elem)] = \
                  data.mcmc_parameters[elem]['initial'][0]
  
      # Initialize random seed
      rd.seed()
  
      # Choice here between sequential and global change of direction
      if data.jumping == 'global':
          for i in range(len(vector)):
              sigmas[i] = (math.sqrt(1/eigv[i]/len(vector))) * \
                  rd.gauss(0, 1)*data.jumping_factor
      elif data.jumping == 'sequential':
          i = k % len(vector)
          sigmas[i] = (math.sqrt(1/eigv[i]))*rd.gauss(0, 1)*data.jumping_factor
      elif data.jumping == 'fast':
          #i = k % len(vector)
          j = k % len(data.over_sampling_indices)
          i = data.over_sampling_indices[j]
          ###############
          # method fast+global
          for index, elem in enumerate(data.block_parameters):
              # When the running index is below the maximum index of a block of
              # parameters, this block is varied, and **only this one** (note the
              # break at the end of the if clause, it is not a continue)
              if i < elem:
                  if index == 0:
                      Range = elem
                      Previous = 0
                  else:
                      Range = elem-data.block_parameters[index-1]
                      Previous = data.block_parameters[index-1]
                  # All the varied parameters are given a random variation with a
                  # sigma of 1. This will translate in a jump for all the
                  # parameters (as long as the Cholesky matrix is non diagonal)
                  for j in range(Range):
                      sigmas[j+Previous] = (math.sqrt(1./Range)) * \
                          rd.gauss(0, 1)*data.jumping_factor
                  break
              else:
                  continue
      else:
          print('\n\n Jumping method unknown (accepted : ')
          print('global, sequential, fast (default))')
  
      # Fill in the new vector
      if data.jumping in ['global', 'sequential']:
          vector_new = vector + np.dot(U, sigmas)
      else:
          vector_new = vector + np.dot(Cholesky, sigmas)
  
      # Check for boundaries problems
      flag = 0
      for i, elem in enumerate(parameter_names):
          value = data.mcmc_parameters[elem]['initial']
          if((str(value[1]) != str(-1) and value[1] is not None) and
                  (vector_new[i] < value[1])):
              flag += 1  # if a boundary value is reached, increment
          elif((str(value[2]) != str(-1) and value[2] is not None) and
                  vector_new[i] > value[2]):
              flag += 1  # same
  
      # At this point, if a boundary condition is not fullfilled, ie, if flag is
      # different from zero, return False
      if flag != 0:
          return False
  
      # Check for a slow step (only after the first time, so we put the test in a
      # try: statement: the first time, the exception KeyError will be raised)
      try:
          data.check_for_slow_step(vector_new)
      except KeyError:
          pass
  
      # If it is not the case, proceed with normal computation. The value of
      # new_vector is then put into the 'current' point in parameter space.
      for index, elem in enumerate(parameter_names):
          data.mcmc_parameters[elem]['current'] = vector_new[index]
  
      # Propagate the information towards the cosmo arguments
      data.update_cosmo1_arguments()
      data.update_cosmo2_arguments()
  
      return True
  
  
  ######################
  # MCMC CHAIN
  ######################
  def chain(cosmo1, cosmo2, data, command_line):
      """
      Run a Markov chain of fixed length with a Metropolis Hastings algorithm.
  
      Main function of this module, this is the actual Markov chain procedure.
      After having selected a starting point in parameter space defining the
      first **last accepted** one, it will, for a given amount of steps :
  
      + choose randomly a new point following the *proposal density*,
      + compute the cosmological *observables* through the cosmological module,
      + compute the value of the *likelihoods* of the desired experiments at this
        point,
      + *accept/reject* this point given its likelihood compared to the one of
        the last accepted one.
  
      Every time the code accepts :code:`data.write_step` number of points
      (quantity defined in the input parameter file), it will write the result to
      disk (flushing the buffer by forcing to exit the output file, and reopen it
      again.
  
      .. note::
  
          to use the code to set a fiducial file for certain fixed parameters,
          you can use two solutions. The first one is to put all input 1-sigma
          proposal density to zero (this method still works, but is not
          recommended anymore). The second one consist in using the flag "-f 0",
          to force a step of zero amplitude.
  
      """
  
      ## Initialisation
      loglike = 0
  
      # In case command_line.silent has been asked, outputs should only contain
      # data.out. Otherwise, it will also contain sys.stdout
      outputs = [data.out]
      if not command_line.silent:
          outputs.append(sys.stdout)
  
      use_mpi = False
      # check for MPI
      try:
          from mpi4py import MPI
          comm = MPI.COMM_WORLD
          rank = comm.Get_rank()
          # suppress duplicate output from slaves
          if rank:
              command_line.quiet = True
          use_mpi = True
      except ImportError:
          # set all chains to master if no MPI
          rank = 0
  
      # Initialise master and slave chains for superupdate.
      # Workaround in order to have one master chain and several slave chains even when
      # communication fails between MPI chains. It could malfunction on some hardware.
      # TODO: Would like to merge with MPI initialization above and make robust and logical
      # TODO: Or if keeping current scheme, store value and delete jumping_factor.txt
      # TODO: automatically if --parallel-chains is enabled
      if command_line.superupdate and data.jumping_factor:
          try:
              jump_file = open(command_line.folder + '/jumping_factor.txt','r')
              #if command_line.restart is None:
              if not use_mpi and command_line.parallel_chains:
                  rank = 1
                  warnings.warn('MPI not in use, flag --parallel-chains enabled, '
                                'superupdate enabled, and a jumping_factor.txt file detected. '
                                'If relaunching in the same folder or restarting a run this '
                                'will cause all chains to be assigned as slaves. In this case '
                                'instead note the value in jumping_factor.txt, delete the '
                                'file, and pass the value with flag -f <value>. This warning '
                                'may then appear again, but you can safely disregard it.')
              else:
                  # For restart runs we want to save the input jumping factor
                  # as starting jumping factor, but continue from the jumping
                  # factor stored in the file.
                  starting_jumping_factor = data.jumping_factor
                  # This will load the value irrespective of whether it starts
                  # with # (i.e. the jumping factor adaptation was started) or not.
                  jump_value = jump_file.read().replace('# ','')
                  data.jumping_factor = float(jump_value)
  	    jump_file.close()
  	    print 'rank = ',rank
          except:
  	    jump_file = open(command_line.folder + '/jumping_factor.txt','w')
  	    jump_file.write(str(data.jumping_factor))
  	    jump_file.close()
  	    rank = 0
  	    print 'rank = ',rank
              starting_jumping_factor = data.jumping_factor
  
      # Recover the covariance matrix according to the input, if the varying set
      # of parameters is non-zero
      if (data.get_mcmc_parameters(['varying']) != []):
          # Read input covariance matrix
          sigma_eig, U, C = sampler.get_covariance_matrix(cosmo1, cosmo2, data, command_line)
  
          # if we want to compute the starting point by minimising lnL (instead of taking it from input file or bestfit file)
          minimum = 0
          if command_line.minimize:
              minimum, min_chi2 = sampler.get_minimum(cosmo1, cosmo2, data, command_line, C)
              parameter_names = data.get_mcmc_parameters(['last_accepted'])
              for index,elem in parameter_names:
                  data.mcmc_parameters[elem]['last_accepted'] = minimum[index]
  
              #FK: write out the results of the minimzer:
              labels = data.get_mcmc_parameters(['varying'])
              fname = os.path.join(command_line.folder, 'results.minimized')
              with open(fname, 'w') as f:
                  f.write('# minimized \chi^2 = {:} \n'.format(min_chi2))
                  f.write('# %s\n' % ', '.join(['%16s' % label for label in labels]))
                  for idx in xrange(len(labels)):
                      bf_value = minimum[idx]
                      if bf_value > 0:
                          f.write(' %.6e\t' % bf_value)
                      else:
                          f.write('%.6e\t' % bf_value)
                  f.write('\n')
              print 'Results of minimizer saved to: \n', fname
  
          # if we want to compute Fisher matrix and then stop
          if command_line.fisher:
              sampler.get_fisher_matrix(cosmo1, cosmo2, data, command_line, C, minimum)
              return
  
          # warning if no jumps are requested
          if data.jumping_factor == 0:
              warnings.warn(
                  "The jumping factor has been set to 0. The above covariance " +
                  "matrix will not be used.")
  
      # In case of a fiducial run (all parameters fixed), simply run once and
      # print out the likelihood. This should not be used any more (one has to
      # modify the log.param, which is never a good idea. Instead, force the code
      # to use a jumping factor of 0 with the option "-f 0".
      else:
          warnings.warn(
              "You are running with no varying parameters... I will compute " +
              "only one point and exit")
          data.update_cosmo1_arguments()  # this fills in the fixed parameters
          data.update_cosmo2_arguments()  # this fills in the fixed parameters
  
          loglike = sampler.compute_lkl(cosmo1, cosmo2, data)
          io_mp.print_vector(outputs, 1, loglike, data)
          return 1, loglike
  
      # In the fast-slow method, one need the Cholesky decomposition of the
      # covariance matrix. Return the Cholesky decomposition as a lower
      # triangular matrix
      Cholesky = None
      Rotation = None
      if command_line.jumping == 'fast':
          Cholesky = la.cholesky(C).T
          Rotation = np.identity(len(sigma_eig))
  
      # define path and covmat
      input_covmat = command_line.cov
      base = os.path.basename(command_line.folder)
      # the previous line fails when "folder" is a string ending with a slash. This issue is cured by the next lines:
      if base == '':
          base = os.path.basename(command_line.folder[:-1])
      command_line.cov = os.path.join(
          command_line.folder, base+'.covmat')
  
      # Fast Parameter Multiplier (fpm) for adjusting update and superupdate numbers.
      # This is equal to N_slow + f_fast N_fast, where N_slow is the number of slow
      # parameters, f_fast is the over sampling number for each fast block and f_fast
      # is the number of parameters in each fast block.
      for i in range(len(data.block_parameters)):
          if i == 0:
              fpm = data.over_sampling[i]*data.block_parameters[i]
          else:
              fpm += data.over_sampling[i]*(data.block_parameters[i] - data.block_parameters[i-1])
  
      # If the update mode was selected, the previous (or original) matrix should be stored
      if command_line.update:
          if not rank and not command_line.silent:
              print 'Update routine is enabled with value %d (recommended: 50)' % command_line.update
              print 'This number is rescaled by cycle length %d (N_slow + f_fast * N_fast) to %d' % (fpm,fpm*command_line.update)
          # Rescale update number by cycle length N_slow + f_fast * N_fast to account for fast parameters
          command_line.update *= fpm
          previous = (sigma_eig, U, C, Cholesky)
  
      # Initialise adaptive
      if command_line.adaptive:
          if not command_line.silent:
              print 'Adaptive routine is enabled with value %d (recommended: 10*dimension)' % command_line.adaptive
              print 'and adaptive_ts = %d (recommended: 100*dimension)' % command_line.adaptive_ts
              print 'Please note: current implementation not suitable for multiple chains'
          if rank > 0:
              raise io_mp.ConfigurationError('Adaptive routine not compatible with MPI')
          if command_line.update:
              warnings.warn('Adaptive routine not compatible with update, overwriting input update value')
          if command_line.superupdate:
              warnings.warn('Adaptive routine not compatible with superupdate, deactivating superupdate')
              command_line.superupdate = 0
          # Define needed parameters
          parameter_names = data.get_mcmc_parameters(['varying'])
          mean = np.zeros(len(parameter_names))
          last_accepted = np.zeros(len(parameter_names),'float64')
          ar = np.zeros(100)
          if command_line.cov == None:
              # If no input covmat was given, the starting jumping factor
              # should be very small until a covmat is obtained and the
              # original start jumping factor should be saved
              start_jumping_factor = command_line.jumping_factor
              data.jumping_factor = command_line.jumping_factor/100.
              # Analyze module will be forced to compute one covmat,
              # after which update flag will be set to False.
              command_line.update = command_line.adaptive
          else:
              # If an input covmat was provided, take mean values from param file
              # Question: is it better to always do this, rather than setting mean
              # to last accepted after the initial update run?
              for elem in parameter_names:
                  mean[parameter_names.index(elem)] = data.mcmc_parameters[elem]['initial'][0]
  
      # Initialize superupdate
      if command_line.superupdate:
          if not rank and not command_line.silent:
              print 'Superupdate routine is enabled with value %d (recommended: 20)' % command_line.superupdate
              if command_line.superupdate < 20:
                  warnings.warn('Superupdate value lower than the recommended value. This '
                                'may increase the risk of poorly converged acceptance rate')
              print 'This number is rescaled by cycle length %d (N_slow + f_fast * N_fast) to %d' % (fpm,fpm*command_line.superupdate)
          # Rescale superupdate number by cycle length N_slow + f_fast * N_fast to account for fast parameters
          command_line.superupdate *= fpm
          # Define needed parameters
  	parameter_names = data.get_mcmc_parameters(['varying'])
          updated_steps = 0
          stop_c = False
          jumping_factor_rescale = 0
          if command_line.restart:
              try:
                  jump_file = open(command_line.cov,'r')
                  jumping_factor_rescale = 1
              except:
                  jumping_factor_rescale = 0
          c_array = np.zeros(command_line.superupdate) # Allows computation of mean of jumping factor
          R_minus_one = np.array([100.,100.]) # 100 to make sure max(R-1) value is high if computation failed
          # Local acceptance rate of last SU*(N_slow + f_fast * N_fast) steps
          ar = np.zeros(command_line.superupdate)
          # Store acceptance rate of last 5*SU*(N_slow + f_fast * N_fast) steps
          backup_ar = np.zeros(5*command_line.superupdate)
          # Make sure update is enabled
          if command_line.update == 0:
              if not rank and not command_line.silent:
                  print 'Update routine required by superupdate. Setting --update 50'
                  print 'This number is then rescaled by cycle length: %d (N_slow + f_fast * N_fast)' % fpm
              command_line.update = 50 * fpm
              previous = (sigma_eig, U, C, Cholesky)
  
      # If restart wanted, pick initial value for arguments
      if command_line.restart is not None:
          sampler.read_args_from_chain(data, command_line.restart)
  
      # If restart from best fit file, read first point (overwrite settings of
      # read_args_from_chain)
      if command_line.bf is not None and not command_line.minimize:
          sampler.read_args_from_bestfit(data, command_line.bf)
  
      # Pick a position (from last accepted point if restart, from the mean value
      # else), with a 100 tries.
      for i in range(100):
          if get_new_position(data, sigma_eig, U, i,
                              Cholesky, Rotation) is True:
              break
          if i == 99:
              raise io_mp.ConfigurationError(
                  "You should probably check your prior boundaries... because " +
                  "no valid starting position was found after 100 tries")
  
      # Compute the starting Likelihood
      loglike = sampler.compute_lkl(cosmo1, cosmo2, data)
  
      # Choose this step as the last accepted value
      # (accept_step), and modify accordingly the max_loglike
      sampler.accept_step(data)
      max_loglike = loglike
  
      # If the jumping factor is 0, the likelihood associated with this point is
      # displayed, and the code exits.
      if data.jumping_factor == 0:
          io_mp.print_vector(outputs, 1, loglike, data)
          return 1, loglike
  
      acc, rej = 0.0, 0.0  # acceptance and rejection number count
      N = 1   # number of time the system stayed in the current position
  
      # Print on screen the computed parameters
      if not command_line.silent and not command_line.quiet:
          io_mp.print_parameters(sys.stdout, data)
  
      # Suppress non-informative output after initializing
      command_line.quiet = True
  
      k = 1
      # Main loop, that goes on while the maximum number of failure is not
      # reached, and while the expected amount of steps (N) is not taken.
      while k <= command_line.N:
          # If the number of steps reaches the number set in the adaptive method plus one,
          # then the proposal distribution should be gradually adapted.
          # If the number of steps also exceeds the number set in adaptive_ts,
          # the jumping factor should be gradually adapted.
  	if command_line.adaptive and k>command_line.adaptive+1:
              # Start of adaptive routine
              # By B. Schroer and T. Brinckmann
              # Modified version of the method outlined in the PhD thesis of Marta Spinelli
  
              # Store last accepted step
              for elem in parameter_names:
                  last_accepted[parameter_names.index(elem)] = data.mcmc_parameters[elem]['last_accepted']
              # Recursion formula for mean and covmat (and jumping factor after ts steps)
              # mean(k) = mean(k-1) + (last_accepted - mean(k-1))/k
              mean += 1./k*(last_accepted-mean)
              # C(k) = C(k-1) + [(last_accepted - mean(k))^T * (last_accepted - mean(k)) - C(k-1)]/k
              C +=1./k*(np.dot(np.transpose(np.asmatrix(last_accepted-mean)),np.asmatrix(last_accepted-mean))-C)
              sigma_eig, U = np.linalg.eig(np.linalg.inv(C))
              if command_line.jumping == 'fast':
                  Cholesky = la.cholesky(C).T
              if k>command_line.adaptive_ts:
                  # c = j^2/d
                  c = data.jumping_factor**2/len(parameter_names)
                  # c(k) = c(k-1) + [acceptance_rate(last 100 steps) - 0.25]/k
                  c +=(np.mean(ar)-0.25)/k
                  data.jumping_factor = np.sqrt(len(parameter_names)*c)
  
              # Save the covariance matrix and the jumping factor in a file
              # For a possible MPI implementation
              #if not (k-command_line.adaptive) % 5:
              #    io_mp.write_covariance_matrix(C,parameter_names,str(command_line.cov))
              #    jump_file = open(command_line.folder + '/jumping_factor.txt','w')
              #    jump_file.write(str(data.jumping_factor))
              #    jump_file.close()
              # End of adaptive routine
  
          # If the number of steps reaches the number set in the update method,
          # then the proposal distribution should be adapted.
          if command_line.update:
              # Start of update routine
              # By M. Ballardini and T. Brinckmann
              # Also used by superupdate and adaptive
  
              # master chain behavior
              if not rank:
                  # Add the folder to the list of files to analyze, and switch on the
                  # options for computing only the covmat
                  from parser_mp import parse
                  info_command_line = parse(
                      'info %s --minimal --noplot --keep-fraction 0.5 --keep-non-markovian --want-covmat' % command_line.folder)
                  info_command_line.update = command_line.update
  
                  if command_line.adaptive:
                      # Keep all points for covmat guess in adaptive
                      info_command_line = parse('info %s --minimal --noplot --keep-non-markovian --want-covmat' % command_line.folder)
                      # Tell the analysis to update the covmat after t0 steps if it is adaptive
                      info_command_line.adaptive = command_line.adaptive
                      # Only compute covmat if no input covmat was provided
                      if input_covmat != None:
                          info_command_line.want_covmat = False
  
                  # This is in order to allow for more frequent R-1 computation with superupdate
                  compute_R_minus_one = False
                  if command_line.superupdate:
                      if not (k+10) % command_line.superupdate:
                          compute_R_minus_one = True
                  # the +10 below is here to ensure that the first master update will take place before the first slave updates,
                  # but this is a detail, the code is robust against situations where updating is not possible, so +10 could be omitted
                  if (not (k+10) % command_line.update or compute_R_minus_one) and k > 10:
                      # Try to launch an analyze (computing a new covmat if successful)
                      try:
                          if not (k+10) % command_line.update:
                              from analyze import analyze
                              R_minus_one = analyze(info_command_line)
                          elif command_line.superupdate:
                              # Compute (only, i.e. no covmat) R-1 more often when using superupdate
                              info_command_line = parse(
                                  'info %s --minimal --noplot --keep-fraction 0.5 --keep-non-markovian' % command_line.folder)
                              info_command_line.update = command_line.update
                              R_minus_one = analyze(info_command_line)
                      except:
                          if not command_line.silent:
                              print 'Step ',k,' chain ', rank,': Failed to calculate covariance matrix'
  
                  if command_line.superupdate:
                      # Start of superupdate routine
                      # By B. Schroer and T. Brinckmann
  
                      c_array[(k-1)%(command_line.superupdate)] = data.jumping_factor
  
                      # If acceptance rate deviates too much from the target acceptance
                      # rate we want to resume adapting the jumping factor
                      # T. Brinckmann 02/2019: use mean a.r. over the last 5*len(ar) steps
                      # instead or the over last len(ar), which is more stable
                      if abs(np.mean(backup_ar) - command_line.superupdate_ar) > 5.*command_line.superupdate_ar_tol:
                          stop_c = False
  
                      # Start adapting the jumping factor after command_line.superupdate steps if R-1 < 10
                      # The lower R-1 criterium is an arbitrary choice to keep from updating when the R-1
                      # calculation fails (i.e. returns only zeros).
                      if (k > updated_steps + command_line.superupdate) and 0.01 < (max(R_minus_one) < 10.) and not stop_c:
                          c = data.jumping_factor**2/len(parameter_names)
                          # To avoid getting trapped in local minima, the jumping factor should
                          # not go below 0.1 (arbitrary) times the starting jumping factor.
                          if (c + (np.mean(ar) - command_line.superupdate_ar)/(k - updated_steps)) > (0.1*starting_jumping_factor)**2./len(parameter_names) or ((np.mean(ar) - command_line.superupdate_ar)/(k - updated_steps) > 0):
                              c += (np.mean(ar) - command_line.superupdate_ar)/(k - updated_steps)
                              data.jumping_factor = np.sqrt(len(parameter_names) * c)
  
                          if not (k-1) % 5:
                              # Check if the jumping factor adaptation should stop.
                              # An acceptance rate of 25% balances the wish for more accepted
                              # points, while ensuring the parameter space is properly sampled.
                              # The convergence criterium is by default (26+/-1)%, so the adaptation
                              # will stop when the code reaches an acceptance rate of at least 25%.
                              # T. Brinckmann 02/2019: use mean a.r. over the last 5*len(ar) steps
                              # instead or the over last len(ar), which is more stable
                              if (max(R_minus_one) < 0.4) and (abs(np.mean(backup_ar) - command_line.superupdate_ar) < command_line.superupdate_ar_tol) and (abs(np.mean(c_array)/c_array[(k-1) % (command_line.superupdate)] - 1) < 0.01):
                                  stop_c = True
                                  data.out.write('# After %d accepted steps: stop adapting the jumping factor at a value of %f with a local acceptance rate %f \n' % (int(acc),data.jumping_factor,np.mean(backup_ar)))
                                  if not command_line.silent:
                                      print 'After %d accepted steps: stop adapting the jumping factor at a value of %f with a local acceptance rate of %f \n' % (int(acc), data.jumping_factor,np.mean(backup_ar))
                                  jump_file = open(command_line.folder + '/jumping_factor.txt','w')
                                  jump_file.write('# '+str(data.jumping_factor))
                                  jump_file.close()
                              else:
                                  jump_file = open(command_line.folder + '/jumping_factor.txt','w')
                                  jump_file.write(str(data.jumping_factor))
                                  jump_file.close()
  
                      # Write the evolution of the jumping factor to a file
                      if not k % (command_line.superupdate):
                          jump_file = open(command_line.folder + '/jumping_factors.txt','a')
                          for i in xrange(command_line.superupdate):
                              jump_file.write(str(c_array[i])+'\n')
                          jump_file.close()
                      # End of main part of superupdate routine
  
                  if not (k-1) % (command_line.update/3):
                      try:
                          # Read the covmat
                          sigma_eig, U, C = sampler.get_covariance_matrix(
                              cosmo1, cosmo2, data, command_line)
                          if command_line.jumping == 'fast':
                              Cholesky = la.cholesky(C).T
                          # Test here whether the covariance matrix has really changed
                          # We should in principle test all terms, but testing the first one should suffice
                          if not C[0,0] == previous[2][0,0]:
                              if k == 1:
                                  if not command_line.silent:
                                      if not input_covmat == None:
                                          warnings.warn(
                                              'Appending to an existing folder: using %s instead of %s. '
                                              'If new input covmat is desired, please delete previous covmat.'
                                              % (command_line.cov, input_covmat))
                                      else:
                                          warnings.warn(
                                              'Appending to an existing folder: using %s. '
                                              'If no starting covmat is desired, please delete previous covmat.'
                                              % command_line.cov)
                              else:
                                  # Start of second part of superupdate routine
  				if command_line.superupdate:
                                      # Adaptation of jumping factor should start again after the covmat is updated
                                      # Save the step number after it updated for superupdate and start adaption of c again
  				    updated_steps = k
  				    stop_c = False
                                      cov_det = np.linalg.det(C)
                                      prev_cov_det = np.linalg.det(previous[2])
                                      # Rescale jumping factor in order to keep the magnitude of the jumps the same.
                                      # Skip this update the first time the covmat is updated in order to prevent
                                      # problems due to a poor initial covmat. Rescale the jumping factor after the
                                      # first calculated covmat to the expected optimal one of 2.4.
                                      if jumping_factor_rescale:
                                          new_jumping_factor = data.jumping_factor * (prev_cov_det/cov_det)**(1./(2 * len(parameter_names)))
                                          data.out.write('# After %d accepted steps: rescaled jumping factor from %f to %f, due to updated covariance matrix \n' % (int(acc), data.jumping_factor, new_jumping_factor))
                                          if not command_line.silent:
                                              print 'After %d accepted steps: rescaled jumping factor from %f to %f, due to updated covariance matrix \n' % (int(acc), data.jumping_factor, new_jumping_factor)
                                          data.jumping_factor = new_jumping_factor
                                      else:
                                          data.jumping_factor = starting_jumping_factor
                                      jumping_factor_rescale += 1
                                  # End of second part of superupdate routine
  
                                  # Write to chains file when the covmat was updated
                                  data.out.write('# After %d accepted steps: update proposal with max(R-1) = %f and jumping factor = %f \n' % (int(acc), max(R_minus_one), data.jumping_factor))
                                  if not command_line.silent:
                                      print 'After %d accepted steps: update proposal with max(R-1) = %f and jumping factor = %f \n' % (int(acc), max(R_minus_one), data.jumping_factor)
                                  try:
                                      if stop-after-update:
                                          k = command_line.N
                                          print 'Covariance matrix updated - stopping run'
                                  except:
                                      pass
  
                              previous = (sigma_eig, U, C, Cholesky)
                      except:
                          pass
  
                      command_line.quiet = True
  
                      # Start of second part of adaptive routine
                      # Stop updating the covmat after t0 steps in adaptive
                      if command_line.adaptive and k > 1:
                          command_line.update = 0
                          data.jumping_factor = start_jumping_factor
                          # Test if there are still enough steps left before the adaption of the jumping factor starts
                          if k > 0.5*command_line.adaptive_ts:
                              command_line.adaptive_ts += k
                          # Set the mean for the recursion formula to the last accepted point
                          for elem in parameter_names:
                              mean[parameter_names.index(elem)] = data.mcmc_parameters[elem]['last_accepted']
                      # End of second part of adaptive routine
  
              # slave chain behavior
              else:
                  # Start of slave superupdate routine
                  if command_line.superupdate:
                      # If acceptance rate deviates too much from the target acceptance
                      # rate we want to resume adapting the jumping factor. This line
                      # will force the slave chains to check if the jumping factor
                      # has been updated
                      if abs(np.mean(backup_ar) - command_line.superupdate_ar) > 5.*command_line.superupdate_ar_tol:
                          stop_c = False
  
                      # Update the jumping factor every 5 steps in superupdate
                      if not k % 5 and k > command_line.superupdate and command_line.superupdate and (not stop_c or (stop_c and k % command_line.update)):
                          try:
                              jump_file = open(command_line.folder + '/jumping_factor.txt','r')
                              # If there is a # in the file, the master has stopped adapting c
                              for line in jump_file:
                                  if line.find('#') == -1:
                                      jump_file.seek(0)
                                      jump_value = jump_file.read()
                                      data.jumping_factor = float(jump_value)
                                  else:
                                      jump_file.seek(0)
                                      jump_value = jump_file.read().replace('# ','')
                                      #if not stop_c or (stop_c and not float(jump_value) == data.jumping_factor):
                                      if not float(jump_value) == data.jumping_factor:
                                          data.jumping_factor = float(jump_value)
                                          stop_c = True
                                          data.out.write('# After %d accepted steps: stop adapting the jumping factor at a value of %f with a local acceptance rate %f \n' % (int(acc),data.jumping_factor,np.mean(backup_ar)))
                                          if not command_line.silent:
                                              print 'After %d accepted steps: stop adapting the jumping factor at a value of %f with a local acceptance rate of %f \n' % (int(acc), data.jumping_factor,np.mean(backup_ar))
                              jump_file.close()
                          except:
                              if not command_line.silent:
                                  print 'Reading jumping_factor file failed'
                                  pass
                  # End of slave superupdate routine
  
                  # Start of slave update routine
                  if not (k-1) % (command_line.update/10):
                      try:
                          sigma_eig, U, C = sampler.get_covariance_matrix(
                              cosmo1, cosmo2, data, command_line)
                          if command_line.jumping == 'fast':
                              Cholesky = la.cholesky(C).T
                          # Test here whether the covariance matrix has really changed
                          # We should in principle test all terms, but testing the first one should suffice
                          if not C[0,0] == previous[2][0,0] and not k == 1:
                              if command_line.superupdate:
                                  # If the covmat was updated, the master has resumed adapting c
                                  stop_c = False
                              data.out.write('# After %d accepted steps: update proposal \n' % int(acc))
                              if not command_line.silent:
                                  print 'After %d accepted steps: update proposal \n' % int(acc)
                              try:
                                  if stop_after_update:
                                      k = command_line.N
                                      print 'Covariance matrix updated - stopping run'
                              except:
                                  pass
                          previous = (sigma_eig, U, C, Cholesky)
  
                      except:
                          pass
                  # End of slave update routine
              # End of update routine
  
          # Pick a new position ('current' flag in mcmc_parameters), and compute
          # its likelihood. If get_new_position returns True, it means it did not
          # encounter any boundary problem. Otherwise, just increase the
          # multiplicity of the point and start the loop again
          if get_new_position(
                  data, sigma_eig, U, k, Cholesky, Rotation) is True:
              newloglike = sampler.compute_lkl(cosmo1, cosmo2, data)
          else:  # reject step
              rej += 1
              if command_line.superupdate:
                  ar[k%len(ar)] = 0 # Local acceptance rate of last SU*(N_slow + f_fast * N_fast) steps
              elif command_line.adaptive:
                  ar[k%len(ar)] = 0 # Local acceptance rate of last 100 steps
              N += 1
              k += 1
              continue
  
          # Harmless trick to avoid exponentiating large numbers. This decides
          # whether or not the system should move.
          if (newloglike != data.boundary_loglike):
              if (newloglike >= loglike):
                  alpha = 1.
              else:
                  alpha = np.exp(newloglike-loglike)
          else:
              alpha = -1
  
          if ((alpha == 1.) or (rd.uniform(0, 1) < alpha)):  # accept step
  
              # Print out the last accepted step (WARNING: this is NOT the one we
              # just computed ('current' flag), but really the previous one.)
              # with its proper multiplicity (number of times the system stayed
              # there).
              io_mp.print_vector(outputs, N, loglike, data)
  
              # Report the 'current' point to the 'last_accepted'
              sampler.accept_step(data)
              loglike = newloglike
              if loglike > max_loglike:
                  max_loglike = loglike
              acc += 1.0
              N = 1  # Reset the multiplicity
              if command_line.superupdate:
                  ar[k%len(ar)] = 1 # Local acceptance rate of last SU*(N_slow + f_fast * N_fast) steps
              elif command_line.adaptive:
                  ar[k%len(ar)] = 1 # Local acceptance rate of last 100 steps
          else:  # reject step
              rej += 1.0
              N += 1  # Increase multiplicity of last accepted point
              if command_line.superupdate:
                  ar[k%len(ar)] = 0 # Local acceptance rate of last SU*(N_slow + f_fast * N_fast) steps
              elif command_line.adaptive:
                  ar[k%len(ar)] = 0 # Local acceptance rate of last 100 steps
  
          # Store a.r. for last 5 x SU*(N_slow + f_fast * N_fast) steps
          if command_line.superupdate:
              backup_ar[k%len(backup_ar)] = ar[k%len(ar)]
  
          # Regularly (option to set in parameter file), close and reopen the
          # buffer to force to write on file.
          if acc % data.write_step == 0:
              io_mp.refresh_file(data)
              # Update the outputs list
              outputs[0] = data.out
          k += 1  # One iteration done
      # END OF WHILE LOOP
  
      # If at this moment, the multiplicity is higher than 1, it means the
      # current point is not yet accepted, but it also mean that we did not print
      # out the last_accepted one yet. So we do.
      if N > 1:
          io_mp.print_vector(outputs, N-1, loglike, data)
  
      # Print out some information on the finished chain
      rate = acc / (acc + rej)
      sys.stdout.write('\n#  {0} steps done, acceptance rate: {1}\n'.
                       format(command_line.N, rate))
  
      # In case the acceptance rate is too low, or too high, print a warning
      if rate < 0.05:
          warnings.warn("The acceptance rate is below 0.05. You might want to "
                        "set the jumping factor to a lower value than the "
                        "default (2.4), with the option `-f 1.5` for instance.")
      elif rate > 0.6:
          warnings.warn("The acceptance rate is above 0.6, which means you might"
                        " have difficulties exploring the entire parameter space"
                        ". Try analysing these chains, and use the output "
                        "covariance matrix to decrease the acceptance rate to a "
                        "value between 0.2 and 0.4 (roughly).")
      # For a restart, erase the starting point to keep only the new, longer
      # chain.
      if command_line.restart is not None:
          os.remove(command_line.restart)
          sys.stdout.write('    deleting starting point of the chain {0}\n'.
                           format(command_line.restart))
  
      return
  