annotate m-toolbox/classes/@ao/mcmc.m @ 52:daf4eab1a51e database-connection-manager tip

Fix. Default password should be [] not an empty string
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 07 Dec 2011 17:29:47 +0100
parents f0afece42f48
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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0
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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1 % MCMC estimates paramters using a Monte Carlo Markov Chain.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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3 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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4 % DESCRIPTION: MCMC estimate the parameters of a given model given
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Daniele Nicolodi <nicolodi@science.unitn.it>
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5 % inputs, outputs and noise using a Metropolis algorithm.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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6 % It handles (1 input / 1 output) systems, (2 input / 1 output) systems,
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Daniele Nicolodi <nicolodi@science.unitn.it>
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7 % and (2 input / 2 output) systems.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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8 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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9 % CALL: b = mcmc(in,out,pl)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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10 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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11 % INPUTS: out - analysis objects with measured outputs
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Daniele Nicolodi <nicolodi@science.unitn.it>
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12 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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13 % pl - parameter list
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Daniele Nicolodi <nicolodi@science.unitn.it>
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14 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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15 % OUTPUTS: b - pest object contatining estimate information
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Daniele Nicolodi <nicolodi@science.unitn.it>
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16 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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17 % <a href="matlab:utils.helper.displayMethodInfo('ao', 'mcmc')">Parameters Description</a>
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Daniele Nicolodi <nicolodi@science.unitn.it>
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18 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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19 % VERSION: $Id: mcmc.m,v 1.24 2011/11/16 15:21:13 nikos Exp $
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Daniele Nicolodi <nicolodi@science.unitn.it>
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20 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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21 % References: "Catching supermassive black holes binaries without a net"
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Daniele Nicolodi <nicolodi@science.unitn.it>
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22 % N.J. Cornish, E.K. Porter, Phys.Rev.D 75, 021301, 2007
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Daniele Nicolodi <nicolodi@science.unitn.it>
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23 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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24 % TODO: multiple chain option not implemented yet
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Daniele Nicolodi <nicolodi@science.unitn.it>
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25 % metropolis/hastings not implemented
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Daniele Nicolodi <nicolodi@science.unitn.it>
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26 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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27 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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28
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Daniele Nicolodi <nicolodi@science.unitn.it>
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29 function varargout = mcmc(varargin)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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30
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Daniele Nicolodi <nicolodi@science.unitn.it>
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31 % Check if this is a call for parameters
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Daniele Nicolodi <nicolodi@science.unitn.it>
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32 if utils.helper.isinfocall(varargin{:})
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Daniele Nicolodi <nicolodi@science.unitn.it>
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33 varargout{1} = getInfo(varargin{3});
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Daniele Nicolodi <nicolodi@science.unitn.it>
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34 return
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Daniele Nicolodi <nicolodi@science.unitn.it>
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35 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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36
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Daniele Nicolodi <nicolodi@science.unitn.it>
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37 import utils.const.*
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Daniele Nicolodi <nicolodi@science.unitn.it>
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38 utils.helper.msg(msg.PROC3, 'running %s/%s', mfilename('class'), mfilename);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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39
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Daniele Nicolodi <nicolodi@science.unitn.it>
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40 % Method can not be used as a modifier
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Daniele Nicolodi <nicolodi@science.unitn.it>
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41 if nargout == 0
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Daniele Nicolodi <nicolodi@science.unitn.it>
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42 error('### mcmc cannot be used as a modifier. Please give an output variable.');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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43 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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44
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Daniele Nicolodi <nicolodi@science.unitn.it>
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45 % Collect input variable names
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Daniele Nicolodi <nicolodi@science.unitn.it>
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46 in_names = cell(size(varargin));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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47 for ii = 1:nargin,in_names{ii} = inputname(ii);end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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48
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Daniele Nicolodi <nicolodi@science.unitn.it>
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49 % Collect all AOs smodels and plists
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Daniele Nicolodi <nicolodi@science.unitn.it>
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50 [as, ao_invars] = utils.helper.collect_objects(varargin(:), 'ao', in_names);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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51 pl = utils.helper.collect_objects(varargin(:), 'plist', in_names);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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52
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Daniele Nicolodi <nicolodi@science.unitn.it>
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53 % Decide on a deep copy or a modify
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Daniele Nicolodi <nicolodi@science.unitn.it>
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54 out = copy(as, nargout);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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55
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Daniele Nicolodi <nicolodi@science.unitn.it>
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56 % Combine plists
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Daniele Nicolodi <nicolodi@science.unitn.it>
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57 pl = parse(pl, getDefaultPlist);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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58
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Daniele Nicolodi <nicolodi@science.unitn.it>
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59
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Daniele Nicolodi <nicolodi@science.unitn.it>
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60 % Get parameters from plist
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Daniele Nicolodi <nicolodi@science.unitn.it>
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61 mtxin = find(pl,'input');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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62 noi = find(pl,'noise');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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63 mdlin = find(pl,'model');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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64
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Daniele Nicolodi <nicolodi@science.unitn.it>
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65 % Decide on a deep copy or a modify
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Daniele Nicolodi <nicolodi@science.unitn.it>
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66 in = copy(mtxin, nargout);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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67 mdl = copy(mdlin, nargout);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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68
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Daniele Nicolodi <nicolodi@science.unitn.it>
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69 numexp = numel(in(1,:));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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70 numchannels_in = numel(in(:,1));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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71 numchannels_out = numel(out(:,1));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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72
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Daniele Nicolodi <nicolodi@science.unitn.it>
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73 if (numel(in) ~= numel(out))
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Daniele Nicolodi <nicolodi@science.unitn.it>
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74 error('### Dimensions of input and output must be equal.');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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75 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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76
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Daniele Nicolodi <nicolodi@science.unitn.it>
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77 % Redefining the ao inputs as matrix objects
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Daniele Nicolodi <nicolodi@science.unitn.it>
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78 for ii = 1:numexp
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Daniele Nicolodi <nicolodi@science.unitn.it>
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79 matin(ii) = matrix(in(:,ii),plist('shape',[numchannels_in 1]));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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80 matout(ii) = matrix(out(:,ii),plist('shape',[numchannels_in 1]));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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81 matnoise(ii) = matrix(noi(:,ii),plist('shape',[numchannels_in 1]));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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82 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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83
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Daniele Nicolodi <nicolodi@science.unitn.it>
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84 switch class(mdl)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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85 case 'smodel'
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Daniele Nicolodi <nicolodi@science.unitn.it>
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86 matmodel = matrix(mdl);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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87 case 'ssm'
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Daniele Nicolodi <nicolodi@science.unitn.it>
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88 matmodel = mdl;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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89 case 'matrix'
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Daniele Nicolodi <nicolodi@science.unitn.it>
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90 matmodel = mdl;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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91 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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92
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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93 pl = pset(pl,'model',matmodel,'input',matin,'noise',matnoise);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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94 mcmc_obj = mcmc(matout,pl);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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95
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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96
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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97 % Set output
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Daniele Nicolodi <nicolodi@science.unitn.it>
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98 varargout{1} = mcmc_obj;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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99
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Daniele Nicolodi <nicolodi@science.unitn.it>
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100 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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101
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Daniele Nicolodi <nicolodi@science.unitn.it>
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102
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Daniele Nicolodi <nicolodi@science.unitn.it>
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103
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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104 %--------------------------------------------------------------------------
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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105 % Get Info Object
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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106 %--------------------------------------------------------------------------
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Daniele Nicolodi <nicolodi@science.unitn.it>
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107 function ii = getInfo(varargin)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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108 if nargin == 1 && strcmpi(varargin{1}, 'None')
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Daniele Nicolodi <nicolodi@science.unitn.it>
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109 sets = {};
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Daniele Nicolodi <nicolodi@science.unitn.it>
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110 pl = [];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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111 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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112 sets = {'Default'};
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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113 pl = getDefaultPlist;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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114 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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115 % Build info object
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Daniele Nicolodi <nicolodi@science.unitn.it>
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116 ii = minfo(mfilename, 'ao', 'ltpda', utils.const.categories.sigproc, '$Id: mcmc.m,v 1.24 2011/11/16 15:21:13 nikos Exp $', sets, pl);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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117 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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118
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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119 %--------------------------------------------------------------------------
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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120 % Get Default Plist
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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121 %--------------------------------------------------------------------------
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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122 function plout = getDefaultPlist()
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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123 persistent pl;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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124 if exist('pl', 'var')==0 || isempty(pl)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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125 pl = buildplist();
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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126 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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127 plout = pl;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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128 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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129
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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130 function pl = buildplist()
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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131 pl = plist();
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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132
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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133 % N
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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134 p = param({'N','number of samples of the chain.'}, paramValue.DOUBLE_VALUE(1000));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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135 pl.append(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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136
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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137 % Sigma
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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138 p = param({'cov','covariance of the gaussian jumping distribution.'}, paramValue.DOUBLE_VALUE(1e-4));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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139 pl.append(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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140
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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141 % Param
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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142 p = param({'Fitparams','A cell array of evaluated parameters.'}, paramValue.EMPTY_DOUBLE);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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143 pl.append(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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144
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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145 % Input
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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146 p = param({'input','A matrix array of input signals.'}, paramValue.EMPTY_STRING);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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147 pl.append(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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148
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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149 % Frequencies
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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150 p = param({'frequencies','Range of frequencies where the analysis is performed. If an array, only first and last are used'}, paramValue.EMPTY_DOUBLE);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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151 pl.append(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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152
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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153 % Noise
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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154 p = param({'noise','An array of noise spectrum (PSD) used to compute the likelihood.<ul>', ...
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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155 '<li>1 channel - Input one object</li>', ...
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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156 '<li>2 channel - Input four objects defining the power spectrum matrix </li>',...
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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157 '</ul>'}, paramValue.EMPTY_STRING);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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158 pl.append(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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159
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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160 % Model
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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161 p = param({'model','An array of models.',...
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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162 '<li>1 input / 1 output - Input one object</li>', ...
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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163 '<li>2 input / 1 output - Input two objects</li>', ...
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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164 '<li>2 channel (2 input/ 2 output) - Input four objects defining the transfer function matrix </li>',...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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165 '</ul>'}, paramValue.EMPTY_STRING);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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166 pl.append(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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167
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Daniele Nicolodi <nicolodi@science.unitn.it>
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168 % Search
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Daniele Nicolodi <nicolodi@science.unitn.it>
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169 p = param({'search','Set to true to use bigger jumps in parameter space during annealing and cool down.'}, paramValue.TRUE_FALSE);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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170 pl.append(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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171
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Daniele Nicolodi <nicolodi@science.unitn.it>
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172 % Simplex
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Daniele Nicolodi <nicolodi@science.unitn.it>
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173 p = param({'simplex','Set to true to perform a simplex search to find the starting parameters of the MCMC chain.'}, paramValue.TRUE_FALSE);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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174 pl.append(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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175
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Daniele Nicolodi <nicolodi@science.unitn.it>
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176 % heat
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Daniele Nicolodi <nicolodi@science.unitn.it>
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177 p = param({'heat','The heat index flattening likelihood surface during annealing.'}, paramValue.DOUBLE_VALUE(1));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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178 pl.append(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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179
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Daniele Nicolodi <nicolodi@science.unitn.it>
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180 % Tc
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Daniele Nicolodi <nicolodi@science.unitn.it>
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181 p = param({'Tc','An array of two values setting the initial and final value for the cooling down.'}, paramValue.EMPTY_DOUBLE);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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182 pl.append(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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183
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Daniele Nicolodi <nicolodi@science.unitn.it>
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184 % x0
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Daniele Nicolodi <nicolodi@science.unitn.it>
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185 p = param({'x0','The proposed initial values.'}, paramValue.EMPTY_DOUBLE);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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186 pl.append(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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187
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Daniele Nicolodi <nicolodi@science.unitn.it>
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188 % jumps
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Daniele Nicolodi <nicolodi@science.unitn.it>
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189 p = param({'jumps','An array of four numbers setting the rescaling of the covariance matrix during the search phase.',...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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190 'The first value is the one applied by default, the following thhree apply just when the chain sample is',...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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191 'mod(10), mod(25) and mod(100) respectively.'}, paramValue.EMPTY_DOUBLE);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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192 pl.append(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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193
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Daniele Nicolodi <nicolodi@science.unitn.it>
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194 % plot
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Daniele Nicolodi <nicolodi@science.unitn.it>
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195 p = param({'plot','Select indexes of the parameters to be plotted.'}, paramValue.EMPTY_DOUBLE);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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196 pl.append(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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197
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Daniele Nicolodi <nicolodi@science.unitn.it>
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198 % debug
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Daniele Nicolodi <nicolodi@science.unitn.it>
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199 p = param({'debug','Set to true to get debug information of the MCMC process.'}, paramValue.FALSE_TRUE);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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200 pl.append(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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201
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Daniele Nicolodi <nicolodi@science.unitn.it>
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202 p = param({'prior','Mean, sigma and normalization factor for priors. Still under test'}, paramValue.EMPTY_STRING);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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203 pl.append(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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204
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Daniele Nicolodi <nicolodi@science.unitn.it>
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205 p = param({'anneal',['Choose type of annealing during sampling. Default value is ',...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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206 'simulated annealing. Choose "thermo" for annealing with a thermostat.',...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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207 ' SNR is computed and if it is larger than a fixed value SNR0 (provided also in the plist), ',...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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208 'then the chains are heated by a factor of (SNR(1)/SNR0)^2. Choosing "simple" ',...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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209 'the deviation of the loglikelihood of every 10 points in the chains is stored. If this deviation ',...
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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210 'is larger or smaller than two fixed values the chains are cooled or heated respectively.']}, {1, {'simul','thermo', 'simple'}, paramValue.SINGLE});
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Daniele Nicolodi <nicolodi@science.unitn.it>
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211 pl.append(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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212
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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213 p = param({'SNR0','Fixed value for thermostated annealing.'}, {1, {200}, paramValue.OPTIONAL});
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Daniele Nicolodi <nicolodi@science.unitn.it>
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214 pl.append(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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215
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Daniele Nicolodi <nicolodi@science.unitn.it>
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216 p = param({'DeltaL',['Deviation of Loglikelihood for 10 points of the chains. Used for',...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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217 'the "simple" choice of annealing with a thermostat.']}, {1, {[100 600 2 3]}, paramValue.OPTIONAL});
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Daniele Nicolodi <nicolodi@science.unitn.it>
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218 pl.append(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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219
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Daniele Nicolodi <nicolodi@science.unitn.it>
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220 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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221
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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222
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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223 % PARAMETERS: J - number of chains to compute.
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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224 % sigma - dispersion of the jumping distribution.
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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225 % range - range where the parameteters are sampled.
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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226 % param - a cell array of evaluated parameters (from the
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Daniele Nicolodi <nicolodi@science.unitn.it>
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227 % smodel).
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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228 % Tc - an array with two values (default: 0, i.e. no annealing).
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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229 % heat - heat index flattening likelihood surface (default: 1)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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230 % x0 - proposed initial values, if empty selected randomly.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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231 % (default: empty)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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232
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Daniele Nicolodi <nicolodi@science.unitn.it>
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233