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annotate m-toolbox/classes/+utils/@math/ppplot.m @ 22:b11e88004fca database-connection-manager

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author Daniele Nicolodi <nicolodi@science.unitn.it>
date Mon, 05 Dec 2011 16:20:06 +0100
parents f0afece42f48
children
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Daniele Nicolodi <nicolodi@science.unitn.it>
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1 % PPPLOT makes probability-probability plot
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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 % h = ppplot(y1,[],ops) Plot a probability-probability plot comparing with
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Daniele Nicolodi <nicolodi@science.unitn.it>
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5 % theoretical model.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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6 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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7 % h = cdfplot(y1,y2,ops) Plot a probability-probability plot comparing two
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Daniele Nicolodi <nicolodi@science.unitn.it>
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8 % empirical cdfs.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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9 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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10 % ops is a cell aray of options
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Daniele Nicolodi <nicolodi@science.unitn.it>
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11 % - 'ProbDist' -> theoretical distribution. Available distributions are:
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Daniele Nicolodi <nicolodi@science.unitn.it>
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12 % - 'Fdist' -> F cumulative distribution function. In this case the
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Daniele Nicolodi <nicolodi@science.unitn.it>
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13 % parameter 'params' should be a vector with distribution degrees of
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Daniele Nicolodi <nicolodi@science.unitn.it>
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14 % freedoms [dof1 dof2]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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15 % - 'Normdist' -> Normal cumulative distribution function. In this case
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Daniele Nicolodi <nicolodi@science.unitn.it>
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16 % the parameter 'params' should be a vector with distribution mean and
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Daniele Nicolodi <nicolodi@science.unitn.it>
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17 % standard deviation [mu sigma]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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18 % - 'Chi2dist' -> Chi square cumulative distribution function. In this
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Daniele Nicolodi <nicolodi@science.unitn.it>
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19 % case the parameter 'params' should be a number indicating
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Daniele Nicolodi <nicolodi@science.unitn.it>
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20 % distribution degrees of freedom
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Daniele Nicolodi <nicolodi@science.unitn.it>
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21 % - 'params' -> Probability distribution parameters
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Daniele Nicolodi <nicolodi@science.unitn.it>
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22 % - 'conflevel' -> requiered confidence for confidence bounds evaluation.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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23 % Default 0.95 (95%)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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24 % - 'FontSize' -> Font size for axis. Default 22
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Daniele Nicolodi <nicolodi@science.unitn.it>
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25 % - 'LineWidth' -> line width. Default 2
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Daniele Nicolodi <nicolodi@science.unitn.it>
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26 % - 'axis' -> set axis properties of the plot. refer to help axis for
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Daniele Nicolodi <nicolodi@science.unitn.it>
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27 % further details
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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 % Luigi Ferraioli 11-02-2011
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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 % % $Id: ppplot.m,v 1.5 2011/03/15 17:16:27 luigi Exp $
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Daniele Nicolodi <nicolodi@science.unitn.it>
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32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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33 function h = ppplot(y1,y2,ops)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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34
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Daniele Nicolodi <nicolodi@science.unitn.it>
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35 %%% check and set imput options
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Daniele Nicolodi <nicolodi@science.unitn.it>
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36 % Default input struct
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Daniele Nicolodi <nicolodi@science.unitn.it>
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37 defaultparams = struct('ProbDist','Fdist',...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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38 'params',[1 1],...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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39 'conflevel',0.95,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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40 'FontSize',22,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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41 'LineWidth',2,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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42 'axis',[]);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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43
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Daniele Nicolodi <nicolodi@science.unitn.it>
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44 names = {'ProbDist','params','conflevel','FontSize','LineWidth','axis'};
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Daniele Nicolodi <nicolodi@science.unitn.it>
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45
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Daniele Nicolodi <nicolodi@science.unitn.it>
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46 % collecting input and default params
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Daniele Nicolodi <nicolodi@science.unitn.it>
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47 if nargin == 3
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Daniele Nicolodi <nicolodi@science.unitn.it>
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48 if ~isempty(ops)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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49 for jj=1:length(names)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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50 if isfield(ops, names(jj))
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Daniele Nicolodi <nicolodi@science.unitn.it>
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51 defaultparams.(names{1,jj}) = ops.(names{1,jj});
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Daniele Nicolodi <nicolodi@science.unitn.it>
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52 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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53 end
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54 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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55 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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56
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Daniele Nicolodi <nicolodi@science.unitn.it>
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57 pdist = defaultparams.ProbDist; % check theoretical distribution
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Daniele Nicolodi <nicolodi@science.unitn.it>
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58 dof = defaultparams.params; % distribution parameters
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Daniele Nicolodi <nicolodi@science.unitn.it>
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59 conf = defaultparams.conflevel; % confidence level for confidence bounds calculation
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Daniele Nicolodi <nicolodi@science.unitn.it>
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60 if conf>1
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Daniele Nicolodi <nicolodi@science.unitn.it>
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61 conf = conf/100;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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62 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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63 fontsize = defaultparams.FontSize;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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64 lwidth = defaultparams.LineWidth;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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65 axvect = defaultparams.axis;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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66
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Daniele Nicolodi <nicolodi@science.unitn.it>
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67
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Daniele Nicolodi <nicolodi@science.unitn.it>
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68 %%% check data input
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Daniele Nicolodi <nicolodi@science.unitn.it>
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69 if isempty(y2) % do theoretical comparison
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Daniele Nicolodi <nicolodi@science.unitn.it>
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70 % get empirical distribution for input data
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Daniele Nicolodi <nicolodi@science.unitn.it>
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71 [ep,ex]=utils.math.ecdf(y1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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72 % switch between input theoretical distributions
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Daniele Nicolodi <nicolodi@science.unitn.it>
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73 switch lower(pdist)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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74 case 'fdist'
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Daniele Nicolodi <nicolodi@science.unitn.it>
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75 % get theoretical probabilities corresponding to empirical quantiles
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Daniele Nicolodi <nicolodi@science.unitn.it>
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76 tp = utils.math.Fcdf(ex,dof(1),dof(2));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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77 case 'normdist'
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Daniele Nicolodi <nicolodi@science.unitn.it>
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78 tp = utils.math.Normcdf(ex,dof(1),dof(2));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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79 case 'chi2dist'
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Daniele Nicolodi <nicolodi@science.unitn.it>
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80 tp = utils.math.Chi2cdf(ex,dof(1));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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81 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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82 % get confidence levels with Kolmogorow - Smirnov test
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Daniele Nicolodi <nicolodi@science.unitn.it>
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83 alp = (1-conf)/2;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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84 cVal = utils.math.SKcriticalvalues(numel(ex),numel(ex),alp);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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85 % get upper and lower bounds for x
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Daniele Nicolodi <nicolodi@science.unitn.it>
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86 pup = CD+cVal;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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87 plw = CD-cVal;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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88
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Daniele Nicolodi <nicolodi@science.unitn.it>
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89 figure
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Daniele Nicolodi <nicolodi@science.unitn.it>
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90 h1 = plot(tp,ep);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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91 grid on
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Daniele Nicolodi <nicolodi@science.unitn.it>
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92 hold on
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Daniele Nicolodi <nicolodi@science.unitn.it>
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93 lnx = [min(tp) max(tp(1:end-1))];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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94 lny = [min(tp) max(tp(1:end-1))];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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95 h2 = line(lnx,lny,'Color','k');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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96 h3 = plot(tp,pup,'b--');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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97 h4 = plot(tp,plw,'b--');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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98 xlabel('Theoretical Probability','FontSize',fontsize);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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99 ylabel('Sample Probability','FontSize',fontsize);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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100 set(h1(1), 'Color','r', 'LineStyle','-','LineWidth',lwidth);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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101 set(h2(1), 'Color','k', 'LineStyle','--','LineWidth',lwidth);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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102 set(h3(1), 'Color','b', 'LineStyle',':','LineWidth',lwidth);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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103 set(h4(1), 'Color','b', 'LineStyle',':','LineWidth',lwidth);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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104 legend([h1(1),h2(1),h3(1)],{'Sample Probability','Reference','Conf. Bounds'},'Location','SouthEast')
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Daniele Nicolodi <nicolodi@science.unitn.it>
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105 if ~isempty(axvect)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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106 axis(axvect);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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107 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
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108 axis([0 0.99 0 0.99])
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Daniele Nicolodi <nicolodi@science.unitn.it>
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109 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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110 h = [h1;h2;h3;h4];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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111
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Daniele Nicolodi <nicolodi@science.unitn.it>
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112 else % do empirical comparison
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Daniele Nicolodi <nicolodi@science.unitn.it>
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113 % get empirical distribution for input data
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Daniele Nicolodi <nicolodi@science.unitn.it>
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114 [eCD1,ex1]=utils.math.ecdf(y1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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115 [eCD2,ex2]=utils.math.ecdf(y2);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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116
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Daniele Nicolodi <nicolodi@science.unitn.it>
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117 % get confidence levels with Kolmogorow - Smirnov test
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Daniele Nicolodi <nicolodi@science.unitn.it>
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118 alp = (1-conf)/2;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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119 cVal = utils.math.SKcriticalvalues(numel(ex1),numel(ex2),alp);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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120 % get confidence levels
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Daniele Nicolodi <nicolodi@science.unitn.it>
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121 CDu = eCD2+cVal;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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122 CDl = eCD2-cVal;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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123
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Daniele Nicolodi <nicolodi@science.unitn.it>
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124 % get probabilities corresponding for second distribution to first empirical
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Daniele Nicolodi <nicolodi@science.unitn.it>
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125 % probabilities
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Daniele Nicolodi <nicolodi@science.unitn.it>
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126 tp = interp1(ex2,eCD2,ex1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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127
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Daniele Nicolodi <nicolodi@science.unitn.it>
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128 % get upper and lower bounds for p
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Daniele Nicolodi <nicolodi@science.unitn.it>
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129 pup = interp1(ex2,CDu,ex1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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130 plw = interp1(ex2,CDl,ex1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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131
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Daniele Nicolodi <nicolodi@science.unitn.it>
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132 % empirical probabilities
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Daniele Nicolodi <nicolodi@science.unitn.it>
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133 ep = eCD1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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134
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Daniele Nicolodi <nicolodi@science.unitn.it>
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135 figure
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Daniele Nicolodi <nicolodi@science.unitn.it>
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136 h1 = plot(tp,ep);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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137 grid on
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Daniele Nicolodi <nicolodi@science.unitn.it>
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138 hold on
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Daniele Nicolodi <nicolodi@science.unitn.it>
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139 lnx = [min(tp) max(tp(1:end-1))];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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140 lny = [min(tp) max(tp(1:end-1))];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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141 h2 = line(lnx,lny,'Color','k');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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142 h3 = plot(tp,pup,'b--');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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143 h4 = plot(tp,plw,'b--');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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144 xlabel('Y2 Probability','FontSize',fontsize);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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145 ylabel('Y1 Probability','FontSize',fontsize);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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146 set(h1(1), 'Color','r', 'LineStyle','-','LineWidth',lwidth);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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147 set(h2(1), 'Color','k', 'LineStyle','--','LineWidth',lwidth);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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148 set(h3(1), 'Color','b', 'LineStyle',':','LineWidth',lwidth);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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149 set(h4(1), 'Color','b', 'LineStyle',':','LineWidth',lwidth);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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150 legend([h1(1),h2(1),h3(1)],{'Sample Probability','Reference','Conf. Bounds'},'Location','SouthEast')
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Daniele Nicolodi <nicolodi@science.unitn.it>
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151 if ~isempty(axvect)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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152 axis(axvect);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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153 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
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154 axis([0 0.99 0 0.99])
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Daniele Nicolodi <nicolodi@science.unitn.it>
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155 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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156 h = [h1;h2;h3;h4];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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157 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
158
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
159 end