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annotate m-toolbox/classes/+utils/@math/qqplot.m @ 52:daf4eab1a51e database-connection-manager tip

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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
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Daniele Nicolodi <nicolodi@science.unitn.it>
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1 % QQPLOT makes quantile-quantile 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 = qqplot(y1,[],ops) Plot a quantile-quantile 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 quantile-quantile 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 % - 'GammaDist' -> Gamma distribution. 'params' should contain the
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Daniele Nicolodi <nicolodi@science.unitn.it>
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22 % shape and scale parameters
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Daniele Nicolodi <nicolodi@science.unitn.it>
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23 % - 'ShapeParam' -> In the case of comparison of a data series with a
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Daniele Nicolodi <nicolodi@science.unitn.it>
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24 % theoretical distribution and the data series is composed of correlated
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Daniele Nicolodi <nicolodi@science.unitn.it>
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25 % elements. K can be adjusted with a shape parameter in order to recover
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Daniele Nicolodi <nicolodi@science.unitn.it>
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26 % test fairness. In such a case the test is performed for K* = Phi *K.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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27 % Phi is the corresponding Shape parameter. The shape parameter depends
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Daniele Nicolodi <nicolodi@science.unitn.it>
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28 % on the correlations and on the significance value. It does not depend
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Daniele Nicolodi <nicolodi@science.unitn.it>
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29 % on data length.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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30 % - 'params' -> Probability distribution parameters
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Daniele Nicolodi <nicolodi@science.unitn.it>
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31 % - 'conflevel' -> requiered confidence for confidence bounds evaluation.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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32 % Default 0.95 (95%)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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33 % - 'FontSize' -> Font size for axis. Default 22
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Daniele Nicolodi <nicolodi@science.unitn.it>
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34 % - 'LineWidth' -> line width. Default 2
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Daniele Nicolodi <nicolodi@science.unitn.it>
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35 % - '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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36 % further details
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Daniele Nicolodi <nicolodi@science.unitn.it>
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37 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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38 % Luigi Ferraioli 11-02-2011
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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 % % $Id: qqplot.m,v 1.8 2011/07/08 10:26:45 luigi Exp $
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Daniele Nicolodi <nicolodi@science.unitn.it>
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41 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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42 function h = qqplot(y1,y2,ops)
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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 %%% check and set imput options
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Daniele Nicolodi <nicolodi@science.unitn.it>
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45 % Default input struct
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Daniele Nicolodi <nicolodi@science.unitn.it>
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46 defaultparams = struct(...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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47 'ProbDist','Fdist',...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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48 'ShapeParam',1,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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49 'params',[1 1],...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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50 'conflevel',0.95,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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51 'FontSize',22,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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52 'LineWidth',2,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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53 'axis',[]);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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54
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Daniele Nicolodi <nicolodi@science.unitn.it>
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55 names = {'ProbDist','ShapeParam','params','conflevel','FontSize','LineWidth','axis'};
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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 % collecting input and default params
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Daniele Nicolodi <nicolodi@science.unitn.it>
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58 if nargin == 3
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Daniele Nicolodi <nicolodi@science.unitn.it>
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59 if ~isempty(ops)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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60 for jj=1:length(names)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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61 if isfield(ops, names(jj))
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Daniele Nicolodi <nicolodi@science.unitn.it>
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62 defaultparams.(names{1,jj}) = ops.(names{1,jj});
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Daniele Nicolodi <nicolodi@science.unitn.it>
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63 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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64 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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65 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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66 end
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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 pdist = defaultparams.ProbDist; % check theoretical distribution
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Daniele Nicolodi <nicolodi@science.unitn.it>
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69 shp = defaultparams.ShapeParam;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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70 dof = defaultparams.params; % distribution parameters
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Daniele Nicolodi <nicolodi@science.unitn.it>
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71 conf = defaultparams.conflevel; % confidence level for confidence bounds calculation
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Daniele Nicolodi <nicolodi@science.unitn.it>
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72 if conf>1
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Daniele Nicolodi <nicolodi@science.unitn.it>
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73 conf = conf/100;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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74 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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75 fontsize = defaultparams.FontSize;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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76 lwidth = defaultparams.LineWidth;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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77 axvect = defaultparams.axis;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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78
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Daniele Nicolodi <nicolodi@science.unitn.it>
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79
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Daniele Nicolodi <nicolodi@science.unitn.it>
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80 %%% check data input
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Daniele Nicolodi <nicolodi@science.unitn.it>
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81 if isempty(y2) % do theoretical comparison
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Daniele Nicolodi <nicolodi@science.unitn.it>
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82 % get empirical distribution for input data
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Daniele Nicolodi <nicolodi@science.unitn.it>
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83 [eCD,ex]=utils.math.ecdf(y1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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84 % switch between input theoretical distributions
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Daniele Nicolodi <nicolodi@science.unitn.it>
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85 switch lower(pdist)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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86 case 'fdist'
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Daniele Nicolodi <nicolodi@science.unitn.it>
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87 % get theoretical Quantile corresponding to empirical probabilities
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Daniele Nicolodi <nicolodi@science.unitn.it>
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88 tx = utils.math.Finv(eCD,dof(1),dof(2));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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89 CD = utils.math.Fcdf(ex,dof(1),dof(2));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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90 case 'normdist'
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Daniele Nicolodi <nicolodi@science.unitn.it>
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91 tx = utils.math.Norminv(eCD,dof(1),dof(2));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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92 CD = utils.math.Normcdf(ex,dof(1),dof(2));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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93 case 'chi2dist'
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Daniele Nicolodi <nicolodi@science.unitn.it>
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94 tx = utils.math.Chi2inv(eCD,dof(1));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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95 CD = utils.math.Chi2cdf(ex,dof(1));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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96 case 'gammadist'
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Daniele Nicolodi <nicolodi@science.unitn.it>
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97 tx = gammaincinv(eCD,dof(1)).*dof(2);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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98 CD = gammainc(ex./dof(2),dof(1));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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99 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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100 % get confidence levels with Kolmogorow - Smirnov test
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Daniele Nicolodi <nicolodi@science.unitn.it>
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101 alp = (1-conf)/2;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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102 cVal = utils.math.SKcriticalvalues(numel(ex)*shp,[],alp);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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103 % get upper and lower bounds for x
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Daniele Nicolodi <nicolodi@science.unitn.it>
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104 CDu = CD+cVal;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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105 CDl = CD-cVal;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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106 xup = interp1(CDl,ex,eCD);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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107 xlw = interp1(CDu,ex,eCD);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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108
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Daniele Nicolodi <nicolodi@science.unitn.it>
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109 figure
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Daniele Nicolodi <nicolodi@science.unitn.it>
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110 h1 = plot(tx,ex);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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111 grid on
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Daniele Nicolodi <nicolodi@science.unitn.it>
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112 hold on
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Daniele Nicolodi <nicolodi@science.unitn.it>
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113 lnx = [min(tx) max(tx(1:end-1))];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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114 lny = [min(tx) max(tx(1:end-1))];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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115 h2 = line(lnx,lny,'Color','k');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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116 h3 = plot(tx,xup,'b--');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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117 h4 = plot(tx,xlw,'b--');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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118 xlabel('Theoretical Quantile','FontSize',fontsize);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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119 ylabel('Sample Quantile','FontSize',fontsize);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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120 set(h1(1), 'Color','r', 'LineStyle','-','LineWidth',lwidth);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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121 set(h2(1), 'Color','k', 'LineStyle','--','LineWidth',lwidth);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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122 set(h3(1), 'Color','b', 'LineStyle',':','LineWidth',lwidth);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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123 set(h4(1), 'Color','b', 'LineStyle',':','LineWidth',lwidth);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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124 legend([h1(1),h2(1),h3(1)],{'Sample Quantile','Reference','Conf. Bounds'},'Location','SouthEast')
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Daniele Nicolodi <nicolodi@science.unitn.it>
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125 if ~isempty(axvect)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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126 axis(axvect);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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127 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
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128 % get limit for quantiles corresponding to 0 and 0.99 prob
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Daniele Nicolodi <nicolodi@science.unitn.it>
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129 xlw = interp1(CD,tx,0.001,'linear');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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130 if isnan(xlw)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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131 xlw = min(CD);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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132 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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133 xup = interp1(CD,tx,0.999,'linear');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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134 % get limit for quantiles corresponding to 0 and 0.99 prob
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Daniele Nicolodi <nicolodi@science.unitn.it>
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135 ylw = interp1(eCD,ex,0.001,'linear');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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136 if isnan(ylw)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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137 ylw = min(eCD);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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138 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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139 yup = interp1(eCD,ex,0.999,'linear');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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140 axis([xlw xup ylw yup]);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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141 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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142 h = [h1;h2;h3;h4];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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143
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Daniele Nicolodi <nicolodi@science.unitn.it>
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144 else % do empirical comparison
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Daniele Nicolodi <nicolodi@science.unitn.it>
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145 % get empirical distribution for input data
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Daniele Nicolodi <nicolodi@science.unitn.it>
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146 [eCD1,ex1]=utils.math.ecdf(y1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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147 [eCD2,ex2]=utils.math.ecdf(y2);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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148
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Daniele Nicolodi <nicolodi@science.unitn.it>
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149 % get confidence levels with Kolmogorow - Smirnov test
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Daniele Nicolodi <nicolodi@science.unitn.it>
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150 alp = (1-conf)/2;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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151 cVal = utils.math.SKcriticalvalues(numel(ex1),numel(ex2),alp);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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152 % get confidence levels
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Daniele Nicolodi <nicolodi@science.unitn.it>
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153 CDu = eCD2+cVal;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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154 CDl = eCD2-cVal;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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155
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Daniele Nicolodi <nicolodi@science.unitn.it>
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156 % get Quantile corresponding for second distribution to first empirical
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
157 % probabilities
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
158 tx = interp1(eCD2,ex2,eCD1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
159
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
160 % get upper and lower bounds for x
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
161 xup = interp1(CDl,ex2,eCD1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
162 xlw = interp1(CDu,ex2,eCD1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
163
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
164 figure
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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165 h1 = plot(tx,ex1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
166 grid on
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
167 hold on
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
168 lnx = [min(tx) max(tx(1:end-1))];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
169 lny = [min(tx) max(tx(1:end-1))];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
170 h2 = line(lnx,lny,'Color','k');
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
171 h3 = plot(tx,xup,'b--');
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
172 h4 = plot(tx,xlw,'b--');
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
173 xlabel('Y2 Quantile','FontSize',fontsize);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
174 ylabel('Y1 Quantile','FontSize',fontsize);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
175 set(h1(1), 'Color','r', 'LineStyle','-','LineWidth',lwidth);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
176 set(h2(1), 'Color','k', 'LineStyle','--','LineWidth',lwidth);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
177 set(h3(1), 'Color','b', 'LineStyle',':','LineWidth',lwidth);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
178 set(h4(1), 'Color','b', 'LineStyle',':','LineWidth',lwidth);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
179 legend([h1(1),h2(1),h3(1)],{'Sample Quantile','Reference','Conf. Bounds'},'Location','SouthEast')
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
180 if ~isempty(axvect)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
181 axis(axvect);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
182 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
183 % get limit for quantiles corresponding to 0 and 0.99 prob
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
184 xlw = interp1(eCD2,ex2,0.001,'linear');
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
185 if isnan(xlw)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
186 xlw = min(eCD2);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
187 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
188 xup = interp1(eCD2,ex2,0.999,'linear');
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
189 % get limit for quantiles corresponding to 0 and 0.99 prob
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
190 ylw = interp1(eCD1,ex1,0.001,'linear');
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
191 if isnan(ylw)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
192 ylw = min(eCD1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
193 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
194 yup = interp1(eCD1,ex1,0.999,'linear');
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
195 axis([xlw xup ylw yup]);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
196 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
197 h = [h1;h2;h3;h4];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
198 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
199
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
200 end