ltpda: m-toolbox/classes/+utils/@math/ppplot.m annotate

author	Daniele Nicolodi <nicolodi@science.unitn.it>
date	Wed, 23 Nov 2011 19:22:13 +0100
parents
children

rev	line source
0 f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	1 % PPPLOT makes probability-probability plot
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	3 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	4 % h = ppplot(y1,[],ops) Plot a probability-probability plot comparing with
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	5 % theoretical model.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	6 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	7 % h = cdfplot(y1,y2,ops) Plot a probability-probability plot comparing two
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	8 % empirical cdfs.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	9 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	10 % ops is a cell aray of options
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	11 % - 'ProbDist' -> theoretical distribution. Available distributions are:
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	12 % - 'Fdist' -> F cumulative distribution function. In this case the
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	13 % parameter 'params' should be a vector with distribution degrees of
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	14 % freedoms [dof1 dof2]
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	15 % - 'Normdist' -> Normal cumulative distribution function. In this case
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	16 % the parameter 'params' should be a vector with distribution mean and
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	17 % standard deviation [mu sigma]
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	18 % - 'Chi2dist' -> Chi square cumulative distribution function. In this
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	19 % case the parameter 'params' should be a number indicating
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	20 % distribution degrees of freedom
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	21 % - 'params' -> Probability distribution parameters
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	22 % - 'conflevel' -> requiered confidence for confidence bounds evaluation.
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	23 % Default 0.95 (95%)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	24 % - 'FontSize' -> Font size for axis. Default 22
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	25 % - 'LineWidth' -> line width. Default 2
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	26 % - 'axis' -> set axis properties of the plot. refer to help axis for
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	27 % further details
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	28 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	29 % Luigi Ferraioli 11-02-2011
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	30 %
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	31 % % $Id: ppplot.m,v 1.5 2011/03/15 17:16:27 luigi Exp $
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	33 function h = ppplot(y1,y2,ops)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	34
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	35 %%% check and set imput options
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	36 % Default input struct
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	37 defaultparams = struct('ProbDist','Fdist',...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	38 'params',[1 1],...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	39 'conflevel',0.95,...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	40 'FontSize',22,...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	41 'LineWidth',2,...
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	42 'axis',[]);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	43
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	44 names = {'ProbDist','params','conflevel','FontSize','LineWidth','axis'};
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	45
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	46 % collecting input and default params
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	47 if nargin == 3
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	48 if ~isempty(ops)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	49 for jj=1:length(names)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	50 if isfield(ops, names(jj))
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	51 defaultparams.(names{1,jj}) = ops.(names{1,jj});
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	52 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	53 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	54 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	55 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	56
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	57 pdist = defaultparams.ProbDist; % check theoretical distribution
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	58 dof = defaultparams.params; % distribution parameters
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	59 conf = defaultparams.conflevel; % confidence level for confidence bounds calculation
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	60 if conf>1
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	61 conf = conf/100;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	62 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	63 fontsize = defaultparams.FontSize;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	64 lwidth = defaultparams.LineWidth;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	65 axvect = defaultparams.axis;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	66
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	67
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	68 %%% check data input
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	69 if isempty(y2) % do theoretical comparison
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	70 % get empirical distribution for input data
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	71 [ep,ex]=utils.math.ecdf(y1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	72 % switch between input theoretical distributions
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	73 switch lower(pdist)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	74 case 'fdist'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	75 % get theoretical probabilities corresponding to empirical quantiles
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	76 tp = utils.math.Fcdf(ex,dof(1),dof(2));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	77 case 'normdist'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	78 tp = utils.math.Normcdf(ex,dof(1),dof(2));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	79 case 'chi2dist'
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	80 tp = utils.math.Chi2cdf(ex,dof(1));
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	81 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	82 % get confidence levels with Kolmogorow - Smirnov test
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	83 alp = (1-conf)/2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	84 cVal = utils.math.SKcriticalvalues(numel(ex),numel(ex),alp);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	85 % get upper and lower bounds for x
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	86 pup = CD+cVal;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	87 plw = CD-cVal;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	88
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	89 figure
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	90 h1 = plot(tp,ep);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	91 grid on
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	92 hold on
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	93 lnx = [min(tp) max(tp(1:end-1))];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	94 lny = [min(tp) max(tp(1:end-1))];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	95 h2 = line(lnx,lny,'Color','k');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	96 h3 = plot(tp,pup,'b--');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	97 h4 = plot(tp,plw,'b--');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	98 xlabel('Theoretical Probability','FontSize',fontsize);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	99 ylabel('Sample Probability','FontSize',fontsize);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	100 set(h1(1), 'Color','r', 'LineStyle','-','LineWidth',lwidth);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	101 set(h2(1), 'Color','k', 'LineStyle','--','LineWidth',lwidth);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	102 set(h3(1), 'Color','b', 'LineStyle',':','LineWidth',lwidth);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	103 set(h4(1), 'Color','b', 'LineStyle',':','LineWidth',lwidth);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	104 legend([h1(1),h2(1),h3(1)],{'Sample Probability','Reference','Conf. Bounds'},'Location','SouthEast')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	105 if ~isempty(axvect)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	106 axis(axvect);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	107 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	108 axis([0 0.99 0 0.99])
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	109 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	110 h = [h1;h2;h3;h4];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	111
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	112 else % do empirical comparison
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	113 % get empirical distribution for input data
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	114 [eCD1,ex1]=utils.math.ecdf(y1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	115 [eCD2,ex2]=utils.math.ecdf(y2);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	116
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	117 % get confidence levels with Kolmogorow - Smirnov test
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	118 alp = (1-conf)/2;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	119 cVal = utils.math.SKcriticalvalues(numel(ex1),numel(ex2),alp);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	120 % get confidence levels
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	121 CDu = eCD2+cVal;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	122 CDl = eCD2-cVal;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	123
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	124 % get probabilities corresponding for second distribution to first empirical
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	125 % probabilities
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	126 tp = interp1(ex2,eCD2,ex1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	127
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	128 % get upper and lower bounds for p
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	129 pup = interp1(ex2,CDu,ex1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	130 plw = interp1(ex2,CDl,ex1);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	131
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	132 % empirical probabilities
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	133 ep = eCD1;
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	134
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	135 figure
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	136 h1 = plot(tp,ep);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	137 grid on
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	138 hold on
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	139 lnx = [min(tp) max(tp(1:end-1))];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	140 lny = [min(tp) max(tp(1:end-1))];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	141 h2 = line(lnx,lny,'Color','k');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	142 h3 = plot(tp,pup,'b--');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	143 h4 = plot(tp,plw,'b--');
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	144 xlabel('Y2 Probability','FontSize',fontsize);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	145 ylabel('Y1 Probability','FontSize',fontsize);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	146 set(h1(1), 'Color','r', 'LineStyle','-','LineWidth',lwidth);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	147 set(h2(1), 'Color','k', 'LineStyle','--','LineWidth',lwidth);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	148 set(h3(1), 'Color','b', 'LineStyle',':','LineWidth',lwidth);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	149 set(h4(1), 'Color','b', 'LineStyle',':','LineWidth',lwidth);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	150 legend([h1(1),h2(1),h3(1)],{'Sample Probability','Reference','Conf. Bounds'},'Location','SouthEast')
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	151 if ~isempty(axvect)
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	152 axis(axvect);
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	153 else
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	154 axis([0 0.99 0 0.99])
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	155 end
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	156 h = [h1;h2;h3;h4];
f0afece42f48 Import. Daniele Nicolodi <nicolodi@science.unitn.it> parents: diff changeset	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

0

f0afece42f48 Import.