function csS = som_stats(D,varargin)%SOM_STATS Calculate descriptive statistics for the data.%  % csS = som_stats(D,[sort]); % %  csS = som_stats(D); %  csS = som_stats(D,'nosort'); %  som_table_print(som_stats_table(csS))%%  Input and output arguments ([]'s are optional): %   D           (matrix) a matrix, size dlen x dim%               (struct) data or map struct%   [sort]      (string) 'sort' (default) or 'nosort'%                        If 'nosort' is specified, the data is not %                        sorted, and therefore the values of%                        nunique, uvalues, ucount, fvalues, fcount, and tiles fields %                        are not calculated. This may be useful if%                        there is a very large amount of data, and%                        one wants to reduce calculation time.%%   csS         (cell array) size dim x 1, of statistics structs with %                        the following fields%      .type             (string) 'som_stat'%      .name             (string) name of the variable%      .normalization    (struct array) variable normalization (see SOM_NORMALIZE)%      .ntotal           (scalar) total number of values%      .nvalid           (scalar) number of valid values (not Inf or NaN)%      .min              (scalar) minimum value %      .max              (scalar) maximum value %      .mean             (scalar) mean value (not Inf or NaN)%      .std              (scalar) standard deviation (not Inf or NaN)%      .nunique          (scalar) number of unique values%      .mfvalue          (vector) most frequent value%      .mfcount          (vector) number of occurances of most frequent value%      .values           (vector) at most MAXDISCRETE (see below) sample values %      .counts           (vector) number of occurances for each sampled value%      .tiles            (vector) NT-tile values, for example%                                    NT=4   for quartiles: 25%, 50% and 75%%                                    NT=100 for percentiles: 1%, 2%, ... and 99%%      .hist             (struct) histogram struct with the following fields%           .type        (string) 'som_hist'%           .bins        (vector) histogram bin centers %           .counts      (vector) count of values in each bin%           .binlabels   (cellstr) labels for the bins (denormalized bin%                                  center values)%           .binlabels2  (cellstr) labels for the bins (denormalized bin%                                  edge values, e.g. '[1.4,2.5['%%   Constants: %      MAXDISCRETE = 10%      NT          = 10%% See also  SOM_STATS_PLOT, SOM_STATS_TABLE, SOM_TABLE_PRINT, SOM_STATS_REPORT.% Contributed to SOM Toolbox 2.0, December 31st, 2001 by Juha Vesanto% Copyright (c) by Juha Vesanto% http://www.cis.hut.fi/projects/somtoolbox/% Version 2.0beta juuso 311201%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5%% arguments% default valuesnosort      = 0; nbins       = 10; maxdiscrete = 20; ntiles      = 10; % first argumentif isstruct(D),     switch D.type,     case 'som_map',  cn = D.comp_names; sN = D.comp_norm; D = D.codebook;     case 'som_data', cn = D.comp_names; sN = D.comp_norm; D = D.data;     otherwise, error('Invalid first argument')    end    else    cn = cell(size(D,2),1);     cn(:) = {'Variable'};    for i=1:length(cn), cn{i} = sprintf('%s%d',cn{i},i); end        sN = cell(size(D,2),1); end[dlen dim] = size(D);% other argumentsif length(varargin)>0,   if strcmp(varargin{1},'nosort'), nosort = 1; endend%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5%% actionsStat = struct('type','som_stat','name','','normalization',[],...               'min',NaN,'max',NaN,'mean',NaN,'std',NaN,...               'nunique',NaN,'values',[],'counts',[],'mfvalue',NaN,'mfcount',NaN,'tiles',[],...               'ntotal',dlen,'nvalid',NaN,'hist',[]);csS = cell(0);           for i=1:dim,     sS = sStat;    sS.name = cn{i};    sS.normalization = sN{i};     x = D(:,i);     x(find(~isfinite(x))) = [];    % basic descriptive statistics    sS.nvalid = length(x);    if length(x),         sS.min  = min(x);        sS.max  = max(x);        sS.mean = mean(x);          sS.std = std(x);        bins = [];        if ~nosort,             xsorted    = sort(x);            % number of unique values            repeated   = (xsorted(1:end-1)==xsorted(2:end));            j          = [1; find(~repeated)+1];                     xunique    = xsorted(j);             sS.nunique = length(xunique);                       ucount     = diff([j; length(xsorted)+1]);            % most frequent value            [fcount,j] = max(ucount);            sS.mfvalue = xunique(j);            sS.mfcount = fcount;            % -tiles (k*100/ntiles % of values, k=1..)            pickind    = round(linspace(1,sS.nvalid,ntiles+1));             pickind    = pickind(2:end-1);            sS.tiles   = xsorted(pickind);            if sS.nunique <= sS.nvalid/2,                 % unique values                sS.values = xunique; 	            sS.counts = ucount;                 bins = sS.values;             else                % just maxdiscrete values, evenly  picked                pickind    = round(linspace(1,sS.nunique,maxdiscrete));                sS.values  = xunique(pickind);                sS.counts  = ucount(pickind); 	                    %% OPTION 2: maxdiscrete most frequent values                %[v,j]     = sort(ucount);                 %pickind   = j(1:maxdiscrete);                             %sS.values = xunique(pickind);                %sS.counts = ucount(pickind);                % OPTION 3: representative values - calculated using k-means                %[y,bm,qe] = kmeans(x,maxdiscrete);               %sS.values = y;                 %sS.counts = full(sum(sparse(bm,1:length(bm),1,maxdiscrete,length(bm)),2));            end         end         if isempty(bins),             bins = linspace(sS.min,sS.max,nbins+1);             bins = (bins(1:end-1)+bins(2:end))/2;         end        sS.hist = som_hist(x,bins,sS.normalization);        else        sS.hist = som_hist(x,0);    end    csS{end+1} = sS; endreturn;%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5%% subfunctionsfunction sH = som_hist(x,bins,sN)    binlabels  = [];     binlabels2 = [];     if nargin<2 | isempty(bins) | isnan(bins),         bins = linspace(min(x),max(x),10);        end    if isstruct(bins),         bins = sH.bins;         binlabels  = sH.binlabels;        binlabels2 = sH.binlabels2;    end     if nargin<3, sN = []; end    sH = struct('type','som_hist','bins',bins,'counts',[],...                'binlabels',binlabels,'binlabels2',binlabels2);                                         if length(bins)==1,        sH.counts = [length(x)];        edges = bins;    elseif length(x),        edges = (bins(1:end-1)+bins(2:end))/2;        counts = histc(x,[-Inf; edges(:); Inf]);        sH.counts = counts(1:end-1);           end     if isempty(sH.binlabels),        b = som_denormalize(bins(:),sN);         sH.binlabels = numtostring(b,4);    end     if isempty(sH.binlabels2),        if length(edges)==1,             sH.binlabels2 = numtostring(som_denormalize(edges,sN),2);            if length(bins)>1,               sH.binlabels2 = sH.binlabels2([1 1]);              sH.binlabels2{1} = [']' sH.binlabels2{1} '['];              sH.binlabels2{2} = ['[' sH.binlabels2{2} '['];            end         else            if size(edges,1)==1, edges = edges'; end            bstr = numtostring(som_denormalize(edges,sN),4);            sH.binlabels2 = bstr([1:end end]);            sH.binlabels2{1} = [bstr{1} '['];            for i=2:length(sH.binlabels2)-1,                sH.binlabels2{i} = ['[' bstr{i-1} ',' bstr{i} '['];             end             sH.binlabels2{end} = ['[' bstr{end}];        end             end         if 0,         if length(bins)==1, sH.binlabels2 = {'constant'};         else                ntiles = 10;             plim = [1:ntiles-1] / ntiles;             cp = cumsum(sH.counts)/sum(sH.counts);            [dummy,i] = histc(cp,[-Inf plim Inf]);                        l2 = cell(length(bins),1);                        for j=1:length(bins), l2{j} = sprintf('Q%d',i(j)); end            if i(1) > 1, l2{1} = ['...' l2{1}]; end                        k = 0;             for j=2:length(bins),                 if i(j)==i(j-1),                     if k==0, l2{j-1} = [l2{j-1} '.1']; k = 1; end                    k = k + 1;                     l2{j} = [l2{j} '.' num2str(k)];                 else k = 0; end            end             if i(end) < ntiles, l2{end} = [l2{end} '...']; end            sH.binlabels2 = l2;         end     end        return;function vstr = numtostring(v,d)    r = max(v)-min(v);     if r==0, r=1; end    nearzero = (abs(v)/r < 10.^-d);    i1 = find(v > 0 & nearzero);     i2 = find(v < 0 & nearzero);         vstr = strrep(cellstr(num2str(v,d)),' ','');    vstr(i1) = {'0.0'};    vstr(i2) = {'-0.0'};    return;