Bin - Assign each input value a bin number between 1 and N.
Assign each input value a bin number between 1 and N. Also return the
corresponding bin values (lower bounds), e.g. assuming that the bins
are [0,1] [1,2] [2,3] ... the value 2.3 falls in bin #3 and the bin
value (lower bound) is 2.
USAGE
% To specify bin limits and # bins
[bins,binned] = Bin(x,limits,nBins)
% To automatically set the limits to [min(x) max(x)]
bins = Bin(x,nBins)
% To specify an explicit list of bins (including the upper bound
% of the last bin)
[bins,binned] = Bin(x,bins)
% To discard values out of limits
bins = Bin(x,...,'trim')
x 1D variable
limits [min_x max_x], where min_x is included and max_x is excluded;
these need not be equal to min(x) and max(x)
by default, x values out of bounds are counted in the first
and last bin, respectively
nBins number of bins
bins explicit list of bins - including the upper bound of the
last bin
NOTE
y = Bin(x,[m M],N) uses N bins b(i). Their size is k=(M-m)/N and their
lower and upper bounds are m+i*k (included) and m+(i+1)*k (excluded),
respectively. As intended, the extreme bounds are equal to m and M,
respectively, but keep in mind that while the first bin starts at m,
the last bin *ends* at M (it actually starts at m+(N-1)*k).
EXAMPLES
Bin([2 2.3 4 4.7],[2 5],3); % returns [1 1 3 3]
Bin([2 2.3 4 4.7],[2 5],6); % returns [1 1 5 6]
Bin([2 2.3 4 4.2 5],[2 5],3); % returns [1 1 3 3 3]
SEE
See also Accumulate.0001 function [bins,binned] = Bin(x,a,b,c) 0002 0003 %Bin - Assign each input value a bin number between 1 and N. 0004 % 0005 % Assign each input value a bin number between 1 and N. Also return the 0006 % corresponding bin values (lower bounds), e.g. assuming that the bins 0007 % are [0,1] [1,2] [2,3] ... the value 2.3 falls in bin #3 and the bin 0008 % value (lower bound) is 2. 0009 % 0010 % USAGE 0011 % 0012 % % To specify bin limits and # bins 0013 % [bins,binned] = Bin(x,limits,nBins) 0014 % 0015 % % To automatically set the limits to [min(x) max(x)] 0016 % bins = Bin(x,nBins) 0017 % 0018 % % To specify an explicit list of bins (including the upper bound 0019 % % of the last bin) 0020 % [bins,binned] = Bin(x,bins) 0021 % 0022 % % To discard values out of limits 0023 % bins = Bin(x,...,'trim') 0024 % 0025 % x 1D variable 0026 % limits [min_x max_x], where min_x is included and max_x is excluded; 0027 % these need not be equal to min(x) and max(x) 0028 % by default, x values out of bounds are counted in the first 0029 % and last bin, respectively 0030 % nBins number of bins 0031 % bins explicit list of bins - including the upper bound of the 0032 % last bin 0033 % 0034 % NOTE 0035 % 0036 % y = Bin(x,[m M],N) uses N bins b(i). Their size is k=(M-m)/N and their 0037 % lower and upper bounds are m+i*k (included) and m+(i+1)*k (excluded), 0038 % respectively. As intended, the extreme bounds are equal to m and M, 0039 % respectively, but keep in mind that while the first bin starts at m, 0040 % the last bin *ends* at M (it actually starts at m+(N-1)*k). 0041 % 0042 % EXAMPLES 0043 % 0044 % Bin([2 2.3 4 4.7],[2 5],3); % returns [1 1 3 3] 0045 % Bin([2 2.3 4 4.7],[2 5],6); % returns [1 1 5 6] 0046 % Bin([2 2.3 4 4.2 5],[2 5],3); % returns [1 1 3 3 3] 0047 % 0048 % SEE 0049 % 0050 % See also Accumulate. 0051 0052 % Copyright (C) 2004-2011 by Michaël Zugaro 0053 % 0054 % This program is free software; you can redistribute it and/or modify 0055 % it under the terms of the GNU General Public License as published by 0056 % the Free Software Foundation; either version 3 of the License, or 0057 % (at your option) any later version. 0058 0059 if nargin < 2, 0060 error('Incorrect number of parameters (type ''help <a href="matlab:help Bin">Bin</a>'' for details).'); 0061 end 0062 0063 if isempty(x), 0064 bins = []; 0065 binned = []; 0066 return 0067 end 0068 if ~isdvector(x), 0069 error('Data is not a vector (type ''help <a href="matlab:help Bin">Bin</a>'' for details).'); 0070 end 0071 0072 if ~isdvector(a), 0073 error('Incorrect second parameter (type ''help <a href="matlab:help Bin">Bin</a>'' for details).'); 0074 end 0075 0076 if length(a) == 1, 0077 % Second parameter is a scalar, i.e. the number of bins 0078 if ~isiscalar(a,'>0'), 0079 error('Incorrect number of bins (type ''help <a href="matlab:help Bin">Bin</a>'' for details).'); 0080 end 0081 nBins = a; 0082 % Automatic limits 0083 limits = [min(x) max(x)]; 0084 % Trim? 0085 trim = nargin == 3 && strcmp(lower(b),'trim'); 0086 elseif length(a) == 2, 0087 % Second parameter is a pair, i.e. the limits 0088 limits = a; 0089 % Third parameter must be # bins 0090 if ~isiscalar(b,'>0'), 0091 error('Incorrect number of bins (type ''help <a href="matlab:help Bin">Bin</a>'' for details).'); 0092 end 0093 nBins = b; 0094 % Trim? 0095 trim = nargin == 4 && strcmp(lower(c),'trim'); 0096 else 0097 % Explicit bins 0098 d = a(2) - a(1); 0099 % if any(abs(diff(a)-d)>eps), 0100 % error('Incorrect list of bins - bins must be evenly spaced (type ''help <a href="matlab:help Bin">Bin</a>'' for details).'); 0101 % end 0102 % Determine limits and # bins 0103 limits = [a(1) a(end)]; 0104 nBins = length(a)-1; 0105 % Trim? 0106 trim = nargin == 3 && strcmp(lower(b),'trim'); 0107 end 0108 0109 if trim, 0110 x(x<limits(1)) = nan; 0111 x(x>=limits(2)) = nan; 0112 else 0113 x(x<limits(1)) = limits(1); 0114 x(x>=limits(2)) = limits(2); 0115 end 0116 0117 bins = floor((x-limits(1))/(limits(2)-limits(1))*nBins)+1; 0118 0119 % The following fixes boundary issues but also Matlab rounding errors 0120 if trim, 0121 bins(bins>nBins) = nan; 0122 else 0123 bins(bins>nBins) = nBins; 0124 end 0125 0126 binSize = (limits(2)-limits(1))/nBins; 0127 i = linspace(limits(1),limits(2),nBins+1); 0128 n = isnan(bins); 0129 binned(~n,1) = i(bins(~n))+binSize/2; 0130 binned(n,1) = NaN;