88 lines
2.6 KiB
Mathematica
88 lines
2.6 KiB
Mathematica
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function A = allcomb(varargin)
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% ALLCOMB - All combinations
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% B = ALLCOMB(A1,A2,A3,...,AN) returns all combinations of the elements
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% in A1, A2, ..., and AN. B is P-by-N matrix is which P is the product
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% of the number of elements of the N inputs.
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% Empty inputs yields an empty matrix B of size 0-by-N. Note that
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% previous versions (1.x) simply ignored empty inputs.
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%
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% Example:
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% allcomb([1 3 5],[-3 8],[0 1]) ;
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% 1 -3 0
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% 1 -3 1
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% 1 8 0
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% ...
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% 5 -3 1
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% 5 8 0
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% 5 8 1
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%
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% ALLCOMB(A1,..AN,'matlab') causes the first column to change fastest.
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% This is more consistent with matlab indexing. Example:
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% allcomb(1:2,3:4,5:6,'matlab') %->
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% 1 3 5
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% 2 3 5
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% 1 4 5
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% ...
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% 2 4 6
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%
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% This functionality is also known as the cartesian product.
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%
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% See also NCHOOSEK, PERMS,
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% and COMBN (Matlab Central FEX)
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% for Matlab R13+
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% version 2.1 (feb 2011)
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% (c) Jos van der Geest
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% email: jos@jasen.nl
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% History
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% 1.1 (feb 2006), removed minor bug when entering empty cell arrays;
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% added option to let the first input run fastest (suggestion by JD)
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% 1.2 (jan 2010), using ii as an index on the left-hand for the multiple
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% output by NDGRID. Thanks to Jan Simon, for showing this little trick
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% 2.0 (dec 2010). Bruno Luong convinced me that an empty input should
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% return an empty output.
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% 2.1 (feb 2011). A cell as input argument caused the check on the last
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% argument (specifying the order) to crash.
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error(nargchk(1,Inf,nargin)) ;
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% check for empty inputs
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q = ~cellfun('isempty',varargin) ;
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if any(~q),
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warning('ALLCOMB:EmptyInput','Empty inputs result in an empty output.') ;
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A = zeros(0,nargin) ;
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else
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ni = sum(q) ;
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argn = varargin{end} ;
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ischar(argn)
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if ischar(argn) && (strcmpi(argn,'matlab') || strcmpi(argn,'john')),
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% based on a suggestion by JD on the FEX
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ni = ni-1 ;
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ii = 1:ni ;
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q(end) = 0 ;
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else
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% enter arguments backwards, so last one (AN) is changing fastest
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ii = ni:-1:1 ;
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end
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if ni==0,
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A = [] ;
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else
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args = varargin(q) ;
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if ~all(cellfun('isclass',args,'double')),
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error('All arguments should be arrays of doubles') ;
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end
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if ni==1,
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A = args{1}(:) ;
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else
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% flip using ii if last column is changing fastest
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[A{ii}] = ndgrid(args{ii}) ;
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% concatenate
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A = reshape(cat(ni+1,A{:}),[],ni) ;
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end
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end
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end
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