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回复 9 # ChaChing 的帖子
- function [M,IND] = combn(V,N)
- % COMBN - all combinations of elements
- % M = COMBN(V,N) returns all combinations of N elements of the elements in
- % vector V. M has the size (length(V).^N)-by-N.
- %
- % [M,I] = COMBN(V,N) also returns the index matrix I so that M = V(I).
- %
- % V can be an array of numbers, cells or strings.
- %
- % Example:
- % M = COMBN([0 1],3) returns the 8-by-3 matrix:
- % 0 0 0
- % 0 0 1
- % 0 1 0
- % 0 1 1
- % ...
- % 1 1 1
- %
- % All elements in V are regarded as unique, so M = COMBN([2 2],3) returns
- % a 8-by-3 matrix with all elements equal to 2.
- %
- % NB Matrix sizes increases exponentially at rate (n^N)*N.
- %
- % See also PERMS, NCHOOSEK
- % and ALLCOMB and PERMPOS on the File Exchange
- % for Matlab R13, R14
- % version 4.1 (jan 2010)
- % (c) Jos van der Geest
- % email: jos@jasen.nl
- % History
- % 1.1 updated help text
- % 2.0 new faster algorithm
- % 3.0 (aug 2006) implemented very fast algorithm
- % 3.1 (may 2007) Improved algorithm Roger Stafford pointed out that for some values, the floor
- % operation on floating points, according to the IEEE 754 standard, could return
- % erroneous values. His excellent solution was to add (1/2) to the values
- % of A.
- % 3.2 (may 2007) changed help and error messages slightly
- % 4.0 (may 2008) again a faster implementation, based on ALLCOMB, suggested on the
- % newsgroup comp.soft-sys.matlab on May 7th 2008 by "Helper". It was
- % pointed out that COMBN(V,N) equals ALLCOMB(V,V,V...) (V repeated N
- % times), ALLCMOB being faster. Actually version 4 is an improvement
- % over version 1 ...
- % 4.1 (jan 2010) removed call to FLIPLR, using refered indexing N:-1:1
- % (is faster, suggestion of Jan Simon, jan 2010), removed REPMAT, and
- % let NDGRID handle this
- error(nargchk(2,2,nargin)) ;
- if isempty(V) || N == 0,
- M = [] ;
- IND = [] ;
- elseif fix(N) ~= N || N < 1 || numel(N) ~= 1 ;
- error('combn:negativeN','Second argument should be a positive integer') ;
- elseif N==1,
- M = V(:).' ;
- IND = 1:numel(V) ;
- else
- % speed depends on the number of output arguments
- if nargout<2,
- M = local_allcomb(V,N) ;
- else
- % indices requested
- IND = local_allcomb(1:numel(V),N) ;
- M = V(IND) ;
- end
- end
- % LOCAL FUNCTIONS
- function Y = local_allcomb(X,N)
- % See ALLCOMB, available on the File Exchange
- if N>1
- % create a list of all possible combinations of N elements
- [Y{N:-1:1}] = ndgrid(X) ;
- % concatenate into one matrix, reshape into 2D and flip columns
- Y = reshape(cat(N+1,Y{:}),[],N) ;
- else
- % no combinations have to be made
- Y = X(:) ;
- end
- % =========================================================================
- % Previous algorithms
- % Version 3.2
- % % COMBN is very fast using a single matrix multiplication, without any
- % explicit for-loops.
- % nV = numel(V) ;
- % % use a math trick
- % A = [0:nV^N-1]+(1/2) ;
- % B = [nV.^(1-N:0)] ;
- % IND = rem(floor((A(:) * B(:)')),nV) + 1 ;
- % M = V(IND) ;
- % Version 2.0
- % for i = N:-1:1
- % X = repmat(1:nV,nV^(N-i),nV^(i-1));
- % IND(:,i) = X(:);
- % end
- % M = V(IND) ;
- % Version 1.0
- % nV = numel(V) ;
- % % don waste space, if only one output is requested
- % [IND{1:N}] = ndgrid(1:nV) ;
- % IND = fliplr(reshape(cat(ndims(IND{1}),IND{:}),[],N)) ;
- % M = V(IND) ;
- % Combinations using for-loops
- % can be implemented in C or VB
- % nv = length(V) ;
- % C = zeros(nv^N,N) ; % declaration
- % for ii=1:N,
- % cc = 1 ;
- % for jj=1:(nv^(ii-1)),
- % for kk=1:nv,
- % for mm=1:(nv^(N-ii)),
- % C(cc,ii) = V(kk) ;
- % cc = cc + 1 ;
- % end
- % end
- % end
- % end
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发表于 2010-9-4 15:27
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发表于 2010-9-4 16:49
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