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The below:

function cnkMatAll = NChooseKRange(nVect, kRange)

% NChooseKRange

%

% Combinations of N taken as k = C of 3 taken as 2 (N = {1,2,3}, k = 2)

%

% NChooseKRange(1:3,2)

%

% ans =

%

% 1 2 % k = 2

% 1 3 % k = 2

% 2 3 % k = 2

% nVect has a range of values: it defines the elements of the N Set

%

% kRange CAN equally a range of k values (not mandatory). If k = 1:2 then:

% NChooseKRange(1:3, 1:2)

%

% ans =

%

% 1 0 % k = 1

% 2 0 % k = 1

% 3 0 % k = 1

% 1 2 % k = 2

% 1 3 % k = 2

% 2 3 % k = 2

lastVal = kRange(end);

parfor i = kRange

cnk = nchoosek(nVect, i);

cnk = padarray(cnk,[0,lastVal-i],0,'post');

cnkMat(i) = {cnk};

end

elRowSizeV = zeros(1,numel(cnkMat));

parfor nr = 1:numel(cnkMat)

el = cnkMat(nr);

elRowSizeV(nr) = size(el{1},1);

end

cumRowSize = cumsum(elRowSizeV);

cnkMatAll = zeros(cumRowSize(end), kRange(end));

for nr = 1:numel(cnkMat)

el = cnkMat(nr);

if nr == 1

cnkMatAll(1:cumRowSize(nr),:) = el{1};

else

cnkMatAll(cumRowSize(nr-1)+1:cumRowSize(nr),:) = el{1};

end

end

end

is an extension of nchoosek as can be seen. Two questions:

1) Is there a better way to obtain this and the more important one is:

2) Can nchoosek be modified such that it returns only "contiguous" value ranges ... such that line:

NChooseKRange(1:3, 1:2) => 1 3 % k = 2

does NOT get returned at all?

Or is there another that would return only contiguous values of the set N (being a subset of what nchoosek currently returns)?

Thanks!

Guillaume
on 10 Aug 2018

Is there a better way to obtain this

I find this function badly designed. What if nVect contains 0?

In my opinion, merging and padding the sets for each k is wrong, keep each one separate in a cell array:

function cnkMatAll = NChooseKRange(nVect, kRange)

%cnkMatAll: a cell array the same size as kRange

cnkMatAll = arrayfun(@(k) nchoosek(nVect, k), kRange, 'UniformOutput', false);

end

Can nchoosek be modified such that it returns only "contiguous" value ranges

It sounds like what you want is nothing like nchoosek. In particular, it sounds like your nVect input has a particular form. Otherwise, what would be the output for nVect = 1:3:12?

If all you want is vectors of continuous values of a given length then there are much faster way to generate this.

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