Random zero-restrictions in vector

I have the following problem and I would be very grateful for support. Let, for instance,

A=[2 0 1]

and

B=[2 1 1 3 0 3]

where the elements of B refer to the index of A. (Context: B is a vector of workers and the elements indicate at which firm (1, 2 or 3) they are employed. 0 indicates unemployment. A is the vector indicating for each firm how many workers they want to lay off. For instance, firm 1 wants to lay of 2 workers. B is such that there is always enough workers to lay off for each firm.) I would like to create a matrix B1 (matrix of workers after random lay-offs) where for each index (firm) in A the corresponding number in A (the number of lay-offs) is randomly set to 0 in B. In the example it would be

B1=[2 0 0 3 0 0] or

B1=[2 0 0 0 0 3]

It would be great to do that without a for-loop. Is that actually possible? Any help is much appreciated! Thank you! Christian

Answer 1

[Matt J]

No loops here, including the ones hidden inside cellfun, num2cell, arrayfun, etc... I still wonder, though, whether avoiding a for-loop is worthwhile.

    nA=length(A); nB=length(B);

    S=accumarray([(1:nB).',B.'+1],1);

    idx=randperm(nB); iidx(idx)=1:nB;

    SS=S(idx,2:end);

    C=bsxfun(@gt,cumsum(SS,1),A).*SS;

    B1=(C(iidx,:)*(1:nA).').'

[Guillaume]

I'd argue that accumarray and bsxfun are just as much loops as arrayfun and co.

[Matt J]

Not sure why. I know bsxfun and accumarray get slower when the user supplies an arbitrary function handle for their FUNC arguments,

   A = accumarray(SUBS,VAL,SZ,FUNC) 
   C = bsxfun(FUNC,A,B)

However, when accumarray is used with its default summation rule and bsxfun is used with its pre-optimized list of bi-operand functions (@plus, @minus, times, etc...) I think they've always been observed to outperform for-loops.

Answer 2

[Alfonso Nieto-Castanon]

 B1 = B; 
 i = randperm(numel(B));
 c = sparse(find(B(i)),nonzeros(B(i)),1);
 B1(i(~any(c&cumsum(c,1)>repmat(A,size(c,1),1),2)))=0;

EDIT: cleaned up the code a bit

[Alfonso Nieto-Castanon]

this is just a variation of what Matt said before me

Answer 3

[Guillaume]

It probably could be done with a loop using accumarray, arrayfun and cellfun, but the following would do and is much clearer. It's arguable that these three functions are not loops, anyway.

%demo data
tofire = [2 0 1 2];
workers = [4 2 1 4 1 3 0 4 3 4];

workersemployed = nonzeros(workers)';
employeecount = histc(workersemployed, unique(workersemployed));
for companyidx = 1:numel(tofire)
    employees = find(ismember(workers, companyidx));
    fired = randperm(employeecount(companyidx), tofire(companyidx));
    workers(employees(fired)) = 0;
end

Answer 4

[Andrei Bobrov]

B1 = B;
ii = B~=0;
C = B(ii);
D = accumarray(C(:),(1:numel(C))',[],@(x){ x(randperm(numel(x))) });
x = cellfun(@(x,y)reshape(x(1:y),[],1),D,num2cell(A(:)),'un',0)
C(cat(1,x{:})) = 0;
B1(ii) = C;

with for..end loop

B1 = B;
for ii = 1:numel(A)
    jj = find(ii == B);
    B1(jj(randperm(numel(jj),A(ii)))) = 0;
end