Create matrix with randomly distributed integers, with exact relative abundances

I want to create a matrix of randomly distributed integers between 0 and 4 (0, 1, 2, 3, or 4). However, I want the abundance of each integer to conform to a predetermined value.

So if I have a vector of abundances (e.g.):

 %     0    1         2         3         4 <--corresponding random numbers
 mo = [0    0.5533    0.1346    0.1167    0.1954]; % abundance of random
 numbers

and I want to fill up a matrix:

 P = zeros(100,100);

I can see that the abundances should be

 abund = round(mo.*size(P,1).*size(P,2));

 = 0        5533        1346        1167        1954

But how do I fill up the matrix P with these randomly distributed numbers? The important thing is that the abundances are exactly as predetermined.

Answer 1

[Thorsten]

values = [0:4];
mo = [0 0.5533 0.1346 0.1167 0.1954];
a = 100; b = 100;

% create a vector where each value appears mo(i)*a*b times
P = [];
for i = 1:numel(mo)
 P = [P values(i)*ones(1, round(a*b*mo(i)))];
end

% randomize and reshape
P = P(randperm(a*b));
P = reshape(P, [a b]);
% check
hi = hist(P(:), [0:4])

[Christopher]

almost correct, but the algorithm fails if i set a=120 and b=120. The array becomes 14399 elements instead of the correct 14400, so reshape fails. Can this be fixed easily?

Edit: sorry the problem is that my vector 'mo' has more decimal places. Is there a way to ensure that the correct size vector for P results (a*b) for any real numbers in the vector 'mo' (as long as mo sums to 1)?

[Thorsten]

P = [];
for i = 1:numel(mo)-1
 P = [P values(i)*ones(1, round(a*b*mo(i)))];
end
P(end+1:a*b) = values(end);