MATLAB: Enumeration of all possible samples with replacement trough base conversion

Question

Hello everybody,

I would like to write a fast efficient code to enumerate all possible samples with replacement. That is, I need a bijective function between the set of all samples of length k taken from a set of n elements and the subset of natural numbers fast to compute in Matlab.

I can identify every member of A as a number between 0 and so that I can consider every element of as a representation in base n, and I would like to convert it in base using the

base2dec('strn',n)    

built-in function of Matlab. The problem I have is the one to convert row vectors containing elements of in strings that could be managed by base2dec.

Indeed, suppose I have generated all the samples with function

X = 0:1:(n-1)
M = VChooseKRO_M_2(X,k)

I would like then to use num2str function to convert every row of M to a string, but for example what I get is

str = num2str(M(8,:))
str = '0  0  0  0  2  1'

while I would like to obtain

str= '000021'

so that then

base2dec(str,3)
ans =  7

is the correct answer.

Could anybody help me or point to a better solution?

Answer 1

Hi Riccardo,

Converting to strings seems inefficient to me (and it not required for this problem either).

Here is an alternative way to get the output:

% I assume all elements in the vector are b/w '0' and 'n-1' inclusive.
N=5;
vec = [1 4 3 1]   % In base 5, this is 241.
% now for the solution.
powN = (length(vec)-1): -1: 0;        % output: powN = 3 2 1 0  (powers of N for each digit)
powN = N.^powN;                       % output: powN = 125 25 5 1  (place value of each digit for base 5)
ans = vec*(powN');                    % output: ans = 241

Explanation: Generate powers of N in a vector and then dot multiply this to get your answer.

You can combine these statements if you wish to speed up your code. Try:

ans = vec*(N.^((length(vec)-1:-1:0)'));

Hope it Helps!