How to find exact number of minimum values in matrix?

Question

I want to find 3 minimum values in my matrix.

For example:

7 7 11 5 6
8 9 6 3 2 
10 15 8 3 4
12 9 6 8 11

3 minimum values: 2,3,4.

Any suggestions?

Answer 1

If the vector is large, sorting a matrix (O(n*log n)) might take more time than doing three linear searches (O(n)). So something like this might actually be faster than sorting the array and selecting the first three values.

On my computer, this approach is faster on vectors larger than 1000-3000 elements.

num_vals = 3
vals = zeros(num_vals,1);
for k = 1:3
   [min_val, idx] = min(A);
   vals(ii) = min_val;
   A(idx) = NaN;
end

To illustrate:

A = rand(1e6,1);
S = A;

%% Linear search:
tic
for ii = 1:10
A = S;
num_vals = 3;
vals = zeros(num_vals,1);
for ii = 1:3
   [min_val, idx] = min(A);
   vals(ii) = min_val;
   A(idx) = NaN;
end
end
t1 = toc
A = S;

%% Sorting first:
tic
for ii = 1:10
   As = sort(A(:),'ascend');
   vals2 = As(1:3);
end
t2 = toc
isequal(vals, vals2)

t1 =
     0.0661
t2 =
     0.4781

ans =
     1

Answer 2

Something like this:

nrItems = 3;
yourAr  = [ 7 7 11 5 6 8 9 6 3 2 10 15 8 3 4 12 9 6 8 11 ];
sortAr  = sort(yourAr, 'ascend');


vals    = sort(1:nrItems)