Extract indices of two related arrays based on uniqueness and minimum WITHOUT FOR LOOP

I have two arrays, A and B, whose indices relate to inputs of an analysis (i.e. A(1) and B(1) are two tracked outputs of run 1 of a simulation with distinct inputs, A(7) and B(7) correspond to the 7th run, whose inputs vary from all other runs).

A          B
0.5          1
0.75         1
0.75         3
1            7
0.5          4
0.75         9
1            2
1            6
0.5          1

I am trying to create a vector of indices which tracks all minimum values of B for each unique value of A So from the above example the desired output is

index
1
2
8 
10

*Note that if there are multiple indices which have the minimum value of B for the same value of A, i want to keep both indices.

I am currently using a for loop (below), but because my array A and B are extremely large (1*10^8 entries) it take hours to run the script

   %Extract unique elements of A
    Unique_A = unique(A);
    %preallocate index vector for speed (no clue how big this will be so intentionally large
    Alternative_index = zeros(1*10^6,1);

    for i = 1:length(Unique_A)     
        %     Find the indices of the Benefit vector which correspond to a each unique value of A
        indices = find(A==Unique_A(i));
             %Now determine which of the corresponding indices in B are equal to the minimum value
       min_B_indices = (indices(B(indices)== min(B(indices))))
  %since the index vector was pre allocated, I need to make sure I am appending the vector without overwriting entries. So determine how many entries will need to be appended:
       length_of_append = length(min_B_indices)
  %Now find the first zero element of the preallocated vector
       first_zero = find(Alternative_index==0, 1, 'first')
  %Now add the indices to the preallocated vector
       Alternative_index(first_zero:first_zero+length_of_append-1,1) = min_B_indices;

    end
    %remove trailing zeros
    Alternative_index = Alternative_index(Alternative_index~=0);

I have wracked my brain on how to do this without a for loop...anyone have a suggestion?

[dpb]

So how did you get that as the expected output from the sample data, again???

[Matt J]

from the above example the desired output is index 1 2 8 10

How are you able to get an index of 10 in the example output when your A,B are only 9 elements long?

[Still Learning Matlab]

Apologies, I meant to create 10 entries.

Answer 1

[Jan]

A leaner version using a cell instead of a pre-allocation:

A = randi([1,1000], 1, 1e6);
B = randi([1,1000], 1, 1e6);

uniqA = unique(A);
OutC  = cell(1, length(uniqA));
for i = 1:length(uniqA)
   index   = find(A == uniqA(i));
   BB      = B(index);
   OutC{i} = index(BB == min(BB));
end
Out = cat(2, OutC{:}).';

It takes 1.60 sec instead of 2.25 sec for the original code.

But Matt J's splitapply approach takes 0.33 sec:

G    = findgroups(A);
C    = 1:numel(B);
OutC = splitapply(@(b,c) {c(b==min(b))}, B, C, G);
Out  = cat(2, OutC{:}).';

[Jan]

I prefer Matt J's solution. I tried it hard to convert it to an accumarray approach, but without success.

It saves some percent to replace G = findgroups(A) by:

[sA, iSA] = sort(A);
groupA    = [true, diff(sA) ~= 0];
G         = cumsum(groupA);
G(iSA)    = G;

Answer 2

[Matt J]

    G=findgroups(A);

    C=(1:numel(B)).';

    output = splitapply( @(b,c) {c(b==min(b))}  , B,C,G),

[Jan]

+1. Much faster than a loop approach.