Vectorize nested for loops with indices and subscripts

How can I vectorize these nested loops?

A=[1 2 0 2;2 1 3 0;0 3 1 3;2 0 3 1];
matArray=unifrnd(-1,1,[4,4,10]);
m=size(matArray,3);
n=size(unique(A),1)-1;
out=zeros(m,n);

 for i = 1 :  m
        mat=matArray(:,:,i);
        for j = 1 : n
            out(i,j) = sum(mat(A(:)==j));
        end
    end

Imo, the main challenge seems to be that if I vectorize i, then I don't seem how to combine indices and subscripts for mat(A(:)==j) to work. I guess one option could be to arrange m copies of A in the same shape as matArray but I am not sure whether that is the best approach.

Answer 1

[Stephen23]

A = [1,2,0,2;2,1,3,0;0,3,1,3;2,0,3,1]

A = 4x4

1 2 0 2 2 1 3 0 0 3 1 3 2 0 3 1

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

matArray = unifrnd(-1,1,[4,4,10])

matArray = 
matArray(:,:,1) =

    0.9181   -0.9570    0.0497    0.6524
    0.4205   -0.6451   -0.5588   -0.5780
    0.7118    0.7484   -0.8464   -0.0865
   -0.4525    0.2185    0.5790   -0.3427


matArray(:,:,2) =

    0.1309    0.5653   -0.5524   -0.1512
    0.7527    0.5233   -0.3332    0.9836
    0.7834   -0.9420   -0.2268    0.6117
   -0.1715   -0.1176   -0.9772    0.9388


matArray(:,:,3) =

    0.4596   -0.3614   -0.4097   -0.7903
   -0.7122   -0.1399   -0.4565    0.4347
   -0.8415    0.8953    0.1029    0.0455
   -0.5326    0.2804   -0.8066    0.6261


matArray(:,:,4) =

    0.4077   -0.0333    0.4346   -0.9412
    0.6351   -0.3117   -0.5348    0.5761
   -0.2888   -0.7777    0.9341    0.3771
    0.4621   -0.6025    0.6449    0.8022


matArray(:,:,5) =

    0.7395    0.6730    0.7379    0.4053
    0.1464   -0.0509    0.6831   -0.8796
   -0.3895    0.1702   -0.5938   -0.2962
    0.4174    0.3532    0.9227   -0.5501


matArray(:,:,6) =

    0.2197    0.1687    0.7668    0.8683
   -0.4941    0.6725    0.6514   -0.9704
    0.3028   -0.1318    0.7828    0.4340
    0.2623    0.0420   -0.5201   -0.4108


matArray(:,:,7) =

   -0.2713    0.9768    0.1635   -0.5738
    0.3383   -0.8399   -0.0359   -0.6835
   -0.7208   -0.3161   -0.9481   -0.8822
    0.0418    0.6457   -0.7966   -0.5913


matArray(:,:,8) =

   -0.6910   -0.4674   -0.7370   -0.6626
   -0.1444   -0.8325   -0.6488    0.3413
    0.9821    0.0235   -0.9698   -0.6879
   -0.4565   -0.1777    0.1102    0.1591


matArray(:,:,9) =

    0.9320   -0.7865   -0.2062   -0.8246
    0.6398    0.6122   -0.8366   -0.6873
    0.2411   -0.1408    0.5993   -0.9460
   -0.4430    0.4233   -0.7198    0.3413


matArray(:,:,10) =

   -0.7914   -0.1586    0.8757   -0.4813
    0.2051   -0.4098   -0.8188   -0.3925
   -0.2224    0.6264    0.3945    0.6536
   -0.8382   -0.3902   -0.8194    0.9986

Method one:

[X,Y] = meshgrid(1:size(matArray,3),A(:));
Z = Y>0;
B = accumarray([X(Z),Y(Z)],matArray(Z))

B = 10x3

-0.9162 -0.3365 0.6820 1.3662 0.9953 -1.6407 1.0488 -2.3965 -0.3223 1.8324 0.1227 -0.2904 -0.4553 1.6421 1.4797 1.2642 0.8051 0.4335 -2.6506 0.7832 -2.0309 -2.3342 -1.7309 -1.2030 2.4848 -1.4144 -2.6432 0.1919 -1.2730 -0.3581

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

Method two:

[X,Y] = meshgrid(1:size(matArray,3),1+A(:));
B = accumarray([X(:),Y(:)],matArray(:));
B = B(:,2:end)

B = 10x3

-0.9162 -0.3365 0.6820 1.3662 0.9953 -1.6407 1.0488 -2.3965 -0.3223 1.8324 0.1227 -0.2904 -0.4553 1.6421 1.4797 1.2642 0.8051 0.4335 -2.6506 0.7832 -2.0309 -2.3342 -1.7309 -1.2030 2.4848 -1.4144 -2.6432 0.1919 -1.2730 -0.3581

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

Method three:

F = @(n)reshape(sum(matArray.*(n==A),1:2),[],1);
C = arrayfun(F,1:max(A(:)),'uni',0);
B = [C{:}]

B = 10x3

-0.9162 -0.3365 0.6820 1.3662 0.9953 -1.6407 1.0488 -2.3965 -0.3223 1.8324 0.1227 -0.2904 -0.4553 1.6421 1.4797 1.2642 0.8051 0.4335 -2.6506 0.7832 -2.0309 -2.3342 -1.7309 -1.2030 2.4848 -1.4144 -2.6432 0.1919 -1.2730 -0.3581

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

Compared against your approach:

m=size(matArray,3);
n=size(unique(A),1)-1;
out=zeros(m,n);

for i = 1:m
    mat = matArray(:,:,i);
    for j = 1:n
        vec = mat(A(:)==j);
        tmp = sum(vec);
        out(i,j) = tmp;
    end
end
out

out = 10x3

-0.9162 -0.3365 0.6820 1.3662 0.9953 -1.6407 1.0488 -2.3965 -0.3223 1.8324 0.1227 -0.2904 -0.4553 1.6421 1.4797 1.2642 0.8051 0.4335 -2.6506 0.7832 -2.0309 -2.3342 -1.7309 -1.2030 2.4848 -1.4144 -2.6432 0.1919 -1.2730 -0.3581

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

[OK]

Thank you!

Answer 2

[Brahmadev]

Hi @OK,

I think we can modify the loop as follows:

for j = 1:n
    mask2 = A == j; % Logical indexing for each unique value in A
    out2(:, j) = squeeze(sum(sum(space .* mask2, 1), 2)); % Assuming space to be similar to matArray
end

Hope this helps!

[OK]

Thank you!