Find Array around Maximum Values of an Array - matlab

Question

i have a quite complicated question here which i am working on. It's extremely difficult to describe in words, so i will try to explain it with an example.
Assume i have a matrix of values:
A =
[31 85 36 71 51]
[12 33 74 39 12]
[67 11 13 14 18]
[35 36 84 33 57]
Now, i want to first find a maximum vector in the first dimension, which is easy:
[max_vector,~] = max(A,[],1);
max_vector=[67,85, 84, 71,57]
Now i want to get a "slimmed" matrix with values around the maxima (periodical indices):
Desired_Matrix =
[12 36 36 33 18]
[67 85 84 71 57]
[35 33 13 39 51]
This is the matrix with the vectors around the maximum values of matrix A. Can someone tell me how to do this without using a double for loop?
Thank you!

Answer 1

% Input.
A = [31 85 36 71 51; 12 33 74 39 12; 67 11 13 14 18; 35 36 84 33 57]
% Dimensions needed.
nRows = size(A, 1);
nCols = size(A, 2);
% Get maxima and corresponding indices in input.
[max_vector, ind] = max(A);
% Get neighbouring indices.
ind = [ind - 1; ind; ind + 1];
% Modulo indices to prevent dimension overflow.
ind = mod(ind, nRows);
% Correct zero indices.
ind(ind == 0) = nRows;
% Calculate correct indices in A.
temp = repmat(0:nRows:nRows*(nCols-1), 3, 1);
ind = ind + temp;
% Output.
B = A(ind)
Since we have max indices per column, but later want to access these elements in the original array A, we need proper linear indices for A. Here, the trick is to add the number of rows multiplied by the column index (starting by 0). The easiest way to understand might be to remove the semicolons, and inspect the intermediate values of ind.

Answer 2

#HansHirse's answer is more efficient, as it does not create an intermediate matrix.
Try this:
[~, ind_max] = max(A,[],1);
A_ext = A([end 1:end 1],:);
ind_lin = bsxfun(#plus, bsxfun(#plus, ind_max, (0:2).'), (0:size(A_ext,2)-1)*size(A_ext,1));
result = reshape(A_ext(ind_lin), 3, []);
For Matlab R2016b or newer, you can simplify the third line:
[~, ind_max] = max(A,[],1);
A_ext = A([end 1:end 1],:);
ind_lin = ind_max + (0:2).' + (0:size(A_ext,2)-1)*size(A_ext,1);
result = reshape(A_ext(ind_lin), 3, []);

Answer 3

Here is another solution. This is similar to HansHirse's answer, with two improvements:
Slightly more elegantly handles the modular indexing
Is more flexible for specifying which neighbours your want
Code:
% Input
A = [31 85 36 71 51;
12 33 74 39 12;
67 11 13 14 18;
35 36 84 33 57];
% Relative rows of neighbours, i.e. this is [-1, 0, 1] for +/- one row
p = -1:1;
% Get A row and column counts for ease
[nr, nc] = size(A);
% Get max indices
[~,idx] = max( A, [], 1 );
% Handle overflowing indices to wrap around rows
% You don't have to redefine "idx", could use this directly in the indexing line
idx = mod( idx + p.' - 1, nr ) + 1;
% Output B. The "+ ... " is to convert to linear indices, as "idx"
% currently just refers to the row number.
B = A(idx + (0:nr:nr*nc-1));

Answer 4

You can use the Image Processing Toolbox to generate the result, though is less efficient than other solutions.
[~,idx] = max(A, [], 1);
d = imdilate( idx == (1:size(A,1) ).', [1;1;1], 'full');
p = padarray(A, 1, 'circular');
Desired_Matrix = reshape(p(d), 3, []);

Answer 5

just for your information, here is the generalized form for the 3D-Case:
A = zeros(3,5,5);
for id = 1: 20
A(:,:,id) = id;
if id == 10
A(:,:,id) = 100;
end
end
% Relative rows of neighbours, i.e. this is [-1, 0, 1] for +/- one row
p = -1:1;
% Get A row and column counts for ease
[nr, nc, nz] = size(A);
% Get max indices
[~,idx] = max( A, [], 3 );
% Handle overflowing indices to wrap around rows
% You don't have to redefine "idx", could use this directly in the indexing line
idx = mod( idx + reshape(p,1,1,3) - 1, nz ) + 1;
% Output B. The "+ ... " is to convert to linear indices, as "idx"
% currently just refers to the row number.
INDICES = ((idx-1) * (nr*nc)+1 )+ reshape(0:1:nc*nr-1,nr,nc);
B = A(INDICES);