element by element subtraction using bsxfun

Question

John Draper 2016-6-25

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https://ww2.mathworks.cn/matlabcentral/answers/292283-element-by-element-subtraction-using-bsxfun

评论： John Draper 2016-6-27

采纳的回答： Stephen23

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Hi everyone,

I have an array, for simplicity let it be:

a = [1 2 3; 4 5 6; 7 8 10];

I would like to perform an element by element subtraction, I have using:

Av = bsxfun(@minus, a(:)', a(:));

However this does not give me the desired result. For the resulting array I want:

Aresult = [0 -1 -2 1 0 -1 2 1 0; -3 -4 -5 -2 -3 -4 -1 -2 -3;-6 -7 -8 -5 -6 -7 -4 -5 -6 ....(continued)]

So to explain the desired result I would like to take an individual element and then subtract the surrounding elements to create a 3x3 sub array in the larger 9x9 array. So in the array above going from left to right

1-0 = 0;
1-2 = -1;
1-3 = -2; (going to the next row down)
1-4 = -3;
1-5 = -4;
1-6 = -5; (going down a row again)
1-7 = -6;
1-8 = -7;
1-9 = -8;

So these results would provide the first 3x3 sub array. This would then be repeated for all elements of the initial array a.

I would be very grateful for any help/ comments you can provide, I hope my explanation wasn't too confusing :).

Thanks, John.

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Answer 1

Stephen23 2016-6-25

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编辑：Stephen23 2016-6-25

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This works for an array whatever its size:

>> A = [1 2 3; 4 5 6; 7 8 9]
A =
     1     2     3
     4     5     6
     7     8     9
>> cell2mat(arrayfun(@(a)a-A,A,'UniformOutput',false))
ans =
     0    -1    -2     1     0    -1     2     1     0
    -3    -4    -5    -2    -3    -4    -1    -2    -3
    -6    -7    -8    -5    -6    -7    -4    -5    -6
     3     2     1     4     3     2     5     4     3
     0    -1    -2     1     0    -1     2     1     0
    -3    -4    -5    -2    -3    -4    -1    -2    -3
     6     5     4     7     6     5     8     7     6
     3     2     1     4     3     2     5     4     3
     0    -1    -2     1     0    -1     2     1     0

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John Draper 2016-6-27

Thank you this works well.

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Answer 2

Andrei Bobrov 2016-6-25

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https://ww2.mathworks.cn/matlabcentral/answers/292283-element-by-element-subtraction-using-bsxfun#answer_226743

编辑：Andrei Bobrov 2016-6-25

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t = ones(size(a));
out = kron(a,t) - kron(t,a);

or

[m,n] = size(a);
out = repelem(a,m,n) - repmat(a,m,n);

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John Draper 2016-6-27

Thank you, this works and produces the desired result!

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Answer 3

John Draper 2016-6-25

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Hi everyone just an update. I have written some code that will return the required result:

if true
a = [1 2 3; 4 5 6; 7 8 9];
Av1 = a(1,1) - a(1:3,1:3);
Av2 = a(1,2) - a(1:3,1:3);
Av3 = a(1,3) - a(1:3,1:3);
Av4 = a(2,1) - a(1:3,1:3);
Av5 = a(2,2) - a(1:3,1:3);
Av6 = a(2,3) - a(1:3,1:3);
Av7 = a(3,1) - a(1:3,1:3);
Av8 = a(3,2) - a(1:3,1:3);
Av9 = a(3,3) - a(1:3,1:3);
Av = [Av1 Av2 Av3; Av4 Av5 Av6; Av7 Av8 Av9];
  % code
end

However I feel there must be a more elegant want to write this, perhaps for an array that doesn't necessarily have a size of 3 x 3. Thanks again, John.