Question related to vectorized matrix operation.

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Pappu Murthy 2017-1-22

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编辑： Pappu Murthy 2017-1-23

i have two matrices A and B; A is say (Nx3) where N is rather large like 1000+... B is (nx2) where n is rather smaller of the order 10 or so.. but it does not matter it is smaller than A row size. i would like to compute

    for i = 1:N
       D = ( A(i,1)- B(1:n,1) )^2 + (A(i,2) - B(1:n,2)^2 )  
    end

for e.g. if N is 4, and n =2 then D = a [4x2] matrix...

I am able to perform this using for loops without much difficulty but would like to try using the vectorized Matrix operations instead for improving the performance and speed. Thanks in advance.

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Answer 1

Stephen23 2017-1-22

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https://ww2.mathworks.cn/matlabcentral/answers/321466-question-related-to-vectorized-matrix-operation#answer_251513

编辑：Andrei Bobrov 2017-1-23

在 MATLAB Online 中打开

>> A = randi(9,4,3)
A =
     4     2     9
     9     4     4
     5     4     8
     4     2     8
>> B = randi(9,3,2)
B =
     3     2
     6     4
     3     1
>> D = bsxfun(@minus,A(:,1),B(:,1).').^2 + bsxfun(@minus,A(:,2),B(:,2).').^2
D =
    1    8    2
   40    9   45
    8    1   13
    1    8    2

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Stephen23 2017-1-23

Thank you Andrei Bobrov.

Pappu Murthy 2017-1-23

thanks to both of you after the corrections I am able to get the right answer and I found this answer to be the most direct and also verified that many times faster than my answer for large size matrices. Thanks again. I will now go ahead and accept the answer.

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Answer 2

Andrei Bobrov 2017-1-23

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https://ww2.mathworks.cn/matlabcentral/answers/321466-question-related-to-vectorized-matrix-operation#answer_251561

编辑：Andrei Bobrov 2017-1-23

在 MATLAB Online 中打开

My variants:

For R2016b and later

>> C2 = squeeze(sum((A(:,1:2) - permute(B,[3,2,1])).^2,2))
C2 =
    1    8    2
   40    9   45
    8    1   13
    1    8    2

and with bsxfun:

>> C3 = squeeze(sum(bsxfun(@minus,A(:,1:2),permute(B,[3,2,1])).^2,2))
C3 =
      1    8    2
     40    9   45
      8    1   13
      1    8    2

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Pappu Murthy 2017-1-23

编辑：Pappu Murthy 2017-1-23

The first solution did not work in 2016a but worked ok in 2016b. Thanks for suggesting the alternative answers, although After testing a lot the original solution and your interpretation with bsxfun appear to be the best from speed point of view. Your first approach was a bit slower. I have tried on huge matrices to establish the speed correctly.

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