Hwo to normalize a Matrix ?

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RT Student 2021-8-15

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https://ww2.mathworks.cn/matlabcentral/answers/898842-hwo-to-normalize-a-matrix

编辑： Image Analyst 2022-1-25

采纳的回答： Fabio Freschi

what is the code to normalize a random complex matrix H according to the following formula:

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Answer 1

Fabio Freschi 2021-8-16

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https://ww2.mathworks.cn/matlabcentral/answers/898842-hwo-to-normalize-a-matrix#answer_768052

编辑：Fabio Freschi 2021-8-16

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Following the formula of the OT the normalization has to be done according to the max and min of each row. Note that the matrix in the comment is actually a real matrix. The solution should be:

% random 4x3 matrix
H = abs(sqrt(1/2)*(randn(16,4)+1j*randn(16,4)));
% min/max along the rows
hMin = min(H,[],2);
hMax = max(H,[],2);
% normalization (binary singleton expansion is implicit since Matlab 2016b)
H = (H-hMin)./(hMax-hMin);

In this way, each element in a row is in the range [0 1]

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RT Student 2021-8-16

Thank you!

영우 오 2022-1-25

Thank you!!

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Answer 2

Image Analyst 2021-8-15

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https://ww2.mathworks.cn/matlabcentral/answers/898842-hwo-to-normalize-a-matrix#answer_767632

编辑：Image Analyst 2022-1-25

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Well I don't know about complex numbers, but for a normal, real valued matrix, you can use the rescale() function, introduced in r2017b:

h = rescale(h, 0, 1);

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Fabio Freschi 2021-8-16

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@Image Analyst suggested

H=rescale(H,0,1); % 0 as second input, 1 as third input

Howewer rescale apply rescaling with respecto to the matrix min and max, while the formula refers to the min and max along each row. See also my answer

Image Analyst 2021-8-16

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@RT Student the code you gave worked just fine. No error at all. Even when I correct rescale(H, 1, 0) to what I had, rescale(H, 0, 1) it still works.

However Fabio is right - the formula normalizes on a row-by-row basis, not globally like my solution did.

His answer is good and more closely follows your formula. Thanks for accepting it. If you wanted to use the built-in rescale(), you'd have to do it on a row-by-row basis:

% Create data.  Note, because of abs() it is all real valued.
H = abs(sqrt(1/2)*(randn(16,4)+1j*randn(16,4)))
% Rescales to global min and max.
%H = rescale(H, 0, 1)
% Rescales min and max to 0-1 on a row-by-row basis.
for row = 1 : size(H, 1)
	H(row, :) = rescale(H(row, :), 0, 1);
end