Hwo to normalize a Matrix ?

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

Answer 1

[Fabio Freschi]

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]

[RT Student]

Thank you!

[영우 오]

Thank you!!

Answer 2

[Image Analyst]

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);

[RT Student]

i got this error message!!

Knowing that H =abs(sqrt(1/2)*(randn(16,4)+1j*randn(16,4)));

H=rescale(H,1,0); ?? like this ??

[Fabio Freschi]

@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]

@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

Answer 3

[Steven Lord]

Take a look at the normalize function.