How to normalize all the matrices in a loop so that each row sums up to 1

N = 4

n = 2

A = cell(1,N);

for i = 1:N

A{i} = rand(n,n)

end

celldisp(A)

From above command I will get 4 matrices.How to normalize all the matrices( ie all 4 matrices) so that each row sums up to 1.

Thanks

Answer 1

[harsha001]

There are two parts to your question - (a) how to normalise each row of a matrix at once, and (b) how to do it independently for each matrix in a cell array.

(a)

use the dot notation to divide each row by the sum of that row

So for a matrix M,

M = M./sum(M,2);     % sum acros the 2nd dimension (column) and do a row-wise division 

will normalise each row to sum to 1.

If instead you want to normalise each column, simply:

M = M./sum(M,1);

(b) You can either use a for loop to do the same for each matrix A{jj} of the cell array

for jj=1:N
    A{jj} = A{jj}./sum(A{jj},2);
end

OR use a neat arrayfun to do the same:

A = arrayfun( @(jj) A{jj}./sum(A{jj},2), 1:N , 'UniformOutput', false );

where i use the array fun to loop over 1 to N, setting uniform output to false so my result is also a cell-array. Imagine it like:

output = arrayfun( @jj, func(something), loop over 1 to N, 'UniformOutput', false)

[parag gupta]

thanks ! :)

[madhan ravi]

@Harsha: How did you know there is two parts to the question?

Answer 2

[Steven Lord]

The sum of the absolute values of the elements of a vector is the 1-norm. You can use the normalize function introduced in release R2018a to normalize each row of a matrix by the 1-norm.

A = rand(6);
B = normalize(A, 2, 'norm', 1);
shouldBeCloseTo1 = sum(B, 2)

You can use a for loop or arrayfun to apply normalize to each matrix in the cell array.

Answer 3

[Moritz Hesse]

If you have the deep learning toolbox installed, you can use normr to normalise matrix rows. You can access cell contents with curly brace notation

N = 4
n = 2
A = cell(1,N);
for i = 1:N
    A{i} = rand(n,n)
end
celldisp(A)

% Loop through cells and normalise matrix rows
for i = 1:N
    A{i} = normr(A{i})
end

[parag gupta]

'normr' requires Deep Learning Toolbox.

Error in Untitledhhho (line 15)

A{i} = normr(A{i})

got this error

[parag gupta]

thanks ! :)