How to make sure each column in a matrix sums exactly to 1?

Question

Marco 2015-8-7

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评论： Marco 2015-8-7

Hello,

I would need to create a matrix of random numbers between 1 and 0, where the diagonal of the matrix is composed of zeros only and where each column sums to 1. I approximately reached the result by the following code, but some of the columns add up to slightly less than 1 (around 0.97). Why doesn't Matlab manage to normalize all of them to 1? Is there a way to solve the problem?

Here's the code:

a = [0:0.0001:1];
b(1:10000) = (0.5/10000);
F=randsrc(100,100,[a;0.5 b]);
columnSums = sum(F);
N=100;
for n=1:N
  F(n,n)=0; 
end
for i = 1:numel(columnSums)
  F(:,i) = F(:,i)./columnSums(i);
end

Thank you! Marco

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Answer 1

Lukas Bystricky 2015-8-7

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It's because you're calculating the column sums and then setting the diagonal entries to 0. If you calculate the sums after you modify the diagonal then what you wrote would work.

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Marco 2015-8-7

Thank you!

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Answer 2

Torsten 2015-8-7

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在 MATLAB Online 中打开

a = [0:0.0001:1];
b(1:10000) = (0.5/10000);
F=randsrc(100,100,[a;0.5 b]);
N=100;
for n=1:N
  F(n,n)=0; 
end
columnSums = sum(F);
for i = 1:numel(columnSums)
  F(:,i) = F(:,i)./columnSums(i);
end