MATLAB实例：对称双随机矩阵

function A=doubly_stochastic(n)
%产生 n 阶双随机矩阵 A
A(1,1)=rand;
for i=2:n-1
    d=1-sum(A(1,1:i-1));
    A(1,i)=d*rand;
end
for i=2:n-1
    d=1-sum(A(1:i-1,1));
    A(i,1)=d*rand;
end
for i=2:n-1
    for j=2:n-1
        d1=1-sum(A(i,1:j-1));
        d2=1-sum(A(1:i-1,j));
        d=min([d1 d2]);
        A(i,j)=d*rand;
    end
end
for i=1:n-1
    A(n,i)=1-sum(A(1:n-1,i));
end
for i=1:n
    A(i,n)=1-sum(A(i,1:n-1));
end
if A(n,n)<0
    A=1/n*ones(n);
end
%对称化A
A=(A'+A)/2;

>> A=doubly_stochastic(5)
 
A =
 
    0.3260    0.2105    0.3017    0.1032    0.0585
    0.2105    0.1132    0.4114    0.1341    0.1308
    0.3017    0.4114    0.0023    0.1947    0.0899
    0.1032    0.1341    0.1947    0.3641    0.2039
    0.0585    0.1308    0.0899    0.2039    0.5169
 
>> sum(A, 1)
 
ans =
 
     1     1     1     1     1
 
>> sum(A, 2)
 
ans =
 
     1
     1
     1
     1
     1
 
>> A'==A
 
ans =
 
  5×5 logical 数组
 
   1   1   1   1   1
   1   1   1   1   1
   1   1   1   1   1
   1   1   1   1   1
   1   1   1   1   1