Generate constrained random vector

Saifullah Khalid

2017 7 14

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I am trying to generate a random vector from two other random vectors and a scaller in Matlabsuch that λ* P - Φ.*μ < 0 where P, Φ, μ are vectors and λ is a scaler value. I have written following code in Matlab. But it stuck in while loop many times when I try to use higher values of λ e.g. λ = 30 or 50. I shall appreciate any help.

    %generate P from uniform distribution: 0≤ P ≤1 and ∑P =1
    a=rand(47,1);
    a=[0;a;1];
    a=sort(a);
    b=zeros(48,1);
    for i=1:48
     b(i)=abs(a(i)-a(i+1));
    end
    P=b';
    %---------------------------------------------
    % Generate μ from uniform distribution: 1≤ μ ≤2 
    %----------------------------------------------
    a=1; b=2; miu = a+(b-a)* rand(48,1);
    %-----------------------------------------------------------------------
    % Generate  from uniform distribution: 0≤ Φ ≤1 such that λ* P - Φ.*μ < 0
    %-----------------------------------------------------------------------
    count=1; lamda=5;
    while(count ~= 49) 
       tPhi = rand(1,1);
       c = lamda* P(count) - tPhi.*miu(count); 
       if(c<0)
            Phi(count,1)= tPhi;
            count=count+1;
       end  
    end
    disp(Phi);

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Jan 2017-7-14

在 MATLAB Online 中打开

Of course this can be an infinite loop:

c = lamda * P(count) - tPhi.*miu(count);

P can have the max value 1, lamda is e.g. 30, tPhi has a max of 1 and miu a max of 2. Then there is no chance the c is negative.

Saifullah Khalid 2017-7-14

编辑：Saifullah Khalid 2017-7-14

在 MATLAB Online 中打开

λ* P - Φ.*μ < 0 is one of the constraints in a research problem I am working on. I have found that if I create P by

x=rand(48,1); P=x./sum(x)

The problem of infinite loops occurs very less. But I do not want to do that way as data generated is probably not uniform. Secondly, if I increase 'u', it can work but I do not know whether that is a practically sound idea.

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