Generating a random matrix with non-static constraints
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Hi,
I would like to generate a random matrix with constraints on both rows and columns. But the problem is I have two parameters for this constraints which are not fix for each element. For explanation, consider the mxn matrix P = [P1 ; P2; ...; Pm], and 2 other vectors lambda and Mu that they should have this constraints:
1. sum of lambda(s) < sum of Mu(s) Now for the random matrix P:
2. each element of the matrix(P[j,i]) should be equal or greater than zero.
3. sum of the elements of each row is equal to one (i.e. for the row of j: sigma_i(P[j,i] = 1)
4. for each column j, sum of the production of each element with the correspond lambda(j) is less than the correspond element in the Mu vector (i.e.Mu(i)). i.e. for the column of i: sigma_j(P[j,i]*lambda(j)) < Mu(i)
I have tried coding all these constraints but because the existence of lambda and Mu vectors, just one of the constraints of 3 or 4 can be feasible. May you please help me for coding this matrix.
Thanks in advance
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