Randomly rearrange rows / columns of a matrix with its own

Question

I am using Eigen and I have a matrix:

MatrixXi x = MatrixXi::Random(5); 

I would like to randomly rearrange rows and columns using an arbitrarily drawn permutation (only one permutation for rows and columns), i.e. if I have a permutation that sends indexes [0,1,2,3,4] → [3,4,2,1,0] than I want to reorder rows and columns with the same permutation.

Part 1: I cannot find an example of PermutationMatrix online, and it is difficult for me to understand the syntax.

Part 2: how do I get a randomly arranged index vector to go to it? Maybe std :: random_shuffle?

update:

Here is a (possibly inefficient) way to get a shuffled set of indices:

 std::vector<int> perm; for (int i=0; i<5; ++i) { perm.push_back(i); } std::random_shuffle(perm.begin(), perm.end()); 

So now the question is, how do I reorder my matrix x so that rows / columns are sorted by perm?

update 2:

Closer, this works (source for ideas: cplusplus.com):

 int myrandom (int i) { return std::rand()%i;} PermutationMatrix<Dynamic,Dynamic> perm(5); perm.setIdentity(); for (int i=dim-1; i>0; --i) { swap (perm.indices()[i],perm.indices()[myrandom(i+1)]); } cout << "original x" << x << endl << endl; cout << "permuted x" << perm * x * perm << endl << endl; 

Does anyone know how to do this with random_shuffle? (see a try that doesn't work below.)

(Bonus: any thoughts on whether perm * x * perm will be effective if perm is a 1e4 x 1e4 matrix?)

Answer 1

Using std :: random_shuffle is fine, then you should use PermutationMatrix:

 PermutationMatrix<Dynamic,Dynamic> perm(size); perm.setIdentity(); std::random_shuffle(perm.indices().data(), perm.indices().data()+perm.indices().size()); A_perm = A * perm; // permute columns A_perm = perm * A; // permute rows