Set coefficients of an Eigen::Matrix according an arbitrary distribution - random

Question

Eigen::Matrix has a setRandom() method which will set all coefficients of the matrix to random values. However, is there a built in way to set all the matrix coefficients to random values while specifying the distribution to use.
Is there a way to achieve something like the following:
Eigen::Matrix3f myMatrix;
std::tr1::mt19937 gen;
std::tr1::uniform_int<int> dist(0,MT_MAX);
myMatrix.setRandom(dist(gen));

Answer 1

You can do what you want using Boost and unaryExpr. The function you pass to unaryExpr needs to accept a dummy input which you can just ignore.
#include <boost/random.hpp>
#include <boost/random/normal_distribution.hpp>
#include <iostream>
#include <Eigen/Dense>
using namespace std;
using namespace boost;
using namespace Eigen;
double sample(double dummy)
{
static mt19937 rng;
static normal_distribution<> nd(3.0,1.0);
return nd(rng);
}
int main()
{
MatrixXd m =MatrixXd::Zero(2,3).unaryExpr(ptr_fun(sample));
cout << m << endl;
return 0;
}

Answer 2

If anyone is coming across this thread, I'm posting an easier answer that is possible nowadays and does not require boost. I found this in an old Eigen Bugzilla Report. All credits go to the author Gael Guennebaud for proposing the following simple method:
#include <Eigen/Sparse>
#include <iostream>
#include <random>
using namespace Eigen;
int main() {
std::default_random_engine generator;
std::poisson_distribution<int> distribution(4.1);
auto poisson = [&] (int) {return distribution(generator);};
RowVectorXi v = RowVectorXi::NullaryExpr(10, poisson );
std::cout << v << "\n";
}
Note that the signature with an int argument of the lambda function is required of Eigen NullaryExpr, despite not being used here in the example.

Answer 3

I had a problem with a similar problem and tried to solve it by using NullaryExpr. But a problem with NullaryExpr is that it cannot be vectorized explicitly. Thus, the solution with NullaryExpr runs quite slowly.
Because of this, I developed EigenRand, an add-on of random distribution for Eigen. I think it will help ones who want to generate random number fast and easily.
#include <Eigen/Dense>
#include <EigenRand/EigenRand>
#include <iostream>
using namespace Eigen;
int main() {
Rand::Vmt19937_64 generator;
// poisson distribution with rate = 4.1
MatrixXi v = Rand::poisson<MatrixXi>(4, 4, generator, 4.1);
std::cout << v << std::endl;
// normal distribution with mean = 3.0, stdev = 1.0
MatrixXf u = Rand::normal<MatrixXf>(4, 4, generator, 3.0, 1.0);
std::cout << u << std::endl;
return 0;
}

Answer 4

Apart the uniform distribution I am not aware of any other types of distribution that can be used directly on a matrix.
What you could do is to map the uniform distribution provided by Eigen directly to your custom distribution (if the mapping exists).
Suppose that your distribution is a sigmoid.
You can map an uniform distribution to the sigmoid distribution using the function y = a / ( b + c exp(x) ).
By temporary converting your matrix to array you can operate element-wise on all values of your matrix:
Matrix3f uniformM;
uniformM.setRandom();
Matrix3f sigmoidM;
sigmoidM.array() = a * ((0.5*uniformM+0.5).array().exp() * c + b).inv();