Question

Matlab code:

invD = inv(D);
Dew=2*invD-E;

D is 1000×1000 matrix of complex numbers. It inverts in 0,5 sec or less.

I tried several ways of porting this code to C++, using different approaches, but it is always slower than 10 seconds. What am I doing wrong? How possibly Matlab optimizes that code?

I did’t write this matlab code, I just have to port it. Sorry, I’m much better in coding that in math.

Answer 1

I am fairly sure you are using Eigen incorrectly. I tried inverting a random 1000×1000 matrix with octave (free alternative to MATLAB, probably slightly less optimized) and with the following Eigen code. Octave takes about 1s, Eigen about 1.5s (I’m using boost::timer instead of your timing solution, but only because it’s less of a hassle):

#include <iostream>
#include <Eigen/Dense>
#include <boost/timer/timer.hpp>

using Eigen::MatrixXcd;

int main() {
    MatrixXcd m,mi;
  {
    boost::timer::auto_cpu_timer t;
    m = MatrixXcd::Random(1000,1000);
  }
  {
    boost::timer::auto_cpu_timer t;
    mi = m.inverse();
  }
    std::cout << mi(4,4) << std::endl;
}

The first possible culprit I can think of are compiler options. Did you compile your C++ code with -O2 at least?

There is still a possibility that your matrices have a special structure, so that numerical considerations make the Eigen algorithm slower in your particular case, but I would look elsewhere for the problem before considering that.