eigen/bench/benchEigenSolver.cpp

// g++ -DNDEBUG -O3 -I.. benchEigenSolver.cpp  -o benchEigenSolver && ./benchEigenSolver
// options:
//  -DBENCH_GMM
//  -DBENCH_GSL -lgsl /usr/lib/libcblas.so.3
//  -DEIGEN_DONT_VECTORIZE
//  -msse2
//  -DREPEAT=100
//  -DTRIES=10
//  -DSCALAR=double

#include <iostream>

#include <Eigen/Core>
#include <Eigen/QR>
#include <bench/BenchUtil.h>
using namespace Eigen;

#ifndef REPEAT
#define REPEAT 1000
#endif

#ifndef TRIES
#define TRIES 4
#endif

#ifndef SCALAR
#define SCALAR float
#endif

typedef SCALAR Scalar;

template <typename MatrixType>
__attribute__((noinline)) void benchEigenSolver(const MatrixType& m) {
  int rows = m.rows();
  int cols = m.cols();

  int stdRepeats = std::max(1, int((REPEAT * 1000) / (rows * rows * sqrt(rows))));
  int saRepeats = stdRepeats * 4;

  typedef typename MatrixType::Scalar Scalar;
  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;

  MatrixType a = MatrixType::Random(rows, cols);
  SquareMatrixType covMat = a * a.adjoint();

  BenchTimer timerSa, timerStd;

  Scalar acc = 0;
  int r = internal::random<int>(0, covMat.rows() - 1);
  int c = internal::random<int>(0, covMat.cols() - 1);
  {
    SelfAdjointEigenSolver<SquareMatrixType> ei(covMat);
    for (int t = 0; t < TRIES; ++t) {
      timerSa.start();
      for (int k = 0; k < saRepeats; ++k) {
        ei.compute(covMat);
        acc += ei.eigenvectors().coeff(r, c);
      }
      timerSa.stop();
    }
  }

  {
    EigenSolver<SquareMatrixType> ei(covMat);
    for (int t = 0; t < TRIES; ++t) {
      timerStd.start();
      for (int k = 0; k < stdRepeats; ++k) {
        ei.compute(covMat);
        acc += ei.eigenvectors().coeff(r, c);
      }
      timerStd.stop();
    }
  }

  if (MatrixType::RowsAtCompileTime == Dynamic)
    std::cout << "dyn   ";
  else
    std::cout << "fixed ";
  std::cout << covMat.rows() << " \t" << timerSa.value() * REPEAT / saRepeats << "s \t"
            << timerStd.value() * REPEAT / stdRepeats << "s";

#ifdef BENCH_GMM
  if (MatrixType::RowsAtCompileTime == Dynamic) {
    timerSa.reset();
    timerStd.reset();

    gmm::dense_matrix<Scalar> gmmCovMat(covMat.rows(), covMat.cols());
    gmm::dense_matrix<Scalar> eigvect(covMat.rows(), covMat.cols());
    std::vector<Scalar> eigval(covMat.rows());
    eiToGmm(covMat, gmmCovMat);
    for (int t = 0; t < TRIES; ++t) {
      timerSa.start();
      for (int k = 0; k < saRepeats; ++k) {
        gmm::symmetric_qr_algorithm(gmmCovMat, eigval, eigvect);
        acc += eigvect(r, c);
      }
      timerSa.stop();
    }
    // the non-selfadjoint solver does not compute the eigen vectors
    //     for (int t=0; t<TRIES; ++t)
    //     {
    //       timerStd.start();
    //       for (int k=0; k<stdRepeats; ++k)
    //       {
    //         gmm::implicit_qr_algorithm(gmmCovMat, eigval, eigvect);
    //         acc += eigvect(r,c);
    //       }
    //       timerStd.stop();
    //     }

    std::cout << " | \t" << timerSa.value() * REPEAT / saRepeats << "s"
              << /*timerStd.value() * REPEAT / stdRepeats << "s"*/ "   na   ";
  }
#endif

#ifdef BENCH_GSL
  if (MatrixType::RowsAtCompileTime == Dynamic) {
    timerSa.reset();
    timerStd.reset();

    gsl_matrix* gslCovMat = gsl_matrix_alloc(covMat.rows(), covMat.cols());
    gsl_matrix* gslCopy = gsl_matrix_alloc(covMat.rows(), covMat.cols());
    gsl_matrix* eigvect = gsl_matrix_alloc(covMat.rows(), covMat.cols());
    gsl_vector* eigval = gsl_vector_alloc(covMat.rows());
    gsl_eigen_symmv_workspace* eisymm = gsl_eigen_symmv_alloc(covMat.rows());

    gsl_matrix_complex* eigvectz = gsl_matrix_complex_alloc(covMat.rows(), covMat.cols());
    gsl_vector_complex* eigvalz = gsl_vector_complex_alloc(covMat.rows());
    gsl_eigen_nonsymmv_workspace* einonsymm = gsl_eigen_nonsymmv_alloc(covMat.rows());

    eiToGsl(covMat, &gslCovMat);
    for (int t = 0; t < TRIES; ++t) {
      timerSa.start();
      for (int k = 0; k < saRepeats; ++k) {
        gsl_matrix_memcpy(gslCopy, gslCovMat);
        gsl_eigen_symmv(gslCopy, eigval, eigvect, eisymm);
        acc += gsl_matrix_get(eigvect, r, c);
      }
      timerSa.stop();
    }
    for (int t = 0; t < TRIES; ++t) {
      timerStd.start();
      for (int k = 0; k < stdRepeats; ++k) {
        gsl_matrix_memcpy(gslCopy, gslCovMat);
        gsl_eigen_nonsymmv(gslCopy, eigvalz, eigvectz, einonsymm);
        acc += GSL_REAL(gsl_matrix_complex_get(eigvectz, r, c));
      }
      timerStd.stop();
    }

    std::cout << " | \t" << timerSa.value() * REPEAT / saRepeats << "s \t" << timerStd.value() * REPEAT / stdRepeats
              << "s";

    gsl_matrix_free(gslCovMat);
    gsl_vector_free(gslCopy);
    gsl_matrix_free(eigvect);
    gsl_vector_free(eigval);
    gsl_matrix_complex_free(eigvectz);
    gsl_vector_complex_free(eigvalz);
    gsl_eigen_symmv_free(eisymm);
    gsl_eigen_nonsymmv_free(einonsymm);
  }
#endif

  std::cout << "\n";

  // make sure the compiler does not optimize too much
  if (acc == 123) std::cout << acc;
}

int main(int argc, char* argv[]) {
  const int dynsizes[] = {4, 6, 8, 12, 16, 24, 32, 64, 128, 256, 512, 0};
  std::cout << "size            selfadjoint       generic";
#ifdef BENCH_GMM
  std::cout << "        GMM++          ";
#endif
#ifdef BENCH_GSL
  std::cout << "       GSL (double + ATLAS)  ";
#endif
  std::cout << "\n";
  for (uint i = 0; dynsizes[i] > 0; ++i) benchEigenSolver(Matrix<Scalar, Dynamic, Dynamic>(dynsizes[i], dynsizes[i]));

  benchEigenSolver(Matrix<Scalar, 2, 2>());
  benchEigenSolver(Matrix<Scalar, 3, 3>());
  benchEigenSolver(Matrix<Scalar, 4, 4>());
  benchEigenSolver(Matrix<Scalar, 6, 6>());
  benchEigenSolver(Matrix<Scalar, 8, 8>());
  benchEigenSolver(Matrix<Scalar, 12, 12>());
  benchEigenSolver(Matrix<Scalar, 16, 16>());
  return 0;
}