benchCholesky.cpp

// g++ -DNDEBUG -O3 -I.. benchCholesky.cpp  -o benchCholesky && ./benchCholesky
// options:
//  -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/Cholesky>
#include <bench/BenchUtil.h>
using namespace Eigen;

#ifndef REPEAT
#define REPEAT 10000
#endif

#ifndef TRIES
#define TRIES 10
#endif

typedef float Scalar;

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

  double cost = 0;
  for (int j = 0; j < rows; ++j) {
    int r = std::max(rows - j - 1, 0);
    cost += 2 * (r * j + r + j);
  }

  int repeats = (REPEAT * 1000) / (rows * rows);

  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 timerNoSqrt, timerSqrt;

  Scalar acc = 0;
  int r = internal::random<int>(0, covMat.rows() - 1);
  int c = internal::random<int>(0, covMat.cols() - 1);
  for (int t = 0; t < TRIES; ++t) {
    timerNoSqrt.start();
    for (int k = 0; k < repeats; ++k) {
      LDLT<SquareMatrixType> cholnosqrt(covMat);
      acc += cholnosqrt.matrixL().coeff(r, c);
    }
    timerNoSqrt.stop();
  }

  for (int t = 0; t < TRIES; ++t) {
    timerSqrt.start();
    for (int k = 0; k < repeats; ++k) {
      LLT<SquareMatrixType> chol(covMat);
      acc += chol.matrixL().coeff(r, c);
    }
    timerSqrt.stop();
  }

  if (MatrixType::RowsAtCompileTime == Dynamic)
    std::cout << "dyn   ";
  else
    std::cout << "fixed ";
  std::cout << covMat.rows() << " \t" << (timerNoSqrt.best()) / repeats << "s "
            << "(" << 1e-9 * cost * repeats / timerNoSqrt.best() << " GFLOPS)\t" << (timerSqrt.best()) / repeats << "s "
            << "(" << 1e-9 * cost * repeats / timerSqrt.best() << " GFLOPS)\n";

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

    gsl_matrix* gslCovMat = gsl_matrix_alloc(covMat.rows(), covMat.cols());
    gsl_matrix* gslCopy = gsl_matrix_alloc(covMat.rows(), covMat.cols());

    eiToGsl(covMat, &gslCovMat);
    for (int t = 0; t < TRIES; ++t) {
      timerSqrt.start();
      for (int k = 0; k < repeats; ++k) {
        gsl_matrix_memcpy(gslCopy, gslCovMat);
        gsl_linalg_cholesky_decomp(gslCopy);
        acc += gsl_matrix_get(gslCopy, r, c);
      }
      timerSqrt.stop();
    }

    std::cout << " | \t" << timerSqrt.value() * REPEAT / repeats << "s";

    gsl_matrix_free(gslCovMat);
  }
#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, 16, 24, 32, 49, 64, 128, 256, 512, 900, 1500, 0};
  std::cout << "size            LDLT                            LLT";
  //   #ifdef BENCH_GSL
  //   std::cout << "       GSL (standard + double + ATLAS)  ";
  //   #endif
  std::cout << "\n";
  for (int i = 0; dynsizes[i] > 0; ++i) benchLLT(Matrix<Scalar, Dynamic, Dynamic>(dynsizes[i], dynsizes[i]));

  benchLLT(Matrix<Scalar, 2, 2>());
  benchLLT(Matrix<Scalar, 3, 3>());
  benchLLT(Matrix<Scalar, 4, 4>());
  benchLLT(Matrix<Scalar, 5, 5>());
  benchLLT(Matrix<Scalar, 6, 6>());
  benchLLT(Matrix<Scalar, 7, 7>());
  benchLLT(Matrix<Scalar, 8, 8>());
  benchLLT(Matrix<Scalar, 12, 12>());
  benchLLT(Matrix<Scalar, 16, 16>());
  return 0;
}