eigen/bench/dense_solvers.cpp

#include <iostream>
#include "BenchTimer.h"
#include <Eigen/Dense>
#include <map>
#include <vector>
#include <string>
#include <sstream>
using namespace Eigen;

std::map<std::string, Array<float, 1, 8, DontAlign | RowMajor> > results;
std::vector<std::string> labels;
std::vector<Array2i> sizes;

template <typename Solver, typename MatrixType>
EIGEN_DONT_INLINE void compute_norm_equation(Solver &solver, const MatrixType &A) {
  if (A.rows() != A.cols())
    solver.compute(A.transpose() * A);
  else
    solver.compute(A);
}

template <typename Solver, typename MatrixType>
EIGEN_DONT_INLINE void compute(Solver &solver, const MatrixType &A) {
  solver.compute(A);
}

template <typename Scalar, int Size>
void bench(int id, int rows, int size = Size) {
  typedef Matrix<Scalar, Dynamic, Size> Mat;
  typedef Matrix<Scalar, Dynamic, Dynamic> MatDyn;
  typedef Matrix<Scalar, Size, Size> MatSquare;
  Mat A(rows, size);
  A.setRandom();
  if (rows == size) A = A * A.adjoint();
  BenchTimer t_llt, t_ldlt, t_lu, t_fplu, t_qr, t_cpqr, t_cod, t_fpqr, t_jsvd, t_bdcsvd;

  int tries = 5;
  int rep = 1000 / size;
  if (rep == 0) rep = 1;
  //   rep = rep*rep;

  LLT<MatSquare> llt(size);
  LDLT<MatSquare> ldlt(size);
  PartialPivLU<MatSquare> lu(size);
  FullPivLU<MatSquare> fplu(size, size);
  HouseholderQR<Mat> qr(A.rows(), A.cols());
  ColPivHouseholderQR<Mat> cpqr(A.rows(), A.cols());
  CompleteOrthogonalDecomposition<Mat> cod(A.rows(), A.cols());
  FullPivHouseholderQR<Mat> fpqr(A.rows(), A.cols());
  JacobiSVD<MatDyn, ComputeThinU | ComputeThinV> jsvd(A.rows(), A.cols());
  BDCSVD<MatDyn, ComputeThinU | ComputeThinV> bdcsvd(A.rows(), A.cols());

  BENCH(t_llt, tries, rep, compute_norm_equation(llt, A));
  BENCH(t_ldlt, tries, rep, compute_norm_equation(ldlt, A));
  BENCH(t_lu, tries, rep, compute_norm_equation(lu, A));
  if (size <= 1000) BENCH(t_fplu, tries, rep, compute_norm_equation(fplu, A));
  BENCH(t_qr, tries, rep, compute(qr, A));
  BENCH(t_cpqr, tries, rep, compute(cpqr, A));
  BENCH(t_cod, tries, rep, compute(cod, A));
  if (size * rows <= 10000000) BENCH(t_fpqr, tries, rep, compute(fpqr, A));
  if (size < 500)  // JacobiSVD is really too slow for too large matrices
    BENCH(t_jsvd, tries, rep, jsvd.compute(A));
  //   if(size*rows<=20000000)
  BENCH(t_bdcsvd, tries, rep, bdcsvd.compute(A));

  results["LLT"][id] = t_llt.best();
  results["LDLT"][id] = t_ldlt.best();
  results["PartialPivLU"][id] = t_lu.best();
  results["FullPivLU"][id] = t_fplu.best();
  results["HouseholderQR"][id] = t_qr.best();
  results["ColPivHouseholderQR"][id] = t_cpqr.best();
  results["CompleteOrthogonalDecomposition"][id] = t_cod.best();
  results["FullPivHouseholderQR"][id] = t_fpqr.best();
  results["JacobiSVD"][id] = t_jsvd.best();
  results["BDCSVD"][id] = t_bdcsvd.best();
}

int main() {
  labels.push_back("LLT");
  labels.push_back("LDLT");
  labels.push_back("PartialPivLU");
  labels.push_back("FullPivLU");
  labels.push_back("HouseholderQR");
  labels.push_back("ColPivHouseholderQR");
  labels.push_back("CompleteOrthogonalDecomposition");
  labels.push_back("FullPivHouseholderQR");
  labels.push_back("JacobiSVD");
  labels.push_back("BDCSVD");

  for (int i = 0; i < labels.size(); ++i) results[labels[i]].fill(-1);

  const int small = 8;
  sizes.push_back(Array2i(small, small));
  sizes.push_back(Array2i(100, 100));
  sizes.push_back(Array2i(1000, 1000));
  sizes.push_back(Array2i(4000, 4000));
  sizes.push_back(Array2i(10000, small));
  sizes.push_back(Array2i(10000, 100));
  sizes.push_back(Array2i(10000, 1000));
  sizes.push_back(Array2i(10000, 4000));

  using namespace std;

  for (int k = 0; k < sizes.size(); ++k) {
    cout << sizes[k](0) << "x" << sizes[k](1) << "...\n";
    bench<float, Dynamic>(k, sizes[k](0), sizes[k](1));
  }

  cout.width(32);
  cout << "solver/size";
  cout << "  ";
  for (int k = 0; k < sizes.size(); ++k) {
    std::stringstream ss;
    ss << sizes[k](0) << "x" << sizes[k](1);
    cout.width(10);
    cout << ss.str();
    cout << " ";
  }
  cout << endl;

  for (int i = 0; i < labels.size(); ++i) {
    cout.width(32);
    cout << labels[i];
    cout << "  ";
    ArrayXf r = (results[labels[i]] * 100000.f).floor() / 100.f;
    for (int k = 0; k < sizes.size(); ++k) {
      cout.width(10);
      if (r(k) >= 1e6)
        cout << "-";
      else
        cout << r(k);
      cout << " ";
    }
    cout << endl;
  }

  // HTML output
  cout << "<table class=\"manual\">" << endl;
  cout << "<tr><th>solver/size</th>" << endl;
  for (int k = 0; k < sizes.size(); ++k) cout << "  <th>" << sizes[k](0) << "x" << sizes[k](1) << "</th>";
  cout << "</tr>" << endl;
  for (int i = 0; i < labels.size(); ++i) {
    cout << "<tr";
    if (i % 2 == 1) cout << " class=\"alt\"";
    cout << "><td>" << labels[i] << "</td>";
    ArrayXf r = (results[labels[i]] * 100000.f).floor() / 100.f;
    for (int k = 0; k < sizes.size(); ++k) {
      if (r(k) >= 1e6)
        cout << "<td>-</td>";
      else {
        cout << "<td>" << r(k);
        if (i > 0) cout << " (x" << numext::round(10.f * results[labels[i]](k) / results["LLT"](k)) / 10.f << ")";
        if (i < 4 && sizes[k](0) != sizes[k](1)) cout << " <sup><a href=\"#note_ls\">*</a></sup>";
        cout << "</td>";
      }
    }
    cout << "</tr>" << endl;
  }
  cout << "</table>" << endl;

  //   cout << "LLT                             (ms)  " << (results["LLT"]*1000.).format(fmt) << "\n";
  //   cout << "LDLT                             (%)  " << (results["LDLT"]/results["LLT"]).format(fmt) << "\n";
  //   cout << "PartialPivLU                     (%)  " << (results["PartialPivLU"]/results["LLT"]).format(fmt) << "\n";
  //   cout << "FullPivLU                        (%)  " << (results["FullPivLU"]/results["LLT"]).format(fmt) << "\n";
  //   cout << "HouseholderQR                    (%)  " << (results["HouseholderQR"]/results["LLT"]).format(fmt) <<
  //   "\n"; cout << "ColPivHouseholderQR              (%)  " <<
  //   (results["ColPivHouseholderQR"]/results["LLT"]).format(fmt) << "\n"; cout << "CompleteOrthogonalDecomposition (%)
  //   " << (results["CompleteOrthogonalDecomposition"]/results["LLT"]).format(fmt) << "\n"; cout <<
  //   "FullPivHouseholderQR             (%)  " << (results["FullPivHouseholderQR"]/results["LLT"]).format(fmt) << "\n";
  //   cout << "JacobiSVD                        (%)  " << (results["JacobiSVD"]/results["LLT"]).format(fmt) << "\n";
  //   cout << "BDCSVD                           (%)  " << (results["BDCSVD"]/results["LLT"]).format(fmt) << "\n";
}