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dense_solvers.cpp
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Thu, Feb 20, 23:07

dense_solvers.cpp
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#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 svd_opt = ComputeThinU|ComputeThinV;
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> jsvd(A.rows(),A.cols());
BDCSVD<MatDyn> 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,svd_opt));
// if(size*rows<=20000000)
BENCH(t_bdcsvd, tries, rep, bdcsvd.compute(A,svd_opt));
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";
}

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