int
main( int argc, char* argv[] )
{
Initialize( argc, argv );
try
{
const Int n = Input("--size","size of matrix",10);
const bool display = Input("--display","display matrix?",true);
const bool print = Input("--print","print matrix?",false);
ProcessInput();
PrintInputReport();
auto J = Legendre<double>( DefaultGrid(), n );
if( display )
{
Display( J, "Jacobi matrix for Legendre polynomials" );
#ifdef HAVE_QT5
Spy( J, "Spy plot for Jacobi matrix" );
#endif
}
if( print )
Print( J, "Jacobi matrix for Legendre polynomials" );
#ifdef HAVE_PMRRR
// We will compute Gaussian quadrature points and weights over [-1,+1]
// using the eigenvalue decomposition of the Jacobi matrix for the
// Legendre polynomials.
DistMatrix<double,VR, STAR> points;
DistMatrix<double,STAR,VR > X;
HermitianTridiagEig
( J.GetDiagonal(), J.GetDiagonal(-1), points, X, ASCENDING );
if( display )
Display( points, "Quadrature points" );
if( print )
Print( points, "points" );
auto firstRow = View( X, 0, 0, 1, n );
DistMatrix<double,STAR,STAR> weights = firstRow;
for( Int j=0; j<n; ++j )
{
const double gamma = weights.Get( 0, j );
weights.Set( 0, j, 2*gamma*gamma );
}
if( display )
Display( weights, "Quadrature weights" );
if( print )
Print( weights, "weights" );
#endif
}
catch( std::exception& e ) { ReportException(e); }
Finalize();
return 0;
}
int
main( int argc, char* argv[] )
{
Environment env( argc, argv );
mpi::Comm comm = mpi::COMM_WORLD;
try
{
const Int m = Input("--numExamples","number of examples",200);
const Int n = Input("--numFeatures","number of features",100);
const bool useIPM = Input("--useIPM","use Interior Point?",true);
const Int maxIter = Input("--maxIter","maximum # of iter's",500);
const Real gamma = Input("--gamma","two-norm coefficient",1.);
const Real rho = Input("--rho","augmented Lagrangian param.",1.);
const bool inv = Input("--inv","use explicit inverse",true);
const bool progress = Input("--progress","print progress?",true);
const bool display = Input("--display","display matrices?",false);
const bool print = Input("--print","print matrices",false);
ProcessInput();
PrintInputReport();
// Define a random (affine) hyperplane
DistMatrix<Real> w;
Gaussian( w, n, 1 );
{
const Real wNorm = FrobeniusNorm( w );
w *= 1/wNorm;
}
Real offset = SampleNormal();
mpi::Broadcast( offset, 0, comm );
// Draw each example (row) from a Gaussian perturbation of a point
// lying on the hyperplane
DistMatrix<Real> G;
Gaussian( G, m, n );
DistMatrix<Real,MR,STAR> w_MR_STAR;
w_MR_STAR.AlignWith( G );
w_MR_STAR = w;
for( Int jLoc=0; jLoc<G.LocalWidth(); ++jLoc )
for( Int iLoc=0; iLoc<G.LocalHeight(); ++iLoc )
G.UpdateLocal( iLoc, jLoc, w_MR_STAR.GetLocal(jLoc,0)*offset );
// Label each example based upon its location relative to the hyperplane
DistMatrix<Real> q;
Ones( q, m, 1 );
Gemv( NORMAL, Real(1), G, w, -offset, q );
auto sgnMap = []( Real alpha )
{ return alpha >= 0 ? Real(1) : Real(-1); };
EntrywiseMap( q, function<Real(Real)>(sgnMap) );
if( mpi::Rank(comm) == 0 )
Output("offset=",offset);
if( print )
{
Print( w, "w" );
Print( G, "G" );
Print( q, "q" );
}
if( display )
Display( G, "G" );
SVMCtrl<Real> ctrl;
ctrl.useIPM = useIPM;
ctrl.modelFitCtrl.rho = rho;
ctrl.modelFitCtrl.maxIter = maxIter;
ctrl.modelFitCtrl.inv = inv;
ctrl.modelFitCtrl.progress = progress;
Timer timer;
DistMatrix<Real> wHatSVM;
if( mpi::Rank() == 0 )
timer.Start();
SVM( G, q, gamma, wHatSVM, ctrl );
if( mpi::Rank() == 0 )
timer.Stop();
auto wSVM = View( wHatSVM, 0, 0, n, 1 );
const Real offsetSVM = -wHatSVM.Get(n,0);
const Real wSVMNorm = FrobeniusNorm( wSVM );
if( mpi::Rank() == 0 )
{
Output("SVM time: ",timer.Total()," secs");
Output
("|| wSVM ||_2=",wSVMNorm,"\n",
"margin =",Real(2)/wSVMNorm,"\n",
"offsetSVM =",offsetSVM,"\n",
"offsetSVM / || wSVM ||_2=",offsetSVM/wSVMNorm);
}
if( print )
Print( wSVM, "wSVM" );
// Report the classification percentage using the returned hyperplane
DistMatrix<Real> qSVM;
Ones( qSVM, m, 1 );
Gemv( NORMAL, Real(1), G, wSVM, -offsetSVM, qSVM );
EntrywiseMap( qSVM, function<Real(Real)>(sgnMap) );
if( print )
Print( qSVM, "qSVM" );
qSVM -= q;
const Real numWrong = OneNorm(qSVM) / Real(2);
if( mpi::Rank(comm) == 0 )
Output("ratio misclassified: ",numWrong,"/",m);
}
catch( exception& e ) { ReportException(e); }
return 0;
}
int
main( int argc, char* argv[] )
{
Initialize( argc, argv );
try
{
const Int m = Input("--numExamples","number of examples",200);
const Int n = Input("--numFeatures","number of features",100);
const Int maxIter = Input("--maxIter","maximum # of iter's",500);
const Real gamma = Input("--gamma","two-norm coefficient",1.);
const Int penaltyInt = Input("--penalty","0: none, 1: l1, 2: l2",1);
const Real rho = Input("--rho","augmented Lagrangian param.",1.);
const bool inv = Input("--inv","use explicit inverse",true);
const bool progress = Input("--progress","print progress?",true);
const bool display = Input("--display","display matrices?",false);
const bool print = Input("--print","print matrices",false);
ProcessInput();
PrintInputReport();
Regularization penalty = static_cast<Regularization>(penaltyInt);
// Define a random (affine) hyperplane
DistMatrix<Real> w;
Gaussian( w, n, 1 );
{
const Real wNorm = FrobeniusNorm( w );
Scale( Real(1)/wNorm, w );
}
Real offset = SampleNormal();
mpi::Broadcast( offset, 0, mpi::COMM_WORLD );
// Draw each example (row) from a Gaussian perturbation of a point
// lying on the hyperplane
DistMatrix<Real> G;
Gaussian( G, m, n );
DistMatrix<Real,MR,STAR> w_MR_STAR;
w_MR_STAR.AlignWith( G );
w_MR_STAR = w;
for( Int jLoc=0; jLoc<G.LocalWidth(); ++jLoc )
for( Int iLoc=0; iLoc<G.LocalHeight(); ++iLoc )
G.UpdateLocal( iLoc, jLoc, w_MR_STAR.GetLocal(jLoc,0)*offset );
// Label each example based upon its location relative to the hyperplane
DistMatrix<Real> q;
Ones( q, m, 1 );
Gemv( NORMAL, Real(1), G, w, -offset, q );
auto sgnMap = []( Real alpha )
{ return alpha >= 0 ? Real(1) : Real(-1); };
EntrywiseMap( q, function<Real(Real)>(sgnMap) );
if( mpi::WorldRank() == 0 )
cout << "offset=" << offset << endl;
if( print )
{
Print( w, "w" );
Print( G, "G" );
Print( q, "q" );
}
if( display )
Display( G, "G" );
DistMatrix<Real> wHatLog;
LogisticRegression
( G, q, wHatLog, gamma, penalty, rho, maxIter, inv, progress );
auto wLog = View( wHatLog, 0, 0, n, 1 );
const Real offsetLog = -wHatLog.Get(n,0);
const Real wLogOneNorm = OneNorm( wLog );
const Real wLogFrobNorm = FrobeniusNorm( wLog );
if( mpi::WorldRank() == 0 )
cout << "|| wLog ||_1=" << wLogOneNorm << "\n"
<< "|| wLog ||_2=" << wLogFrobNorm << "\n"
<< "margin =" << Real(2)/wLogFrobNorm << "\n"
<< "offsetLog=" << offsetLog << "\n"
<< "offsetLog / || wLog ||_2=" << offsetLog/wLogFrobNorm
<< endl;
if( print )
Print( wLog, "wLog" );
// Report the classification percentage using the returned hyperplane
// TODO: Evaluate probabilities implied by logistic function
DistMatrix<Real> qLog;
Ones( qLog, m, 1 );
Gemv( NORMAL, Real(1), G, wLog, -offsetLog, qLog );
EntrywiseMap( qLog, function<Real(Real)>(sgnMap) );
if( print )
Print( qLog, "qLog" );
Axpy( Real(-1), q, qLog );
const Real numWrong = OneNorm(qLog) / Real(2);
if( mpi::WorldRank() == 0 )
cout << "ratio misclassified: " << numWrong << "/" << m << endl;
}
catch( exception& e ) { ReportException(e); }
Finalize();
return 0;
}