void TestGemv
( El::Int height,
El::Int width,
El::Orientation orientation,
const El::Grid& grid,
bool print )
{
El::DistMatrix<Field> A(grid);
El::Uniform( A, height, width );
// Draw the entries of the original x and y from uniform distributions
// over the complex unit ball
El::DistMatrix<Field,El::VC,El::STAR> x(grid), y(grid);
if( orientation == El::NORMAL )
{
El::Uniform( x, width, 1 );
El::Uniform( y, height, 1 );
}
else
{
El::Uniform( x, height, 1 );
El::Uniform( y, width, 1 );
}
if( print )
{
El::Print( A, "A" );
El::Print( x, "x" );
El::Print( y, "y" );
}
// Run the matrix-vector product
if( grid.Rank() == 0 )
El::Output("Starting Gemv (with Field=",El::TypeName<Field>(),")");
El::Timer gemvElem;
gemvElem.Start();
// Form y := 3 A x + 4 y
El::Gemv( orientation, Field(3), A, x, Field(4), y );
gemvElem.Stop();
if( grid.Rank() == 0 )
El::Output(" Time: ",gemvElem.Total());
if( print )
{
if( orientation == El::NORMAL )
El::Print( y, "y := 3 A x + 4 y" );
else
El::Print( y, "y := 3 A^H x + 4 y" );
}
}
int
main( int argc, char* argv[] )
{
El::Environment env( argc, argv );
El::mpi::Comm comm = El::mpi::COMM_WORLD;
try
{
typedef double Real;
typedef El::Complex<Real> Scalar;
const El::Int m = El::Input("--height","height of matrix",100);
const El::Int n = El::Input("--width","width of matrix",100);
const bool print = El::Input("--print","print matrices?",false);
El::ProcessInput();
El::PrintInputReport();
El::DistMatrix<Scalar> A;
El::Uniform( A, m, n );
El::Timer timer;
// Compute the pseudoinverseof A (but do not overwrite A)
El::DistMatrix<Scalar> pinvA( A );
if( El::mpi::Rank(comm) == 0 )
timer.Start();
El::Pseudoinverse( pinvA );
if( El::mpi::Rank(comm) == 0 )
timer.Stop();
if( print )
{
El::Print( A, "A" );
El::Print( pinvA, "pinv(A)" );
}
const Real frobA = El::FrobeniusNorm( A );
const Real frobPinvA = El::FrobeniusNorm( pinvA );
if( El::mpi::Rank(comm) == 0 )
{
El::Output("PseudoInverse time: ",timer.Total()," secs");
El::Output
("|| A ||_F = ",frobA,"\n",
"|| pinv(A) ||_F = ",frobPinvA,"\n");
}
}
catch( std::exception& e ) { El::ReportException(e); }
return 0;
}
int main( int argc, char* argv[] )
{
El::Environment env( argc, argv );
try
{
typedef double Real;
typedef El::Complex<Real> Scalar;
const El::Int m = El::Input("--height","height of matrix",20);
const El::Int n = El::Input("--width","width of matrix",100);
const El::Int r = El::Input("--rank","rank of matrix",5);
const El::Int maxSteps =
El::Input("--maxSteps","max # of steps of QR",10);
const Real tol = El::Input("--tol","tolerance for ID",Real(-1));
const bool print = El::Input("--print","print matrices?",false);
const bool smallestFirst =
El::Input("--smallestFirst","smallest norm first?",false);
El::ProcessInput();
El::PrintInputReport();
El::mpi::Comm comm = El::mpi::COMM_WORLD;
const El::Grid& grid = El::Grid::Default();
El::DistMatrix<Scalar> U(grid), V(grid), A(grid);
El::Uniform( U, m, r );
El::Uniform( V, n, r );
El::Gemm( El::NORMAL, El::ADJOINT, Scalar(1), U, V, A );
const Real frobA = El::FrobeniusNorm( A );
if( print )
El::Print( A, "A" );
El::DistPermutation Omega(grid);
El::DistMatrix<Scalar,El::STAR,El::VR> Z(grid);
El::QRCtrl<Real> ctrl;
ctrl.boundRank = true;
ctrl.maxRank = maxSteps;
if( tol != -1. )
{
ctrl.adaptive = true;
ctrl.tol = tol;
}
ctrl.smallestFirst = smallestFirst;
El::Timer timer;
if( El::mpi::Rank(comm) == 0 )
timer.Start();
El::ID( A, Omega, Z, ctrl );
if( El::mpi::Rank(comm) == 0 )
timer.Stop();
const El::Int rank = Z.Height();
if( print )
{
El::DistMatrix<El::Int> OmegaFull(grid);
Omega.ExplicitMatrix( OmegaFull );
El::Print( OmegaFull, "Omega" );
El::Print( Z, "Z" );
}
// Pivot A and form the matrix of its (hopefully) dominant columns
El::Timer permTimer("permTimer");
permTimer.Start();
Omega.PermuteCols( A );
permTimer.Stop();
auto hatA( A );
hatA.Resize( m, rank );
if( print )
{
El::Print( A, "A Omega^T" );
El::Print( hatA, "\\hat{A}" );
}
// Check || A Omega^T - \hat{A} [I, Z] ||_F / || A ||_F
El::DistMatrix<Scalar> AL(grid), AR(grid);
El::PartitionRight( A, AL, AR, rank );
El::Zero( AL );
{
El::DistMatrix<Scalar,El::MC,El::STAR> hatA_MC_STAR(grid);
El::DistMatrix<Scalar,El::STAR,El::MR> Z_STAR_MR(grid);
hatA_MC_STAR.AlignWith( AR );
Z_STAR_MR.AlignWith( AR );
hatA_MC_STAR = hatA;
Z_STAR_MR = Z;
El::LocalGemm
( El::NORMAL, El::NORMAL,
Scalar(-1), hatA_MC_STAR, Z_STAR_MR, Scalar(1), AR );
}
const Real frobError = El::FrobeniusNorm( A );
if( print )
El::Print( A, "A Omega^T - \\hat{A} [I, Z]" );
if( El::mpi::Rank(comm) == 0 )
{
El::Output(" ID time: ",timer.Total()," secs");
El::Output
("|| A ||_F = ",frobA,"\n",
"|| A Omega^T - \\hat{A} [I, Z] ||_F / || A ||_F = ",
frobError/frobA);
}
}
catch( std::exception& e ) { El::ReportException(e); }
return 0;
}
int main( int argc, char* argv[] )
{
El::Environment env( argc, argv );
try
{
const El::Int n = El::Input("--n","problem size",200);
const El::Int maxIter =
El::Input("--maxIter","maximum # of iter's",500);
const Real lb = El::Input("--lb","lower bound for x",0.5);
const Real ub = El::Input("--ub","upper bound for x",1.0);
const Real lbEig = El::Input("--lbEig","spectral lower bound",1.);
const Real ubEig = El::Input("--ubEig","spectral upper bound",2.);
const Real rho = El::Input("--rho","augmented Lagrangian param.",1.);
const Real alpha = El::Input("--alpha","over-relaxation",1.2);
const Real absTol = El::Input("--absTol","absolute tolerance",1e-6);
const Real relTol = El::Input("--relTol","relative tolerance",1e-4);
const bool inv = El::Input("--inv","form inv(LU) to avoid trsv?",true);
const bool progress = El::Input("--progress","print progress?",true);
const bool display = El::Input("--display","display matrices?",false);
const bool print = El::Input("--print","print matrices",false);
El::ProcessInput();
El::PrintInputReport();
El::ADMMCtrl<Real> ctrl;
ctrl.rho = rho;
ctrl.alpha = alpha;
ctrl.maxIter = maxIter;
ctrl.absTol = absTol;
ctrl.relTol = relTol;
ctrl.inv = inv;
ctrl.print = progress;
El::DistMatrix<Real> Q, c, xTrue;
El::HermitianUniformSpectrum( Q, n, lbEig, ubEig );
// Alternate the entries of xTrue between ub and lb
El::Zeros( xTrue, n, 1 );
if( xTrue.LocalWidth() == 1 )
for( El::Int iLoc=0; iLoc<xTrue.LocalHeight(); ++iLoc )
xTrue.SetLocal( iLoc, 0,
( xTrue.GlobalRow(iLoc)%2==0 ? lb : ub ) );
// Set c := - Q xTrue - du + dl
El::Zeros( c, n, 1 );
El::Hemv( El::LOWER, Real(-1), Q, xTrue, Real(0), c );
if( c.LocalWidth() == 1 )
for( El::Int iLoc=0; iLoc<c.LocalHeight(); ++iLoc )
c.UpdateLocal( iLoc, 0,
( c.GlobalRow(iLoc)%2==0 ? 0.5 : -0.5 ) );
if( print )
{
El::Print( Q, "Q" );
El::Print( c, "c" );
El::Print( xTrue, "xTrue" );
}
if( display )
El::Display( Q, "Q" );
El::Timer timer;
El::DistMatrix<Real> z;
if( El::mpi::Rank() == 0 )
timer.Start();
El::qp::box::ADMM( Q, c, lb, ub, z, ctrl );
if( El::mpi::Rank() == 0 )
timer.Stop();
if( print )
El::Print( z, "z" );
if( El::mpi::Rank() == 0 )
El::Output("QPBox time: ",timer.Total(),"secs");
}
catch( std::exception& e ) { El::ReportException(e); }
return 0;
}
int
main( int argc, char* argv[] )
{
El::Environment env( argc, argv );
try
{
const El::Int m = El::Input("--m","height of matrix",100);
const El::Int n = El::Input("--n","width of matrix",200);
// TODO(poulson): Add options for controlling IPM
const El::Int maxIter =
El::Input("--maxIter","maximum # of iter's",500);
const Real lambda = El::Input("--lambda","DS parameter",0.5);
const bool display = El::Input("--display","display matrices?",false);
const bool print = El::Input("--print","print matrices",false);
El::ProcessInput();
El::PrintInputReport();
El::SparseMatrix<Real> A;
El::Matrix<Real> b, xTrue;
El::Identity( A, m, n );
El::Uniform( b, m, 1 );
if( print )
{
El::Print( A, "A" );
El::Print( b, "b" );
}
if( display )
El::Display( A, "A" );
El::lp::affine::Ctrl<Real> affineCtrl;
affineCtrl.mehrotraCtrl.print = true;
El::Matrix<Real> x;
El::Timer timer;
if( El::mpi::Rank() == 0 )
timer.Start();
El::DS( A, b, lambda, x, affineCtrl );
if( El::mpi::Rank() == 0 )
timer.Stop();
if( print )
El::Print( x, "x" );
const El::Int xZeroNorm = El::ZeroNorm( x );
if( El::mpi::Rank() == 0 )
{
El::Output("Dantzig Selector time: ",timer.Total()," secs");
El::Output("|| x ||_0 = ",xZeroNorm);
}
SoftThreshold( x, El::Sqrt(El::limits::Epsilon<Real>()) );
if( print )
El::Print( x, "xThresh" );
const El::Int xZeroNormThresh = El::ZeroNorm( x );
if( El::mpi::Rank() == 0 )
{
El::Output("|| xThresh ||_0 = ",xZeroNormThresh);
}
}
catch( std::exception& e ) { El::ReportException(e); }
return 0;
}
int
main( int argc, char* argv[] )
{
El::Environment env( argc, argv );
try
{
const El::Int n = El::Input("--size","width of matrix",100);
const bool display = El::Input("--display","display matrices?",false);
const bool print = El::Input("--print","print matrices?",false);
const bool smallestFirst =
El::Input("--smallestFirst","smallest norm first?",false);
El::ProcessInput();
El::PrintInputReport();
const El::Int m = n;
El::QRCtrl<double> ctrl;
ctrl.smallestFirst = smallestFirst;
El::DistMatrix<El::Complex<double>> A;
El::GKS( A, n );
const double frobA = El::FrobeniusNorm( A );
if( display )
El::Display( A, "A" );
if( print )
El::Print( A, "A" );
// Compute the pivoted QR decomposition of A, but do not overwrite A
auto QRPiv( A );
El::DistMatrix<El::Complex<double>> householderScalarsPiv;
El::DistMatrix<double> signaturePiv;
El::DistPermutation Omega;
El::Timer PQRtimer;
if( El::mpi::Rank() == 0 )
PQRtimer.Start();
El::QR( QRPiv, householderScalarsPiv, signaturePiv, Omega );
if( El::mpi::Rank() == 0 )
PQRtimer.Stop();
if( display )
{
El::Display( QRPiv, "QRPiv" );
El::Display( householderScalarsPiv, "householderScalarsPiv" );
El::Display( signaturePiv, "signaturePiv" );
El::DistMatrix<El::Int> OmegaFull;
Omega.ExplicitMatrix( OmegaFull );
El::Display( OmegaFull, "Omega" );
}
if( print )
{
El::Print( QRPiv, "QRPiv" );
El::Print( householderScalarsPiv, "householderScalarsPiv" );
El::Print( signaturePiv, "signaturePiv" );
El::DistMatrix<El::Int> OmegaFull;
Omega.ExplicitMatrix( OmegaFull );
El::Print( OmegaFull, "Omega" );
}
// Compute the standard QR decomposition of A
auto QRNoPiv( A );
El::DistMatrix<El::Complex<double>> householderScalarsNoPiv;
El::DistMatrix<double> signatureNoPiv;
El::Timer QRtimer;
if( El::mpi::Rank() == 0 )
QRtimer.Start();
El::QR( QRNoPiv, householderScalarsNoPiv, signatureNoPiv );
if( El::mpi::Rank() == 0 )
QRtimer.Start();
if( display )
{
El::Display( QRNoPiv, "QRNoPiv" );
El::Display( householderScalarsNoPiv, "householderScalarsNoPiv" );
El::Display( signatureNoPiv, "signatureNoPiv" );
}
if( print )
{
El::Print( QRNoPiv, "QRNoPiv" );
El::Print( householderScalarsNoPiv, "householderScalarsNoPiv" );
El::Print( signatureNoPiv, "signatureNoPiv" );
}
// Check the error in the pivoted QR factorization,
// || A Omega^T - Q R ||_F / || A ||_F
auto E( QRPiv );
El::MakeTrapezoidal( El::UPPER, E );
El::qr::ApplyQ
( El::LEFT, El::NORMAL, QRPiv, householderScalarsPiv, signaturePiv, E );
Omega.InversePermuteCols( E );
E -= A;
const double frobQRPiv = El::FrobeniusNorm( E );
if( display )
El::Display( E, "A P - Q R" );
if( print )
El::Print( E, "A P - Q R" );
// Check the error in the standard QR factorization,
// || A - Q R ||_F / || A ||_F
E = QRNoPiv;
El::MakeTrapezoidal( El::UPPER, E );
El::qr::ApplyQ
( El::LEFT, El::NORMAL,
QRNoPiv, householderScalarsNoPiv, signatureNoPiv, E );
E -= A;
const double frobQRNoPiv = El::FrobeniusNorm( E );
if( display )
El::Display( E, "A - Q R" );
if( print )
El::Print( E, "A - Q R" );
// Check orthogonality of pivoted Q, || I - Q^H Q ||_F / || A ||_F
El::Identity( E, m, n );
El::qr::ApplyQ
( El::LEFT, El::NORMAL,
QRPiv, householderScalarsPiv, signaturePiv, E );
El::qr::ApplyQ
( El::LEFT, El::ADJOINT,
QRPiv, householderScalarsPiv, signaturePiv, E );
const El::Int k = El::Min(m,n);
auto EUpper = E( El::IR(0,k), El::IR(0,k) );
El::ShiftDiagonal( EUpper, El::Complex<double>(-1) );
const double frobOrthogPiv = El::FrobeniusNorm( EUpper );
if( display )
El::Display( E, "pivoted I - Q^H Q" );
if( print )
El::Print( E, "pivoted I - Q^H Q" );
// Check orthogonality of unpivoted Q, || I - Q^H Q ||_F / || A ||_F
El::Identity( E, m, n );
El::qr::ApplyQ
( El::LEFT, El::NORMAL,
QRPiv, householderScalarsPiv, signaturePiv, E );
El::qr::ApplyQ
( El::LEFT, El::ADJOINT,
QRPiv, householderScalarsPiv, signaturePiv, E );
EUpper = E( El::IR(0,k), El::IR(0,k) );
El::ShiftDiagonal( EUpper, El::Complex<double>(-1) );
const double frobOrthogNoPiv = El::FrobeniusNorm( EUpper );
if( display )
El::Display( E, "unpivoted I - Q^H Q" );
if( print )
El::Print( E, "unpivoted I - Q^H Q" );
if( El::mpi::Rank() == 0 )
{
El::Output("Pivot QR time: ",PQRtimer.Total()," secs\n",
" QR time: ",QRtimer.Total()," secs");
El::Output
("|| A ||_F = ",frobA,"\n\n",
"With pivoting: \n",
" || A P - Q R ||_F / || A ||_F = ",frobQRPiv/frobA,"\n",
" || I - Q^H Q ||_F / || A ||_F = ",frobOrthogPiv/frobA,"\n\n",
"Without pivoting: \n",
" || A - Q R ||_F / || A ||_F = ",frobQRNoPiv/frobA,"\n",
" || I - Q^H Q ||_F / || A ||_F = ",frobOrthogNoPiv/frobA,"\n");
}
}
catch( std::exception& e ) { El::ReportException(e); }
return 0;
}
int
main( int argc, char* argv[] )
{
El::Environment env( argc, argv );
try
{
const El::Int m = El::Input("--m","height of matrix",100);
const El::Int n = El::Input("--n","width of matrix",200);
const bool useIPM = El::Input("--useIPM","use Interior Point?",true);
// TODO(poulson): Add options for controlling IPM
const El::Int maxIter =
El::Input("--maxIter","maximum # of iter's",500);
const Real rho = El::Input("--rho","augmented Lagrangian param.",1.);
const Real alpha = El::Input("--alpha","over-relaxation",1.2);
const Real absTol = El::Input("--absTol","absolute tolerance",1e-6);
const Real relTol = El::Input("--relTol","relative tolerance",1e-4);
const Real pinvTol = El::Input("--pinvTol","pseudoinv tolerance",0.);
const bool usePinv =
El::Input("--usePinv","Directly compute pinv(A)",true);
const bool progress = El::Input("--progress","print progress?",true);
const bool display = El::Input("--display","display matrices?",false);
const bool print = El::Input("--print","print matrices",false);
El::ProcessInput();
El::PrintInputReport();
El::DistMatrix<Real> A, b, xTrue;
El::Uniform( A, m, n );
El::Uniform( b, m, 1 );
if( print )
{
El::Print( A, "A" );
El::Print( b, "b" );
}
if( display )
El::Display( A, "A" );
const bool sparse = false;
El::BPCtrl<Real> ctrl(sparse);
ctrl.useIPM = useIPM;
ctrl.admmCtrl.rho = rho;
ctrl.admmCtrl.alpha = alpha;
ctrl.admmCtrl.maxIter = maxIter;
ctrl.admmCtrl.absTol = absTol;
ctrl.admmCtrl.relTol = relTol;
ctrl.admmCtrl.usePinv = usePinv;
ctrl.admmCtrl.pinvTol = pinvTol;
ctrl.admmCtrl.progress = progress;
ctrl.lpIPMCtrl.mehrotraCtrl.print = true;
El::DistMatrix<Real> x;
El::Timer timer;
if( El::mpi::Rank() == 0 )
timer.Start();
El::BP( A, b, x, ctrl );
if( El::mpi::Rank() == 0 )
timer.Stop();
if( print )
El::Print( x, "x" );
const El::Int xZeroNorm = El::ZeroNorm( x );
if( El::mpi::Rank() == 0 )
{
El::Output("Basis Pursuit time: ",timer.Total()," secs");
El::Output("|| x ||_0 = ",xZeroNorm);
}
SoftThreshold( x, El::Sqrt(El::limits::Epsilon<Real>()) );
if( print )
El::Print( x, "xThresh" );
const El::Int xZeroNormThresh = El::ZeroNorm( x );
if( El::mpi::Rank() == 0 )
{
El::Output("|| xThresh ||_0 = ",xZeroNormThresh);
}
}
catch( std::exception& e ) { El::ReportException(e); }
return 0;
}