inline SafeProduct<F>
AfterLUPartialPiv( const Matrix<F>& A, const Matrix<Int>& p )
{
#ifndef RELEASE
CallStackEntry entry("determinant::AfterLUPartialPiv");
#endif
if( A.Height() != A.Width() )
LogicError("Cannot compute determinant of nonsquare matrix");
if( A.Height() != p.Height() )
LogicError("Pivot vector is incorrect length");
typedef BASE(F) R;
const Int n = A.Height();
Matrix<F> d;
A.GetDiagonal( d );
const R scale(n);
SafeProduct<F> det( n );
for( Int i=0; i<n; ++i )
{
const F delta = d.Get(i,0);
R alpha = Abs(delta);
det.rho *= delta/alpha;
det.kappa += Log(alpha)/scale;
}
const bool isOdd = PivotParity( p );
if( isOdd )
det.rho = -det.rho;
return det;
}
inline SafeProduct<F>
SafeDeterminant( DistMatrix<F,MC,MR>& A )
{
#ifndef RELEASE
PushCallStack("SafeDeterminant");
#endif
if( A.Height() != A.Width() )
throw std::logic_error
("Cannot compute determinant of nonsquare matrix");
typedef typename Base<F>::type R;
const int n = A.Height();
SafeProduct<F> det( n );
const Grid& g = A.Grid();
try
{
DistMatrix<int,VC,STAR> p;
LU( A, p );
const bool isOdd = PivotParity( p );
DistMatrix<F,MD,STAR> d(g);
A.GetDiagonal( d );
F localRho = 1;
R localKappa = 0;
if( d.InDiagonal() )
{
const int nLocalDiag = d.LocalHeight();
for( int iLocal=0; iLocal<nLocalDiag; ++iLocal )
{
const F delta = d.GetLocalEntry(iLocal,0);
R alpha = Abs(delta);
localRho *= delta/alpha;
localKappa += std::log(alpha)/n;
}
}
mpi::AllReduce( &localRho, &det.rho, 1, mpi::PROD, g.VCComm() );
mpi::AllReduce( &localKappa, &det.kappa, 1, mpi::SUM, g.VCComm() );
if( isOdd )
det.rho = -det.rho;
}
catch( SingularMatrixException& e )
{
det.rho = 0;
det.kappa = 0;
}
#ifndef RELEASE
PopCallStack();
#endif
return det;
}
inline SafeProduct<F>
LUPartialPiv( DistMatrix<F>& A )
{
#ifndef RELEASE
CallStackEntry entry("determinant::LUPartialPiv");
#endif
if( A.Height() != A.Width() )
throw std::logic_error
("Cannot compute determinant of nonsquare matrix");
typedef BASE(F) R;
const int n = A.Height();
const R scale(n);
SafeProduct<F> det( n );
const Grid& g = A.Grid();
try
{
DistMatrix<int,VC,STAR> p(g);
elem::LU( A, p );
const bool isOdd = PivotParity( p );
DistMatrix<F,MD,STAR> d(g);
A.GetDiagonal( d );
F localRho = 1;
R localKappa = 0;
if( d.Participating() )
{
const int nLocalDiag = d.LocalHeight();
for( int iLocal=0; iLocal<nLocalDiag; ++iLocal )
{
const F delta = d.GetLocal(iLocal,0);
R alpha = Abs(delta);
localRho *= delta/alpha;
localKappa += Log(alpha)/scale;
}
}
mpi::AllReduce( &localRho, &det.rho, 1, mpi::PROD, g.VCComm() );
mpi::AllReduce( &localKappa, &det.kappa, 1, mpi::SUM, g.VCComm() );
if( isOdd )
det.rho = -det.rho;
}
catch( SingularMatrixException& e )
{
det.rho = 0;
det.kappa = 0;
}
return det;
}
inline SafeProduct<F>
AfterLUPartialPiv( const DistMatrix<F>& A, const DistMatrix<Int,VC,STAR>& p )
{
#ifndef RELEASE
CallStackEntry entry("determinant::AfterLUPartialPiv");
#endif
if( A.Height() != A.Width() )
LogicError("Cannot compute determinant of nonsquare matrix");
if( A.Grid() != p.Grid() )
LogicError("A and p must have the same grid");
if( A.Height() != p.Height() )
LogicError("Pivot vector is incorrect length");
typedef BASE(F) R;
const Int n = A.Height();
const Grid& g = A.Grid();
DistMatrix<F,MD,STAR> d(g);
A.GetDiagonal( d );
F localRho = 1;
R localKappa = 0;
if( d.Participating() )
{
const R scale(n);
const Int nLocalDiag = d.LocalHeight();
for( Int iLoc=0; iLoc<nLocalDiag; ++iLoc )
{
const F delta = d.GetLocal(iLoc,0);
R alpha = Abs(delta);
localRho *= delta/alpha;
localKappa += Log(alpha)/scale;
}
}
SafeProduct<F> det( n );
det.rho = mpi::AllReduce( localRho, mpi::PROD, g.VCComm() );
det.kappa = mpi::AllReduce( localKappa, mpi::SUM, g.VCComm() );
const bool isOdd = PivotParity( p );
if( isOdd )
det.rho = -det.rho;
return det;
}
inline SafeProduct<F>
SafeDeterminant( Matrix<F>& A )
{
#ifndef RELEASE
PushCallStack("SafeDeterminant");
#endif
if( A.Height() != A.Width() )
throw std::logic_error
("Cannot compute determinant of nonsquare matrix");
typedef typename Base<F>::type R;
const int n = A.Height();
SafeProduct<F> det( n );
try
{
Matrix<int> p;
LU( A, p );
const bool isOdd = PivotParity( p );
Matrix<F> d;
A.GetDiagonal( d );
for( int i=0; i<n; ++i )
{
const F delta = d.Get(i,0);
R alpha = Abs(delta);
det.rho *= delta/alpha;
det.kappa += std::log(alpha)/n;
}
if( isOdd )
det.rho = -det.rho;
}
catch( SingularMatrixException& e )
{
det.rho = 0;
det.kappa = 0;
}
#ifndef RELEASE
PopCallStack();
#endif
return det;
}
inline SafeProduct<F>
LUPartialPiv( Matrix<F>& A )
{
#ifndef RELEASE
CallStackEntry entry("determinant::LUPartialPiv");
#endif
if( A.Height() != A.Width() )
throw std::logic_error
("Cannot compute determinant of nonsquare matrix");
typedef BASE(F) R;
const int n = A.Height();
const R scale(n);
SafeProduct<F> det( n );
try
{
Matrix<int> p;
elem::LU( A, p );
const bool isOdd = PivotParity( p );
Matrix<F> d;
A.GetDiagonal( d );
for( int i=0; i<n; ++i )
{
const F delta = d.Get(i,0);
R alpha = Abs(delta);
det.rho *= delta/alpha;
det.kappa += Log(alpha)/scale;
}
if( isOdd )
det.rho = -det.rho;
}
catch( SingularMatrixException& e )
{
det.rho = 0;
det.kappa = 0;
}
return det;
}
