void ExplicitUnitary
( ElementalMatrix<F>& APre, bool thinQR, const QRCtrl<Base<F>>& ctrl )
{
DEBUG_CSE
DistMatrixReadWriteProxy<F,F,MC,MR> AProx( APre );
auto& A = AProx.Get();
const Grid& g = A.Grid();
DistMatrix<F,MD,STAR> householderScalars(g);
DistMatrix<Base<F>,MD,STAR> signature(g);
if( ctrl.colPiv )
{
DistPermutation Omega(g);
QR( A, householderScalars, signature, Omega, ctrl );
}
else
QR( A, householderScalars, signature );
if( thinQR )
{
A.Resize( A.Height(), householderScalars.Height() );
ExpandPackedReflectors
( LOWER, VERTICAL, CONJUGATED, 0, A, householderScalars );
DiagonalScale( RIGHT, NORMAL, signature, A );
}
else
{
auto ACopy = A;
// TODO: Use an extension of ExpandPackedReflectors to make this faster
Identity( A, A.Height(), A.Height() );
qr::ApplyQ( LEFT, NORMAL, ACopy, householderScalars, signature, A );
}
}
inline void
Explicit( DistMatrix<F>& A, DistMatrix<F>& R, bool colPiv=false )
{
#ifndef RELEASE
CallStackEntry cse("qr::Explicit");
#endif
const Grid& g = A.Grid();
DistMatrix<F,MD,STAR> t(g);
if( colPiv )
{
DistMatrix<Int,VR,STAR> p(g);
QR( A, t, p );
}
else
{
QR( A, t );
}
DistMatrix<F> AT(g),
AB(g);
PartitionDown
( A, AT,
AB, Min(A.Height(),A.Width()) );
R = AT;
MakeTriangular( UPPER, R );
ExpandPackedReflectors( LOWER, VERTICAL, UNCONJUGATED, 0, A, t );
}
void ExplicitUnitary
( Matrix<F>& A, bool thinQR, const QRCtrl<Base<F>>& ctrl )
{
DEBUG_CSE
Matrix<F> householderScalars;
Matrix<Base<F>> signature;
if( ctrl.colPiv )
{
Permutation Omega;
QR( A, householderScalars, signature, Omega, ctrl );
}
else
QR( A, householderScalars, signature );
if( thinQR )
{
A.Resize( A.Height(), householderScalars.Height() );
ExpandPackedReflectors
( LOWER, VERTICAL, CONJUGATED, 0, A, householderScalars );
DiagonalScale( RIGHT, NORMAL, signature, A );
}
else
{
auto ACopy = A;
// TODO: Use an extension of ExpandPackedReflectors to make this faster
Identity( A, A.Height(), A.Height() );
qr::ApplyQ( LEFT, NORMAL, ACopy, householderScalars, signature, A );
}
}
void ExplicitUnitary
( Matrix<F>& A, bool thinQR, const QRCtrl<Base<F>>& ctrl )
{
DEBUG_ONLY(CSE cse("qr::ExplicitUnitary"))
Matrix<F> t;
Matrix<Base<F>> d;
if( ctrl.colPiv )
{
Permutation Omega;
QR( A, t, d, Omega, ctrl );
}
else
QR( A, t, d );
if( thinQR )
{
A.Resize( A.Height(), t.Height() );
ExpandPackedReflectors( LOWER, VERTICAL, CONJUGATED, 0, A, t );
DiagonalScale( RIGHT, NORMAL, d, A );
}
else
{
auto ACopy = A;
// TODO: Use an extension of ExpandPackedReflectors to make this faster
Identity( A, A.Height(), A.Height() );
qr::ApplyQ( LEFT, NORMAL, ACopy, t, d, A );
}
}
inline void
Explicit( Matrix<F>& A, Matrix<F>& R, bool colPiv=false )
{
#ifndef RELEASE
CallStackEntry cse("qr::Explicit");
#endif
Matrix<F> t;
if( colPiv )
{
Matrix<Int> p;
QR( A, t, p );
}
else
{
QR( A, t );
}
Matrix<F> AT,
AB;
PartitionDown
( A, AT,
AB, Min(A.Height(),A.Width()) );
R = AT;
MakeTriangular( UPPER, R );
ExpandPackedReflectors( LOWER, VERTICAL, UNCONJUGATED, 0, A, t );
}
inline void
ExpandPackedReflectors
( UpperOrLower uplo, VerticalOrHorizontal dir, Conjugation conjugation,
int offset,
DistMatrix<Complex<R> >& H,
const DistMatrix<Complex<R>,STAR,STAR>& t )
{
#ifndef RELEASE
CallStackEntry entry("ExpandPackedReflectors");
#endif
DistMatrix<Complex<R>,MD,STAR> tDiag(H.Grid());
tDiag.AlignWithDiagonal( H, offset );
tDiag = t;
ExpandPackedReflectors( uplo, dir, conjugation, offset, H, tDiag );
}
inline void
Explicit( Matrix<F>& A, bool colPiv=false )
{
DEBUG_ONLY(CallStackEntry cse("qr::Explicit"))
Matrix<F> t;
if( colPiv )
{
Matrix<Int> p;
QR( A, t, p );
}
else
{
QR( A, t );
}
ExpandPackedReflectors( LOWER, VERTICAL, CONJUGATED, 0, A, t );
}
void ExplicitUnitary( Matrix<F>& A, const QRCtrl<Base<F>>& ctrl )
{
DEBUG_ONLY(CallStackEntry cse("qr::ExplicitUnitary"))
Matrix<F> t;
Matrix<Base<F>> d;
if( ctrl.colPiv )
{
Matrix<Int> p;
QR( A, t, d, p, ctrl );
}
else
QR( A, t, d );
A.Resize( A.Height(), t.Height() );
ExpandPackedReflectors( LOWER, VERTICAL, CONJUGATED, 0, A, t );
DiagonalScale( RIGHT, NORMAL, d, A );
}
inline void
Explicit( Matrix<F>& A, bool colPiv=false )
{
#ifndef RELEASE
CallStackEntry cse("qr::Explicit");
#endif
Matrix<F> t;
if( colPiv )
{
Matrix<Int> p;
QR( A, t, p );
}
else
{
QR( A, t );
}
ExpandPackedReflectors( LOWER, VERTICAL, UNCONJUGATED, 0, A, t );
}
void Explicit
( ElementalMatrix<F>& APre,
ElementalMatrix<F>& R,
bool thinQR,
const QRCtrl<Base<F>>& ctrl )
{
DEBUG_ONLY(CSE cse("qr::Explicit"))
DistMatrixReadWriteProxy<F,F,MC,MR> AProx( APre );
auto& A = AProx.Get();
const Grid& g = A.Grid();
DistMatrix<F,MD,STAR> t(g);
DistMatrix<Base<F>,MD,STAR> d(g);
if( ctrl.colPiv )
{
DistPermutation Omega(g);
QR( A, t, d, Omega, ctrl );
}
else
QR( A, t, d );
const Int m = A.Height();
const Int n = A.Width();
const Int numIts = t.Height();
auto AT = A( IR(0,numIts), IR(0,n) );
Copy( AT, R );
MakeTrapezoidal( UPPER, R );
if( thinQR )
{
A.Resize( m, numIts );
ExpandPackedReflectors( LOWER, VERTICAL, CONJUGATED, 0, A, t );
DiagonalScale( RIGHT, NORMAL, d, A );
}
else
{
auto ACopy = A;
// TODO: Use an extension of ExpandPackedReflectors to make this faster
Identity( A, A.Height(), A.Height() );
qr::ApplyQ( LEFT, NORMAL, ACopy, t, d, A );
}
}
void Explicit
( ElementalMatrix<F>& APre,
ElementalMatrix<F>& R,
ElementalMatrix<Int>& OmegaFull,
bool thinQR,
const QRCtrl<Base<F>>& ctrl )
{
DEBUG_CSE
DistMatrixReadWriteProxy<F,F,MC,MR> AProx( APre );
auto& A = AProx.Get();
const Grid& g = A.Grid();
DistMatrix<F,MD,STAR> householderScalars(g);
DistMatrix<Base<F>,MD,STAR> signature(g);
DistPermutation Omega(g);
QR( A, householderScalars, signature, Omega, ctrl );
const Int m = A.Height();
const Int n = A.Width();
const Int numIts = householderScalars.Height();
auto AT = A( IR(0,numIts), IR(0,n) );
Copy( AT, R );
MakeTrapezoidal( UPPER, R );
if( thinQR )
{
A.Resize( m, numIts );
ExpandPackedReflectors
( LOWER, VERTICAL, CONJUGATED, 0, A, householderScalars );
DiagonalScale( RIGHT, NORMAL, signature, A );
}
else
{
auto ACopy = A;
// TODO: Use an extension of ExpandPackedReflectors to make this faster
Identity( A, A.Height(), A.Height() );
qr::ApplyQ( LEFT, NORMAL, ACopy, householderScalars, signature, A );
}
Omega.ExplicitMatrix( OmegaFull );
}
inline void
Explicit( DistMatrix<F>& A, bool colPiv=false )
{
#ifndef RELEASE
CallStackEntry cse("qr::Explicit");
#endif
const Grid& g = A.Grid();
DistMatrix<F,MD,STAR> t(g);
if( colPiv )
{
DistMatrix<Int,VR,STAR> p(g);
QR( A, t, p );
}
else
{
QR( A, t );
}
ExpandPackedReflectors( LOWER, VERTICAL, UNCONJUGATED, 0, A, t );
}
void Explicit
( Matrix<F>& A,
Matrix<F>& R,
bool thinQR,
const QRCtrl<Base<F>>& ctrl )
{
DEBUG_CSE
Matrix<F> householderScalars;
Matrix<Base<F>> signature;
if( ctrl.colPiv )
{
Permutation Omega;
QR( A, householderScalars, signature, Omega, ctrl );
}
else
QR( A, householderScalars, signature );
const Int m = A.Height();
const Int n = A.Width();
const Int numIts = householderScalars.Height();
auto AT = A( IR(0,numIts), IR(0,n) );
R = AT;
MakeTrapezoidal( UPPER, R );
if( thinQR )
{
A.Resize( m, numIts );
ExpandPackedReflectors
( LOWER, VERTICAL, CONJUGATED, 0, A, householderScalars );
DiagonalScale( RIGHT, NORMAL, signature, A );
}
else
{
auto ACopy = A;
// TODO: Use an extension of ExpandPackedReflectors to make this faster
Identity( A, A.Height(), A.Height() );
qr::ApplyQ( LEFT, NORMAL, ACopy, householderScalars, signature, A );
}
}
inline ValueInt<BASE(F)>
QDWHDivide
( UpperOrLower uplo, DistMatrix<F>& A, DistMatrix<F>& G, bool returnQ=false )
{
DEBUG_ONLY(CallStackEntry cse("herm_eig::QDWHDivide"))
// G := sgn(G)
// G := 1/2 ( G + I )
herm_polar::QDWH( uplo, G );
UpdateDiagonal( G, F(1) );
Scale( F(1)/F(2), G );
// Compute the pivoted QR decomposition of the spectral projection
const Grid& g = A.Grid();
DistMatrix<F,MD,STAR> t(g);
DistMatrix<Int,VR,STAR> p(g);
elem::QR( G, t, p );
// A := Q^H A Q
MakeHermitian( uplo, A );
const Base<F> oneA = OneNorm( A );
if( returnQ )
{
ExpandPackedReflectors( LOWER, VERTICAL, CONJUGATED, 0, G, t );
DistMatrix<F> B(g);
Gemm( ADJOINT, NORMAL, F(1), G, A, B );
Gemm( NORMAL, NORMAL, F(1), B, G, A );
}
else
{
qr::ApplyQ( LEFT, ADJOINT, G, t, A );
qr::ApplyQ( RIGHT, NORMAL, G, t, A );
}
// Return || E21 ||1 / || A ||1 and the chosen rank
auto part = ComputePartition( A );
part.value /= oneA;
return part;
}
void Explicit
( Matrix<F>& A,
Matrix<F>& R,
Matrix<Int>& OmegaFull,
bool thinQR,
const QRCtrl<Base<F>>& ctrl )
{
DEBUG_ONLY(CSE cse("qr::Explicit"))
Matrix<F> t;
Matrix<Base<F>> d;
Permutation Omega;
QR( A, t, d, Omega, ctrl );
const Int m = A.Height();
const Int n = A.Width();
const Int numIts = t.Height();
auto AT = A( IR(0,numIts), IR(0,n) );
R = AT;
MakeTrapezoidal( UPPER, R );
if( thinQR )
{
A.Resize( m, numIts );
ExpandPackedReflectors( LOWER, VERTICAL, CONJUGATED, 0, A, t );
DiagonalScale( RIGHT, NORMAL, d, A );
}
else
{
auto ACopy = A;
// TODO: Use an extension of ExpandPackedReflectors to make this faster
Identity( A, A.Height(), A.Height() );
qr::ApplyQ( LEFT, NORMAL, ACopy, t, d, A );
}
Omega.ExplicitMatrix( OmegaFull );
}