inline void
Syr2kLN
( T alpha, const DistMatrix<T>& A, const DistMatrix<T>& B,
T beta, DistMatrix<T>& C )
{
#ifndef RELEASE
PushCallStack("internal::Syr2kLN");
if( A.Grid() != B.Grid() || B.Grid() != C.Grid() )
throw std::logic_error
("{A,B,C} must be distributed over the same grid");
if( A.Height() != C.Height() || A.Height() != C.Width() ||
B.Height() != C.Height() || B.Height() != C.Width() ||
A.Width() != B.Width() )
{
std::ostringstream msg;
msg << "Nonconformal Syr2kLN:\n"
<< " A ~ " << A.Height() << " x " << A.Width() << "\n"
<< " B ~ " << B.Height() << " x " << B.Width() << "\n"
<< " C ~ " << C.Height() << " x " << C.Width() << "\n";
throw std::logic_error( msg.str().c_str() );
}
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<T> AL(g), AR(g),
A0(g), A1(g), A2(g);
DistMatrix<T> BL(g), BR(g),
B0(g), B1(g), B2(g);
// Temporary distributions
DistMatrix<T,MC, STAR> A1_MC_STAR(g);
DistMatrix<T,MC, STAR> B1_MC_STAR(g);
DistMatrix<T,VR, STAR> A1_VR_STAR(g);
DistMatrix<T,VR, STAR> B1_VR_STAR(g);
DistMatrix<T,STAR,MR > A1Trans_STAR_MR(g);
DistMatrix<T,STAR,MR > B1Trans_STAR_MR(g);
A1_MC_STAR.AlignWith( C );
B1_MC_STAR.AlignWith( C );
A1_VR_STAR.AlignWith( C );
B1_VR_STAR.AlignWith( C );
A1Trans_STAR_MR.AlignWith( C );
B1Trans_STAR_MR.AlignWith( C );
// Start the algorithm
ScaleTrapezoid( beta, LEFT, LOWER, 0, C );
LockedPartitionRight( A, AL, AR, 0 );
LockedPartitionRight( B, BL, BR, 0 );
while( AR.Width() > 0 )
{
LockedRepartitionRight
( AL, /**/ AR,
A0, /**/ A1, A2 );
LockedRepartitionRight
( BL, /**/ BR,
B0, /**/ B1, B2 );
//--------------------------------------------------------------------//
A1_VR_STAR = A1_MC_STAR = A1;
A1Trans_STAR_MR.TransposeFrom( A1_VR_STAR );
B1_VR_STAR = B1_MC_STAR = B1;
B1Trans_STAR_MR.TransposeFrom( B1_VR_STAR );
LocalTrr2k
( LOWER,
alpha, A1_MC_STAR, B1Trans_STAR_MR,
B1_MC_STAR, A1Trans_STAR_MR,
T(1), C );
//--------------------------------------------------------------------//
SlideLockedPartitionRight
( AL, /**/ AR,
A0, A1, /**/ A2 );
SlideLockedPartitionRight
( BL, /**/ BR,
B0, B1, /**/ B2 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
TrmmLLNCOld
( UnitOrNonUnit diag,
T alpha, const DistMatrix<T>& L,
DistMatrix<T>& X )
{
#ifndef RELEASE
PushCallStack("internal::TrmmLLNCOld");
if( L.Grid() != X.Grid() )
throw std::logic_error
("L and X must be distributed over the same grid");
if( L.Height() != L.Width() || L.Width() != X.Height() )
{
std::ostringstream msg;
msg << "Nonconformal TrmmLLNC: \n"
<< " L ~ " << L.Height() << " x " << L.Width() << "\n"
<< " X ~ " << X.Height() << " x " << X.Width() << "\n";
throw std::logic_error( msg.str().c_str() );
}
#endif
const Grid& g = L.Grid();
// Matrix views
DistMatrix<T>
LTL(g), LTR(g), L00(g), L01(g), L02(g),
LBL(g), LBR(g), L10(g), L11(g), L12(g),
L20(g), L21(g), L22(g);
DistMatrix<T> XT(g), X0(g),
XB(g), X1(g),
X2(g);
// Temporary distributions
DistMatrix<T,STAR,MC > L10_STAR_MC(g);
DistMatrix<T,STAR,STAR> L11_STAR_STAR(g);
DistMatrix<T,STAR,VR > X1_STAR_VR(g);
DistMatrix<T,MR, STAR> D1Trans_MR_STAR(g);
DistMatrix<T,MR, MC > D1Trans_MR_MC(g);
DistMatrix<T,MC, MR > D1(g);
// Start the algorithm
Scale( alpha, X );
LockedPartitionUpDiagonal
( L, LTL, LTR,
LBL, LBR, 0 );
PartitionUp
( X, XT,
XB, 0 );
while( XT.Height() > 0 )
{
LockedRepartitionUpDiagonal
( LTL, /**/ LTR, L00, L01, /**/ L02,
/**/ L10, L11, /**/ L12,
/*************/ /******************/
LBL, /**/ LBR, L20, L21, /**/ L22 );
RepartitionUp
( XT, X0,
X1,
/**/ /**/
XB, X2 );
L10_STAR_MC.AlignWith( X0 );
D1Trans_MR_STAR.AlignWith( X1 );
D1Trans_MR_MC.AlignWith( X1 );
D1.AlignWith( X1 );
Zeros( X1.Width(), X1.Height(), D1Trans_MR_STAR );
Zeros( X1.Height(), X1.Width(), D1 );
//--------------------------------------------------------------------//
L11_STAR_STAR = L11;
X1_STAR_VR = X1;
LocalTrmm( LEFT, LOWER, NORMAL, diag, T(1), L11_STAR_STAR, X1_STAR_VR );
X1 = X1_STAR_VR;
L10_STAR_MC = L10;
LocalGemm
( TRANSPOSE, TRANSPOSE, T(1), X0, L10_STAR_MC, T(0), D1Trans_MR_STAR );
D1Trans_MR_MC.SumScatterFrom( D1Trans_MR_STAR );
Transpose( D1Trans_MR_MC.LocalMatrix(), D1.LocalMatrix() );
Axpy( T(1), D1, X1 );
//--------------------------------------------------------------------//
D1.FreeAlignments();
D1Trans_MR_MC.FreeAlignments();
D1Trans_MR_STAR.FreeAlignments();
L10_STAR_MC.FreeAlignments();
SlideLockedPartitionUpDiagonal
( LTL, /**/ LTR, L00, /**/ L01, L02,
/*************/ /******************/
/**/ L10, /**/ L11, L12,
LBL, /**/ LBR, L20, /**/ L21, L22 );
SlidePartitionUp
( XT, X0,
/**/ /**/
X1,
XB, X2 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
TwoSidedTrmmLVar4( UnitOrNonUnit diag, Matrix<F>& A, const Matrix<F>& L )
{
#ifndef RELEASE
PushCallStack("internal::TwoSidedTrmmLVar4");
if( A.Height() != A.Width() )
throw std::logic_error("A must be square");
if( L.Height() != L.Width() )
throw std::logic_error("Triangular matrices must be square");
if( A.Height() != L.Height() )
throw std::logic_error("A and L must be the same size");
#endif
// Matrix views
Matrix<F>
ATL, ATR, A00, A01, A02,
ABL, ABR, A10, A11, A12,
A20, A21, A22;
Matrix<F>
LTL, LTR, L00, L01, L02,
LBL, LBR, L10, L11, L12,
L20, L21, L22;
// Temporary products
Matrix<F> Y10;
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
LockedPartitionDownDiagonal
( L, LTL, LTR,
LBL, LBR, 0 );
while( ATL.Height() < A.Height() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
LockedRepartitionDownDiagonal
( LTL, /**/ LTR, L00, /**/ L01, L02,
/*************/ /******************/
/**/ L10, /**/ L11, L12,
LBL, /**/ LBR, L20, /**/ L21, L22 );
//--------------------------------------------------------------------//
// Y10 := A11 L10
Zeros( A10.Height(), A10.Width(), Y10 );
Hemm( LEFT, LOWER, F(1), A11, L10, F(0), Y10 );
// A10 := A10 + 1/2 Y10
Axpy( F(1)/F(2), Y10, A10 );
// A00 := A00 + (A10' L10 + L10' A10)
Her2k( LOWER, ADJOINT, F(1), A10, L10, F(1), A00 );
// A10 := A10 + 1/2 Y10
Axpy( F(1)/F(2), Y10, A10 );
// A10 := L11' A10
Trmm( LEFT, LOWER, ADJOINT, diag, F(1), L11, A10 );
// A20 := A20 + A21 L10
Gemm( NORMAL, NORMAL, F(1), A21, L10, F(1), A20 );
// A11 := L11' A11 L11
TwoSidedTrmmLUnb( diag, A11, L11 );
// A21 := A21 L11
Trmm( RIGHT, LOWER, NORMAL, diag, F(1), L11, A21 );
//--------------------------------------------------------------------//
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
SlideLockedPartitionDownDiagonal
( LTL, /**/ LTR, L00, L01, /**/ L02,
/**/ L10, L11, /**/ L12,
/*************/ /******************/
LBL, /**/ LBR, L20, L21, /**/ L22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
Var3( Orientation orientation, DistMatrix<F>& A, DistMatrix<F,MC,STAR>& d )
{
#ifndef RELEASE
PushCallStack("ldl::Var3");
if( orientation == NORMAL )
throw std::logic_error("Can only perform LDL^T and LDL^H");
if( A.Height() != A.Width() )
throw std::logic_error("A must be square");
if( A.Grid() != d.Grid() )
throw std::logic_error("A and d must use the same grid");
if( d.Viewing() && (d.Height() != A.Height() || d.Width() != 1) )
throw std::logic_error
("d must be a column vector of the same height as A");
if( d.Viewing() && d.ColAlignment() != A.ColAlignment() )
throw std::logic_error("d must be aligned with A");
#endif
const Grid& g = A.Grid();
if( !d.Viewing() )
{
d.AlignWith( A );
d.ResizeTo( A.Height(), 1 );
}
// Matrix views
DistMatrix<F>
ATL(g), ATR(g), A00(g), A01(g), A02(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
DistMatrix<F,MC,STAR>
dT(g), d0(g),
dB(g), d1(g),
d2(g);
// Temporary matrices
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,STAR,STAR> d1_STAR_STAR(g);
DistMatrix<F,VC, STAR> A21_VC_STAR(g);
DistMatrix<F,VR, STAR> A21_VR_STAR(g);
DistMatrix<F,STAR,MC > S21Trans_STAR_MC(g);
DistMatrix<F,STAR,MR > A21AdjOrTrans_STAR_MR(g);
const bool conjugate = ( orientation == ADJOINT );
// Start the algorithm
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
PartitionDown
( d, dT,
dB, 0 );
while( ABR.Height() > 0 )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
RepartitionDown
( dT, d0,
/**/ /**/
d1,
dB, d2 );
A21_VC_STAR.AlignWith( A22 );
A21_VR_STAR.AlignWith( A22 );
S21Trans_STAR_MC.AlignWith( A22 );
A21AdjOrTrans_STAR_MR.AlignWith( A22 );
//--------------------------------------------------------------------//
A11_STAR_STAR = A11;
LocalLDL( orientation, A11_STAR_STAR, d1_STAR_STAR );
A11 = A11_STAR_STAR;
d1 = d1_STAR_STAR;
A21_VC_STAR = A21;
LocalTrsm
( RIGHT, LOWER, orientation, UNIT,
F(1), A11_STAR_STAR, A21_VC_STAR );
S21Trans_STAR_MC.TransposeFrom( A21_VC_STAR );
DiagonalSolve( RIGHT, NORMAL, d1_STAR_STAR, A21_VC_STAR );
A21_VR_STAR = A21_VC_STAR;
A21AdjOrTrans_STAR_MR.TransposeFrom( A21_VR_STAR, conjugate );
LocalTrrk
( LOWER, TRANSPOSE,
F(-1), S21Trans_STAR_MC, A21AdjOrTrans_STAR_MR, F(1), A22 );
A21 = A21_VC_STAR;
//--------------------------------------------------------------------//
A21_VC_STAR.FreeAlignments();
A21_VR_STAR.FreeAlignments();
S21Trans_STAR_MC.FreeAlignments();
A21AdjOrTrans_STAR_MR.FreeAlignments();
SlidePartitionDown
( dT, d0,
d1,
/**/ /**/
dB, d2 );
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
Var3( Orientation orientation, Matrix<F>& A, Matrix<F>& d )
{
#ifndef RELEASE
PushCallStack("ldl::Var3");
if( A.Height() != A.Width() )
throw std::logic_error("A must be square");
if( d.Viewing() && (d.Height() != A.Height() || d.Width() != 1) )
throw std::logic_error
("d must be a column vector the same height as A");
if( orientation == NORMAL )
throw std::logic_error("Can only perform LDL^T or LDL^H");
#endif
const int n = A.Height();
if( !d.Viewing() )
d.ResizeTo( n, 1 );
Matrix<F>
ATL, ATR, A00, A01, A02,
ABL, ABR, A10, A11, A12,
A20, A21, A22;
Matrix<F>
dT, d0,
dB, d1,
d2;
Matrix<F> S21;
// Start the algorithm
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
PartitionDown
( d, dT,
dB, 0 );
while( ABR.Height() > 0 )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
RepartitionDown
( dT, d0,
/**/ /**/
d1,
dB, d2 );
//--------------------------------------------------------------------//
ldl::Var3Unb( orientation, A11, d1 );
Trsm( RIGHT, LOWER, orientation, UNIT, F(1), A11, A21 );
S21 = A21;
DiagonalSolve( RIGHT, NORMAL, d1, A21 );
internal::TrrkNT( LOWER, orientation, F(-1), S21, A21, F(1), A22 );
//--------------------------------------------------------------------//
SlidePartitionDown
( dT, d0,
d1,
/**/ /**/
dB, d2 );
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
MakeTrapezoidal
( LeftOrRight side, UpperOrLower uplo, int offset, Matrix<T>& A )
{
#ifndef RELEASE
PushCallStack("MakeTrapezoidal");
#endif
const int height = A.Height();
const int width = A.Width();
const int ldim = A.LDim();
T* buffer = A.Buffer();
if( uplo == LOWER )
{
if( side == LEFT )
{
#ifdef HAVE_OPENMP
#pragma omp parallel for
#endif
for( int j=std::max(0,offset+1); j<width; ++j )
{
const int lastZeroRow = j-offset-1;
const int numZeroRows = std::min( lastZeroRow+1, height );
MemZero( &buffer[j*ldim], numZeroRows );
}
}
else
{
#ifdef HAVE_OPENMP
#pragma omp parallel for
#endif
for( int j=std::max(0,offset-height+width+1); j<width; ++j )
{
const int lastZeroRow = j-offset+height-width-1;
const int numZeroRows = std::min( lastZeroRow+1, height );
MemZero( &buffer[j*ldim], numZeroRows );
}
}
}
else
{
if( side == LEFT )
{
#ifdef HAVE_OPENMP
#pragma omp parallel for
#endif
for( int j=0; j<width; ++j )
{
const int firstZeroRow = std::max(j-offset+1,0);
if( firstZeroRow < height )
MemZero
( &buffer[firstZeroRow+j*ldim], height-firstZeroRow );
}
}
else
{
#ifdef HAVE_OPENMP
#pragma omp parallel for
#endif
for( int j=0; j<width; ++j )
{
const int firstZeroRow = std::max(j-offset+height-width+1,0);
if( firstZeroRow < height )
MemZero
( &buffer[firstZeroRow+j*ldim], height-firstZeroRow );
}
}
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
internal::HPDInverseUVar2( DistMatrix<F,MC,MR>& A )
{
#ifndef RELEASE
PushCallStack("internal::HPDInverseUVar2");
if( A.Height() != A.Width() )
throw std::logic_error("Nonsquare matrices cannot be triangular");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<F,MC,MR>
ATL(g), ATR(g), A00(g), A01(g), A02(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
// Temporary distributions
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,VC, STAR> A01_VC_STAR(g);
DistMatrix<F,VR, STAR> A01_VR_STAR(g);
DistMatrix<F,STAR,VR > A12_STAR_VR(g);
DistMatrix<F,STAR,MC > A01Trans_STAR_MC(g);
DistMatrix<F,MR, STAR> A01_MR_STAR(g);
DistMatrix<F,STAR,MR > A01Adj_STAR_MR(g);
DistMatrix<F,STAR,MR > A12_STAR_MR(g);
DistMatrix<F,STAR,MC > A12_STAR_MC(g);
// Start the algorithm
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
while( ATL.Height() < A.Height() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
A01_VC_STAR.AlignWith( A00 );
A12_STAR_VR.AlignWith( A02 );
A01Trans_STAR_MC.AlignWith( A00 );
A01_VR_STAR.AlignWith( A00 );
A01Adj_STAR_MR.AlignWith( A00 );
A12_STAR_MR.AlignWith( A02 );
A12_STAR_MC.AlignWith( A22 );
//--------------------------------------------------------------------//
A11_STAR_STAR = A11;
internal::LocalCholesky( UPPER, A11_STAR_STAR );
A01_VC_STAR = A01;
internal::LocalTrsm
( RIGHT, UPPER, NORMAL, NON_UNIT, (F)1, A11_STAR_STAR, A01_VC_STAR );
A12_STAR_VR = A12;
internal::LocalTrsm
( LEFT, UPPER, ADJOINT, NON_UNIT, (F)1, A11_STAR_STAR, A12_STAR_VR );
A01Trans_STAR_MC.TransposeFrom( A01_VC_STAR );
A01_VR_STAR = A01_VC_STAR;
A01Adj_STAR_MR.AdjointFrom( A01_VR_STAR );
internal::LocalTrrk
( UPPER, TRANSPOSE,
(F)1, A01Trans_STAR_MC, A01Adj_STAR_MR, (F)1, A00 );
A12_STAR_MR = A12_STAR_VR;
internal::LocalGemm
( TRANSPOSE, NORMAL, (F)-1, A01Trans_STAR_MC, A12_STAR_MR, (F)1, A02 );
A12_STAR_MC = A12_STAR_VR;
internal::LocalTrrk
( UPPER, ADJOINT,
(F)-1, A12_STAR_MC, A12_STAR_MR, (F)1, A22 );
internal::LocalTrsm
( RIGHT, UPPER, ADJOINT, NON_UNIT, (F)1, A11_STAR_STAR, A01_VC_STAR );
internal::LocalTrsm
( LEFT, UPPER, NORMAL, NON_UNIT, (F)-1, A11_STAR_STAR, A12_STAR_VR );
internal::LocalTriangularInverse
( UPPER, NON_UNIT, A11_STAR_STAR );
internal::LocalHetrmm( UPPER, A11_STAR_STAR );
A11 = A11_STAR_STAR;
A01 = A01_VC_STAR;
A12 = A12_STAR_VR;
//--------------------------------------------------------------------//
A01_VC_STAR.FreeAlignments();
A12_STAR_VR.FreeAlignments();
A01Trans_STAR_MC.FreeAlignments();
A01_VR_STAR.FreeAlignments();
A01Adj_STAR_MR.FreeAlignments();
A12_STAR_MR.FreeAlignments();
A12_STAR_MC.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
Trr2kNNTT
( UpperOrLower uplo,
Orientation orientationOfC, Orientation orientationOfD,
T alpha, const DistMatrix<T,MC,MR>& A, const DistMatrix<T,MC,MR>& B,
const DistMatrix<T,MC,MR>& C, const DistMatrix<T,MC,MR>& D,
T beta, DistMatrix<T,MC,MR>& E )
{
#ifndef RELEASE
PushCallStack("internal::Trr2kNNTT");
if( E.Height() != E.Width() || A.Width() != C.Height() ||
A.Height() != E.Height() || C.Width() != E.Height() ||
B.Width() != E.Width() || D.Height() != E.Width() ||
A.Width() != B.Height() || C.Height() != D.Width() )
throw std::logic_error("Nonconformal Trr2kNNTT");
#endif
const Grid& g = E.Grid();
DistMatrix<T,MC,MR> AL(g), AR(g),
A0(g), A1(g), A2(g);
DistMatrix<T,MC,MR> BT(g), B0(g),
BB(g), B1(g),
B2(g);
DistMatrix<T,MC,MR> CT(g), C0(g),
CB(g), C1(g),
C2(g);
DistMatrix<T,MC,MR> DL(g), DR(g),
D0(g), D1(g), D2(g);
DistMatrix<T,MC, STAR> A1_MC_STAR(g);
DistMatrix<T,MR, STAR> B1Trans_MR_STAR(g);
DistMatrix<T,STAR,MC > C1_STAR_MC(g);
DistMatrix<T,VR, STAR> D1_VR_STAR(g);
DistMatrix<T,STAR,MR > D1AdjOrTrans_STAR_MR(g);
A1_MC_STAR.AlignWith( E );
B1Trans_MR_STAR.AlignWith( E );
C1_STAR_MC.AlignWith( E );
D1_VR_STAR.AlignWith( E );
D1AdjOrTrans_STAR_MR.AlignWith( E );
LockedPartitionRight( A, AL, AR, 0 );
LockedPartitionDown
( B, BT,
BB, 0 );
LockedPartitionDown
( C, CT,
CB, 0 );
LockedPartitionRight( D, DL, DR, 0 );
while( AL.Width() < A.Width() )
{
LockedRepartitionRight
( AL, /**/ AR,
A0, /**/ A1, A2 );
LockedRepartitionDown
( BT, B0,
/**/ /**/
B1,
BB, B2 );
LockedRepartitionDown
( CT, C0,
/**/ /**/
C1,
CB, C2 );
LockedRepartitionRight
( DL, /**/ DR,
D0, /**/ D1, D2 );
//--------------------------------------------------------------------//
A1_MC_STAR = A1;
C1_STAR_MC = C1;
B1Trans_MR_STAR.TransposeFrom( B1 );
D1_VR_STAR = D1;
if( orientationOfD == ADJOINT )
D1AdjOrTrans_STAR_MR.AdjointFrom( D1_VR_STAR );
else
D1AdjOrTrans_STAR_MR.TransposeFrom( D1_VR_STAR );
LocalTrr2k
( uplo, TRANSPOSE, orientationOfC,
alpha, A1_MC_STAR, B1Trans_MR_STAR,
C1_STAR_MC, D1AdjOrTrans_STAR_MR,
beta, E );
//--------------------------------------------------------------------//
SlideLockedPartitionRight
( DL, /**/ DR,
D0, D1, /**/ D2 );
SlideLockedPartitionDown
( CT, C0,
C1,
/**/ /**/
CB, C2 );
SlideLockedPartitionDown
( BT, B0,
B1,
/**/ /**/
BB, B2 );
SlideLockedPartitionRight
( AL, /**/ AR,
A0, A1, /**/ A2 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
CallStackEntry(const std::string& s) {
if (!std::uncaught_exception())
PushCallStack(s);
}
inline void
TwoSidedTrmmUVar2
( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& U )
{
#ifndef RELEASE
PushCallStack("internal::TwoSidedTrmmUVar2");
if( A.Height() != A.Width() )
throw std::logic_error("A must be square");
if( U.Height() != U.Width() )
throw std::logic_error("Triangular matrices must be square");
if( A.Height() != U.Height() )
throw std::logic_error("A and U must be the same size");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<F>
ATL(g), ATR(g), A00(g), A01(g), A02(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
DistMatrix<F>
UTL(g), UTR(g), U00(g), U01(g), U02(g),
UBL(g), UBR(g), U10(g), U11(g), U12(g),
U20(g), U21(g), U22(g);
// Temporary distributions
DistMatrix<F,VC, STAR> A01_VC_STAR(g);
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,STAR,VR > A12_STAR_VR(g);
DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
DistMatrix<F,STAR,MC > U12_STAR_MC(g);
DistMatrix<F,STAR,VR > U12_STAR_VR(g);
DistMatrix<F,MR, STAR> U12Adj_MR_STAR(g);
DistMatrix<F,VC, STAR> U12Adj_VC_STAR(g);
DistMatrix<F,MC, STAR> X01_MC_STAR(g);
DistMatrix<F,STAR,STAR> X11_STAR_STAR(g);
DistMatrix<F,MR, MC > Z12Adj_MR_MC(g);
DistMatrix<F,MC, STAR> Z12Adj_MC_STAR(g);
DistMatrix<F,MR, STAR> Z12Adj_MR_STAR(g);
DistMatrix<F> Y12(g);
DistMatrix<F> Z12Adj(g);
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
LockedPartitionDownDiagonal
( U, UTL, UTR,
UBL, UBR, 0 );
while( ATL.Height() < A.Height() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
LockedRepartitionDownDiagonal
( UTL, /**/ UTR, U00, /**/ U01, U02,
/*************/ /******************/
/**/ U10, /**/ U11, U12,
UBL, /**/ UBR, U20, /**/ U21, U22 );
A12_STAR_VR.AlignWith( A12 );
U12_STAR_MC.AlignWith( A22 );
U12_STAR_VR.AlignWith( A12 );
U12Adj_MR_STAR.AlignWith( A22 );
U12Adj_VC_STAR.AlignWith( A22 );
X01_MC_STAR.AlignWith( A01 );
Y12.AlignWith( A12 );
Z12Adj.AlignWith( A12 );
Z12Adj_MR_MC.AlignWith( A12 );
Z12Adj_MC_STAR.AlignWith( A22 );
Z12Adj_MR_STAR.AlignWith( A22 );
//--------------------------------------------------------------------//
// A01 := A01 U11'
U11_STAR_STAR = U11;
A01_VC_STAR = A01;
LocalTrmm
( RIGHT, UPPER, ADJOINT, diag, F(1), U11_STAR_STAR, A01_VC_STAR );
A01 = A01_VC_STAR;
// A01 := A01 + A02 U12'
U12Adj_MR_STAR.AdjointFrom( U12 );
X01_MC_STAR.ResizeTo( A01.Height(), A01.Width() );
LocalGemm
( NORMAL, NORMAL, F(1), A02, U12Adj_MR_STAR, F(0), X01_MC_STAR );
A01.SumScatterUpdate( F(1), X01_MC_STAR );
// Y12 := U12 A22
U12Adj_VC_STAR = U12Adj_MR_STAR;
U12_STAR_MC.AdjointFrom( U12Adj_VC_STAR );
Z12Adj_MC_STAR.ResizeTo( A12.Width(), A12.Height() );
Z12Adj_MR_STAR.ResizeTo( A12.Width(), A12.Height() );
Zero( Z12Adj_MC_STAR );
Zero( Z12Adj_MR_STAR );
LocalSymmetricAccumulateRU
( ADJOINT,
F(1), A22, U12_STAR_MC, U12Adj_MR_STAR,
Z12Adj_MC_STAR, Z12Adj_MR_STAR );
Z12Adj.SumScatterFrom( Z12Adj_MC_STAR );
Z12Adj_MR_MC = Z12Adj;
Z12Adj_MR_MC.SumScatterUpdate( F(1), Z12Adj_MR_STAR );
Y12.ResizeTo( A12.Height(), A12.Width() );
Adjoint( Z12Adj_MR_MC.LockedLocalMatrix(), Y12.LocalMatrix() );
// A12 := U11 A12
A12_STAR_VR = A12;
U11_STAR_STAR = U11;
LocalTrmm
( LEFT, UPPER, NORMAL, diag, F(1), U11_STAR_STAR, A12_STAR_VR );
A12 = A12_STAR_VR;
// A12 := A12 + 1/2 Y12
Axpy( F(1)/F(2), Y12, A12 );
// A11 := U11 A11 U11'
A11_STAR_STAR = A11;
LocalTwoSidedTrmm( UPPER, diag, A11_STAR_STAR, U11_STAR_STAR );
A11 = A11_STAR_STAR;
// A11 := A11 + (A12 U12' + U12 A12')
A12_STAR_VR = A12;
U12_STAR_VR = U12;
X11_STAR_STAR.ResizeTo( A11.Height(), A11.Width() );
Her2k
( UPPER, NORMAL,
F(1), A12_STAR_VR.LocalMatrix(), U12_STAR_VR.LocalMatrix(),
F(0), X11_STAR_STAR.LocalMatrix() );
A11.SumScatterUpdate( F(1), X11_STAR_STAR );
// A12 := A12 + 1/2 Y12
Axpy( F(1)/F(2), Y12, A12 );
//--------------------------------------------------------------------//
A12_STAR_VR.FreeAlignments();
U12_STAR_MC.FreeAlignments();
U12_STAR_VR.FreeAlignments();
U12Adj_MR_STAR.FreeAlignments();
U12Adj_VC_STAR.FreeAlignments();
X01_MC_STAR.FreeAlignments();
Y12.FreeAlignments();
Z12Adj.FreeAlignments();
Z12Adj_MR_MC.FreeAlignments();
Z12Adj_MC_STAR.FreeAlignments();
Z12Adj_MR_STAR.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
SlideLockedPartitionDownDiagonal
( UTL, /**/ UTR, U00, U01, /**/ U02,
/**/ U10, U11, /**/ U12,
/*************/ /******************/
UBL, /**/ UBR, U20, U21, /**/ U22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
TwoSidedTrmmUVar2( UnitOrNonUnit diag, Matrix<F>& A, const Matrix<F>& U )
{
#ifndef RELEASE
PushCallStack("internal::TwoSidedTrmmUVar2");
if( A.Height() != A.Width() )
throw std::logic_error("A must be square");
if( U.Height() != U.Width() )
throw std::logic_error("Triangular matrices must be square");
if( A.Height() != U.Height() )
throw std::logic_error("A and U must be the same size");
#endif
// Matrix views
Matrix<F>
ATL, ATR, A00, A01, A02,
ABL, ABR, A10, A11, A12,
A20, A21, A22;
Matrix<F>
UTL, UTR, U00, U01, U02,
UBL, UBR, U10, U11, U12,
U20, U21, U22;
// Temporary products
Matrix<F> Y12;
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
LockedPartitionDownDiagonal
( U, UTL, UTR,
UBL, UBR, 0 );
while( ATL.Height() < A.Height() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
LockedRepartitionDownDiagonal
( UTL, /**/ UTR, U00, /**/ U01, U02,
/*************/ /******************/
/**/ U10, /**/ U11, U12,
UBL, /**/ UBR, U20, /**/ U21, U22 );
//--------------------------------------------------------------------//
// A01 := A01 U11'
Trmm( RIGHT, UPPER, ADJOINT, diag, F(1), U11, A01 );
// A01 := A01 + A02 U12'
Gemm( NORMAL, ADJOINT, F(1), A02, U12, F(1), A01 );
// Y12 := U12 A22
Zeros( A12.Height(), A12.Width(), Y12 );
Hemm( RIGHT, UPPER, F(1), A22, U12, F(0), Y12 );
// A12 := U11 A12
Trmm( LEFT, UPPER, NORMAL, diag, F(1), U11, A12 );
// A12 := A12 + 1/2 Y12
Axpy( F(1)/F(2), Y12, A12 );
// A11 := U11 A11 U11'
TwoSidedTrmmUUnb( diag, A11, U11 );
// A11 := A11 + (A12 U12' + U12 A12')
Her2k( UPPER, NORMAL, F(1), A12, U12, F(1), A11 );
// A12 := A12 + 1/2 Y12
Axpy( F(1)/F(2), Y12, A12 );
//--------------------------------------------------------------------//
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
SlideLockedPartitionDownDiagonal
( UTL, /**/ UTR, U00, U01, /**/ U02,
/**/ U10, U11, /**/ U12,
/*************/ /******************/
UBL, /**/ UBR, U20, U21, /**/ U22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
internal::CholeskyLVar3( DistMatrix<F,MC,MR>& A )
{
#ifndef RELEASE
PushCallStack("internal::CholeskyLVar3");
if( A.Height() != A.Width() )
throw std::logic_error
("Can only compute Cholesky factor of square matrices");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<F,MC,MR>
ATL(g), ATR(g), A00(g), A01(g), A02(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
// Temporary matrices
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,VC, STAR> A21_VC_STAR(g);
DistMatrix<F,VR, STAR> A21_VR_STAR(g);
DistMatrix<F,STAR,MC > A21Trans_STAR_MC(g);
DistMatrix<F,STAR,MR > A21Adj_STAR_MR(g);
// Start the algorithm
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
while( ABR.Height() > 0 )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
A21_VR_STAR.AlignWith( A22 );
A21_VC_STAR.AlignWith( A22 );
A21Trans_STAR_MC.AlignWith( A22 );
A21Adj_STAR_MR.AlignWith( A22 );
//--------------------------------------------------------------------//
A11_STAR_STAR = A11;
internal::LocalCholesky( LOWER, A11_STAR_STAR );
A11 = A11_STAR_STAR;
A21_VC_STAR = A21;
internal::LocalTrsm
( RIGHT, LOWER, ADJOINT, NON_UNIT, (F)1, A11_STAR_STAR, A21_VC_STAR );
A21_VR_STAR = A21_VC_STAR;
A21Trans_STAR_MC.TransposeFrom( A21_VC_STAR );
A21Adj_STAR_MR.AdjointFrom( A21_VR_STAR );
// (A21^T[* ,MC])^T A21^H[* ,MR] = A21[MC,* ] A21^H[* ,MR]
// = (A21 A21^H)[MC,MR]
internal::LocalTrrk
( LOWER, TRANSPOSE,
(F)-1, A21Trans_STAR_MC, A21Adj_STAR_MR, (F)1, A22 );
A21.TransposeFrom( A21Trans_STAR_MC );
//--------------------------------------------------------------------//
A21_VR_STAR.FreeAlignments();
A21_VC_STAR.FreeAlignments();
A21Trans_STAR_MC.FreeAlignments();
A21Adj_STAR_MR.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
internal::CholeskyLVar3Naive( DistMatrix<F,MC,MR>& A )
{
#ifndef RELEASE
PushCallStack("internal::CholeskyLVar3Naive");
if( A.Height() != A.Width() )
throw std::logic_error
("Can only compute Cholesky factor of square matrices");
if( A.Grid().VCRank() == 0 )
{
std::cout
<< "CholeskyLVar3Naive exists solely for academic purposes. Please "
"use CholeskyLVar3 in real applications." << std::endl;
}
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<F,MC,MR>
ATL(g), ATR(g), A00(g), A01(g), A02(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
// Temporary matrices
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,VC, STAR> A21_VC_STAR(g);
DistMatrix<F,MC, STAR> A21_MC_STAR(g);
DistMatrix<F,MR, STAR> A21_MR_STAR(g);
// Start the algorithm
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
while( ABR.Height() > 0 )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
A21_VC_STAR.AlignWith( A22 );
A21_MC_STAR.AlignWith( A22 );
A21_MR_STAR.AlignWith( A22 );
//--------------------------------------------------------------------//
A11_STAR_STAR = A11;
internal::LocalCholesky( LOWER, A11_STAR_STAR );
A11 = A11_STAR_STAR;
A21_VC_STAR = A21;
internal::LocalTrsm
( RIGHT, LOWER, ADJOINT, NON_UNIT, (F)1, A11_STAR_STAR, A21_VC_STAR );
A21_MC_STAR = A21_VC_STAR;
A21_MR_STAR = A21_VC_STAR;
// (A21^T[* ,MC])^T A21^H[* ,MR] = A21[MC,* ] A21^H[* ,MR]
// = (A21 A21^H)[MC,MR]
internal::LocalTrrk
( LOWER, ADJOINT, (F)-1, A21_MC_STAR, A21_MR_STAR, (F)1, A22 );
A21 = A21_MC_STAR;
//--------------------------------------------------------------------//
A21_VC_STAR.FreeAlignments();
A21_MC_STAR.FreeAlignments();
A21_MR_STAR.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
TwoSidedTrsmUVar2
( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& U )
{
#ifndef RELEASE
PushCallStack("internal::TwoSidedTrsmUVar2");
if( A.Height() != A.Width() )
throw std::logic_error("A must be square");
if( U.Height() != U.Width() )
throw std::logic_error("Triangular matrices must be square");
if( A.Height() != U.Height() )
throw std::logic_error("A and U must be the same size");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<F>
ATL(g), ATR(g), A00(g), A01(g), A02(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
DistMatrix<F>
UTL(g), UTR(g), U00(g), U01(g), U02(g),
UBL(g), UBR(g), U10(g), U11(g), U12(g),
U20(g), U21(g), U22(g);
// Temporary distributions
DistMatrix<F,MC, STAR> A01_MC_STAR(g);
DistMatrix<F,VC, STAR> A01_VC_STAR(g);
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,STAR,VR > A12_STAR_VR(g);
DistMatrix<F,MC, STAR> F01_MC_STAR(g);
DistMatrix<F,MC, STAR> U01_MC_STAR(g);
DistMatrix<F,VR, STAR> U01_VR_STAR(g);
DistMatrix<F,STAR,MR > U01Adj_STAR_MR(g);
DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
DistMatrix<F,STAR,MR > X11_STAR_MR(g);
DistMatrix<F,MR, STAR> X12Adj_MR_STAR(g);
DistMatrix<F,MR, MC > X12Adj_MR_MC(g);
DistMatrix<F,MR, MC > Y01_MR_MC(g);
DistMatrix<F,MR, STAR> Y01_MR_STAR(g);
DistMatrix<F> X11(g);
DistMatrix<F> Y01(g);
Matrix<F> X12Local;
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
LockedPartitionDownDiagonal
( U, UTL, UTR,
UBL, UBR, 0 );
while( ATL.Height() < A.Height() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
LockedRepartitionDownDiagonal
( UTL, /**/ UTR, U00, /**/ U01, U02,
/*************/ /******************/
/**/ U10, /**/ U11, U12,
UBL, /**/ UBR, U20, /**/ U21, U22 );
A01_MC_STAR.AlignWith( U01 );
Y01.AlignWith( A01 );
Y01_MR_STAR.AlignWith( A00 );
U01_MC_STAR.AlignWith( A00 );
U01_VR_STAR.AlignWith( A00 );
U01Adj_STAR_MR.AlignWith( A00 );
X11_STAR_MR.AlignWith( U01 );
X11.AlignWith( A11 );
X12Adj_MR_STAR.AlignWith( A02 );
X12Adj_MR_MC.AlignWith( A12 );
F01_MC_STAR.AlignWith( A00 );
//--------------------------------------------------------------------//
// Y01 := A00 U01
U01_MC_STAR = U01;
U01_VR_STAR = U01_MC_STAR;
U01Adj_STAR_MR.AdjointFrom( U01_VR_STAR );
Y01_MR_STAR.ResizeTo( A01.Height(), A01.Width() );
F01_MC_STAR.ResizeTo( A01.Height(), A01.Width() );
Zero( Y01_MR_STAR );
Zero( F01_MC_STAR );
LocalSymmetricAccumulateLU
( ADJOINT,
F(1), A00, U01_MC_STAR, U01Adj_STAR_MR, F01_MC_STAR, Y01_MR_STAR );
Y01_MR_MC.SumScatterFrom( Y01_MR_STAR );
Y01 = Y01_MR_MC;
Y01.SumScatterUpdate( F(1), F01_MC_STAR );
// X11 := U01' A01
X11_STAR_MR.ResizeTo( A11.Height(), A11.Width() );
LocalGemm( ADJOINT, NORMAL, F(1), U01_MC_STAR, A01, F(0), X11_STAR_MR );
// A01 := A01 - Y01
Axpy( F(-1), Y01, A01 );
A01_MC_STAR = A01;
// A11 := A11 - triu(X11 + A01' U01) = A11 - (U01 A01 + A01' U01)
LocalGemm( ADJOINT, NORMAL, F(1), A01_MC_STAR, U01, F(1), X11_STAR_MR );
X11.SumScatterFrom( X11_STAR_MR );
MakeTrapezoidal( LEFT, UPPER, 0, X11 );
Axpy( F(-1), X11, A11 );
// A01 := A01 inv(U11)
U11_STAR_STAR = U11;
A01_VC_STAR = A01_MC_STAR;
LocalTrsm
( RIGHT, UPPER, NORMAL, diag, F(1), U11_STAR_STAR, A01_VC_STAR );
A01 = A01_VC_STAR;
// A11 := inv(U11)' A11 inv(U11)
A11_STAR_STAR = A11;
LocalTwoSidedTrsm( UPPER, diag, A11_STAR_STAR, U11_STAR_STAR );
A11 = A11_STAR_STAR;
// A12 := A12 - A02' U01
X12Adj_MR_STAR.ResizeTo( A12.Width(), A12.Height() );
LocalGemm
( ADJOINT, NORMAL, F(1), A02, U01_MC_STAR, F(0), X12Adj_MR_STAR );
X12Adj_MR_MC.SumScatterFrom( X12Adj_MR_STAR );
Adjoint( X12Adj_MR_MC.LockedLocalMatrix(), X12Local );
Axpy( F(-1), X12Local, A12.LocalMatrix() );
// A12 := inv(U11)' A12
A12_STAR_VR = A12;
LocalTrsm
( LEFT, UPPER, ADJOINT, diag, F(1), U11_STAR_STAR, A12_STAR_VR );
A12 = A12_STAR_VR;
//--------------------------------------------------------------------//
A01_MC_STAR.FreeAlignments();
F01_MC_STAR.FreeAlignments();
U01_MC_STAR.FreeAlignments();
U01_VR_STAR.FreeAlignments();
U01Adj_STAR_MR.FreeAlignments();
X11.FreeAlignments();
X11_STAR_MR.FreeAlignments();
X12Adj_MR_STAR.FreeAlignments();
X12Adj_MR_MC.FreeAlignments();
Y01.FreeAlignments();
Y01_MR_STAR.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
SlideLockedPartitionDownDiagonal
( UTL, /**/ UTR, U00, U01, /**/ U02,
/**/ U10, U11, /**/ U12,
/*************/ /******************/
UBL, /**/ UBR, U20, U21, /**/ U22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
TrtrsmLLN
( UnitOrNonUnit diag, F alpha, const Matrix<F>& L, Matrix<F>& X,
bool checkIfSingular )
{
#ifndef RELEASE
PushCallStack("internal::TrtrsmLLN");
#endif
// Matrix views
Matrix<F>
LTL, LTR, L00, L01, L02,
LBL, LBR, L10, L11, L12,
L20, L21, L22;
Matrix<F>
XTL, XTR, X00, X01, X02,
XBL, XBR, X10, X11, X12,
X20, X21, X22;
Matrix<F> Z11;
// Start the algorithm
ScaleTrapezoid( alpha, LEFT, LOWER, 0, X );
LockedPartitionDownDiagonal
( L, LTL, LTR,
LBL, LBR, 0 );
PartitionDownDiagonal
( X, XTL, XTR,
XBL, XBR, 0 );
while( XBR.Height() > 0 )
{
LockedRepartitionDownDiagonal
( LTL, /**/ LTR, L00, /**/ L01, L02,
/*************/ /******************/
/**/ L10, /**/ L11, L12,
LBL, /**/ LBR, L20, /**/ L21, L22 );
RepartitionDownDiagonal
( XTL, /**/ XTR, X00, /**/ X01, X02,
/*************/ /******************/
/**/ X10, /**/ X11, X12,
XBL, /**/ XBR, X20, /**/ X21, X22 );
//--------------------------------------------------------------------//
Trsm( LEFT, LOWER, NORMAL, diag, F(1), L11, X10, checkIfSingular );
TrtrsmLLNUnb( diag, F(1), L11, X11 );
Gemm( NORMAL, NORMAL, F(-1), L21, X10, F(1), X20 );
Z11 = X11;
MakeTrapezoidal( LEFT, LOWER, 0, Z11 );
Gemm( NORMAL, NORMAL, F(-1), L21, Z11, F(1), X21 );
//--------------------------------------------------------------------//
SlideLockedPartitionDownDiagonal
( LTL, /**/ LTR, L00, L01, /**/ L02,
/**/ L10, L11, /**/ L12,
/*************/ /******************/
LBL, /**/ LBR, L20, L21, /**/ L22 );
SlidePartitionDownDiagonal
( XTL, /**/ XTR, X00, X01, /**/ X02,
/**/ X10, X11, /**/ X12,
/*************/ /******************/
XBL, /**/ XBR, X20, X21, /**/ X22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
internal::ApplyPackedReflectorsLUVF
( Conjugation conjugation, int offset,
const DistMatrix<Complex<R>,MC,MR >& H,
const DistMatrix<Complex<R>,MD,STAR>& t,
DistMatrix<Complex<R>,MC,MR >& A )
{
#ifndef RELEASE
PushCallStack("internal::ApplyPackedReflectorsLUVF");
if( H.Grid() != t.Grid() || t.Grid() != A.Grid() )
throw std::logic_error
("{H,t,A} must be distributed over the same grid");
if( offset > H.Height() )
throw std::logic_error("Transforms cannot extend above matrix");
if( offset < 0 )
throw std::logic_error("Transforms cannot extend below matrix");
if( H.Width() != A.Height() )
throw std::logic_error
("Width of transforms must equal height of target matrix");
if( t.Height() != H.DiagonalLength( offset ) )
throw std::logic_error("t must be the same length as H's offset diag");
if( !t.AlignedWithDiagonal( H, offset ) )
throw std::logic_error("t must be aligned with H's 'offset' diagonal");
#endif
typedef Complex<R> C;
const Grid& g = H.Grid();
// Matrix views
DistMatrix<C,MC,MR>
HTL(g), HTR(g), H00(g), H01(g), H02(g), HPan(g),
HBL(g), HBR(g), H10(g), H11(g), H12(g),
H20(g), H21(g), H22(g);
DistMatrix<C,MC,MR>
AT(g), A0(g), ATop(g),
AB(g), A1(g),
A2(g);
DistMatrix<C,MD,STAR>
tT(g), t0(g),
tB(g), t1(g),
t2(g);
DistMatrix<C,MC, MR > HPanCopy(g);
DistMatrix<C,VC, STAR> HPan_VC_STAR(g);
DistMatrix<C,MC, STAR> HPan_MC_STAR(g);
DistMatrix<C,STAR,STAR> t1_STAR_STAR(g);
DistMatrix<C,STAR,STAR> SInv_STAR_STAR(g);
DistMatrix<C,STAR,MR > Z_STAR_MR(g);
DistMatrix<C,STAR,VR > Z_STAR_VR(g);
LockedPartitionDownDiagonal
( H, HTL, HTR,
HBL, HBR, 0 );
LockedPartitionDown
( t, tT,
tB, 0 );
PartitionDown
( A, AT,
AB, 0 );
while( HTL.Height() < H.Height() && HTL.Width() < H.Width() )
{
LockedRepartitionDownDiagonal
( HTL, /**/ HTR, H00, /**/ H01, H02,
/*************/ /******************/
/**/ H10, /**/ H11, H12,
HBL, /**/ HBR, H20, /**/ H21, H22 );
const int HPanHeight = H01.Height() + H11.Height();
const int HPanOffset =
std::min( H11.Width(), std::max(offset-H00.Width(),0) );
const int HPanWidth = H11.Width()-HPanOffset;
HPan.LockedView( H, 0, H00.Width()+HPanOffset, HPanHeight, HPanWidth );
LockedRepartitionDown
( tT, t0,
/**/ /**/
t1,
tB, t2, HPanWidth );
RepartitionDown
( AT, A0,
/**/ /**/
A1,
AB, A2 );
ATop.View2x1( A0,
A1 );
HPan_MC_STAR.AlignWith( ATop );
Z_STAR_MR.AlignWith( ATop );
Z_STAR_VR.AlignWith( ATop );
Z_STAR_MR.ResizeTo( HPan.Width(), ATop.Width() );
SInv_STAR_STAR.ResizeTo( HPan.Width(), HPan.Width() );
Zero( SInv_STAR_STAR );
//--------------------------------------------------------------------//
HPanCopy = HPan;
MakeTrapezoidal( RIGHT, UPPER, offset, HPanCopy );
SetDiagonalToOne( RIGHT, offset, HPanCopy );
HPan_VC_STAR = HPanCopy;
Herk
( UPPER, ADJOINT,
(C)1, HPan_VC_STAR.LockedLocalMatrix(),
(C)0, SInv_STAR_STAR.LocalMatrix() );
SInv_STAR_STAR.SumOverGrid();
t1_STAR_STAR = t1;
FixDiagonal( conjugation, t1_STAR_STAR, SInv_STAR_STAR );
HPan_MC_STAR = HPanCopy;
internal::LocalGemm
( ADJOINT, NORMAL, (C)1, HPan_MC_STAR, ATop, (C)0, Z_STAR_MR );
Z_STAR_VR.SumScatterFrom( Z_STAR_MR );
internal::LocalTrsm
( LEFT, UPPER, ADJOINT, NON_UNIT, (C)1, SInv_STAR_STAR, Z_STAR_VR );
Z_STAR_MR = Z_STAR_VR;
internal::LocalGemm
( NORMAL, NORMAL, (C)-1, HPan_MC_STAR, Z_STAR_MR, (C)1, ATop );
//--------------------------------------------------------------------//
HPan_MC_STAR.FreeAlignments();
Z_STAR_MR.FreeAlignments();
Z_STAR_VR.FreeAlignments();
SlideLockedPartitionDownDiagonal
( HTL, /**/ HTR, H00, H01, /**/ H02,
/**/ H10, H11, /**/ H12,
/*************/ /******************/
HBL, /**/ HBR, H20, H21, /**/ H22 );
SlideLockedPartitionDown
( tT, t0,
t1,
/**/ /**/
tB, t2 );
SlidePartitionDown
( AT, A0,
A1,
/**/ /**/
AB, A2 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
int QDWH
( Matrix<F>& A,
typename Base<F>::type lowerBound,
typename Base<F>::type upperBound )
{
#ifndef RELEASE
PushCallStack("QDWH");
#endif
typedef typename Base<F>::type R;
const int height = A.Height();
const int width = A.Width();
const R oneHalf = R(1)/R(2);
const R oneThird = R(1)/R(3);
if( height < width )
throw std::logic_error("Height cannot be less than width");
const R epsilon = lapack::MachineEpsilon<R>();
const R tol = 5*epsilon;
const R cubeRootTol = Pow(tol,oneThird);
// Form the first iterate
Scale( 1/upperBound, A );
int numIts=0;
R frobNormADiff;
Matrix<F> ALast;
Matrix<F> Q( height+width, width );
Matrix<F> QT, QB;
PartitionDown( Q, QT,
QB, height );
Matrix<F> C;
Matrix<F> ATemp;
do
{
++numIts;
ALast = A;
R L2;
Complex<R> dd, sqd;
if( Abs(1-lowerBound) < tol )
{
L2 = 1;
dd = 0;
sqd = 1;
}
else
{
L2 = lowerBound*lowerBound;
dd = Pow( 4*(1-L2)/(L2*L2), oneThird );
sqd = Sqrt( 1+dd );
}
const Complex<R> arg = 8 - 4*dd + 8*(2-L2)/(L2*sqd);
const R a = (sqd + Sqrt( arg )/2).real;
const R b = (a-1)*(a-1)/4;
const R c = a+b-1;
const Complex<R> alpha = a-b/c;
const Complex<R> beta = b/c;
lowerBound = lowerBound*(a+b*L2)/(1+c*L2);
if( c > 100 )
{
//
// The standard QR-based algorithm
//
QT = A;
Scale( Sqrt(c), QT );
MakeIdentity( QB );
ExplicitQR( Q );
Gemm( NORMAL, ADJOINT, alpha/Sqrt(c), QT, QB, beta, A );
}
else
{
//
// Use faster Cholesky-based algorithm since A is well-conditioned
//
Identity( width, width, C );
Herk( LOWER, ADJOINT, F(c), A, F(1), C );
Cholesky( LOWER, C );
ATemp = A;
Trsm( RIGHT, LOWER, ADJOINT, NON_UNIT, F(1), C, ATemp );
Trsm( RIGHT, LOWER, NORMAL, NON_UNIT, F(1), C, ATemp );
Scale( beta, A );
Axpy( alpha, ATemp, A );
}
Axpy( F(-1), A, ALast );
frobNormADiff = Norm( ALast, FROBENIUS_NORM );
}
while( frobNormADiff > cubeRootTol || Abs(1-lowerBound) > tol );
#ifndef RELEASE
PopCallStack();
#endif
return numIts;
}
inline void
internal::ApplyPackedReflectorsLUVF
( int offset,
const DistMatrix<R,MC,MR>& H,
DistMatrix<R,MC,MR>& A )
{
#ifndef RELEASE
PushCallStack("internal::ApplyPackedReflectorsLUVF");
if( H.Grid() != A.Grid() )
throw std::logic_error("{H,A} must be distributed over the same grid");
if( offset > H.Height() )
throw std::logic_error("Transforms cannot extend above matrix");
if( offset < 0 )
throw std::logic_error("Transforms cannot extend below matrix");
if( H.Width() != A.Height() )
throw std::logic_error
("Width of transforms must equal height of target matrix");
#endif
const Grid& g = H.Grid();
// Matrix views
DistMatrix<R,MC,MR>
HTL(g), HTR(g), H00(g), H01(g), H02(g), HPan(g),
HBL(g), HBR(g), H10(g), H11(g), H12(g),
H20(g), H21(g), H22(g);
DistMatrix<R,MC,MR>
AT(g), A0(g), ATop(g),
AB(g), A1(g),
A2(g);
DistMatrix<R,MC, MR > HPanCopy(g);
DistMatrix<R,VC, STAR> HPan_VC_STAR(g);
DistMatrix<R,MC, STAR> HPan_MC_STAR(g);
DistMatrix<R,STAR,STAR> SInv_STAR_STAR(g);
DistMatrix<R,STAR,MR > Z_STAR_MR(g);
DistMatrix<R,STAR,VR > Z_STAR_VR(g);
LockedPartitionDownDiagonal
( H, HTL, HTR,
HBL, HBR, 0 );
PartitionDown
( A, AT,
AB, 0 );
while( HTL.Height() < H.Height() && HTL.Width() < H.Width() )
{
LockedRepartitionDownDiagonal
( HTL, /**/ HTR, H00, /**/ H01, H02,
/*************/ /******************/
/**/ H10, /**/ H11, H12,
HBL, /**/ HBR, H20, /**/ H21, H22 );
const int HPanHeight = H01.Height() + H11.Height();
const int HPanOffset =
std::min( H11.Width(), std::max(offset-H00.Width(),0) );
const int HPanWidth = H11.Width()-HPanOffset;
HPan.LockedView( H, 0, H00.Width()+HPanOffset, HPanHeight, HPanWidth );
RepartitionDown
( AT, A0,
/**/ /**/
A1,
AB, A2 );
ATop.View2x1( A0,
A1 );
HPan_MC_STAR.AlignWith( ATop );
Z_STAR_MR.AlignWith( ATop );
Z_STAR_VR.AlignWith( ATop );
Z_STAR_MR.ResizeTo( HPan.Width(), ATop.Width() );
SInv_STAR_STAR.ResizeTo( HPan.Width(), HPan.Width() );
Zero( SInv_STAR_STAR );
//--------------------------------------------------------------------//
HPanCopy = HPan;
MakeTrapezoidal( RIGHT, UPPER, offset, HPanCopy );
SetDiagonalToOne( RIGHT, offset, HPanCopy );
HPan_VC_STAR = HPanCopy;
Syrk
( UPPER, TRANSPOSE,
(R)1, HPan_VC_STAR.LockedLocalMatrix(),
(R)0, SInv_STAR_STAR.LocalMatrix() );
SInv_STAR_STAR.SumOverGrid();
HalveMainDiagonal( SInv_STAR_STAR );
HPan_MC_STAR = HPanCopy;
internal::LocalGemm
( TRANSPOSE, NORMAL,
(R)1, HPan_MC_STAR, ATop, (R)0, Z_STAR_MR );
Z_STAR_VR.SumScatterFrom( Z_STAR_MR );
internal::LocalTrsm
( LEFT, UPPER, TRANSPOSE, NON_UNIT,
(R)1, SInv_STAR_STAR, Z_STAR_VR );
Z_STAR_MR = Z_STAR_VR;
internal::LocalGemm
( NORMAL, NORMAL,
(R)-1, HPan_MC_STAR, Z_STAR_MR, (R)1, ATop );
//--------------------------------------------------------------------//
HPan_MC_STAR.FreeAlignments();
Z_STAR_MR.FreeAlignments();
Z_STAR_VR.FreeAlignments();
SlideLockedPartitionDownDiagonal
( HTL, /**/ HTR, H00, H01, /**/ H02,
/**/ H10, H11, /**/ H12,
/*************/ /******************/
HBL, /**/ HBR, H20, H21, /**/ H22 );
SlidePartitionDown
( AT, A0,
A1,
/**/ /**/
AB, A2 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
MakeTrapezoidal
( LeftOrRight side, UpperOrLower uplo, int offset,
DistMatrix<T,U,V>& A )
{
#ifndef RELEASE
PushCallStack("MakeTrapezoidal");
#endif
const int height = A.Height();
const int width = A.Width();
const int localHeight = A.LocalHeight();
const int localWidth = A.LocalWidth();
const int colShift = A.ColShift();
const int rowShift = A.RowShift();
const int colStride = A.ColStride();
const int rowStride = A.RowStride();
T* buffer = A.Buffer();
const int ldim = A.LDim();
if( uplo == LOWER )
{
#ifdef HAVE_OPENMP
#pragma omp parallel for
#endif
for( int jLocal=0; jLocal<localWidth; ++jLocal )
{
const int j = rowShift + jLocal*rowStride;
const int lastZeroRow =
( side==LEFT ? j-offset-1
: j-offset+height-width-1 );
if( lastZeroRow >= 0 )
{
const int boundary = std::min( lastZeroRow+1, height );
const int numZeroRows =
Length_( boundary, colShift, colStride );
MemZero( &buffer[jLocal*ldim], numZeroRows );
}
}
}
else
{
#ifdef HAVE_OPENMP
#pragma omp parallel for
#endif
for( int jLocal=0; jLocal<localWidth; ++jLocal )
{
const int j = rowShift + jLocal*rowStride;
const int firstZeroRow =
( side==LEFT ? std::max(j-offset+1,0)
: std::max(j-offset+height-width+1,0) );
const int numNonzeroRows =
Length_(firstZeroRow,colShift,colStride);
if( numNonzeroRows < localHeight )
{
T* col = &buffer[numNonzeroRows+jLocal*ldim];
MemZero( col, localHeight-numNonzeroRows );
}
}
}
#ifndef RELEASE
PopCallStack();
#endif
}
CallStackEntry( string s )
{
if( !uncaught_exception() )
PushCallStack(s);
}
inline void
Trsm
( LeftOrRight side, UpperOrLower uplo,
Orientation orientation, UnitOrNonUnit diag,
F alpha, const DistMatrix<F>& A, DistMatrix<F>& B,
bool checkIfSingular )
{
#ifndef RELEASE
PushCallStack("Trsm");
if( A.Grid() != B.Grid() )
throw std::logic_error("A and B must use the same grid");
if( A.Height() != A.Width() )
throw std::logic_error("A must be square");
if( side == LEFT )
{
if( A.Height() != B.Height() )
throw std::logic_error("Nonconformal Trsm");
}
else
{
if( A.Height() != B.Width() )
throw std::logic_error("Nonconformal Trsm");
}
#endif
const int p = B.Grid().Size();
if( side == LEFT && uplo == LOWER )
{
if( orientation == NORMAL )
{
if( B.Width() > 5*p )
internal::TrsmLLNLarge( diag, alpha, A, B, checkIfSingular );
else
internal::TrsmLLNMedium( diag, alpha, A, B, checkIfSingular );
}
else
{
if( B.Width() > 5*p )
internal::TrsmLLTLarge
( orientation, diag, alpha, A, B, checkIfSingular );
else
internal::TrsmLLTMedium
( orientation, diag, alpha, A, B, checkIfSingular );
}
}
else if( side == LEFT && uplo == UPPER )
{
if( orientation == NORMAL )
{
if( B.Width() > 5*p )
internal::TrsmLUNLarge( diag, alpha, A, B, checkIfSingular );
else
internal::TrsmLUNMedium( diag, alpha, A, B, checkIfSingular );
}
else
{
if( B.Width() > 5*p )
internal::TrsmLUTLarge
( orientation, diag, alpha, A, B, checkIfSingular );
else
internal::TrsmLUTMedium
( orientation, diag, alpha, A, B, checkIfSingular );
}
}
else if( side == RIGHT && uplo == LOWER )
{
if( orientation == NORMAL )
internal::TrsmRLN( diag, alpha, A, B, checkIfSingular );
else
internal::TrsmRLT
( orientation, diag, alpha, A, B, checkIfSingular );
}
else if( side == RIGHT && uplo == UPPER )
{
if( orientation == NORMAL )
internal::TrsmRUN( diag, alpha, A, B, checkIfSingular );
else
internal::TrsmRUT
( orientation, diag, alpha, A, B, checkIfSingular );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
ReformNormalMatrix
( DistMatrix<Complex<R>,MC,MR >& A,
const DistMatrix<R, VR,STAR>& w,
const DistMatrix<Complex<R>,MC,MR >& Z,
const ComplexFunctor& f )
{
#ifndef RELEASE
PushCallStack("hermitian_function::ReformNormalMatrix");
#endif
const Grid& g = A.Grid();
typedef Complex<R> C;
DistMatrix<C,MC,MR> ZL(g), ZR(g),
Z0(g), Z1(g), Z2(g);
DistMatrix<R,VR,STAR> wT(g), w0(g),
wB(g), w1(g),
w2(g);
DistMatrix<C,MC, STAR> Z1_MC_STAR(g);
DistMatrix<C,VR, STAR> Z1_VR_STAR(g);
DistMatrix<C,STAR,MR > Z1Adj_STAR_MR(g);
DistMatrix<R,STAR,STAR> w1_STAR_STAR(g);
Zero( A );
LockedPartitionRight( Z, ZL, ZR, 0 );
LockedPartitionDown
( w, wT,
wB, 0 );
while( ZL.Width() < Z.Width() )
{
LockedRepartitionRight
( ZL, /**/ ZR,
Z0, /**/ Z1, Z2 );
LockedRepartitionDown
( wT, w0,
/**/ /**/
w1,
wB, w2 );
Z1_MC_STAR.AlignWith( A );
Z1_VR_STAR.AlignWith( A );
Z1Adj_STAR_MR.AlignWith( A );
//--------------------------------------------------------------------//
Z1_MC_STAR = Z1;
Z1_VR_STAR = Z1_MC_STAR;
w1_STAR_STAR = w1;
// Scale Z1[VR,* ] with the modified eigenvalues
const int width = Z1_VR_STAR.Width();
const int localHeight = Z1_VR_STAR.LocalHeight();
for( int j=0; j<width; ++j )
{
const C conjOmega = Conj(f(w1_STAR_STAR.GetLocalEntry(j,0)));
C* buffer = Z1_VR_STAR.LocalBuffer(0,j);
for( int iLocal=0; iLocal<localHeight; ++iLocal )
buffer[iLocal] *= conjOmega;
}
Z1Adj_STAR_MR.AdjointFrom( Z1_VR_STAR );
internal::LocalGemm
( NORMAL, NORMAL, (C)1, Z1_MC_STAR, Z1Adj_STAR_MR, (C)1, A );
//--------------------------------------------------------------------//
Z1Adj_STAR_MR.FreeAlignments();
Z1_VR_STAR.FreeAlignments();
Z1_MC_STAR.FreeAlignments();
SlideLockedPartitionDown
( wT, w0,
w1,
/**/ /**/
wB, w2 );
SlideLockedPartitionRight
( ZL, /**/ ZR,
Z0, Z1, /**/ Z2 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
Var3Unb( Orientation orientation, Matrix<F>& A, Matrix<F>& d )
{
#ifndef RELEASE
PushCallStack("ldl::Var3Unb");
if( A.Height() != A.Width() )
throw std::logic_error("A must be square");
if( d.Viewing() && (d.Height() != A.Height() || d.Width() != 1) )
throw std::logic_error
("d must be a column vector the same height as A");
if( orientation == NORMAL )
throw std::logic_error("Can only perform LDL^T or LDL^H");
#endif
const int n = A.Height();
if( !d.Viewing() )
d.ResizeTo( n, 1 );
F* ABuffer = A.Buffer();
F* dBuffer = d.Buffer();
const int ldim = A.LDim();
for( int j=0; j<n; ++j )
{
const int a21Height = n - (j+1);
// Extract and store the diagonal of D
const F alpha11 = ABuffer[j+j*ldim];
if( alpha11 == F(0) )
throw SingularMatrixException();
dBuffer[j] = alpha11;
F* RESTRICT a21 = &ABuffer[(j+1)+j*ldim];
if( orientation == ADJOINT )
{
// A22 := A22 - a21 (a21 / alpha11)^H
for( int k=0; k<a21Height; ++k )
{
const F beta = Conj(a21[k]/alpha11);
F* RESTRICT A22Col = &ABuffer[(j+1)+(j+1+k)*ldim];
for( int i=k; i<a21Height; ++i )
A22Col[i] -= a21[i]*beta;
}
}
else
{
// A22 := A22 - a21 (a21 / alpha11)^T
for( int k=0; k<a21Height; ++k )
{
const F beta = a21[k]/alpha11;
F* RESTRICT A22Col = &ABuffer[(j+1)+(j+1+k)*ldim];
for( int i=k; i<a21Height; ++i )
A22Col[i] -= a21[i]*beta;
}
}
// a21 := a21 / alpha11
for( int i=0; i<a21Height; ++i )
a21[i] /= alpha11;
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
ReformHermitianMatrix
( UpperOrLower uplo,
DistMatrix<R,MC,MR>& A,
const DistMatrix<R,VR,STAR>& w,
const DistMatrix<R,MC,MR>& Z,
const RealFunctor& f )
{
#ifndef RELEASE
PushCallStack("hermitian_function::ReformHermitianMatrix");
#endif
const Grid& g = A.Grid();
DistMatrix<R,MC,MR> ZL(g), ZR(g),
Z0(g), Z1(g), Z2(g);
DistMatrix<R,VR,STAR> wT(g), w0(g),
wB(g), w1(g),
w2(g);
DistMatrix<R,MC, STAR> Z1_MC_STAR(g);
DistMatrix<R,VR, STAR> Z1_VR_STAR(g);
DistMatrix<R,STAR,MR > Z1Trans_STAR_MR(g);
DistMatrix<R,STAR,STAR> w1_STAR_STAR(g);
if( uplo == LOWER )
MakeTrapezoidal( LEFT, UPPER, 1, A );
else
MakeTrapezoidal( LEFT, LOWER, -1, A );
LockedPartitionRight( Z, ZL, ZR, 0 );
LockedPartitionDown
( w, wT,
wB, 0 );
while( ZL.Width() < Z.Width() )
{
LockedRepartitionRight
( ZL, /**/ ZR,
Z0, /**/ Z1, Z2 );
LockedRepartitionDown
( wT, w0,
/**/ /**/
w1,
wB, w2 );
Z1_MC_STAR.AlignWith( A );
Z1_VR_STAR.AlignWith( A );
Z1Trans_STAR_MR.AlignWith( A );
//--------------------------------------------------------------------//
Z1_MC_STAR = Z1;
Z1_VR_STAR = Z1_MC_STAR;
w1_STAR_STAR = w1;
// Scale Z1[VR,* ] with the modified eigenvalues
const int width = Z1_VR_STAR.Width();
const int localHeight = Z1_VR_STAR.LocalHeight();
for( int j=0; j<width; ++j )
{
const R omega = f(w1_STAR_STAR.GetLocalEntry(j,0));
R* buffer = Z1_VR_STAR.LocalBuffer(0,j);
for( int iLocal=0; iLocal<localHeight; ++iLocal )
buffer[iLocal] *= omega;
}
Z1Trans_STAR_MR.TransposeFrom( Z1_VR_STAR );
internal::LocalTrrk( uplo, (R)1, Z1_MC_STAR, Z1Trans_STAR_MR, (R)1, A );
//--------------------------------------------------------------------//
Z1Trans_STAR_MR.FreeAlignments();
Z1_VR_STAR.FreeAlignments();
Z1_MC_STAR.FreeAlignments();
SlideLockedPartitionDown
( wT, w0,
w1,
/**/ /**/
wB, w2 );
SlideLockedPartitionRight
( ZL, /**/ ZR,
Z0, Z1, /**/ Z2 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
LocalTrmmAccumulateLLN
( Orientation orientation, UnitOrNonUnit diag, T alpha,
const DistMatrix<T,MC, MR >& L,
const DistMatrix<T,STAR,MR >& XAdjOrTrans_STAR_MR,
DistMatrix<T,MC, STAR>& Z_MC_STAR )
{
#ifndef RELEASE
PushCallStack("internal::LocalTrmmAccumulateLLN");
if( L.Grid() != XAdjOrTrans_STAR_MR.Grid() ||
XAdjOrTrans_STAR_MR.Grid() != Z_MC_STAR.Grid() )
throw std::logic_error
("{L,X,Z} must be distributed over the same grid");
if( L.Height() != L.Width() ||
L.Height() != XAdjOrTrans_STAR_MR.Width() ||
L.Height() != Z_MC_STAR.Height() ||
XAdjOrTrans_STAR_MR.Height() != Z_MC_STAR.Width() )
{
std::ostringstream msg;
msg << "Nonconformal LocalTrmmAccumulateLLN: \n"
<< " L ~ " << L.Height() << " x " << L.Width() << "\n"
<< " X^H/T[* ,MR] ~ " << XAdjOrTrans_STAR_MR.Height() << " x "
<< XAdjOrTrans_STAR_MR.Width() << "\n"
<< " Z[MC,* ] ~ " << Z_MC_STAR.Height() << " x "
<< Z_MC_STAR.Width() << "\n";
throw std::logic_error( msg.str().c_str() );
}
if( XAdjOrTrans_STAR_MR.RowAlignment() != L.RowAlignment() ||
Z_MC_STAR.ColAlignment() != L.ColAlignment() )
throw std::logic_error("Partial matrix distributions are misaligned");
#endif
const Grid& g = L.Grid();
// Matrix views
DistMatrix<T>
LTL(g), LTR(g), L00(g), L01(g), L02(g),
LBL(g), LBR(g), L10(g), L11(g), L12(g),
L20(g), L21(g), L22(g);
DistMatrix<T> D11(g);
DistMatrix<T,STAR,MR>
XLAdjOrTrans_STAR_MR(g), XRAdjOrTrans_STAR_MR(g),
X0AdjOrTrans_STAR_MR(g), X1AdjOrTrans_STAR_MR(g),
X2AdjOrTrans_STAR_MR(g);
DistMatrix<T,MC,STAR>
ZT_MC_STAR(g), Z0_MC_STAR(g),
ZB_MC_STAR(g), Z1_MC_STAR(g),
Z2_MC_STAR(g);
const int ratio = std::max( g.Height(), g.Width() );
PushBlocksizeStack( ratio*Blocksize() );
LockedPartitionDownDiagonal
( L, LTL, LTR,
LBL, LBR, 0 );
LockedPartitionRight
( XAdjOrTrans_STAR_MR, XLAdjOrTrans_STAR_MR, XRAdjOrTrans_STAR_MR, 0 );
PartitionDown
( Z_MC_STAR, ZT_MC_STAR,
ZB_MC_STAR, 0 );
while( LTL.Height() < L.Height() )
{
LockedRepartitionDownDiagonal
( LTL, /**/ LTR, L00, /**/ L01, L02,
/*************/ /******************/
/**/ L10, /**/ L11, L12,
LBL, /**/ LBR, L20, /**/ L21, L22 );
LockedRepartitionRight
( XLAdjOrTrans_STAR_MR, /**/ XRAdjOrTrans_STAR_MR,
X0AdjOrTrans_STAR_MR, /**/ X1AdjOrTrans_STAR_MR,
X2AdjOrTrans_STAR_MR );
RepartitionDown
( ZT_MC_STAR, Z0_MC_STAR,
/**********/ /**********/
Z1_MC_STAR,
ZB_MC_STAR, Z2_MC_STAR );
D11.AlignWith( L11 );
//--------------------------------------------------------------------//
D11 = L11;
MakeTrapezoidal( LEFT, LOWER, 0, D11 );
if( diag == UNIT )
SetDiagonalToOne( D11 );
LocalGemm
( NORMAL, orientation,
alpha, D11, X1AdjOrTrans_STAR_MR, T(1), Z1_MC_STAR );
LocalGemm
( NORMAL, orientation,
alpha, L21, X1AdjOrTrans_STAR_MR, T(1), Z2_MC_STAR );
//--------------------------------------------------------------------//
D11.FreeAlignments();
SlideLockedPartitionDownDiagonal
( LTL, /**/ LTR, L00, L01, /**/ L02,
/**/ L10, L11, /**/ L12,
/*************/ /******************/
LBL, /**/ LBR, L20, L21, /**/ L22 );
SlideLockedPartitionRight
( XLAdjOrTrans_STAR_MR, /**/ XRAdjOrTrans_STAR_MR,
X0AdjOrTrans_STAR_MR, X1AdjOrTrans_STAR_MR, /**/ X2AdjOrTrans_STAR_MR
);
SlidePartitionDown
( ZT_MC_STAR, Z0_MC_STAR,
Z1_MC_STAR,
/**********/ /**********/
ZB_MC_STAR, Z2_MC_STAR );
}
PopBlocksizeStack();
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
TrtrmmUVar1( Orientation orientation, DistMatrix<T>& U )
{
#ifndef RELEASE
PushCallStack("internal::TrtrmmUVar1");
if( U.Height() != U.Width() )
throw std::logic_error("U must be square");
#endif
const Grid& g = U.Grid();
// Matrix views
DistMatrix<T>
UTL(g), UTR(g), U00(g), U01(g), U02(g),
UBL(g), UBR(g), U10(g), U11(g), U12(g),
U20(g), U21(g), U22(g);
// Temporary distributions
DistMatrix<T,MC, STAR> U01_MC_STAR(g);
DistMatrix<T,VC, STAR> U01_VC_STAR(g);
DistMatrix<T,VR, STAR> U01_VR_STAR(g);
DistMatrix<T,STAR,MR > U01AdjOrTrans_STAR_MR(g);
DistMatrix<T,STAR,STAR> U11_STAR_STAR(g);
U01_MC_STAR.AlignWith( U );
U01_VC_STAR.AlignWith( U );
U01_VR_STAR.AlignWith( U );
U01AdjOrTrans_STAR_MR.AlignWith( U );
PartitionDownDiagonal
( U, UTL, UTR,
UBL, UBR, 0 );
while( UTL.Height() < U.Height() && UTL.Width() < U.Height() )
{
RepartitionDownDiagonal
( UTL, /**/ UTR, U00, /**/ U01, U02,
/*************/ /******************/
/**/ U10, /**/ U11, U12,
UBL, /**/ UBR, U20, /**/ U21, U22 );
//--------------------------------------------------------------------//
U01_MC_STAR = U01;
U01_VC_STAR = U01_MC_STAR;
U01_VR_STAR = U01_VC_STAR;
if( orientation == ADJOINT )
U01AdjOrTrans_STAR_MR.AdjointFrom( U01_VR_STAR );
else
U01AdjOrTrans_STAR_MR.TransposeFrom( U01_VR_STAR );
LocalTrrk( UPPER, T(1), U01_MC_STAR, U01AdjOrTrans_STAR_MR, T(1), U00 );
U11_STAR_STAR = U11;
LocalTrmm
( RIGHT, UPPER, orientation, NON_UNIT,
T(1), U11_STAR_STAR, U01_VC_STAR );
U01 = U01_VC_STAR;
LocalTrtrmm( orientation, UPPER, U11_STAR_STAR );
U11 = U11_STAR_STAR;
//--------------------------------------------------------------------//
SlidePartitionDownDiagonal
( UTL, /**/ UTR, U00, U01, /**/ U02,
/**/ U10, U11, /**/ U12,
/*************/ /******************/
UBL, /**/ UBR, U20, U21, /**/ U22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
TwoSidedTrmmLVar4
( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& L )
{
#ifndef RELEASE
PushCallStack("internal::TwoSidedTrmmLVar4");
if( A.Height() != A.Width() )
throw std::logic_error("A must be square");
if( L.Height() != L.Width() )
throw std::logic_error("Triangular matrices must be square");
if( A.Height() != L.Height() )
throw std::logic_error("A and L must be the same size");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<F>
ATL(g), ATR(g), A00(g), A01(g), A02(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
DistMatrix<F>
LTL(g), LTR(g), L00(g), L01(g), L02(g),
LBL(g), LBR(g), L10(g), L11(g), L12(g),
L20(g), L21(g), L22(g);
// Temporary distributions
DistMatrix<F,STAR,VR > A10_STAR_VR(g);
DistMatrix<F,STAR,MR > A10_STAR_MR(g);
DistMatrix<F,STAR,MC > A10_STAR_MC(g);
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,VC, STAR> A21_VC_STAR(g);
DistMatrix<F,MC, STAR> A21_MC_STAR(g);
DistMatrix<F,STAR,VR > L10_STAR_VR(g);
DistMatrix<F,MR, STAR> L10Adj_MR_STAR(g);
DistMatrix<F,STAR,MC > L10_STAR_MC(g);
DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
DistMatrix<F,STAR,VR > Y10_STAR_VR(g);
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
LockedPartitionDownDiagonal
( L, LTL, LTR,
LBL, LBR, 0 );
while( ATL.Height() < A.Height() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
LockedRepartitionDownDiagonal
( LTL, /**/ LTR, L00, /**/ L01, L02,
/*************/ /******************/
/**/ L10, /**/ L11, L12,
LBL, /**/ LBR, L20, /**/ L21, L22 );
A10_STAR_VR.AlignWith( A00 );
A10_STAR_MR.AlignWith( A00 );
A10_STAR_MC.AlignWith( A00 );
A21_MC_STAR.AlignWith( A20 );
L10_STAR_VR.AlignWith( A00 );
L10Adj_MR_STAR.AlignWith( A00 );
L10_STAR_MC.AlignWith( A00 );
Y10_STAR_VR.AlignWith( A10 );
//--------------------------------------------------------------------//
// Y10 := A11 L10
A11_STAR_STAR = A11;
L10Adj_MR_STAR.AdjointFrom( L10 );
L10_STAR_VR.AdjointFrom( L10Adj_MR_STAR );
Y10_STAR_VR.ResizeTo( A10.Height(), A10.Width() );
Zero( Y10_STAR_VR );
Hemm
( LEFT, LOWER,
F(1), A11_STAR_STAR.LockedLocalMatrix(),
L10_STAR_VR.LockedLocalMatrix(),
F(0), Y10_STAR_VR.LocalMatrix() );
// A10 := A10 + 1/2 Y10
A10_STAR_VR = A10;
Axpy( F(1)/F(2), Y10_STAR_VR, A10_STAR_VR );
// A00 := A00 + (A10' L10 + L10' A10)
A10_STAR_MR = A10_STAR_VR;
A10_STAR_MC = A10_STAR_VR;
L10_STAR_MC = L10_STAR_VR;
LocalTrr2k
( LOWER, ADJOINT, ADJOINT, ADJOINT,
F(1), A10_STAR_MC, L10Adj_MR_STAR,
L10_STAR_MC, A10_STAR_MR,
F(1), A00 );
// A10 := A10 + 1/2 Y10
Axpy( F(1)/F(2), Y10_STAR_VR, A10_STAR_VR );
// A10 := L11' A10
L11_STAR_STAR = L11;
LocalTrmm
( LEFT, LOWER, ADJOINT, diag, F(1), L11_STAR_STAR, A10_STAR_VR );
A10 = A10_STAR_VR;
// A20 := A20 + A21 L10
A21_MC_STAR = A21;
LocalGemm
( NORMAL, ADJOINT, F(1), A21_MC_STAR, L10Adj_MR_STAR, F(1), A20 );
// A11 := L11' A11 L11
LocalTwoSidedTrmm( LOWER, diag, A11_STAR_STAR, L11_STAR_STAR );
A11 = A11_STAR_STAR;
// A21 := A21 L11
A21_VC_STAR = A21_MC_STAR;
LocalTrmm
( RIGHT, LOWER, NORMAL, diag, F(1), L11_STAR_STAR, A21_VC_STAR );
A21 = A21_VC_STAR;
//--------------------------------------------------------------------//
A10_STAR_VR.FreeAlignments();
A10_STAR_MR.FreeAlignments();
A10_STAR_MC.FreeAlignments();
A21_MC_STAR.FreeAlignments();
L10_STAR_VR.FreeAlignments();
L10Adj_MR_STAR.FreeAlignments();
L10_STAR_MC.FreeAlignments();
Y10_STAR_VR.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
SlideLockedPartitionDownDiagonal
( LTL, /**/ LTR, L00, L01, /**/ L02,
/**/ L10, L11, /**/ L12,
/*************/ /******************/
LBL, /**/ LBR, L20, L21, /**/ L22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
TrtrsmLLN
( UnitOrNonUnit diag, F alpha, const DistMatrix<F>& L, DistMatrix<F>& X,
bool checkIfSingular )
{
#ifndef RELEASE
PushCallStack("internal::TrtrsmLLN");
#endif
const Grid& g = L.Grid();
// Matrix views
DistMatrix<F>
LTL(g), LTR(g), L00(g), L01(g), L02(g),
LBL(g), LBR(g), L10(g), L11(g), L12(g),
L20(g), L21(g), L22(g);
DistMatrix<F>
XTL(g), XTR(g), X00(g), X01(g), X02(g),
XBL(g), XBR(g), X10(g), X11(g), X12(g),
X20(g), X21(g), X22(g);
// Temporary distributions
DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
DistMatrix<F,MC, STAR> L21_MC_STAR(g);
DistMatrix<F,STAR,MR > X10_STAR_MR(g);
DistMatrix<F,STAR,VR > X10_STAR_VR(g);
DistMatrix<F,STAR,MR > X11_STAR_MR(g);
DistMatrix<F,STAR,STAR> X11_STAR_STAR(g);
// Start the algorithm
ScaleTrapezoid( alpha, LEFT, LOWER, 0, X );
LockedPartitionDownDiagonal
( L, LTL, LTR,
LBL, LBR, 0 );
PartitionDownDiagonal
( X, XTL, XTR,
XBL, XBR, 0 );
while( XBR.Height() > 0 )
{
LockedRepartitionDownDiagonal
( LTL, /**/ LTR, L00, /**/ L01, L02,
/*************/ /******************/
/**/ L10, /**/ L11, L12,
LBL, /**/ LBR, L20, /**/ L21, L22 );
RepartitionDownDiagonal
( XTL, /**/ XTR, X00, /**/ X01, X02,
/*************/ /******************/
/**/ X10, /**/ X11, X12,
XBL, /**/ XBR, X20, /**/ X21, X22 );
L21_MC_STAR.AlignWith( X20 );
X10_STAR_MR.AlignWith( X20 );
X11_STAR_MR.AlignWith( X21 );
//--------------------------------------------------------------------//
L11_STAR_STAR = L11;
X11_STAR_STAR = X11;
X10_STAR_VR = X10;
LocalTrsm
( LEFT, LOWER, NORMAL, diag, F(1), L11_STAR_STAR, X10_STAR_VR,
checkIfSingular );
LocalTrtrsm
( LEFT, LOWER, NORMAL, diag, F(1), L11_STAR_STAR, X11_STAR_STAR,
checkIfSingular );
X11 = X11_STAR_STAR;
X11_STAR_MR = X11_STAR_STAR;
MakeTrapezoidal( LEFT, LOWER, 0, X11_STAR_MR );
X10_STAR_MR = X10_STAR_VR;
X10 = X10_STAR_MR;
L21_MC_STAR = L21;
LocalGemm
( NORMAL, NORMAL, F(-1), L21_MC_STAR, X10_STAR_MR, F(1), X20 );
LocalGemm
( NORMAL, NORMAL, F(-1), L21_MC_STAR, X11_STAR_MR, F(1), X21 );
//--------------------------------------------------------------------//
L21_MC_STAR.FreeAlignments();
X10_STAR_MR.FreeAlignments();
X11_STAR_MR.FreeAlignments();
SlideLockedPartitionDownDiagonal
( LTL, /**/ LTR, L00, L01, /**/ L02,
/**/ L10, L11, /**/ L12,
/*************/ /******************/
LBL, /**/ LBR, L20, L21, /**/ L22 );
SlidePartitionDownDiagonal
( XTL, /**/ XTR, X00, X01, /**/ X02,
/**/ X10, X11, /**/ X12,
/*************/ /******************/
XBL, /**/ XBR, X20, X21, /**/ X22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
SimpleSVDUpper
( DistMatrix<Real>& A,
DistMatrix<Real,VR,STAR>& s,
DistMatrix<Real>& V )
{
#ifndef RELEASE
PushCallStack("svd::SimpleSVDUpper");
#endif
const int m = A.Height();
const int n = A.Width();
const int k = std::min( m, n );
const int offdiagonal = ( m>=n ? 1 : -1 );
const char uplo = ( m>=n ? 'U' : 'L' );
const Grid& g = A.Grid();
// Bidiagonalize A
Bidiag( A );
// Grab copies of the diagonal and sub/super-diagonal of A
DistMatrix<Real,MD,STAR> d_MD_STAR( g ),
e_MD_STAR( g );
A.GetDiagonal( d_MD_STAR );
A.GetDiagonal( e_MD_STAR, offdiagonal );
// In order to use serial QR kernels, we need the full bidiagonal matrix
// on each process.
//
// NOTE: lapack::BidiagQRAlg expects e to be of length k
DistMatrix<Real,STAR,STAR> d_STAR_STAR( d_MD_STAR );
DistMatrix<Real,STAR,STAR> eHat_STAR_STAR( k, 1, g );
DistMatrix<Real,STAR,STAR> e_STAR_STAR( g );
e_STAR_STAR.View( eHat_STAR_STAR, 0, 0, k-1, 1 );
e_STAR_STAR = e_MD_STAR;
// Initialize U and VTrans to the appropriate identity matrices.
DistMatrix<Real,VC,STAR> U_VC_STAR( g );
DistMatrix<Real,STAR,VC> VTrans_STAR_VC( g );
U_VC_STAR.AlignWith( A );
VTrans_STAR_VC.AlignWith( V );
Identity( m, k, U_VC_STAR );
Identity( k, n, VTrans_STAR_VC );
// Compute the SVD of the bidiagonal matrix and accumulate the Givens
// rotations into our local portion of U and VTrans
Matrix<Real>& ULocal = U_VC_STAR.LocalMatrix();
Matrix<Real>& VTransLocal = VTrans_STAR_VC.LocalMatrix();
lapack::BidiagQRAlg
( uplo, k, VTransLocal.Width(), ULocal.Height(),
d_STAR_STAR.LocalBuffer(), e_STAR_STAR.LocalBuffer(),
VTransLocal.Buffer(), VTransLocal.LDim(),
ULocal.Buffer(), ULocal.LDim() );
// Make a copy of A (for the Householder vectors) and pull the necessary
// portions of U and VTrans into a standard matrix dist.
DistMatrix<Real> B( A );
if( m >= n )
{
DistMatrix<Real> AT( g ),
AB( g );
DistMatrix<Real,VC,STAR> UT_VC_STAR( g ),
UB_VC_STAR( g );
PartitionDown( A, AT,
AB, n );
PartitionDown( U_VC_STAR, UT_VC_STAR,
UB_VC_STAR, n );
AT = UT_VC_STAR;
MakeZeros( AB );
Transpose( VTrans_STAR_VC, V );
}
else
{
DistMatrix<Real> VT( g ),
VB( g );
DistMatrix<Real,STAR,VC>
VTransL_STAR_VC( g ), VTransR_STAR_VC( g );
PartitionDown( V, VT,
VB, m );
PartitionRight( VTrans_STAR_VC, VTransL_STAR_VC, VTransR_STAR_VC, m );
Transpose( VTransL_STAR_VC, VT );
MakeZeros( VB );
}
// Backtransform U and V
if( m >= n )
{
ApplyPackedReflectors
( LEFT, LOWER, VERTICAL, BACKWARD, 0, B, A );
ApplyPackedReflectors
( LEFT, UPPER, HORIZONTAL, BACKWARD, 1, B, V );
}
else
{
ApplyPackedReflectors
( LEFT, LOWER, VERTICAL, BACKWARD, -1, B, A );
ApplyPackedReflectors
( LEFT, UPPER, HORIZONTAL, BACKWARD, 0, B, V );
}
// Copy out the appropriate subset of the singular values
s = d_STAR_STAR;
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
Her2kUC
( T alpha, const DistMatrix<T>& A, const DistMatrix<T>& B,
T beta, DistMatrix<T>& C )
{
#ifndef RELEASE
PushCallStack("internal::Her2kUC");
if( A.Grid() != B.Grid() || B.Grid() != C.Grid() )
throw std::logic_error
("{A,B,C} must be distributed over the same grid");
if( A.Width() != C.Height() ||
A.Width() != C.Width() ||
B.Width() != C.Height() ||
B.Width() != C.Width() ||
A.Height() != B.Height() )
{
std::ostringstream msg;
msg << "Nonconformal Her2kUC:\n"
<< " A ~ " << A.Height() << " x " << A.Width() << "\n"
<< " B ~ " << B.Height() << " x " << B.Width() << "\n"
<< " C ~ " << C.Height() << " x " << C.Width() << "\n";
throw std::logic_error( msg.str().c_str() );
}
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<T> AT(g), A0(g),
AB(g), A1(g),
A2(g);
DistMatrix<T> BT(g), B0(g),
BB(g), B1(g),
B2(g);
// Temporary distributions
DistMatrix<T,MR, STAR> A1Trans_MR_STAR(g);
DistMatrix<T,MR, STAR> B1Trans_MR_STAR(g);
DistMatrix<T,STAR,VR > A1_STAR_VR(g);
DistMatrix<T,STAR,VR > B1_STAR_VR(g);
DistMatrix<T,STAR,MC > A1_STAR_MC(g);
DistMatrix<T,STAR,MC > B1_STAR_MC(g);
A1Trans_MR_STAR.AlignWith( C );
B1Trans_MR_STAR.AlignWith( C );
A1_STAR_MC.AlignWith( C );
B1_STAR_MC.AlignWith( C );
// Start the algorithm
ScaleTrapezoid( beta, LEFT, UPPER, 0, C );
LockedPartitionDown
( A, AT,
AB, 0 );
LockedPartitionDown
( B, BT,
BB, 0 );
while( AB.Height() > 0 )
{
LockedRepartitionDown
( AT, A0,
/**/ /**/
A1,
AB, A2 );
LockedRepartitionDown
( BT, B0,
/**/ /**/
B1,
BB, B2 );
//--------------------------------------------------------------------//
A1Trans_MR_STAR.TransposeFrom( A1 );
A1_STAR_VR.TransposeFrom( A1Trans_MR_STAR );
A1_STAR_MC = A1_STAR_VR;
B1Trans_MR_STAR.TransposeFrom( B1 );
B1_STAR_VR.TransposeFrom( B1Trans_MR_STAR );
B1_STAR_MC = B1_STAR_VR;
LocalTrr2k
( UPPER, ADJOINT, TRANSPOSE, ADJOINT, TRANSPOSE,
alpha, A1_STAR_MC, B1Trans_MR_STAR,
B1_STAR_MC, A1Trans_MR_STAR,
T(1), C );
//--------------------------------------------------------------------//
SlideLockedPartitionDown
( AT, A0,
A1,
/**/ /**/
AB, A2 );
SlideLockedPartitionDown
( BT, B0,
B1,
/**/ /**/
BB, B2 );
}
#ifndef RELEASE
PopCallStack();
#endif
}