inline void
internal::HegstRLVar3( DistMatrix<F,MC,MR>& A, const DistMatrix<F,MC,MR>& L )
{
#ifndef RELEASE
PushCallStack("internal::HegstRLVar4");
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,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);
DistMatrix<F,MC,MR>
YTL(g), YTR(g), Y00(g), Y01(g), Y02(g),
YBL(g), YBR(g), Y10(g), Y11(g), Y12(g),
Y20(g), Y21(g), Y22(g);
DistMatrix<F,MC,MR>
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,MR > A11_STAR_MR(g);
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,VC, STAR> A21_VC_STAR(g);
DistMatrix<F,STAR,VR > A10_STAR_VR(g);
DistMatrix<F,STAR,MR > A10_STAR_MR(g);
DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
DistMatrix<F,STAR,VR > L10_STAR_VR(g);
DistMatrix<F,STAR,MR > L10_STAR_MR(g);
DistMatrix<F,MC, STAR> L21_MC_STAR(g);
DistMatrix<F,STAR,STAR> X11_STAR_STAR(g);
DistMatrix<F,MC, STAR> X21_MC_STAR(g);
DistMatrix<F,MC, STAR> Z21_MC_STAR(g);
// We will use an entire extra matrix as temporary storage. If this is not
// acceptable, use HegstRLVar4 instead.
DistMatrix<F,MC,MR> Y(g);
Y.AlignWith( A );
Y.ResizeTo( A.Height(), A.Width() );
Zero( Y );
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
PartitionDownDiagonal
( Y, YTL, YTR,
YBL, YBR, 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 );
RepartitionDownDiagonal
( YTL, /**/ YTR, Y00, /**/ Y01, Y02,
/*************/ /******************/
/**/ Y10, /**/ Y11, Y12,
YBL, /**/ YBR, Y20, /**/ Y21, Y22 );
LockedRepartitionDownDiagonal
( LTL, /**/ LTR, L00, /**/ L01, L02,
/*************/ /******************/
/**/ L10, /**/ L11, L12,
LBL, /**/ LBR, L20, /**/ L21, L22 );
A11_STAR_MR.AlignWith( Y21 );
A21_VC_STAR.AlignWith( A21 );
A10_STAR_VR.AlignWith( A10 );
A10_STAR_MR.AlignWith( A10 );
L10_STAR_VR.AlignWith( A10 );
L10_STAR_MR.AlignWith( A10 );
L21_MC_STAR.AlignWith( Y21 );
X21_MC_STAR.AlignWith( A20 );
Z21_MC_STAR.AlignWith( L20 );
//--------------------------------------------------------------------//
// A10 := A10 - 1/2 Y10
Axpy( (F)-0.5, Y10, A10 );
// A11 := A11 - (A10 L10' + L10 A10')
A10_STAR_VR = A10;
L10_STAR_VR = L10;
X11_STAR_STAR.ResizeTo( A11.Height(), A11.Width() );
Her2k
( LOWER, NORMAL,
(F)1, A10_STAR_VR.LocalMatrix(), L10_STAR_VR.LocalMatrix(),
(F)0, X11_STAR_STAR.LocalMatrix() );
MakeTrapezoidal( LEFT, LOWER, 0, X11_STAR_STAR );
A11.SumScatterUpdate( (F)-1, X11_STAR_STAR );
// A11 := inv(L11) A11 inv(L11)'
A11_STAR_STAR = A11;
L11_STAR_STAR = L11;
internal::LocalHegst( RIGHT, LOWER, A11_STAR_STAR, L11_STAR_STAR );
A11 = A11_STAR_STAR;
// A21 := A21 - A20 L10'
L10_STAR_MR = L10_STAR_VR;
X21_MC_STAR.ResizeTo( A21.Height(), A21.Width() );
internal::LocalGemm
( NORMAL, ADJOINT, (F)1, A20, L10_STAR_MR, (F)0, X21_MC_STAR );
A21.SumScatterUpdate( (F)-1, X21_MC_STAR );
// A21 := A21 inv(L11)'
A21_VC_STAR = A21;
internal::LocalTrsm
( RIGHT, LOWER, ADJOINT, NON_UNIT, (F)1, L11_STAR_STAR, A21_VC_STAR );
A21 = A21_VC_STAR;
// A10 := A10 - 1/2 Y10
Axpy( (F)-0.5, Y10, A10 );
// A10 := inv(L11) A10
A10_STAR_VR = A10;
internal::LocalTrsm
( LEFT, LOWER, NORMAL, NON_UNIT,
(F)1, L11_STAR_STAR, A10_STAR_VR );
// Y20 := Y20 + L21 A10
A10_STAR_MR = A10_STAR_VR;
A10 = A10_STAR_MR;
L21_MC_STAR = L21;
internal::LocalGemm
( NORMAL, NORMAL, (F)1, L21_MC_STAR, A10_STAR_MR, (F)1, Y20 );
// Y21 := L21 A11
//
// Symmetrize A11[* ,* ] by copying the lower triangle into the upper
// so that we can call a local gemm instead of worrying about
// reproducing a hemm with nonsymmetric local matrices.
{
const int height = A11_STAR_STAR.LocalHeight();
const int ldim = A11_STAR_STAR.LocalLDim();
F* A11Buffer = A11_STAR_STAR.LocalBuffer();
for( int i=1; i<height; ++i )
for( int j=0; j<i; ++j )
A11Buffer[j+i*ldim] = Conj(A11Buffer[i+j*ldim]);
}
A11_STAR_MR = A11_STAR_STAR;
internal::LocalGemm
( NORMAL, NORMAL, (F)1, L21_MC_STAR, A11_STAR_MR, (F)0, Y21 );
// Y21 := Y21 + L20 A10'
Z21_MC_STAR.ResizeTo( A21.Height(), A21.Width() );
internal::LocalGemm
( NORMAL, ADJOINT, (F)1, L20, A10_STAR_MR, (F)0, Z21_MC_STAR );
Y21.SumScatterUpdate( (F)1, Z21_MC_STAR );
//--------------------------------------------------------------------//
A11_STAR_MR.FreeAlignments();
A21_VC_STAR.FreeAlignments();
A10_STAR_VR.FreeAlignments();
A10_STAR_MR.FreeAlignments();
L10_STAR_VR.FreeAlignments();
L10_STAR_MR.FreeAlignments();
L21_MC_STAR.FreeAlignments();
X21_MC_STAR.FreeAlignments();
Z21_MC_STAR.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
SlidePartitionDownDiagonal
( YTL, /**/ YTR, Y00, Y01, /**/ Y02,
/**/ Y10, Y11, /**/ Y12,
/*************/ /******************/
YBL, /**/ YBR, Y20, Y21, /**/ Y22 );
SlideLockedPartitionDownDiagonal
( LTL, /**/ LTR, L00, L01, /**/ L02,
/**/ L10, L11, /**/ L12,
/**********************************/
LBL, /**/ LBR, L20, L21, /**/ L22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
TwoSidedTrsmLVar5
( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& L )
{
#ifndef RELEASE
CallStackEntry entry("internal::TwoSidedTrsmLVar5");
if( A.Height() != A.Width() )
LogicError("A must be square");
if( L.Height() != L.Width() )
LogicError("Triangular matrices must be square");
if( A.Height() != L.Height() )
LogicError("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,STAR> A11_STAR_STAR(g);
DistMatrix<F,MC, STAR> A21_MC_STAR(g);
DistMatrix<F,VC, STAR> A21_VC_STAR(g);
DistMatrix<F,VR, STAR> A21_VR_STAR(g);
DistMatrix<F,STAR,MR > A21Adj_STAR_MR(g);
DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
DistMatrix<F,MC, STAR> L21_MC_STAR(g);
DistMatrix<F,VC, STAR> L21_VC_STAR(g);
DistMatrix<F,VR, STAR> L21_VR_STAR(g);
DistMatrix<F,STAR,MR > L21Adj_STAR_MR(g);
DistMatrix<F,VC, STAR> Y21_VC_STAR(g);
DistMatrix<F> Y21(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 );
A21_MC_STAR.AlignWith( A22 );
A21_VC_STAR.AlignWith( A22 );
A21_VR_STAR.AlignWith( A22 );
A21Adj_STAR_MR.AlignWith( A22 );
L21_MC_STAR.AlignWith( A22 );
L21_VC_STAR.AlignWith( A22 );
L21_VR_STAR.AlignWith( A22 );
L21Adj_STAR_MR.AlignWith( A22 );
Y21.AlignWith( A21 );
Y21_VC_STAR.AlignWith( A22 );
//--------------------------------------------------------------------//
// A11 := inv(L11) A11 inv(L11)'
L11_STAR_STAR = L11;
A11_STAR_STAR = A11;
LocalTwoSidedTrsm( LOWER, diag, A11_STAR_STAR, L11_STAR_STAR );
A11 = A11_STAR_STAR;
// Y21 := L21 A11
L21_VC_STAR = L21;
Zeros( Y21_VC_STAR, A21.Height(), A21.Width() );
Hemm
( RIGHT, LOWER,
F(1), A11_STAR_STAR.Matrix(), L21_VC_STAR.Matrix(),
F(0), Y21_VC_STAR.Matrix() );
Y21 = Y21_VC_STAR;
// A21 := A21 inv(L11)'
A21_VC_STAR = A21;
LocalTrsm
( RIGHT, LOWER, ADJOINT, diag, F(1), L11_STAR_STAR, A21_VC_STAR );
A21 = A21_VC_STAR;
// A21 := A21 - 1/2 Y21
Axpy( F(-1)/F(2), Y21, A21 );
// A22 := A22 - (L21 A21' + A21 L21')
A21_MC_STAR = A21;
L21_MC_STAR = L21;
A21_VC_STAR = A21_MC_STAR;
A21_VR_STAR = A21_VC_STAR;
L21_VR_STAR = L21_VC_STAR;
A21Adj_STAR_MR.AdjointFrom( A21_VR_STAR );
L21Adj_STAR_MR.AdjointFrom( L21_VR_STAR );
LocalTrr2k
( LOWER,
F(-1), L21_MC_STAR, A21Adj_STAR_MR,
A21_MC_STAR, L21Adj_STAR_MR,
F(1), A22 );
// A21 := A21 - 1/2 Y21
Axpy( F(-1)/F(2), Y21, A21 );
// A21 := inv(L22) A21
//
// This is the bottleneck because A21 only has blocksize columns
Trsm( LEFT, LOWER, NORMAL, diag, F(1), L22, 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 );
}
}
inline void
TwoSidedTrmmLVar2
( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& L )
{
#ifndef RELEASE
PushCallStack("internal::TwoSidedTrmmLVar2");
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,STAR> A11_STAR_STAR(g);
DistMatrix<F,VC, STAR> A21_VC_STAR(g);
DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
DistMatrix<F,MC, STAR> L21_MC_STAR(g);
DistMatrix<F,STAR,MR > L21Adj_STAR_MR(g);
DistMatrix<F,VC, STAR> L21_VC_STAR(g);
DistMatrix<F,VR, STAR> L21_VR_STAR(g);
DistMatrix<F,STAR,MR > X10_STAR_MR(g);
DistMatrix<F,STAR,STAR> X11_STAR_STAR(g);
DistMatrix<F,MC, STAR> Z21_MC_STAR(g);
DistMatrix<F,MR, STAR> Z21_MR_STAR(g);
DistMatrix<F,MR, MC > Z21_MR_MC(g);
DistMatrix<F> Y21(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 );
A21_VC_STAR.AlignWith( A22 );
L21_MC_STAR.AlignWith( A20 );
L21_VC_STAR.AlignWith( A22 );
L21_VR_STAR.AlignWith( A22 );
L21Adj_STAR_MR.AlignWith( A22 );
X10_STAR_MR.AlignWith( A10 );
Y21.AlignWith( A21 );
Z21_MC_STAR.AlignWith( A22 );
Z21_MR_STAR.AlignWith( A22 );
//--------------------------------------------------------------------//
// A10 := L11' A10
L11_STAR_STAR = L11;
A10_STAR_VR = A10;
LocalTrmm
( LEFT, LOWER, ADJOINT, diag, F(1), L11_STAR_STAR, A10_STAR_VR );
A10 = A10_STAR_VR;
// A10 := A10 + L21' A20
L21_MC_STAR = L21;
X10_STAR_MR.ResizeTo( A10.Height(), A10.Width() );
LocalGemm( ADJOINT, NORMAL, F(1), L21_MC_STAR, A20, F(0), X10_STAR_MR );
A10.SumScatterUpdate( F(1), X10_STAR_MR );
// Y21 := A22 L21
L21_VC_STAR = L21_MC_STAR;
L21_VR_STAR = L21_VC_STAR;
L21Adj_STAR_MR.AdjointFrom( L21_VR_STAR );
Z21_MC_STAR.ResizeTo( A21.Height(), A21.Width() );
Z21_MR_STAR.ResizeTo( A21.Height(), A21.Width() );
Zero( Z21_MC_STAR );
Zero( Z21_MR_STAR );
LocalSymmetricAccumulateLL
( ADJOINT,
F(1), A22, L21_MC_STAR, L21Adj_STAR_MR, Z21_MC_STAR, Z21_MR_STAR );
Z21_MR_MC.SumScatterFrom( Z21_MR_STAR );
Y21 = Z21_MR_MC;
Y21.SumScatterUpdate( F(1), Z21_MC_STAR );
// A21 := A21 L11
A21_VC_STAR = A21;
LocalTrmm
( RIGHT, LOWER, NORMAL, diag, F(1), L11_STAR_STAR, A21_VC_STAR );
A21 = A21_VC_STAR;
// A21 := A21 + 1/2 Y21
Axpy( F(1)/F(2), Y21, A21 );
// A11 := L11' A11 L11
A11_STAR_STAR = A11;
LocalTwoSidedTrmm( LOWER, diag, A11_STAR_STAR, L11_STAR_STAR );
A11 = A11_STAR_STAR;
// A11 := A11 + (A21' L21 + L21' A21)
A21_VC_STAR = A21;
X11_STAR_STAR.ResizeTo( A11.Height(), A11.Width() );
Her2k
( LOWER, ADJOINT,
F(1), A21_VC_STAR.LocalMatrix(), L21_VC_STAR.LocalMatrix(),
F(0), X11_STAR_STAR.LocalMatrix() );
A11.SumScatterUpdate( F(1), X11_STAR_STAR );
// A21 := A21 + 1/2 Y21
Axpy( F(1)/F(2), Y21, A21 );
//--------------------------------------------------------------------//
A21_VC_STAR.FreeAlignments();
L21_MC_STAR.FreeAlignments();
L21_VC_STAR.FreeAlignments();
L21_VR_STAR.FreeAlignments();
L21Adj_STAR_MR.FreeAlignments();
X10_STAR_MR.FreeAlignments();
Y21.FreeAlignments();
Z21_MC_STAR.FreeAlignments();
Z21_MR_STAR.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
}