inline void
LQ( DistMatrix<Complex<R>,MC,MR >& A,
DistMatrix<Complex<R>,MD,STAR>& t )
{
#ifndef RELEASE
PushCallStack("LQ");
if( A.Grid() != t.Grid() )
throw std::logic_error("{A,t} must be distributed over the same grid");
#endif
typedef Complex<R> C;
const Grid& g = A.Grid();
if( t.Viewing() )
{
if( !t.AlignedWithDiagonal( A ) )
throw std::logic_error("t was not aligned with A");
if( t.Height() != std::min(A.Height(),A.Width()) || t.Width() != 1 )
throw std::logic_error("t was not the appropriate shape");
}
else
{
t.AlignWithDiagonal( A );
t.ResizeTo( std::min(A.Height(),A.Width()), 1 );
}
// Matrix views
DistMatrix<C,MC,MR>
ATL(g), ATR(g), A00(g), A01(g), A02(g), ATopPan(g), ABottomPan(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
DistMatrix<C,MD,STAR>
tT(g), t0(g),
tB(g), t1(g),
t2(g);
PartitionDownLeftDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
PartitionDown
( t, tT,
tB, 0 );
while( ATL.Height() < A.Height() && ATL.Width() < A.Width() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
RepartitionDown
( tT, t0,
/**/ /**/
t1,
tB, t2 );
ATopPan.View1x2( A11, A12 );
ABottomPan.View1x2( A21, A22 );
//--------------------------------------------------------------------//
internal::PanelLQ( ATopPan, t1 );
ApplyPackedReflectors
( RIGHT, UPPER, HORIZONTAL, FORWARD, CONJUGATED,
0, ATopPan, t1, ABottomPan );
//--------------------------------------------------------------------//
SlidePartitionDown
( tT, t0,
t1,
/**/ /**/
tB, t2 );
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
Householder( DistMatrix<F>& A, DistMatrix<F,MD,STAR>& t )
{
#ifndef RELEASE
CallStackEntry entry("qr::Householder");
if( A.Grid() != t.Grid() )
LogicError("{A,s} must be distributed over the same grid");
#endif
const Grid& g = A.Grid();
if( t.Viewing() )
{
if( !t.AlignedWithDiagonal( A ) )
LogicError("t was not aligned with A");
}
else
{
t.AlignWithDiagonal( A );
}
t.ResizeTo( Min(A.Height(),A.Width()), 1 );
// Matrix views
DistMatrix<F>
ATL(g), ATR(g), A00(g), A01(g), A02(g), ALeftPan(g), ARightPan(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
DistMatrix<F,MD,STAR>
tT(g), t0(g),
tB(g), t1(g),
t2(g);
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
PartitionDown
( t, tT,
tB, 0 );
while( ATL.Height() < A.Height() && ATL.Width() < A.Width() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
RepartitionDown
( tT, t0,
/**/ /**/
t1,
tB, t2 );
View2x1
( ALeftPan, A11,
A21 );
View2x1
( ARightPan, A12,
A22 );
//--------------------------------------------------------------------//
PanelHouseholder( ALeftPan, t1 );
ApplyQ( LEFT, ADJOINT, ALeftPan, t1, ARightPan );
//--------------------------------------------------------------------//
SlidePartitionDown
( tT, t0,
t1,
/**/ /**/
tB, t2 );
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
}
}
void LSquare
( DistMatrix<Complex<R> >& A,
DistMatrix<Complex<R>,STAR,STAR>& t )
{
#ifndef RELEASE
CallStackEntry entry("hermitian_tridiag::LSquare");
if( A.Grid() != t.Grid() )
throw std::logic_error("{A,t} must be distributed over the same grid");
#endif
const Grid& g = A.Grid();
#ifndef RELEASE
if( g.Height() != g.Width() )
throw std::logic_error("The process grid must be square");
if( A.Height() != A.Width() )
throw std::logic_error("A must be square");
if( t.Viewing() )
throw std::logic_error("t must not be a view");
#endif
typedef Complex<R> C;
DistMatrix<C,MD,STAR> tDiag(g);
tDiag.AlignWithDiagonal( A, -1 );
tDiag.ResizeTo( A.Height()-1, 1 );
// Matrix views
DistMatrix<C>
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<C,MD,STAR> tT(g), t0(g),
tB(g), t1(g),
t2(g);
// Temporary distributions
DistMatrix<C> WPan(g);
DistMatrix<C,STAR,STAR> t1_STAR_STAR(g);
DistMatrix<C,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<C,MC, STAR> APan_MC_STAR(g), A11_MC_STAR(g),
A21_MC_STAR(g);
DistMatrix<C,MR, STAR> APan_MR_STAR(g), A11_MR_STAR(g),
A21_MR_STAR(g);
DistMatrix<C,MC, STAR> WPan_MC_STAR(g), W11_MC_STAR(g),
W21_MC_STAR(g);
DistMatrix<C,MR, STAR> WPan_MR_STAR(g), W11_MR_STAR(g),
W21_MR_STAR(g);
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
PartitionDown
( tDiag, tT,
tB, 0 );
while( ATL.Height() < A.Height() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
RepartitionDown
( tT, t0,
/**/ /**/
t1,
tB, t2 );
if( A22.Height() > 0 )
{
WPan.AlignWith( A11 );
APan_MC_STAR.AlignWith( A11 );
WPan_MC_STAR.AlignWith( A11 );
APan_MR_STAR.AlignWith( A11 );
WPan_MR_STAR.AlignWith( A11 );
//----------------------------------------------------------------//
WPan.ResizeTo( ABR.Height(), A11.Width() );
APan_MC_STAR.ResizeTo( ABR.Height(), A11.Width() );
WPan_MC_STAR.ResizeTo( ABR.Height(), A11.Width() );
APan_MR_STAR.ResizeTo( ABR.Height(), A11.Width() );
WPan_MR_STAR.ResizeTo( ABR.Height(), A11.Width() );
hermitian_tridiag::PanelLSquare
( ABR, WPan, t1,
APan_MC_STAR, APan_MR_STAR, WPan_MC_STAR, WPan_MR_STAR );
PartitionDown
( APan_MC_STAR, A11_MC_STAR,
A21_MC_STAR, A11.Height() );
PartitionDown
( APan_MR_STAR, A11_MR_STAR,
A21_MR_STAR, A11.Height() );
PartitionDown
( WPan_MC_STAR, W11_MC_STAR,
W21_MC_STAR, A11.Height() );
PartitionDown
( WPan_MR_STAR, W11_MR_STAR,
W21_MR_STAR, A11.Height() );
LocalTrr2k
( LOWER, ADJOINT, ADJOINT,
C(-1), A21_MC_STAR, W21_MR_STAR,
W21_MC_STAR, A21_MR_STAR,
C(1), A22 );
//----------------------------------------------------------------//
WPan_MR_STAR.FreeAlignments();
APan_MR_STAR.FreeAlignments();
WPan_MC_STAR.FreeAlignments();
APan_MC_STAR.FreeAlignments();
WPan.FreeAlignments();
}
else
{
A11_STAR_STAR = A11;
t1_STAR_STAR.ResizeTo( t1.Height(), 1 );
HermitianTridiag
( LOWER, A11_STAR_STAR.Matrix(), t1_STAR_STAR.Matrix() );
A11 = A11_STAR_STAR;
t1 = t1_STAR_STAR;
}
SlidePartitionDown
( tT, t0,
t1,
/**/ /**/
tB, t2 );
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
}
// Redistribute from matrix-diagonal form to fully replicated
t = tDiag;
}
inline void
LU( DistMatrix<F>& A, DistMatrix<int,VC,STAR>& p )
{
#ifndef RELEASE
CallStackEntry entry("LU");
if( A.Grid() != p.Grid() )
throw std::logic_error("{A,p} must be distributed over the same grid");
if( p.Viewing() &&
(std::min(A.Height(),A.Width()) != p.Height() || p.Width() != 1) )
throw std::logic_error
("p must be a vector of the same height as the min dimension of A.");
#endif
const Grid& g = A.Grid();
if( !p.Viewing() )
p.ResizeTo( std::min(A.Height(),A.Width()), 1 );
// Matrix views
DistMatrix<F>
ATL(g), ATR(g), A00(g), A01(g), A02(g), AB(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
DistMatrix<int,VC,STAR>
pT(g), p0(g),
pB(g), p1(g),
p2(g);
// Temporary distributions
DistMatrix<F, STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F, MC, STAR> A21_MC_STAR(g);
DistMatrix<F, STAR,VR > A12_STAR_VR(g);
DistMatrix<F, STAR,MR > A12_STAR_MR(g);
DistMatrix<int,STAR,STAR> p1_STAR_STAR(g);
// Pivot composition
std::vector<int> image, preimage;
// Start the algorithm
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
PartitionDown
( p, pT,
pB, 0 );
while( ATL.Height() < A.Height() && ATL.Width() < A.Width() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
RepartitionDown
( pT, p0,
/**/ /**/
p1,
pB, p2 );
View1x2( AB, ABL, ABR );
const int pivotOffset = A01.Height();
A12_STAR_VR.AlignWith( A22 );
A12_STAR_MR.AlignWith( A22 );
A21_MC_STAR.AlignWith( A22 );
A11_STAR_STAR.ResizeTo( A11.Height(), A11.Width() );
p1_STAR_STAR.ResizeTo( p1.Height(), 1 );
//--------------------------------------------------------------------//
A21_MC_STAR = A21;
A11_STAR_STAR = A11;
lu::Panel( A11_STAR_STAR, A21_MC_STAR, p1_STAR_STAR, pivotOffset );
ComposePivots( p1_STAR_STAR, pivotOffset, image, preimage );
ApplyRowPivots( AB, image, preimage );
// Perhaps we should give up perfectly distributing this operation since
// it's total contribution is only O(n^2)
A12_STAR_VR = A12;
LocalTrsm
( LEFT, LOWER, NORMAL, UNIT, F(1), A11_STAR_STAR, A12_STAR_VR );
A12_STAR_MR = A12_STAR_VR;
LocalGemm( NORMAL, NORMAL, F(-1), A21_MC_STAR, A12_STAR_MR, F(1), A22 );
A11 = A11_STAR_STAR;
A12 = A12_STAR_MR;
A21 = A21_MC_STAR;
p1 = p1_STAR_STAR;
//--------------------------------------------------------------------//
A12_STAR_VR.FreeAlignments();
A12_STAR_MR.FreeAlignments();
A21_MC_STAR.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
SlidePartitionDown
( pT, p0,
p1,
/**/ /**/
pB, p2 );
}
}
inline void
internal::HermitianTridiagU
( DistMatrix<Complex<R>,MC, MR >& A,
DistMatrix<Complex<R>,STAR,STAR>& t )
{
#ifndef RELEASE
PushCallStack("internal::HermitianTridiagU");
if( A.Grid() != t.Grid() )
throw std::logic_error("{A,t} must be distributed over the same grid");
if( A.Height() != A.Width() )
throw std::logic_error("A must be square");
if( t.Viewing() )
throw std::logic_error("t must not be a view");
#endif
typedef Complex<R> C;
const Grid& g = A.Grid();
DistMatrix<C,MD,STAR> tDiag(g);
tDiag.AlignWithDiagonal( A, 1 );
tDiag.ResizeTo( A.Height()-1, 1 );
if( g.InGrid() )
{
// Matrix views
DistMatrix<C,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<C,MD,STAR> tT(g), t0(g),
tB(g), t1(g),
t2(g);
// Temporary distributions
DistMatrix<C,MC, MR > WPan(g);
DistMatrix<C,STAR,STAR> t1_STAR_STAR(g);
DistMatrix<C,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<C,MC, STAR> APan_MC_STAR(g), A01_MC_STAR(g),
A11_MC_STAR(g);
DistMatrix<C,MR, STAR> APan_MR_STAR(g), A01_MR_STAR(g),
A11_MR_STAR(g);
DistMatrix<C,MC, STAR> WPan_MC_STAR(g), W01_MC_STAR(g),
W11_MC_STAR(g);
DistMatrix<C,MR, STAR> WPan_MR_STAR(g), W01_MR_STAR(g),
W11_MR_STAR(g);
PartitionUpDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
PartitionUp
( tDiag, tT,
tB, 0 );
while( ABR.Height() < A.Height() )
{
RepartitionUpDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
RepartitionUp
( tT, t0,
t1,
/**/ /**/
tB, t2 );
if( A00.Height() > 0 )
{
WPan.AlignWith( A01 );
APan_MC_STAR.AlignWith( A00 );
WPan_MC_STAR.AlignWith( A00 );
APan_MR_STAR.AlignWith( A00 );
WPan_MR_STAR.AlignWith( A00 );
//------------------------------------------------------------//
WPan.ResizeTo( ATL.Height(), A11.Width() );
APan_MC_STAR.ResizeTo( ATL.Height(), A11.Width() );
WPan_MC_STAR.ResizeTo( ATL.Height(), A11.Width() );
APan_MR_STAR.ResizeTo( ATL.Height(), A11.Width() );
WPan_MR_STAR.ResizeTo( ATL.Height(), A11.Width() );
internal::HermitianPanelTridiagU
( ATL, WPan, t1,
APan_MC_STAR, APan_MR_STAR, WPan_MC_STAR, WPan_MR_STAR );
PartitionUp
( APan_MC_STAR, A01_MC_STAR,
A11_MC_STAR, A11.Height() );
PartitionUp
( APan_MR_STAR, A01_MR_STAR,
A11_MR_STAR, A11.Height() );
PartitionUp
( WPan_MC_STAR, W01_MC_STAR,
W11_MC_STAR, A11.Height() );
PartitionUp
( WPan_MR_STAR, W01_MR_STAR,
W11_MR_STAR, A11.Height() );
internal::LocalTrr2k
( UPPER, ADJOINT, ADJOINT,
(C)-1, A01_MC_STAR, W01_MR_STAR,
W01_MC_STAR, A01_MR_STAR,
(C)1, A00 );
//------------------------------------------------------------//
WPan_MR_STAR.FreeAlignments();
APan_MR_STAR.FreeAlignments();
WPan_MC_STAR.FreeAlignments();
APan_MC_STAR.FreeAlignments();
WPan.FreeAlignments();
}
else
{
A11_STAR_STAR = A11;
t1_STAR_STAR.ResizeTo( t1.Height(), 1 );
HermitianTridiag
( UPPER, A11_STAR_STAR.LocalMatrix(),
t1_STAR_STAR.LocalMatrix() );
A11 = A11_STAR_STAR;
t1 = t1_STAR_STAR;
}
SlidePartitionUp
( tT, t0,
/**/ /**/
t1,
tB, t2 );
SlidePartitionUpDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
}
}
// Redistribute from matrix-diagonal form to fully replicated
t = tDiag;
#ifndef RELEASE
PopCallStack();
#endif
}
inline void UnblockedBidiagU
( DistMatrix<Complex<R> >& A,
DistMatrix<Complex<R>,MD,STAR>& tP,
DistMatrix<Complex<R>,MD,STAR>& tQ )
{
#ifndef RELEASE
PushCallStack("BidiagU");
#endif
const int tPHeight = std::max(A.Width()-1,0);
const int tQHeight = A.Width();
#ifndef RELEASE
if( A.Grid() != tP.Grid() || tP.Grid() != tQ.Grid() )
throw std::logic_error("Process grids do not match");
if( A.Height() < A.Width() )
throw std::logic_error("A must be at least as tall as it is wide");
if( tP.Viewing() && (tP.Height() != tPHeight || tP.Width() != 1) )
throw std::logic_error("tP is the wrong height");
if( tQ.Viewing() && (tQ.Height() != tQHeight || tQ.Width() != 1) )
throw std::logic_error("tQ is the wrong height");
#endif
typedef Complex<R> C;
const Grid& g = A.Grid();
if( !tP.Viewing() )
tP.ResizeTo( tPHeight, 1 );
if( !tQ.Viewing() )
tQ.ResizeTo( tQHeight, 1 );
// Matrix views
DistMatrix<C>
ATL(g), ATR(g), A00(g), a01(g), A02(g), alpha12L(g), a12R(g),
ABL(g), ABR(g), a10(g), alpha11(g), a12(g), aB1(g), AB2(g),
A20(g), a21(g), A22(g);
// Temporary matrices
DistMatrix<C,STAR,MR > a12_STAR_MR(g);
DistMatrix<C,MC, STAR> aB1_MC_STAR(g);
DistMatrix<C,MR, STAR> x12Adj_MR_STAR(g);
DistMatrix<C,MC, STAR> w21_MC_STAR(g);
PushBlocksizeStack( 1 );
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
while( ATL.Width() < A.Width() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ a01, A02,
/*************/ /**********************/
/**/ a10, /**/ alpha11, a12,
ABL, /**/ ABR, A20, /**/ a21, A22 );
View2x1
( aB1, alpha11,
a21 );
View2x1
( AB2, a12,
A22 );
aB1_MC_STAR.AlignWith( aB1 );
a12_STAR_MR.AlignWith( a12 );
x12Adj_MR_STAR.AlignWith( AB2 );
w21_MC_STAR.AlignWith( A22 );
Zeros( a12.Width(), 1, x12Adj_MR_STAR );
Zeros( a21.Height(), 1, w21_MC_STAR );
const bool thisIsMyRow = ( g.Row() == alpha11.ColAlignment() );
const bool thisIsMyCol = ( g.Col() == alpha11.RowAlignment() );
const bool nextIsMyCol = ( g.Col() == a12.RowAlignment() );
//--------------------------------------------------------------------//
// Find tauQ, u, and epsilonQ such that
// I - conj(tauQ) | 1 | | 1, u^H | | alpha11 | = | epsilonQ |
// | u | | a21 | | 0 |
const C tauQ = Reflector( alpha11, a21 );
tQ.Set(A00.Height(),0,tauQ );
C epsilonQ=0;
if( thisIsMyCol && thisIsMyRow )
epsilonQ = alpha11.GetLocal(0,0);
// Set aB1 = | 1 | and form x12^H := (aB1^H AB2)^H = AB2^H aB1
// | u |
alpha11.Set(0,0,C(1));
aB1_MC_STAR = aB1;
internal::LocalGemv
( ADJOINT, C(1), AB2, aB1_MC_STAR, C(0), x12Adj_MR_STAR );
x12Adj_MR_STAR.SumOverCol();
// Update AB2 := AB2 - conj(tauQ) aB1 x12
// = AB2 - conj(tauQ) aB1 aB1^H AB2
// = (I - conj(tauQ) aB1 aB1^H) AB2
internal::LocalGer( -Conj(tauQ), aB1_MC_STAR, x12Adj_MR_STAR, AB2 );
// Put epsilonQ back instead of the temporary value, 1
if( thisIsMyCol && thisIsMyRow )
alpha11.SetLocal(0,0,epsilonQ);
if( A22.Width() != 0 )
{
// Due to the deficiencies in the BLAS ?gemv routines, this section
// is easier if we temporarily conjugate a12
Conjugate( a12 );
// Expose the subvector we seek to zero, a12R
PartitionRight( a12, alpha12L, a12R );
// Find tauP, v, and epsilonP such that
// I - conj(tauP) | 1 | | 1, v^H | | alpha12L | = | epsilonP |
// | v | | a12R^T | | 0 |
const C tauP = Reflector( alpha12L, a12R );
tP.Set(A00.Height(),0,tauP);
C epsilonP=0;
if( nextIsMyCol && thisIsMyRow )
epsilonP = alpha12L.GetLocal(0,0);
// Set a12^T = | 1 | and form w21 := A22 a12^T = A22 | 1 |
// | v | | v |
alpha12L.Set(0,0,C(1));
a12_STAR_MR = a12;
internal::LocalGemv
( NORMAL, C(1), A22, a12_STAR_MR, C(0), w21_MC_STAR );
w21_MC_STAR.SumOverRow();
// A22 := A22 - tauP w21 conj(a12)
// = A22 - tauP A22 a12^T conj(a12)
// = A22 (I - tauP a12^T conj(a12))
// = A22 conj(I - conj(tauP) a12^H a12)
// which compensates for the fact that the reflector was generated
// on the conjugated a12.
internal::LocalGer( -tauP, w21_MC_STAR, a12_STAR_MR, A22 );
// Put epsilonP back instead of the temporary value, 1
if( nextIsMyCol && thisIsMyRow )
alpha12L.SetLocal(0,0,epsilonP);
// Undue the temporary conjugation
Conjugate( a12 );
}
//--------------------------------------------------------------------//
aB1_MC_STAR.FreeAlignments();
a12_STAR_MR.FreeAlignments();
x12Adj_MR_STAR.FreeAlignments();
w21_MC_STAR.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, a01, /**/ A02,
/**/ a10, alpha11, /**/ a12,
/*************/ /**********************/
ABL, /**/ ABR, A20, a21, /**/ A22 );
}
PopBlocksizeStack();
#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
}