int main()
{
DoubleMatrix A(3,3);
DoubleInterval A00(2,3);
DoubleInterval A10(5,9);
DoubleInterval A11(3,4);
DoubleInterval A20(-2,5);
DoubleInterval A21(3,8);
A(0,0) = A00;
A(0,1) = 0;
A(0,2) = 0;
A(1,0) = A10;
A(1,1) = A11;
A(1,2) = 0;
A(2,0) = A20;
A(2,1) = A21;
A(2,2) = 5;
DoubleInterval X(0,0);
mtl::dense_vector<DoubleInterval> b(3,X);
b[0] = 5;
b[1] = 3;
b[2] = -6;
mtl::dense_vector<DoubleInterval> x(3,X);
x = mtl::mat::upper_trisolve(A,b);
std::cout << x << std::endl;
return 0;
}
void MakeExplicitlyHermitian( UpperOrLower uplo, DistMatrix<F,MC,MR>& A )
{
const Grid& g = A.Grid();
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> A11Adj(g);
DistMatrix<F,MR,MC> A11_MR_MC(g);
DistMatrix<F,MR,MC> A21_MR_MC(g);
DistMatrix<F,MR,MC> A12_MR_MC(g);
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 );
A11Adj.AlignWith( A11 );
A11_MR_MC.AlignWith( A11 );
A12_MR_MC.AlignWith( A21 );
A21_MR_MC.AlignWith( A12 );
//--------------------------------------------------------------------//
A11_MR_MC = A11;
A11Adj.ResizeTo( A11.Height(), A11.Width() );
Adjoint( A11_MR_MC.LocalMatrix(), A11Adj.LocalMatrix() );
if( uplo == LOWER )
{
MakeTrapezoidal( LEFT, UPPER, 1, A11Adj );
Axpy( (F)1, A11Adj, A11 );
A21_MR_MC = A21;
Adjoint( A21_MR_MC.LocalMatrix(), A12.LocalMatrix() );
}
else
{
MakeTrapezoidal( LEFT, LOWER, -1, A11Adj );
Axpy( (F)1, A11Adj, A11 );
A12_MR_MC = A12;
Adjoint( A12_MR_MC.LocalMatrix(), A21.LocalMatrix() );
}
//--------------------------------------------------------------------//
A21_MR_MC.FreeAlignments();
A12_MR_MC.FreeAlignments();
A11_MR_MC.FreeAlignments();
A11Adj.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
}
}
int main()
{
Rat a1(-1,2);
Rat a2(2,9);
Rat b2(3,2);
Rat c1(-1,9);
DoubleInterval A11(a2,b2);
DoubleInterval A12(a1,0);
DoubleInterval A21(-1,c1);
DoubleInterval A22(a2,b2);
DoubleMatrix A(2,2);
A(0,0) = A11;
A(0,1) = A12;
A(1,0) = A21;
A(1,1) = A22;
DoubleInterval B1(1,3);
DoubleInterval B2(3,4);
DoubleVector b(2, (DoubleInterval)0);
b[0] = B1;
b[1] = B2;
std::cout << A << std::endl;
std::cout << b << std::endl;
DoubleVector x(2, (DoubleInterval)0);
x = A * b;
std::cout << x << std::endl;
//Need to sort this out
DoubleInterval test(-1,2);
DoubleInterval testb(5,100);
DoubleInterval ans;
ans = testb/test;
std::cout << ans << std::endl;
DoubleInterval k00(0,2);
DoubleInterval k01(1,3);
DoubleInterval k10(3,5);
DoubleInterval k11(5,7);
std::cout << "INVERSE IS " << std::endl;
std::cout << boost::numeric::Doubleinterval_lib::multiplicative_inverse(k11) << std::endl;
std::cout << boost::numeric::norm(k11) << std::endl;
std::cout << k00 * k11 << std::endl;
std::cout << k01 * k10 << std::endl;
std::cout << (k00 * k11) - (k01 * k10) << std::endl;
return 0;
}
inline void
LQ( DistMatrix<R,MC,MR>& A )
{
#ifndef RELEASE
PushCallStack("LQ");
#endif
if( IsComplex<R>::val )
throw std::logic_error("Called real routine with complex datatype");
const Grid& g = A.Grid();
// Matrix views
DistMatrix<R,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);
PartitionDownLeftDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
while( ATL.Height() < A.Height() && ATL.Width() < A.Width() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
ATopPan.View1x2( A11, A12 );
ABottomPan.View1x2( A21, A22 );
//--------------------------------------------------------------------//
internal::PanelLQ( ATopPan );
ApplyPackedReflectors
( RIGHT, UPPER, HORIZONTAL, FORWARD, 0, ATopPan, ABottomPan );
//--------------------------------------------------------------------//
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
Inverse( DistMatrix<F>& A )
{
#ifndef RELEASE
PushCallStack("Inverse");
if( A.Height() != A.Width() )
throw std::logic_error("Cannot invert non-square matrices");
#endif
const Grid& g = A.Grid();
DistMatrix<int,VC,STAR> p( g );
LU( A, p );
TriangularInverse( UPPER, NON_UNIT, A );
// Solve inv(A) L = inv(U) for inv(A)
DistMatrix<F> ATL(g), ATR(g),
ABL(g), ABR(g);
DistMatrix<F> A00(g), A01(g), A02(g),
A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
DistMatrix<F> A1(g), A2(g);
DistMatrix<F,VC, STAR> A1_VC_STAR(g);
DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
DistMatrix<F,VR, STAR> L21_VR_STAR(g);
DistMatrix<F,STAR,MR > L21Trans_STAR_MR(g);
DistMatrix<F,MC, STAR> Z1(g);
PartitionUpDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
while( ABR.Height() < A.Height() )
{
RepartitionUpDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
View( A1, A, 0, A00.Width(), A.Height(), A01.Width() );
View( A2, A, 0, A00.Width()+A01.Width(), A.Height(), A02.Width() );
L21_VR_STAR.AlignWith( A2 );
L21Trans_STAR_MR.AlignWith( A2 );
Z1.AlignWith( A01 );
Z1.ResizeTo( A.Height(), A01.Width() );
//--------------------------------------------------------------------//
// Copy out L1
L11_STAR_STAR = A11;
L21_VR_STAR = A21;
L21Trans_STAR_MR.TransposeFrom( L21_VR_STAR );
// Zero the strictly lower triangular portion of A1
MakeTrapezoidal( LEFT, UPPER, 0, A11 );
Zero( A21 );
// Perform the lazy update of A1
internal::LocalGemm
( NORMAL, TRANSPOSE,
F(-1), A2, L21Trans_STAR_MR, F(0), Z1 );
A1.SumScatterUpdate( F(1), Z1 );
// Solve against this diagonal block of L11
A1_VC_STAR = A1;
internal::LocalTrsm
( RIGHT, LOWER, NORMAL, UNIT, F(1), L11_STAR_STAR, A1_VC_STAR );
A1 = A1_VC_STAR;
//--------------------------------------------------------------------//
Z1.FreeAlignments();
L21Trans_STAR_MR.FreeAlignments();
L21_VR_STAR.FreeAlignments();
SlidePartitionUpDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /*******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
}
// inv(A) := inv(A) P
ApplyInverseColumnPivots( A, p );
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
SymmLLC
( T alpha, const DistMatrix<T>& A, const DistMatrix<T>& B,
T beta, DistMatrix<T>& C )
{
#ifndef RELEASE
PushCallStack("internal::SymmLLC");
if( A.Grid() != B.Grid() || B.Grid() != C.Grid() )
throw std::logic_error
("{A,B,C} must be distributed over the same grid");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<T>
ATL(g), ATR(g), A00(g), A01(g), A02(g), AColPan(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g), ARowPan(g),
A20(g), A21(g), A22(g);
DistMatrix<T>
BT(g), B0(g),
BB(g), B1(g),
B2(g);
DistMatrix<T>
CT(g), C0(g), CAbove(g),
CB(g), C1(g), CBelow(g),
C2(g);
// Temporary distributions
DistMatrix<T,MC, STAR> AColPan_MC_STAR(g);
DistMatrix<T,STAR,MC > ARowPan_STAR_MC(g);
DistMatrix<T,MR, STAR> B1Trans_MR_STAR(g);
B1Trans_MR_STAR.AlignWith( C );
// Start the algorithm
Scale( beta, C );
LockedPartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
LockedPartitionDown
( B, BT,
BB, 0 );
PartitionDown
( C, CT,
CB, 0 );
while( CB.Height() > 0 )
{
LockedRepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
LockedRepartitionDown
( BT, B0,
/**/ /**/
B1,
BB, B2 );
RepartitionDown
( CT, C0,
/**/ /**/
C1,
CB, C2 );
LockedView1x2( ARowPan, A10, A11 );
LockedView2x1
( AColPan, A11,
A21 );
View2x1
( CAbove, C0,
C1 );
View2x1
( CBelow, C1,
C2 );
AColPan_MC_STAR.AlignWith( CBelow );
ARowPan_STAR_MC.AlignWith( CAbove );
//--------------------------------------------------------------------//
AColPan_MC_STAR = AColPan;
ARowPan_STAR_MC = ARowPan;
MakeTrapezoidal( LEFT, LOWER, 0, AColPan_MC_STAR );
MakeTrapezoidal( RIGHT, LOWER, -1, ARowPan_STAR_MC );
B1Trans_MR_STAR.TransposeFrom( B1 );
LocalGemm
( NORMAL, TRANSPOSE,
alpha, AColPan_MC_STAR, B1Trans_MR_STAR, T(1), CBelow );
LocalGemm
( TRANSPOSE, TRANSPOSE,
alpha, ARowPan_STAR_MC, B1Trans_MR_STAR, T(1), CAbove );
//--------------------------------------------------------------------//
AColPan_MC_STAR.FreeAlignments();
ARowPan_STAR_MC.FreeAlignments();
SlideLockedPartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
SlideLockedPartitionDown
( BT, B0,
B1,
/**/ /**/
BB, B2 );
SlidePartitionDown
( CT, C0,
C1,
/**/ /**/
CB, C2 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
TwoSidedTrsmUVar1
( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& U )
{
#ifndef RELEASE
CallStackEntry entry("internal::TwoSidedTrsmUVar1");
if( A.Height() != A.Width() )
LogicError("A must be square");
if( U.Height() != U.Width() )
LogicError("Triangular matrices must be square");
if( A.Height() != U.Height() )
LogicError("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,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,VC, STAR> A01_VC_STAR(g);
DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
DistMatrix<F,MC, STAR> U01_MC_STAR(g);
DistMatrix<F,VC, STAR> U01_VC_STAR(g);
DistMatrix<F,VR, STAR> U01_VR_STAR(g);
DistMatrix<F,STAR,MR > U01Adj_STAR_MR(g);
DistMatrix<F,STAR,STAR> X11_STAR_STAR(g);
DistMatrix<F,MR, MC > Z01_MR_MC(g);
DistMatrix<F,MC, STAR> Z01_MC_STAR(g);
DistMatrix<F,MR, STAR> Z01_MR_STAR(g);
DistMatrix<F> Y01(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 );
A01_VC_STAR.AlignWith( A01 );
U01_MC_STAR.AlignWith( A00 );
U01_VR_STAR.AlignWith( A00 );
U01_VC_STAR.AlignWith( A00 );
U01Adj_STAR_MR.AlignWith( A00 );
Y01.AlignWith( A01 );
Z01_MR_MC.AlignWith( A01 );
Z01_MC_STAR.AlignWith( A00 );
Z01_MR_STAR.AlignWith( A00 );
//--------------------------------------------------------------------//
// Y01 := A00 U01
U01_MC_STAR = U01;
U01_VR_STAR = U01_MC_STAR;
U01Adj_STAR_MR.AdjointFrom( U01_VR_STAR );
Zeros( Z01_MC_STAR, A01.Height(), A01.Width() );
Zeros( Z01_MR_STAR, A01.Height(), A01.Width() );
LocalSymmetricAccumulateLU
( ADJOINT,
F(1), A00, U01_MC_STAR, U01Adj_STAR_MR, Z01_MC_STAR, Z01_MR_STAR );
Z01_MR_MC.SumScatterFrom( Z01_MR_STAR );
Y01 = Z01_MR_MC;
Y01.SumScatterUpdate( F(1), Z01_MC_STAR );
// A01 := inv(U00)' A01
//
// This is the bottleneck because A01 only has blocksize columns
Trsm( LEFT, UPPER, ADJOINT, diag, F(1), U00, A01 );
// A01 := A01 - 1/2 Y01
Axpy( F(-1)/F(2), Y01, A01 );
// A11 := A11 - (U01' A01 + A01' U01)
A01_VC_STAR = A01;
U01_VC_STAR = U01_MC_STAR;
Zeros( X11_STAR_STAR, A11.Height(), A11.Width() );
Her2k
( UPPER, ADJOINT,
F(-1), A01_VC_STAR.Matrix(), U01_VC_STAR.Matrix(),
F(0), X11_STAR_STAR.Matrix() );
A11.SumScatterUpdate( F(1), X11_STAR_STAR );
// A11 := inv(U11)' A11 inv(U11)
A11_STAR_STAR = A11;
U11_STAR_STAR = U11;
LocalTwoSidedTrsm( UPPER, diag, A11_STAR_STAR, U11_STAR_STAR );
A11 = A11_STAR_STAR;
// A01 := A01 - 1/2 Y01
Axpy( F(-1)/F(2), Y01, A01 );
// A01 := A01 inv(U11)
A01_VC_STAR = A01;
LocalTrsm
( RIGHT, UPPER, NORMAL, diag, F(1), U11_STAR_STAR, A01_VC_STAR );
A01 = A01_VC_STAR;
//--------------------------------------------------------------------//
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 );
}
}
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 );
}
}
inline void
internal::HermitianTridiagU( DistMatrix<R,MC,MR>& A )
{
#ifndef RELEASE
PushCallStack("internal::HermitianTridiagU");
if( A.Height() != A.Width() )
throw std::logic_error( "A must be square." );
#endif
const Grid& g = A.Grid();
if( g.InGrid() )
{
// Matrix views
DistMatrix<R,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<R,MC, MR > WPan(g);
DistMatrix<R,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<R,MC, STAR> APan_MC_STAR(g), A01_MC_STAR(g),
A11_MC_STAR(g);
DistMatrix<R,MR, STAR> APan_MR_STAR(g), A01_MR_STAR(g),
A11_MR_STAR(g);
DistMatrix<R,MC, STAR> WPan_MC_STAR(g), W01_MC_STAR(g),
W11_MC_STAR(g);
DistMatrix<R,MR, STAR> WPan_MR_STAR(g), W01_MR_STAR(g),
W11_MR_STAR(g);
PartitionUpDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
while( ABR.Height() < A.Height() )
{
RepartitionUpDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
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,
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, TRANSPOSE, TRANSPOSE,
(R)-1, A01_MC_STAR, W01_MR_STAR,
W01_MC_STAR, A01_MR_STAR,
(R)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;
HermitianTridiag( UPPER, A11_STAR_STAR.LocalMatrix() );
A11 = A11_STAR_STAR;
}
SlidePartitionUpDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
}
}
#ifndef RELEASE
PopCallStack();
#endif
}
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
TwoSidedTrsmLVar2
( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& L )
{
#ifndef RELEASE
PushCallStack("internal::TwoSidedTrsmLVar2");
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,MR, STAR> A10Adj_MR_STAR(g);
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,MR, STAR> F10Adj_MR_STAR(g);
DistMatrix<F,MR, STAR> L10Adj_MR_STAR(g);
DistMatrix<F,VC, STAR> L10Adj_VC_STAR(g);
DistMatrix<F,STAR,MC > L10_STAR_MC(g);
DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
DistMatrix<F,MC, STAR> X11_MC_STAR(g);
DistMatrix<F,MC, STAR> X21_MC_STAR(g);
DistMatrix<F,MC, STAR> Y10Adj_MC_STAR(g);
DistMatrix<F,MR, MC > Y10Adj_MR_MC(g);
DistMatrix<F> X11(g);
DistMatrix<F> Y10Adj(g);
Matrix<F> Y10Local;
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 );
A10Adj_MR_STAR.AlignWith( L10 );
F10Adj_MR_STAR.AlignWith( A00 );
L10Adj_MR_STAR.AlignWith( A00 );
L10Adj_VC_STAR.AlignWith( A00 );
L10_STAR_MC.AlignWith( A00 );
X11.AlignWith( A11 );
X11_MC_STAR.AlignWith( L10 );
X21_MC_STAR.AlignWith( A20 );
Y10Adj_MC_STAR.AlignWith( A00 );
Y10Adj_MR_MC.AlignWith( A10 );
//--------------------------------------------------------------------//
// Y10 := L10 A00
L10Adj_MR_STAR.AdjointFrom( L10 );
L10Adj_VC_STAR = L10Adj_MR_STAR;
L10_STAR_MC.AdjointFrom( L10Adj_VC_STAR );
Y10Adj_MC_STAR.ResizeTo( A10.Width(), A10.Height() );
F10Adj_MR_STAR.ResizeTo( A10.Width(), A10.Height() );
Zero( Y10Adj_MC_STAR );
Zero( F10Adj_MR_STAR );
LocalSymmetricAccumulateRL
( ADJOINT,
F(1), A00, L10_STAR_MC, L10Adj_MR_STAR,
Y10Adj_MC_STAR, F10Adj_MR_STAR );
Y10Adj.SumScatterFrom( Y10Adj_MC_STAR );
Y10Adj_MR_MC = Y10Adj;
Y10Adj_MR_MC.SumScatterUpdate( F(1), F10Adj_MR_STAR );
Adjoint( Y10Adj_MR_MC.LockedLocalMatrix(), Y10Local );
// X11 := A10 L10'
X11_MC_STAR.ResizeTo( A11.Height(), A11.Width() );
LocalGemm
( NORMAL, NORMAL, F(1), A10, L10Adj_MR_STAR, F(0), X11_MC_STAR );
// A10 := A10 - Y10
Axpy( F(-1), Y10Local, A10.LocalMatrix() );
A10Adj_MR_STAR.AdjointFrom( A10 );
// A11 := A11 - (X11 + L10 A10') = A11 - (A10 L10' + L10 A10')
LocalGemm
( NORMAL, NORMAL, F(1), L10, A10Adj_MR_STAR, F(1), X11_MC_STAR );
X11.SumScatterFrom( X11_MC_STAR );
MakeTrapezoidal( LEFT, LOWER, 0, X11 );
Axpy( F(-1), X11, A11 );
// A10 := inv(L11) A10
L11_STAR_STAR = L11;
A10_STAR_VR.AdjointFrom( A10Adj_MR_STAR );
LocalTrsm
( LEFT, LOWER, NORMAL, diag, F(1), L11_STAR_STAR, A10_STAR_VR );
A10 = A10_STAR_VR;
// A11 := inv(L11) A11 inv(L11)'
A11_STAR_STAR = A11;
LocalTwoSidedTrsm( LOWER, diag, A11_STAR_STAR, L11_STAR_STAR );
A11 = A11_STAR_STAR;
// A21 := A21 - A20 L10'
X21_MC_STAR.ResizeTo( A21.Height(), A21.Width() );
LocalGemm
( NORMAL, NORMAL, F(1), A20, L10Adj_MR_STAR, F(0), X21_MC_STAR );
A21.SumScatterUpdate( F(-1), X21_MC_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;
//--------------------------------------------------------------------//
A10Adj_MR_STAR.FreeAlignments();
F10Adj_MR_STAR.FreeAlignments();
L10Adj_MR_STAR.FreeAlignments();
L10Adj_VC_STAR.FreeAlignments();
L10_STAR_MC.FreeAlignments();
X11.FreeAlignments();
X11_MC_STAR.FreeAlignments();
X21_MC_STAR.FreeAlignments();
Y10Adj_MC_STAR.FreeAlignments();
Y10Adj_MR_MC.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
}
void CudaModule::printDeviceInfo(CUdevice device)
{
static const struct
{
CUdevice_attribute attrib;
const char* name;
} attribs[] =
{
#define A21(ENUM, NAME) { CU_DEVICE_ATTRIBUTE_ ## ENUM, NAME },
#if (CUDA_VERSION >= 4000)
# define A40(ENUM, NAME) A21(ENUM, NAME)
#else
# define A40(ENUM, NAME) // TODO: Some of these may exist in earlier versions, too.
#endif
A21(CLOCK_RATE, "Clock rate")
A40(MEMORY_CLOCK_RATE, "Memory clock rate")
A21(MULTIPROCESSOR_COUNT, "Number of SMs")
// A40(GLOBAL_MEMORY_BUS_WIDTH, "DRAM bus width")
// A40(L2_CACHE_SIZE, "L2 cache size")
A21(MAX_THREADS_PER_BLOCK, "Max threads per block")
A40(MAX_THREADS_PER_MULTIPROCESSOR, "Max threads per SM")
A21(REGISTERS_PER_BLOCK, "Registers per block")
// A40(MAX_REGISTERS_PER_BLOCK, "Max registers per block")
A21(SHARED_MEMORY_PER_BLOCK, "Shared mem per block")
// A40(MAX_SHARED_MEMORY_PER_BLOCK, "Max shared mem per block")
A21(TOTAL_CONSTANT_MEMORY, "Constant memory")
// A21(WARP_SIZE, "Warp size")
A21(MAX_BLOCK_DIM_X, "Max blockDim.x")
// A21(MAX_BLOCK_DIM_Y, "Max blockDim.y")
// A21(MAX_BLOCK_DIM_Z, "Max blockDim.z")
A21(MAX_GRID_DIM_X, "Max gridDim.x")
// A21(MAX_GRID_DIM_Y, "Max gridDim.y")
// A21(MAX_GRID_DIM_Z, "Max gridDim.z")
// A40(MAXIMUM_TEXTURE1D_WIDTH, "Max tex1D.x")
// A40(MAXIMUM_TEXTURE2D_WIDTH, "Max tex2D.x")
// A40(MAXIMUM_TEXTURE2D_HEIGHT, "Max tex2D.y")
// A40(MAXIMUM_TEXTURE3D_WIDTH, "Max tex3D.x")
// A40(MAXIMUM_TEXTURE3D_HEIGHT, "Max tex3D.y")
// A40(MAXIMUM_TEXTURE3D_DEPTH, "Max tex3D.z")
// A40(MAXIMUM_TEXTURE1D_LAYERED_WIDTH, "Max layerTex1D.x")
// A40(MAXIMUM_TEXTURE1D_LAYERED_LAYERS, "Max layerTex1D.y")
// A40(MAXIMUM_TEXTURE2D_LAYERED_WIDTH, "Max layerTex2D.x")
// A40(MAXIMUM_TEXTURE2D_LAYERED_HEIGHT, "Max layerTex2D.y")
// A40(MAXIMUM_TEXTURE2D_LAYERED_LAYERS, "Max layerTex2D.z")
// A40(MAXIMUM_TEXTURE2D_ARRAY_WIDTH, "Max array.x")
// A40(MAXIMUM_TEXTURE2D_ARRAY_HEIGHT, "Max array.y")
// A40(MAXIMUM_TEXTURE2D_ARRAY_NUMSLICES, "Max array.z")
// A21(MAX_PITCH, "Max memcopy pitch")
// A21(TEXTURE_ALIGNMENT, "Texture alignment")
// A40(SURFACE_ALIGNMENT, "Surface alignment")
A40(CONCURRENT_KERNELS, "Concurrent launches supported")
A21(GPU_OVERLAP, "Concurrent memcopy supported")
A40(ASYNC_ENGINE_COUNT, "Max concurrent memcopies")
// A40(KERNEL_EXEC_TIMEOUT, "Kernel launch time limited")
// A40(INTEGRATED, "Integrated with host memory")
A40(UNIFIED_ADDRESSING, "Unified addressing supported")
A40(CAN_MAP_HOST_MEMORY, "Can map host memory")
A40(ECC_ENABLED, "ECC enabled")
// A40(TCC_DRIVER, "Driver is TCC")
// A40(COMPUTE_MODE, "Compute exclusivity mode")
// A40(PCI_BUS_ID, "PCI bus ID")
// A40(PCI_DEVICE_ID, "PCI device ID")
// A40(PCI_DOMAIN_ID, "PCI domain ID")
#undef A21
#undef A40
};
char name[256];
int major;
int minor;
size_t memory;
checkError("cuDeviceGetName", cuDeviceGetName(name, FW_ARRAY_SIZE(name) - 1, device));
checkError("cuDeviceComputeCapability", cuDeviceComputeCapability(&major, &minor, device));
checkError("cuDeviceTotalMem", cuDeviceTotalMem(&memory, device));
name[FW_ARRAY_SIZE(name) - 1] = '\0';
printf("\n");
char deviceIdStr[16];
sprintf( deviceIdStr, "CUDA device %d", device);
printf("%-32s%s\n",deviceIdStr, name);
printf("%-32s%s\n", "---", "---");
int version = getDriverVersion();
printf("%-32s%d.%d\n", "CUDA driver API version", version/10, version%10);
printf("%-32s%d.%d\n", "Compute capability", major, minor);
printf("%-32s%.0f megs\n", "Total memory", (F32)memory * exp2(-20));
for (int i = 0; i < (int)FW_ARRAY_SIZE(attribs); i++)
{
int value;
if (cuDeviceGetAttribute(&value, attribs[i].attrib, device) == CUDA_SUCCESS)
printf("%-32s%d\n", attribs[i].name, value);
}
printf("\n");
}
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
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
HemmRUC
( T alpha, const DistMatrix<T>& A,
const DistMatrix<T>& B,
T beta, DistMatrix<T>& C )
{
#ifndef RELEASE
PushCallStack("internal::HemmRUC");
if( A.Grid() != B.Grid() || B.Grid() != C.Grid() )
throw std::logic_error("{A,B,C} must be distributed on the same grid");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<T>
ATL(g), ATR(g), A00(g), A01(g), A02(g), AColPan(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g), ARowPan(g),
A20(g), A21(g), A22(g);
DistMatrix<T> BL(g), BR(g),
B0(g), B1(g), B2(g);
DistMatrix<T> CL(g), CR(g),
C0(g), C1(g), C2(g),
CLeft(g), CRight(g);
// Temporary distributions
DistMatrix<T,MC,STAR> B1_MC_STAR(g);
DistMatrix<T,VR, STAR> AColPan_VR_STAR(g);
DistMatrix<T,STAR,MR > AColPanAdj_STAR_MR(g);
DistMatrix<T,MR, STAR> ARowPanAdj_MR_STAR(g);
B1_MC_STAR.AlignWith( C );
// Start the algorithm
Scale( beta, C );
LockedPartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
LockedPartitionRight( B, BL, BR, 0 );
PartitionRight( C, CL, CR, 0 );
while( CR.Width() > 0 )
{
LockedRepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
LockedRepartitionRight
( BL, /**/ BR,
B0, /**/ B1, B2 );
RepartitionRight
( CL, /**/ CR,
C0, /**/ C1, C2 );
ARowPan.LockedView1x2( A11, A12 );
AColPan.LockedView2x1
( A01,
A11 );
CLeft.View1x2( C0, C1 );
CRight.View1x2( C1, C2 );
AColPan_VR_STAR.AlignWith( CLeft );
AColPanAdj_STAR_MR.AlignWith( CLeft );
ARowPanAdj_MR_STAR.AlignWith( CRight );
//--------------------------------------------------------------------//
B1_MC_STAR = B1;
AColPan_VR_STAR = AColPan;
AColPanAdj_STAR_MR.AdjointFrom( AColPan_VR_STAR );
ARowPanAdj_MR_STAR.AdjointFrom( ARowPan );
MakeTrapezoidal( LEFT, LOWER, 0, ARowPanAdj_MR_STAR );
MakeTrapezoidal( RIGHT, LOWER, -1, AColPanAdj_STAR_MR );
LocalGemm
( NORMAL, ADJOINT,
alpha, B1_MC_STAR, ARowPanAdj_MR_STAR, T(1), CRight );
LocalGemm
( NORMAL, NORMAL,
alpha, B1_MC_STAR, AColPanAdj_STAR_MR, T(1), CLeft );
//--------------------------------------------------------------------//
AColPan_VR_STAR.FreeAlignments();
AColPanAdj_STAR_MR.FreeAlignments();
ARowPanAdj_MR_STAR.FreeAlignments();
SlideLockedPartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
SlideLockedPartitionRight
( BL, /**/ BR,
B0, B1, /**/ B2 );
SlidePartitionRight
( CL, /**/ CR,
C0, C1, /**/ C2 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
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;
}
void LSquare( DistMatrix<R>& A )
{
#ifndef RELEASE
CallStackEntry entry("hermitian_tridiag::LSquare");
if( A.Height() != A.Width() )
throw std::logic_error("A must be square");
if( A.Grid().Height() != A.Grid().Width() )
throw std::logic_error("The process grid must be square");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<R>
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<R> WPan(g);
DistMatrix<R,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<R,MC, STAR> APan_MC_STAR(g), A11_MC_STAR(g),
A21_MC_STAR(g);
DistMatrix<R,MR, STAR> APan_MR_STAR(g), A11_MR_STAR(g),
A21_MR_STAR(g);
DistMatrix<R,MC, STAR> WPan_MC_STAR(g), W11_MC_STAR(g),
W21_MC_STAR(g);
DistMatrix<R,MR, STAR> WPan_MR_STAR(g), W11_MR_STAR(g),
W21_MR_STAR(g);
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 );
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,
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, TRANSPOSE, TRANSPOSE,
R(-1), A21_MC_STAR, W21_MR_STAR,
W21_MC_STAR, A21_MR_STAR,
R(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;
HermitianTridiag( LOWER, A11_STAR_STAR.Matrix() );
A11 = A11_STAR_STAR;
}
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
}
}
inline void
internal::CholeskyUVar3Square( DistMatrix<F,MC,MR>& A )
{
#ifndef RELEASE
PushCallStack("internal::CholeskyUVar3Square");
if( A.Height() != A.Width() )
throw std::logic_error
("Can only compute Cholesky factor of square matrices.");
if( A.Grid().Height() != A.Grid().Width() )
throw std::logic_error
("CholeskyUVar3Square assumes a square process grid.");
#endif
const Grid& g = A.Grid();
// Find the process holding our transposed data
const int r = g.Height();
int transposeRank;
{
const int colAlignment = A.ColAlignment();
const int rowAlignment = A.RowAlignment();
const int colShift = A.ColShift();
const int rowShift = A.RowShift();
const int transposeRow = (colAlignment+rowShift) % r;
const int transposeCol = (rowAlignment+colShift) % r;
transposeRank = transposeRow + r*transposeCol;
}
const bool onDiagonal = ( transposeRank == g.VCRank() );
// 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 matrix distributions
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,STAR,VR > A12_STAR_VR(g);
DistMatrix<F,STAR,MC > A12_STAR_MC(g);
DistMatrix<F,STAR,MR > A12_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 );
A12_STAR_MC.AlignWith( A22 );
A12_STAR_MR.AlignWith( A22 );
A12_STAR_VR.AlignWith( A22 );
//--------------------------------------------------------------------//
A11_STAR_STAR = A11;
internal::LocalCholesky( UPPER, A11_STAR_STAR );
A11 = A11_STAR_STAR;
A12_STAR_VR = A12;
internal::LocalTrsm
( LEFT, UPPER, ADJOINT, NON_UNIT, (F)1, A11_STAR_STAR, A12_STAR_VR );
A12_STAR_MR = A12_STAR_VR;
// SendRecv to form A12[* ,MC] from A12[* ,MR]
A12_STAR_MC.ResizeTo( A12.Height(), A12.Width() );
{
if( onDiagonal )
{
const int size = A11.Height()*A22.LocalWidth();
MemCopy
( A12_STAR_MC.LocalBuffer(),
A12_STAR_MR.LocalBuffer(), size );
}
else
{
const int sendSize = A11.Height()*A22.LocalWidth();
const int recvSize = A11.Width()*A22.LocalHeight();
// We know that the ldim is the height since we have manually
// created both temporary matrices.
mpi::SendRecv
( A12_STAR_MR.LocalBuffer(), sendSize, transposeRank, 0,
A12_STAR_MC.LocalBuffer(), recvSize, transposeRank, 0,
g.VCComm() );
}
}
internal::LocalTrrk
( UPPER, ADJOINT, (F)-1, A12_STAR_MC, A12_STAR_MR, (F)1, A22 );
A12 = A12_STAR_MR;
//--------------------------------------------------------------------//
A12_STAR_MC.FreeAlignments();
A12_STAR_MR.FreeAlignments();
A12_STAR_VR.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
TwoSidedTrmmUVar5
( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& U )
{
#ifndef RELEASE
PushCallStack("internal::TwoSidedTrmmUVar5");
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,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,MC, STAR> A01_MC_STAR(g);
DistMatrix<F,MR, STAR> A01_MR_STAR(g);
DistMatrix<F,VC, STAR> A01_VC_STAR(g);
DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
DistMatrix<F,MC, STAR> U01_MC_STAR(g);
DistMatrix<F,MR, STAR> U01_MR_STAR(g);
DistMatrix<F,VC, STAR> U01_VC_STAR(g);
DistMatrix<F,VC, STAR> Y01_VC_STAR(g);
DistMatrix<F> Y01(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 );
A01_MC_STAR.AlignWith( A00 );
A01_MR_STAR.AlignWith( A00 );
A01_VC_STAR.AlignWith( A00 );
U01_MC_STAR.AlignWith( A00 );
U01_MR_STAR.AlignWith( A00 );
U01_VC_STAR.AlignWith( A00 );
Y01.AlignWith( A01 );
Y01_VC_STAR.AlignWith( A01 );
//--------------------------------------------------------------------//
// Y01 := U01 A11
A11_STAR_STAR = A11;
U01_VC_STAR = U01;
Y01_VC_STAR.ResizeTo( A01.Height(), A01.Width() );
Hemm
( RIGHT, UPPER,
F(1), A11_STAR_STAR.LocalMatrix(), U01_VC_STAR.LocalMatrix(),
F(0), Y01_VC_STAR.LocalMatrix() );
Y01 = Y01_VC_STAR;
// A01 := U00 A01
Trmm( LEFT, UPPER, NORMAL, diag, F(1), U00, A01 );
// A01 := A01 + 1/2 Y01
Axpy( F(1)/F(2), Y01, A01 );
// A00 := A00 + (U01 A01' + A01 U01')
A01_MC_STAR = A01;
U01_MC_STAR = U01;
A01_VC_STAR = A01_MC_STAR;
A01_MR_STAR = A01_VC_STAR;
U01_MR_STAR = U01_MC_STAR;
LocalTrr2k
( UPPER, ADJOINT, ADJOINT,
F(1), U01_MC_STAR, A01_MR_STAR,
A01_MC_STAR, U01_MR_STAR,
F(1), A00 );
// A01 := A01 + 1/2 Y01
Axpy( F(1)/F(2), Y01_VC_STAR, A01_VC_STAR );
// A01 := A01 U11'
U11_STAR_STAR = U11;
LocalTrmm
( RIGHT, UPPER, ADJOINT, diag, F(1), U11_STAR_STAR, A01_VC_STAR );
A01 = A01_VC_STAR;
// A11 := U11 A11 U11'
LocalTwoSidedTrmm( UPPER, diag, A11_STAR_STAR, U11_STAR_STAR );
A11 = A11_STAR_STAR;
//--------------------------------------------------------------------//
A01_MC_STAR.FreeAlignments();
A01_MR_STAR.FreeAlignments();
A01_VC_STAR.FreeAlignments();
U01_MC_STAR.FreeAlignments();
U01_MR_STAR.FreeAlignments();
U01_VC_STAR.FreeAlignments();
Y01.FreeAlignments();
Y01_VC_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
internal::HegstLLVar4( DistMatrix<F,MC,MR>& A, const DistMatrix<F,MC,MR>& L )
{
#ifndef RELEASE
PushCallStack("internal::HegstLLVar4");
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>
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,STAR,MR > L10_STAR_MR(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 );
L10_STAR_MR.AlignWith( A00 );
L10_STAR_MC.AlignWith( A00 );
Y10_STAR_VR.AlignWith( A10 );
//--------------------------------------------------------------------//
// Y10 := A11 L10
A11_STAR_STAR = A11;
L10_STAR_VR = L10;
Y10_STAR_VR.ResizeTo( A10.Height(), A10.Width() );
Zero( Y10_STAR_VR );
Hemm
( LEFT, LOWER,
(F)0.5, 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, 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_MR = L10_STAR_VR;
L10_STAR_MC = L10_STAR_VR;
internal::LocalTrr2k
( LOWER, ADJOINT, ADJOINT,
(F)1, A10_STAR_MC, L10_STAR_MR,
L10_STAR_MC, A10_STAR_MR,
(F)1, A00 );
// A10 := A10 + 1/2 Y10
Axpy( (F)1, Y10_STAR_VR, A10_STAR_VR );
// A10 := L11' A10
L11_STAR_STAR = L11;
internal::LocalTrmm
( LEFT, LOWER, ADJOINT, NON_UNIT, (F)1, L11_STAR_STAR, A10_STAR_VR );
A10 = A10_STAR_VR;
// A20 := A20 + A21 L10
A21_MC_STAR = A21;
internal::LocalGemm
( NORMAL, NORMAL, (F)1, A21_MC_STAR, L10_STAR_MR, (F)1, A20 );
// A11 := L11' A11 L11
internal::LocalHegst
( LEFT, LOWER, A11_STAR_STAR, L11_STAR_STAR );
A11 = A11_STAR_STAR;
// A21 := A21 L11
A21_VC_STAR = A21_MC_STAR;
internal::LocalTrmm
( RIGHT, LOWER, NORMAL, NON_UNIT, (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();
L10_STAR_MR.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
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
TwoSidedTrsmUVar4
( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& U )
{
#ifndef RELEASE
CallStackEntry entry("internal::TwoSidedTrsmUVar4");
if( A.Height() != A.Width() )
LogicError("A must be square");
if( U.Height() != U.Width() )
LogicError("Triangular matrices must be square");
if( A.Height() != U.Height() )
LogicError("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,MC > A01Trans_STAR_MC(g);
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,STAR,VR > A12_STAR_VR(g);
DistMatrix<F,STAR,VC > A12_STAR_VC(g);
DistMatrix<F,STAR,MC > A12_STAR_MC(g);
DistMatrix<F,STAR,MR > A12_STAR_MR(g);
DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
DistMatrix<F,MR, STAR> U12Trans_MR_STAR(g);
DistMatrix<F,VR, STAR> U12Trans_VR_STAR(g);
DistMatrix<F,STAR,VR > U12_STAR_VR(g);
DistMatrix<F,STAR,VC > U12_STAR_VC(g);
DistMatrix<F,STAR,MC > U12_STAR_MC(g);
DistMatrix<F,STAR,VR > Y12_STAR_VR(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 );
A01_VC_STAR.AlignWith( A02 );
A01Trans_STAR_MC.AlignWith( A02 );
A12_STAR_VR.AlignWith( A22 );
A12_STAR_VC.AlignWith( A22 );
A12_STAR_MC.AlignWith( A22 );
A12_STAR_MR.AlignWith( A22 );
U12Trans_MR_STAR.AlignWith( A02 );
U12Trans_VR_STAR.AlignWith( A02 );
U12_STAR_VR.AlignWith( A02 );
U12_STAR_VC.AlignWith( A22 );
U12_STAR_MC.AlignWith( A22 );
Y12_STAR_VR.AlignWith( A12 );
//--------------------------------------------------------------------//
// A01 := A01 inv(U11)
A01_VC_STAR = A01;
U11_STAR_STAR = U11;
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;
// A02 := A02 - A01 U12
A01Trans_STAR_MC.TransposeFrom( A01_VC_STAR );
U12Trans_MR_STAR.TransposeFrom( U12 );
LocalGemm
( TRANSPOSE, TRANSPOSE,
F(-1), A01Trans_STAR_MC, U12Trans_MR_STAR, F(1), A02 );
// Y12 := A11 U12
U12Trans_VR_STAR = U12Trans_MR_STAR;
Zeros( U12_STAR_VR, A12.Height(), A12.Width() );
Transpose( U12Trans_VR_STAR.Matrix(), U12_STAR_VR.Matrix() );
Zeros( Y12_STAR_VR, A12.Height(), A12.Width() );
Hemm
( LEFT, UPPER,
F(1), A11_STAR_STAR.Matrix(), U12_STAR_VR.Matrix(),
F(0), Y12_STAR_VR.Matrix() );
// A12 := inv(U11)' A12
A12_STAR_VR = A12;
LocalTrsm
( LEFT, UPPER, ADJOINT, diag, F(1), U11_STAR_STAR, A12_STAR_VR );
// A12 := A12 - 1/2 Y12
Axpy( F(-1)/F(2), Y12_STAR_VR, A12_STAR_VR );
// A22 := A22 - (A12' U12 + U12' A12)
A12_STAR_MR = A12_STAR_VR;
A12_STAR_VC = A12_STAR_VR;
U12_STAR_VC = U12_STAR_VR;
A12_STAR_MC = A12_STAR_VC;
U12_STAR_MC = U12_STAR_VC;
LocalTrr2k
( UPPER, ADJOINT, TRANSPOSE, ADJOINT,
F(-1), A12_STAR_MC, U12Trans_MR_STAR,
U12_STAR_MC, A12_STAR_MR,
F(1), A22 );
// A12 := A12 - 1/2 Y12
Axpy( F(-1)/F(2), Y12_STAR_VR, A12_STAR_VR );
A12 = A12_STAR_VR;
//--------------------------------------------------------------------//
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 );
}
}
inline void
LocalSymmetricAccumulateLU
( Orientation orientation, T alpha,
const DistMatrix<T>& A,
const DistMatrix<T,MC, STAR>& B_MC_STAR,
const DistMatrix<T,STAR,MR >& BAdjOrTrans_STAR_MR,
DistMatrix<T,MC, STAR>& Z_MC_STAR,
DistMatrix<T,MR, STAR>& Z_MR_STAR )
{
#ifndef RELEASE
PushCallStack("internal::LocalSymmetricAccumulateLU");
if( A.Grid() != B_MC_STAR.Grid() ||
B_MC_STAR.Grid() != BAdjOrTrans_STAR_MR.Grid() ||
BAdjOrTrans_STAR_MR.Grid() != Z_MC_STAR.Grid() ||
Z_MC_STAR.Grid() != Z_MR_STAR.Grid() )
throw std::logic_error
("{A,B,Z} must be distributed over the same grid");
if( A.Height() != A.Width() ||
A.Height() != B_MC_STAR.Height() ||
A.Height() != BAdjOrTrans_STAR_MR.Width() ||
A.Height() != Z_MC_STAR.Height() ||
A.Height() != Z_MR_STAR.Height() ||
B_MC_STAR.Width() != BAdjOrTrans_STAR_MR.Height() ||
BAdjOrTrans_STAR_MR.Height() != Z_MC_STAR.Width() ||
Z_MC_STAR.Width() != Z_MR_STAR.Width() )
{
std::ostringstream msg;
msg << "Nonconformal LocalSymmetricAccumulateLU: \n"
<< " A ~ " << A.Height() << " x " << A.Width() << "\n"
<< " B[MC,* ] ~ " << B_MC_STAR.Height() << " x "
<< B_MC_STAR.Width() << "\n"
<< " B^H/T[* ,MR] ~ " << BAdjOrTrans_STAR_MR.Height() << " x "
<< BAdjOrTrans_STAR_MR.Width() << "\n"
<< " Z[MC,* ] ~ " << Z_MC_STAR.Height() << " x "
<< Z_MC_STAR.Width() << "\n"
<< " Z[MR,* ] ` " << Z_MR_STAR.Height() << " x "
<< Z_MR_STAR.Width() << "\n";
throw std::logic_error( msg.str().c_str() );
}
if( B_MC_STAR.ColAlignment() != A.ColAlignment() ||
BAdjOrTrans_STAR_MR.RowAlignment() != A.RowAlignment() ||
Z_MC_STAR.ColAlignment() != A.ColAlignment() ||
Z_MR_STAR.ColAlignment() != A.RowAlignment() )
throw std::logic_error("Partial matrix distributions are misaligned");
#endif
const Grid& g = A.Grid();
DistMatrix<T>
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<T> D11(g);
DistMatrix<T,MC,STAR>
BT_MC_STAR(g), B0_MC_STAR(g),
BB_MC_STAR(g), B1_MC_STAR(g),
B2_MC_STAR(g);
DistMatrix<T,STAR,MR>
BLAdjOrTrans_STAR_MR(g), BRAdjOrTrans_STAR_MR(g),
B0AdjOrTrans_STAR_MR(g), B1AdjOrTrans_STAR_MR(g),
B2AdjOrTrans_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);
DistMatrix<T,MR,STAR>
ZT_MR_STAR(g), Z0_MR_STAR(g),
ZB_MR_STAR(g), Z1_MR_STAR(g),
Z2_MR_STAR(g);
const int ratio = std::max( g.Height(), g.Width() );
PushBlocksizeStack( ratio*Blocksize() );
LockedPartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
LockedPartitionDown
( B_MC_STAR, BT_MC_STAR,
BB_MC_STAR, 0 );
LockedPartitionRight
( BAdjOrTrans_STAR_MR, BLAdjOrTrans_STAR_MR, BRAdjOrTrans_STAR_MR, 0 );
PartitionDown
( Z_MC_STAR, ZT_MC_STAR,
ZB_MC_STAR, 0 );
PartitionDown
( Z_MR_STAR, ZT_MR_STAR,
ZB_MR_STAR, 0 );
while( ATL.Height() < A.Height() )
{
LockedRepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
LockedRepartitionDown
( BT_MC_STAR, B0_MC_STAR,
/**********/ /**********/
B1_MC_STAR,
BB_MC_STAR, B2_MC_STAR );
LockedRepartitionRight
( BLAdjOrTrans_STAR_MR, /**/ BRAdjOrTrans_STAR_MR,
B0AdjOrTrans_STAR_MR, /**/ B1AdjOrTrans_STAR_MR,
B2AdjOrTrans_STAR_MR );
RepartitionDown
( ZT_MC_STAR, Z0_MC_STAR,
/**********/ /**********/
Z1_MC_STAR,
ZB_MC_STAR, Z2_MC_STAR );
RepartitionDown
( ZT_MR_STAR, Z0_MR_STAR,
/**********/ /**********/
Z1_MR_STAR,
ZB_MR_STAR, Z2_MR_STAR );
D11.AlignWith( A11 );
//--------------------------------------------------------------------//
D11 = A11;
MakeTrapezoidal( LEFT, UPPER, 0, D11 );
LocalGemm
( NORMAL, orientation,
alpha, D11, B1AdjOrTrans_STAR_MR, T(1), Z1_MC_STAR );
MakeTrapezoidal( LEFT, UPPER, 1, D11 );
LocalGemm
( orientation, NORMAL, alpha, D11, B1_MC_STAR, T(1), Z1_MR_STAR );
LocalGemm
( NORMAL, orientation,
alpha, A12, B2AdjOrTrans_STAR_MR, T(1), Z1_MC_STAR );
LocalGemm
( orientation, NORMAL, alpha, A12, B1_MC_STAR, T(1), Z2_MR_STAR );
//--------------------------------------------------------------------//
D11.FreeAlignments();
SlideLockedPartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
SlideLockedPartitionDown
( BT_MC_STAR, B0_MC_STAR,
B1_MC_STAR,
/**********/ /**********/
BB_MC_STAR, B2_MC_STAR );
SlideLockedPartitionRight
( BLAdjOrTrans_STAR_MR, /**/ BRAdjOrTrans_STAR_MR,
B0AdjOrTrans_STAR_MR, B1AdjOrTrans_STAR_MR, /**/ B2AdjOrTrans_STAR_MR );
SlidePartitionDown
( ZT_MC_STAR, Z0_MC_STAR,
Z1_MC_STAR,
/**********/ /**********/
ZB_MC_STAR, Z2_MC_STAR );
SlidePartitionDown
( ZT_MR_STAR, Z0_MR_STAR,
Z1_MR_STAR,
/**********/ /**********/
ZB_MR_STAR, Z2_MR_STAR );
}
PopBlocksizeStack();
#ifndef RELEASE
PopCallStack();
#endif
}
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
CholeskyUVar3( DistMatrix<F>& A )
{
#ifndef RELEASE
PushCallStack("internal::CholeskyUVar3");
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>
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 matrix distributions
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,STAR,VR > A12_STAR_VR(g);
DistMatrix<F,STAR,MC > A12_STAR_MC(g);
DistMatrix<F,STAR,MR > A12_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 );
A12_STAR_MC.AlignWith( A22 );
A12_STAR_MR.AlignWith( A22 );
A12_STAR_VR.AlignWith( A22 );
//--------------------------------------------------------------------//
A11_STAR_STAR = A11;
LocalCholesky( UPPER, A11_STAR_STAR );
A11 = A11_STAR_STAR;
A12_STAR_VR = A12;
LocalTrsm
( LEFT, UPPER, ADJOINT, NON_UNIT, F(1), A11_STAR_STAR, A12_STAR_VR );
A12_STAR_MC = A12_STAR_VR;
A12_STAR_MR = A12_STAR_VR;
LocalTrrk
( UPPER, ADJOINT, F(-1), A12_STAR_MC, A12_STAR_MR, F(1), A22 );
A12 = A12_STAR_MR;
//--------------------------------------------------------------------//
A12_STAR_MC.FreeAlignments();
A12_STAR_MR.FreeAlignments();
A12_STAR_VR.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
LU( DistMatrix<F>& A )
{
#ifndef RELEASE
CallStackEntry entry("LU");
#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);
// 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);
// Start the algorithm
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
while( ATL.Height() < A.Height() && ATL.Width() < A.Width() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
A12_STAR_VR.AlignWith( A22 );
A12_STAR_MR.AlignWith( A22 );
A21_MC_STAR.AlignWith( A22 );
A11_STAR_STAR.ResizeTo( A11.Height(), A11.Width() );
//--------------------------------------------------------------------//
A11_STAR_STAR = A11;
LocalLU( A11_STAR_STAR );
A11 = A11_STAR_STAR;
A21_MC_STAR = A21;
LocalTrsm
( RIGHT, UPPER, NORMAL, NON_UNIT, F(1), A11_STAR_STAR, A21_MC_STAR );
A21 = A21_MC_STAR;
// 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 );
A12 = A12_STAR_MR;
//--------------------------------------------------------------------//
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 );
}
}
inline void
HPDInverseLVar2( DistMatrix<F>& A )
{
#ifndef RELEASE
PushCallStack("internal::HPDInverseLVar2");
if( A.Height() != A.Width() )
throw std::logic_error("Nonsquare matrices cannot be triangular");
#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);
// Temporary distributions
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,STAR,VR > A10_STAR_VR(g);
DistMatrix<F,VC, STAR> A21_VC_STAR(g);
DistMatrix<F,STAR,MC > A10_STAR_MC(g);
DistMatrix<F,STAR,MR > A10_STAR_MR(g);
DistMatrix<F,STAR,MC > A21Trans_STAR_MC(g);
DistMatrix<F,VR, STAR> A21_VR_STAR(g);
DistMatrix<F,STAR,MR > A21Adj_STAR_MR(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 );
A10_STAR_VR.AlignWith( A00 );
A21_VC_STAR.AlignWith( A20 );
A10_STAR_MC.AlignWith( A00 );
A10_STAR_MR.AlignWith( A00 );
A21Trans_STAR_MC.AlignWith( A20 );
A21_VR_STAR.AlignWith( A22 );
A21Adj_STAR_MR.AlignWith( A22 );
//--------------------------------------------------------------------//
A11_STAR_STAR = A11;
LocalCholesky( LOWER, A11_STAR_STAR );
A10_STAR_VR = A10;
LocalTrsm
( LEFT, LOWER, NORMAL, NON_UNIT, F(1), A11_STAR_STAR, A10_STAR_VR );
A21_VC_STAR = A21;
LocalTrsm
( RIGHT, LOWER, ADJOINT, NON_UNIT, F(1), A11_STAR_STAR, A21_VC_STAR );
A10_STAR_MC = A10_STAR_VR;
A10_STAR_MR = A10_STAR_VR;
LocalTrrk
( LOWER, ADJOINT,
F(1), A10_STAR_MC, A10_STAR_MR, F(1), A00 );
A21Trans_STAR_MC.TransposeFrom( A21_VC_STAR );
LocalGemm
( TRANSPOSE, NORMAL, F(-1), A21Trans_STAR_MC, A10_STAR_MR, F(1), A20 );
A21_VR_STAR = A21_VC_STAR;
A21Adj_STAR_MR.AdjointFrom( A21_VR_STAR );
LocalTrrk
( LOWER, TRANSPOSE,
F(-1), A21Trans_STAR_MC, A21Adj_STAR_MR, F(1), A22 );
LocalTrsm
( LEFT, LOWER, ADJOINT, NON_UNIT, F(1), A11_STAR_STAR, A10_STAR_VR );
LocalTrsm
( RIGHT, LOWER, NORMAL, NON_UNIT, F(-1), A11_STAR_STAR, A21_VC_STAR );
LocalTriangularInverse( LOWER, NON_UNIT, A11_STAR_STAR );
LocalTrtrmm( ADJOINT, LOWER, A11_STAR_STAR );
A11 = A11_STAR_STAR;
A10 = A10_STAR_VR;
A21 = A21_VC_STAR;
//--------------------------------------------------------------------//
A10_STAR_VR.FreeAlignments();
A21_VC_STAR.FreeAlignments();
A10_STAR_MC.FreeAlignments();
A10_STAR_MR.FreeAlignments();
A21Trans_STAR_MC.FreeAlignments();
A21_VR_STAR.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
TwoSidedTrmmLVar4
( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& L )
{
#ifndef RELEASE
CallStackEntry entry("internal::TwoSidedTrmmLVar4");
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,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 );
Zeros( Y10_STAR_VR, A10.Height(), A10.Width() );
Hemm
( LEFT, LOWER,
F(1), A11_STAR_STAR.LockedMatrix(), L10_STAR_VR.LockedMatrix(),
F(0), Y10_STAR_VR.Matrix() );
// 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;
//--------------------------------------------------------------------//
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
LVar2( DistMatrix<F>& A )
{
#ifndef RELEASE
CallStackEntry entry("cholesky::LVar2");
if( A.Height() != A.Width() )
LogicError("Can only compute Cholesky factor of square matrices");
#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);
// Temporary distributions
DistMatrix<F,MR, STAR> A10Adj_MR_STAR(g);
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,VC, STAR> A21_VC_STAR(g);
DistMatrix<F,MC, STAR> X11_MC_STAR(g);
DistMatrix<F,MC, STAR> X21_MC_STAR(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 );
A10Adj_MR_STAR.AlignWith( A10 );
X11_MC_STAR.AlignWith( A10 );
X21_MC_STAR.AlignWith( A20 );
//--------------------------------------------------------------------//
A10Adj_MR_STAR.AdjointFrom( A10 );
LocalGemm( NORMAL, NORMAL, F(1), A10, A10Adj_MR_STAR, X11_MC_STAR );
A11.SumScatterUpdate( F(-1), X11_MC_STAR );
A11_STAR_STAR = A11;
LocalCholesky( LOWER, A11_STAR_STAR );
A11 = A11_STAR_STAR;
LocalGemm( NORMAL, NORMAL, F(1), A20, A10Adj_MR_STAR, X21_MC_STAR );
A21.SumScatterUpdate( F(-1), X21_MC_STAR );
A21_VC_STAR = A21;
LocalTrsm
( RIGHT, LOWER, ADJOINT, NON_UNIT, F(1), A11_STAR_STAR, A21_VC_STAR );
A21 = A21_VC_STAR;
//--------------------------------------------------------------------//
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
}
}
inline void
TwoSidedTrsmUVar5
( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& U )
{
#ifndef RELEASE
PushCallStack("internal::TwoSidedTrsmUVar5");
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,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,STAR,MC > A12_STAR_MC(g);
DistMatrix<F,STAR,MR > A12_STAR_MR(g);
DistMatrix<F,STAR,VC > A12_STAR_VC(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,MR > U12_STAR_MR(g);
DistMatrix<F,STAR,VC > U12_STAR_VC(g);
DistMatrix<F,STAR,VR > U12_STAR_VR(g);
DistMatrix<F,STAR,VR > Y12_STAR_VR(g);
DistMatrix<F> Y12(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_MC.AlignWith( A22 );
A12_STAR_MR.AlignWith( A22 );
A12_STAR_VC.AlignWith( A22 );
A12_STAR_VR.AlignWith( A22 );
U12_STAR_MC.AlignWith( A22 );
U12_STAR_MR.AlignWith( A22 );
U12_STAR_VC.AlignWith( A22 );
U12_STAR_VR.AlignWith( A22 );
Y12.AlignWith( A12 );
Y12_STAR_VR.AlignWith( A12 );
//--------------------------------------------------------------------//
// A11 := inv(U11)' A11 inv(U11)
U11_STAR_STAR = U11;
A11_STAR_STAR = A11;
LocalTwoSidedTrsm( UPPER, diag, A11_STAR_STAR, U11_STAR_STAR );
A11 = A11_STAR_STAR;
// Y12 := A11 U12
U12_STAR_VR = U12;
Y12_STAR_VR.ResizeTo( A12.Height(), A12.Width() );
Hemm
( LEFT, UPPER,
F(1), A11_STAR_STAR.LocalMatrix(), U12_STAR_VR.LocalMatrix(),
F(0), Y12_STAR_VR.LocalMatrix() );
Y12 = Y12_STAR_VR;
// 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;
// A12 := A12 - 1/2 Y12
Axpy( F(-1)/F(2), Y12, A12 );
// A22 := A22 - (A12' U12 + U12' A12)
A12_STAR_VR = A12;
A12_STAR_VC = A12_STAR_VR;
U12_STAR_VC = U12_STAR_VR;
A12_STAR_MC = A12_STAR_VC;
U12_STAR_MC = U12_STAR_VC;
A12_STAR_MR = A12_STAR_VR;
U12_STAR_MR = U12_STAR_VR;
LocalTrr2k
( UPPER, ADJOINT, ADJOINT,
F(-1), U12_STAR_MC, A12_STAR_MR,
A12_STAR_MC, U12_STAR_MR,
F(1), A22 );
// A12 := A12 - 1/2 Y12
Axpy( F(-1)/F(2), Y12, A12 );
// A12 := A12 inv(U22)
//
// This is the bottleneck because A12 only has blocksize rows
Trsm( RIGHT, UPPER, NORMAL, diag, F(1), U22, A12 );
//--------------------------------------------------------------------//
A12_STAR_MC.FreeAlignments();
A12_STAR_MR.FreeAlignments();
A12_STAR_VC.FreeAlignments();
A12_STAR_VR.FreeAlignments();
U12_STAR_MC.FreeAlignments();
U12_STAR_MR.FreeAlignments();
U12_STAR_VC.FreeAlignments();
U12_STAR_VR.FreeAlignments();
Y12.FreeAlignments();
Y12_STAR_VR.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
}