inline void
SlidePartitionDown
( DM& AT, DM& A0,
DM& A1,
DM& AB, DM& A2 )
{
DEBUG_ONLY(CallStackEntry cse("SlidePartitionDown"))
View2x1( AT, A0, A1 );
View( AB, A2 );
}
inline void
SlidePartitionUp
( M& AT, M& A0,
M& A1,
M& AB, M& A2 )
{
DEBUG_ONLY(CallStackEntry cse("SlidePartitionUp"))
View( AT, A0 );
View2x1( AB, A1, A2 );
}
inline void
SlidePartitionDownDiagonal
( DM& ATL, DM& ATR, DM& A00, DM& A01, DM& A02,
DM& A10, DM& A11, DM& A12,
DM& ABL, DM& ABR, DM& A20, DM& A21, DM& A22 )
{
DEBUG_ONLY(CallStackEntry cse("SlidePartitionDownDiagonal"))
View2x2( ATL, A00, A01,
A10, A11 );
View2x1( ATR, A02, A12 );
View1x2( ABL, A20, A21 );
View( ABR, A22 );
}
inline void
SlidePartitionUpDiagonal
( M& ATL, M& ATR, M& A00, M& A01, M& A02,
M& A10, M& A11, M& A12,
M& ABL, M& ABR, M& A20, M& A21, M& A22 )
{
DEBUG_ONLY(CallStackEntry cse("SlidePartitionUpDiagonal"))
View( ATL, A00 );
View1x2( ATR, A01, A02 );
View2x1( ABL, A10, A20 );
View2x2( ABR, A11, A12,
A21, A22 );
}
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
Householder( Matrix<F>& A, Matrix<F>& t )
{
#ifndef RELEASE
CallStackEntry entry("qr::Householder");
#endif
t.ResizeTo( Min(A.Height(),A.Width()), 1 );
// Matrix views
Matrix<F>
ATL, ATR, A00, A01, A02, ALeftPan, ARightPan,
ABL, ABR, A10, A11, A12,
A20, A21, A22;
Matrix<F>
tT, t0,
tB, t1,
t2;
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
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 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 UnblockedBidiagU( DistMatrix<R>& A )
{
#ifndef RELEASE
PushCallStack("bidiag::UnblockedBidiagU");
if( A.Height() < A.Width() )
throw std::logic_error("A must be at least as tall as it is wide");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<R>
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<R,STAR,MR > a12_STAR_MR(g);
DistMatrix<R,MC, STAR> aB1_MC_STAR(g);
DistMatrix<R,MR, STAR> x12Trans_MR_STAR(g);
DistMatrix<R,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 );
x12Trans_MR_STAR.AlignWith( AB2 );
w21_MC_STAR.AlignWith( A22 );
Zeros( a12.Width(), 1, x12Trans_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 - tauQ | 1 | | 1, u^T | | alpha11 | = | epsilonQ |
// | u | | a21 | = | 0 |
const R tauQ = Reflector( alpha11, a21 );
R epsilonQ=0;
if( thisIsMyCol && thisIsMyRow )
epsilonQ = alpha11.GetLocal(0,0);
// Set aB1 = | 1 | and form x12^T := (aB1^T AB2)^T = AB2^T aB1
// | u |
alpha11.Set(0,0,R(1));
aB1_MC_STAR = aB1;
internal::LocalGemv
( TRANSPOSE, R(1), AB2, aB1_MC_STAR, R(0), x12Trans_MR_STAR );
x12Trans_MR_STAR.SumOverCol();
// Update AB2 := AB2 - tauQ aB1 x12
// = AB2 - tauQ aB1 aB1^T AB2
// = (I - tauQ aB1 aB1^T) AB2
internal::LocalGer( -tauQ, aB1_MC_STAR, x12Trans_MR_STAR, AB2 );
// Put epsilonQ back instead of the temporary value, 1
if( thisIsMyCol && thisIsMyRow )
alpha11.SetLocal(0,0,epsilonQ);
if( A22.Width() != 0 )
{
// Expose the subvector we seek to zero, a12R
PartitionRight( a12, alpha12L, a12R );
// Find tauP, v, and epsilonP such that
// I - tauP | 1 | | 1, v^T | | alpha12L | = | epsilonP |
// | v | | a12R^T | = | 0 |
const R tauP = Reflector( alpha12L, a12R );
R 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,R(1));
a12_STAR_MR = a12;
internal::LocalGemv
( NORMAL, R(1), A22, a12_STAR_MR, R(0), w21_MC_STAR );
w21_MC_STAR.SumOverRow();
// A22 := A22 - tauP w21 a12
// = A22 - tauP A22 a12^T a12
// = A22 (I - tauP a12^T 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);
}
//--------------------------------------------------------------------//
aB1_MC_STAR.FreeAlignments();
a12_STAR_MR.FreeAlignments();
x12Trans_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
RowEchelon( DistMatrix<F>& A, DistMatrix<F>& B )
{
#ifndef RELEASE
CallStackEntry entry("RowEchelon");
if( A.Grid() != B.Grid() )
LogicError("{A,B} must be distributed over the same grid");
if( A.Height() != B.Height() )
LogicError("A and B must be the same height");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<F>
ATL(g), ATR(g), A00(g), A01(g), A02(g), APan(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
DistMatrix<F>
BT(g), B0(g),
BB(g), B1(g),
B2(g);
// Temporary distributions
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,STAR,VR > A12_STAR_VR(g);
DistMatrix<F,STAR,MR > A12_STAR_MR(g);
DistMatrix<F,MC, STAR> A21_MC_STAR(g);
DistMatrix<F,STAR,VR > B1_STAR_VR(g);
DistMatrix<F,STAR,MR > B1_STAR_MR(g);
DistMatrix<Int,STAR,STAR> p1_STAR_STAR(g);
// In case B's columns are not aligned with A's
const bool BAligned = ( B.ColShift() == A.ColShift() );
DistMatrix<F,MC,STAR> A21_MC_STAR_B(g);
// Pivot composition
std::vector<Int> image, preimage;
// Start the algorithm
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
PartitionDown
( B, BT,
BB, 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
( BT, B0,
/**/ /**/
B1,
BB, B2 );
View2x1
( APan, A12,
A22 );
A12_STAR_VR.AlignWith( A22 );
A12_STAR_MR.AlignWith( A22 );
A21_MC_STAR.AlignWith( A22 );
B1_STAR_VR.AlignWith( B1 );
B1_STAR_MR.AlignWith( B1 );
if( ! BAligned )
A21_MC_STAR_B.AlignWith( B2 );
p1_STAR_STAR.ResizeTo( A11.Height(), 1 );
//--------------------------------------------------------------------//
A11_STAR_STAR = A11;
A21_MC_STAR = A21;
lu::Panel( A11_STAR_STAR, A21_MC_STAR, p1_STAR_STAR, A00.Height() );
ComposePivots( p1_STAR_STAR, A00.Height(), image, preimage );
ApplyRowPivots( APan, image, preimage );
ApplyRowPivots( BB, image, preimage );
A12_STAR_VR = A12;
B1_STAR_VR = B1;
LocalTrsm
( LEFT, LOWER, NORMAL, UNIT, F(1), A11_STAR_STAR, A12_STAR_VR );
LocalTrsm( LEFT, LOWER, NORMAL, UNIT, F(1), A11_STAR_STAR, B1_STAR_VR );
A12_STAR_MR = A12_STAR_VR;
B1_STAR_MR = B1_STAR_VR;
LocalGemm( NORMAL, NORMAL, F(-1), A21_MC_STAR, A12_STAR_MR, F(1), A22 );
if( BAligned )
{
LocalGemm
( NORMAL, NORMAL, F(-1), A21_MC_STAR, B1_STAR_MR, F(1), B2 );
}
else
{
A21_MC_STAR_B = A21_MC_STAR;
LocalGemm
( NORMAL, NORMAL, F(-1), A21_MC_STAR_B, B1_STAR_MR, F(1), B2 );
}
A11 = A11_STAR_STAR;
A12 = A12_STAR_MR;
B1 = B1_STAR_MR;
//--------------------------------------------------------------------//
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
SlidePartitionDown
( BT, B0,
B1,
/**/ /**/
BB, B2 );
}
}
inline void
RowEchelon( Matrix<F>& A, Matrix<F>& B )
{
#ifndef RELEASE
CallStackEntry entry("RowEchelon");
if( A.Height() != B.Height() )
LogicError("A and B must be the same height");
#endif
// Matrix views
Matrix<F>
ATL, ATR, A00, A01, A02, APan,
ABL, ABR, A10, A11, A12,
A20, A21, A22;
Matrix<F>
BT, B0,
BB, B1,
B2;
Matrix<Int> p1;
// Pivot composition
std::vector<Int> image, preimage;
// Start the algorithm
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
PartitionDown
( B, BT,
BB, 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
( BT, B0,
/**/ /**/
B1,
BB, B2 );
View2x1
( APan, A12,
A22 );
//--------------------------------------------------------------------//
lu::Panel( APan, p1, A00.Height() );
ComposePivots( p1, A00.Height(), image, preimage );
ApplyRowPivots( BB, image, preimage );
Trsm( LEFT, LOWER, NORMAL, UNIT, F(1), A11, A12 );
Trsm( LEFT, LOWER, NORMAL, UNIT, F(1), A11, B1 );
Gemm( NORMAL, NORMAL, F(-1), A21, A12, F(1), A22 );
Gemm( NORMAL, NORMAL, F(-1), A21, B1, F(1), B2 );
//--------------------------------------------------------------------//
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
SlidePartitionDown
( BT, B0,
B1,
/**/ /**/
BB, B2 );
}
}
