void UUnb( Matrix<F>& A, Matrix<F>& householderScalars )
{
DEBUG_CSE
const Int n = A.Height();
const Int householderScalarsHeight = Max(n-1,0);
householderScalars.Resize( householderScalarsHeight, 1 );
// Temporary products
Matrix<F> x1, x12Adj;
for( Int k=0; k<n-1; ++k )
{
const Range<Int> ind1( k, k+1 ),
ind2( k+1, n );
auto a21 = A( ind2, ind1 );
auto A22 = A( ind2, ind2 );
auto A2 = A( IR(0,n), ind2 );
auto alpha21T = A( IR(k+1,k+2), ind1 );
auto a21B = A( IR(k+2,n), ind1 );
// Find tau and v such that
// / I - tau | 1 | | 1, v^H | \ | alpha21T | = | beta |
// \ | v | / | a21B | | 0 |
const F tau = LeftReflector( alpha21T, a21B );
householderScalars(k) = tau;
// Temporarily set a21 := | 1 |
// | v |
const F beta = alpha21T(0);
alpha21T(0) = F(1);
// A2 := A2 Hous(a21,tau)^H
// = A2 (I - conj(tau) a21 a21^H)
// = A2 - conj(tau) (A2 a21) a21^H
// -----------------------------------
// x1 := A2 a21
Zeros( x1, n, 1 );
Gemv( NORMAL, F(1), A2, a21, F(0), x1 );
// A2 := A2 - conj(tau) x1 a21^H
Ger( -Conj(tau), x1, a21, A2 );
// A22 := Hous(a21,tau) A22
// = (I - tau a21 a21^H) A22
// = A22 - tau a21 (A22^H a21)^H
// ----------------------------------
// x12^H := (a21^H A22)^H = A22^H a21
Zeros( x12Adj, A22.Width(), 1 );
Gemv( ADJOINT, F(1), A22, a21, F(0), x12Adj );
// A22 := A22 - tau a21 x12
Ger( -tau, a21, x12Adj, A22 );
// Put beta back
alpha21T(0) = beta;
}
}
void QP
( const Matrix<Real>& A,
const Matrix<Real>& B,
Matrix<Real>& X,
const qp::direct::Ctrl<Real>& ctrl )
{
DEBUG_CSE
const Int n = A.Width();
const Int k = B.Width();
Matrix<Real> Q, AHat, bHat, c;
Herk( LOWER, ADJOINT, Real(1), A, Q );
Zeros( AHat, 0, n );
Zeros( bHat, 0, 1 );
Zeros( X, n, k );
Matrix<Real> y, z;
for( Int j=0; j<k; ++j )
{
auto x = X( ALL, IR(j) );
auto b = B( ALL, IR(j) );
Zeros( c, n, 1 );
Gemv( ADJOINT, Real(-1), A, b, Real(0), c );
El::QP( Q, AHat, bHat, c, x, y, z, ctrl );
}
}
void
PanelHouseholder
( Matrix<F>& A,
Matrix<F>& householderScalars,
Matrix<Base<F>>& signature )
{
DEBUG_CSE
typedef Base<F> Real;
const Int m = A.Height();
const Int n = A.Width();
const Int minDim = Min(m,n);
householderScalars.Resize( minDim, 1 );
signature.Resize( minDim, 1 );
Matrix<F> z21;
for( Int k=0; k<minDim; ++k )
{
const Range<Int> ind1( k ), ind2( k+1, END ), indR( k, n );
F& alpha11 = A(k,k);
auto a12 = A( ind1, ind2 );
auto a1R = A( ind1, indR );
auto A2R = A( ind2, indR );
// Find tau and v such that
// |alpha11 a12| /I - tau |1 | |1 conj(v)|\ = |beta 0|
// \ |v^T| /
const F tau = RightReflector( alpha11, a12 );
householderScalars(k) = tau;
// Temporarily set a1R = | 1 v |
const F alpha = alpha11;
alpha11 = 1;
// A2R := A2R Hous(a1R^T,tau)
// = A2R (I - tau a1R^T conj(a1R))
// = A2R - tau (A2R a1R^T) conj(a1R)
Zeros( z21, A2R.Height(), 1 );
Gemv( NORMAL, F(1), A2R, a1R, F(0), z21 );
Ger( -tau, z21, a1R, A2R );
// Reset alpha11's value
alpha11 = alpha;
}
// Form d and rescale L
auto L = A( ALL, IR(0,minDim) );
GetRealPartOfDiagonal(L,signature);
auto sgn = []( const Real& delta )
{
return delta >= Real(0) ? Real(1) : Real(-1);
};
EntrywiseMap( signature, function<Real(Real)>(sgn) );
DiagonalScaleTrapezoid( RIGHT, LOWER, NORMAL, signature, L );
}
inline void
PanelQR( Matrix<Real>& A )
{
#ifndef RELEASE
PushCallStack("internal::PanelQR");
#endif
Matrix<Real>
ATL, ATR, A00, a01, A02, aLeftCol, ARightPan,
ABL, ABR, a10, alpha11, a12,
A20, a21, A22;
Matrix<Real> z;
PushBlocksizeStack( 1 );
PartitionDownLeftDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
while( ATL.Height() < A.Height() && ATL.Width() < A.Width() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ a01, A02,
/*************/ /**********************/
/**/ a10, /**/ alpha11, a12,
ABL, /**/ ABR, A20, /**/ a21, A22 );
aLeftCol.View2x1( alpha11,
a21 );
ARightPan.View2x1( a12,
A22 );
Zeros( ARightPan.Width(), 1, z );
//--------------------------------------------------------------------//
const Real tau = Reflector( alpha11, a21 );
const Real alpha = alpha11.Get(0,0);
alpha11.Set(0,0,1);
Gemv( TRANSPOSE, Real(1), ARightPan, aLeftCol, Real(0), z );
Ger( -tau, aLeftCol, z, ARightPan );
alpha11.Set(0,0,alpha);
//--------------------------------------------------------------------//
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, a01, /**/ A02,
/**/ a10, alpha11, /**/ a12,
/*************/ /**********************/
ABL, /**/ ABR, A20, a21, /**/ A22 );
}
PopBlocksizeStack();
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
PanelLQ( Matrix<Real>& A )
{
#ifndef RELEASE
PushCallStack("internal::PanelLQ");
#endif
Matrix<Real>
ATL, ATR, A00, a01, A02, aTopRow, ABottomPan,
ABL, ABR, a10, alpha11, a12,
A20, a21, A22;
Matrix<Real> z;
PushBlocksizeStack( 1 );
PartitionDownLeftDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
while( ATL.Height() < A.Height() && ATL.Width() < A.Width() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ a01, A02,
/*************/ /**********************/
/**/ a10, /**/ alpha11, a12,
ABL, /**/ ABR, A20, /**/ a21, A22 );
aTopRow.View1x2( alpha11, a12 );
ABottomPan.View1x2( a21, A22 );
Zeros( ABottomPan.Height(), 1, z );
//--------------------------------------------------------------------//
const Real tau = Reflector( alpha11, a12 );
const Real alpha = alpha11.Get(0,0);
alpha11.Set(0,0,1);
Gemv( NORMAL, Real(1), ABottomPan, aTopRow, Real(0), z );
Ger( -tau, z, aTopRow, ABottomPan );
alpha11.Set(0,0,alpha);
//--------------------------------------------------------------------//
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, a01, /**/ A02,
/**/ a10, alpha11, /**/ a12,
/*************/ /**********************/
ABL, /**/ ABR, A20, a21, /**/ A22 );
}
PopBlocksizeStack();
#ifndef RELEASE
PopCallStack();
#endif
}
void QP
( const ElementalMatrix<Real>& APre,
const ElementalMatrix<Real>& BPre,
ElementalMatrix<Real>& XPre,
const qp::direct::Ctrl<Real>& ctrl )
{
DEBUG_CSE
DistMatrixReadProxy<Real,Real,MC,MR>
AProx( APre ),
BProx( BPre );
DistMatrixWriteProxy<Real,Real,MC,MR>
XProx( XPre );
auto& A = AProx.GetLocked();
auto& B = BProx.GetLocked();
auto& X = XProx.Get();
const Int n = A.Width();
const Int k = B.Width();
const Grid& g = A.Grid();
DistMatrix<Real> Q(g), AHat(g), bHat(g), c(g);
Herk( LOWER, ADJOINT, Real(1), A, Q );
Zeros( AHat, 0, n );
Zeros( bHat, 0, 1 );
Zeros( X, n, k );
DistMatrix<Real> y(g), z(g);
for( Int j=0; j<k; ++j )
{
auto x = X( ALL, IR(j) );
auto b = B( ALL, IR(j) );
Zeros( c, n, 1 );
Gemv( ADJOINT, Real(-1), A, b, Real(0), c );
El::QP( Q, AHat, bHat, c, x, y, z, ctrl );
}
}
void Covariance( const Matrix<F>& D, Matrix<F>& S )
{
DEBUG_CSE
const Int numObs = D.Height();
const Int n = D.Width();
// Compute the average column
Matrix<F> ones, xMean;
Ones( ones, numObs, 1 );
Gemv( TRANSPOSE, F(1)/F(numObs), D, ones, xMean );
// Subtract the mean from each column of D
Matrix<F> DDev( D );
for( Int i=0; i<numObs; ++i )
blas::Axpy
( n, F(-1), xMean.LockedBuffer(), 1, DDev.Buffer(i,0), DDev.LDim() );
// Form S := 1/(numObs-1) DDev DDev'
Herk( LOWER, ADJOINT, Base<F>(1)/Base<F>(numObs-1), DDev, S );
Conjugate( S );
MakeHermitian( LOWER, S );
}
void Covariance
( const ElementalMatrix<F>& DPre, ElementalMatrix<F>& SPre )
{
DEBUG_CSE
DistMatrixReadProxy<F,F,MC,MR>
DProx( DPre );
DistMatrixWriteProxy<F,F,MC,MR>
SProx( SPre );
auto& D = DProx.GetLocked();
auto& S = SProx.Get();
const Grid& g = D.Grid();
const Int numObs = D.Height();
// Compute the average column
DistMatrix<F> ones(g), xMean(g);
Ones( ones, numObs, 1 );
Gemv( TRANSPOSE, F(1)/F(numObs), D, ones, xMean );
DistMatrix<F,MR,STAR> xMean_MR(g);
xMean_MR.AlignWith( D );
xMean_MR = xMean;
// Subtract the mean from each column of D
DistMatrix<F> DDev( D );
for( Int iLoc=0; iLoc<DDev.LocalHeight(); ++iLoc )
blas::Axpy
( DDev.LocalWidth(), F(-1),
xMean_MR.LockedBuffer(), 1,
DDev.Buffer(iLoc,0), DDev.LDim() );
// Form S := 1/(numObs-1) DDev DDev'
Herk( LOWER, ADJOINT, Base<F>(1)/Base<F>(numObs-1), DDev, S );
Conjugate( S );
MakeHermitian( LOWER, S );
}
inline void
TrsvUN( UnitOrNonUnit diag, const DistMatrix<F>& U, DistMatrix<F>& x )
{
#ifndef RELEASE
PushCallStack("internal::TrsvUN");
if( U.Grid() != x.Grid() )
throw std::logic_error("{U,x} must be distributed over the same grid");
if( U.Height() != U.Width() )
throw std::logic_error("U must be square");
if( x.Width() != 1 && x.Height() != 1 )
throw std::logic_error("x must be a vector");
const int xLength = ( x.Width() == 1 ? x.Height() : x.Width() );
if( U.Width() != xLength )
throw std::logic_error("Nonconformal TrsvUN");
#endif
const Grid& g = U.Grid();
if( x.Width() == 1 )
{
// Matrix views
DistMatrix<F> U01(g),
U11(g);
DistMatrix<F>
xT(g), x0(g),
xB(g), x1(g),
x2(g);
// Temporary distributions
DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
DistMatrix<F,STAR,STAR> x1_STAR_STAR(g);
DistMatrix<F,MR, STAR> x1_MR_STAR(g);
DistMatrix<F,MC, STAR> z_MC_STAR(g);
// Views of z[MC,* ], which will store updates to x
DistMatrix<F,MC,STAR> z0_MC_STAR(g),
z1_MC_STAR(g);
z_MC_STAR.AlignWith( U );
Zeros( x.Height(), 1, z_MC_STAR );
// Start the algorithm
PartitionUp
( x, xT,
xB, 0 );
while( xT.Height() > 0 )
{
RepartitionUp
( xT, x0,
x1,
/**/ /**/
xB, x2 );
const int n0 = x0.Height();
const int n1 = x1.Height();
LockedView( U01, U, 0, n0, n0, n1 );
LockedView( U11, U, n0, n0, n1, n1 );
View( z0_MC_STAR, z_MC_STAR, 0, 0, n0, 1 );
View( z1_MC_STAR, z_MC_STAR, n0, 0, n1, 1 );
x1_MR_STAR.AlignWith( U01 );
//----------------------------------------------------------------//
if( x2.Height() != 0 )
x1.SumScatterUpdate( F(1), z1_MC_STAR );
x1_STAR_STAR = x1;
U11_STAR_STAR = U11;
Trsv
( UPPER, NORMAL, diag,
U11_STAR_STAR.LockedLocalMatrix(),
x1_STAR_STAR.LocalMatrix() );
x1 = x1_STAR_STAR;
x1_MR_STAR = x1_STAR_STAR;
Gemv
( NORMAL, F(-1),
U01.LockedLocalMatrix(),
x1_MR_STAR.LockedLocalMatrix(),
F(1), z0_MC_STAR.LocalMatrix() );
//----------------------------------------------------------------//
x1_MR_STAR.FreeAlignments();
SlidePartitionUp
( xT, x0,
/**/ /**/
x1,
xB, x2 );
}
}
else
{
// Matrix views
DistMatrix<F> U01(g),
U11(g);
DistMatrix<F>
xL(g), xR(g),
x0(g), x1(g), x2(g);
// Temporary distributions
DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
DistMatrix<F,STAR,STAR> x1_STAR_STAR(g);
DistMatrix<F,STAR,MR > x1_STAR_MR(g);
DistMatrix<F,MC, MR > z1(g);
DistMatrix<F,MR, MC > z1_MR_MC(g);
DistMatrix<F,STAR,MC > z_STAR_MC(g);
// Views of z[* ,MC]
DistMatrix<F,STAR,MC> z0_STAR_MC(g),
z1_STAR_MC(g);
z_STAR_MC.AlignWith( U );
Zeros( 1, x.Width(), z_STAR_MC );
// Start the algorithm
PartitionLeft( x, xL, xR, 0 );
while( xL.Width() > 0 )
{
RepartitionLeft
( xL, /**/ xR,
x0, x1, /**/ x2 );
const int n0 = x0.Width();
const int n1 = x1.Width();
LockedView( U01, U, 0, n0, n0, n1 );
LockedView( U11, U, n0, n0, n1, n1 );
View( z0_STAR_MC, z_STAR_MC, 0, 0, 1, n0 );
View( z1_STAR_MC, z_STAR_MC, 0, n0, 1, n1 );
x1_STAR_MR.AlignWith( U01 );
z1.AlignWith( x1 );
//----------------------------------------------------------------//
if( x2.Width() != 0 )
{
z1_MR_MC.SumScatterFrom( z1_STAR_MC );
z1 = z1_MR_MC;
Axpy( F(1), z1, x1 );
}
x1_STAR_STAR = x1;
U11_STAR_STAR = U11;
Trsv
( UPPER, NORMAL, diag,
U11_STAR_STAR.LockedLocalMatrix(),
x1_STAR_STAR.LocalMatrix() );
x1 = x1_STAR_STAR;
x1_STAR_MR = x1_STAR_STAR;
Gemv
( NORMAL, F(-1),
U01.LockedLocalMatrix(),
x1_STAR_MR.LockedLocalMatrix(),
F(1), z0_STAR_MC.LocalMatrix() );
//----------------------------------------------------------------//
x1_STAR_MR.FreeAlignments();
z1.FreeAlignments();
SlidePartitionLeft
( xL, /**/ xR,
x0, /**/ x1, x2 );
}
}
#ifndef RELEASE
PopCallStack();
#endif
}
bool LatticeCoordinates
( const Matrix<F>& B,
const Matrix<F>& y,
Matrix<F>& x )
{
DEBUG_CSE
typedef Base<F> Real;
const Int m = B.Height();
const Int n = B.Width();
if( y.Height() != m || y.Width() != 1 )
LogicError("y should have been an ",m," x 1 vector");
if( FrobeniusNorm(y) == Real(0) )
{
Zeros( x, n, 1 );
return true;
}
Matrix<F> BRed( B );
Matrix<F> UB, RB;
auto infoB = LLL( BRed, UB, RB );
auto MB = BRed( ALL, IR(0,infoB.rank) );
Matrix<F> A;
Zeros( A, m, infoB.rank+1 );
{
auto AL = A( ALL, IR(0,infoB.rank) );
auto aR = A( ALL, IR(infoB.rank) );
AL = MB;
aR = y;
}
// Reduce A in-place
Matrix<F> UA, RA;
auto infoA = LLL( A, UA, RA );
if( infoA.nullity != 1 )
return false;
// Solve for x_M such that M_B x_M = y
// NOTE: The last column of U_A should hold the coordinates of the single
// member of the null-space of (the original) A
Matrix<F> xM;
xM = UA( IR(0,infoA.rank), IR(infoB.rank) );
const F gamma = UA(infoA.rank,infoB.rank);
if( Abs(gamma) != Real(1) )
LogicError("Invalid member of null space");
else
xM *= -Conj(gamma);
// Map xM back to the original coordinates using the portion of the
// unimodular transformation of B (U_B) which produced the image of B
auto UBM = UB( ALL, IR(0,infoB.rank) );
Zeros( x, n, 1 );
Gemv( NORMAL, F(1), UBM, xM, F(0), x );
/*
if( infoB.nullity != 0 )
{
Matrix<F> C;
Zeros( C, m, infoB.nullity+1 );
auto cL = C( ALL, IR(infoB.rank-1) );
auto CR = C( ALL, IR(infoB.rank,END) );
// Reduce the kernel of B
CR = UB( ALL, IR(infoB.rank,END) );
LLL( CR );
// Attempt to reduce the (reduced) kernel out of the coordinates
// TODO: Which column to grab from the result?!?
cL = x;
LLL( C );
x = cL;
}
*/
return true;
}
inline void
PanelHouseholder( Matrix<F>& A, Matrix<F>& t )
{
#ifndef RELEASE
CallStackEntry entry("lq::PanelHouseholder");
if( t.Height() != Min(A.Height(),A.Width()) || t.Width() != 1 )
LogicError
("t must be a vector of height equal to the minimum dimension of A");
#endif
Matrix<F>
ATL, ATR, A00, a01, A02, aTopRow, ABottomPan,
ABL, ABR, a10, alpha11, a12,
A20, a21, A22;
Matrix<F>
tT, t0,
tB, tau1,
t2;
Matrix<F> z, aTopRowConj;
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, /**/ alpha11, a12,
ABL, /**/ ABR, A20, /**/ a21, A22, 1 );
RepartitionDown
( tT, t0,
/**/ /****/
tau1,
tB, t2, 1 );
View1x2( aTopRow, alpha11, a12 );
View1x2( ABottomPan, a21, A22 );
//--------------------------------------------------------------------//
// Compute the Householder reflector
const F tau = Reflector( alpha11, a12 );
tau1.Set( 0, 0, tau );
// Apply the Householder reflector
const F alpha = alpha11.Get(0,0);
alpha11.Set(0,0,1);
Conjugate( aTopRow, aTopRowConj );
Zeros( z, ABottomPan.Height(), 1 );
Gemv( NORMAL, F(1), ABottomPan, aTopRowConj, F(0), z );
Ger( -Conj(tau), z, aTopRowConj, ABottomPan );
alpha11.Set(0,0,alpha);
//--------------------------------------------------------------------//
SlidePartitionDown
( tT, t0,
tau1,
/**/ /****/
tB, t2 );
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, a01, /**/ A02,
/**/ a10, alpha11, /**/ a12,
/*************/ /**********************/
ABL, /**/ ABR, A20, a21, /**/ A22 );
}
}
inline void
internal::TrsvUN
( UnitOrNonUnit diag,
const DistMatrix<F,MC,MR>& U,
DistMatrix<F,MC,MR>& x )
{
#ifndef RELEASE
PushCallStack("internal::TrsvUN");
if( U.Grid() != x.Grid() )
throw std::logic_error("{U,x} must be distributed over the same grid");
if( U.Height() != U.Width() )
throw std::logic_error("U must be square");
if( x.Width() != 1 && x.Height() != 1 )
throw std::logic_error("x must be a vector");
const int xLength = ( x.Width() == 1 ? x.Height() : x.Width() );
if( U.Width() != xLength )
throw std::logic_error("Nonconformal TrsvUN");
#endif
const Grid& g = U.Grid();
if( x.Width() == 1 )
{
// Matrix views
DistMatrix<F,MC,MR>
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);
DistMatrix<F,MC,MR>
xT(g), x0(g),
xB(g), x1(g),
x2(g);
// Temporary distributions
DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
DistMatrix<F,STAR,STAR> x1_STAR_STAR(g);
DistMatrix<F,MR, STAR> x1_MR_STAR(g);
DistMatrix<F,MC, STAR> z0_MC_STAR(g);
// Start the algorithm
LockedPartitionUpDiagonal
( U, UTL, UTR,
UBL, UBR, 0 );
PartitionUp
( x, xT,
xB, 0 );
while( xT.Height() > 0 )
{
LockedRepartitionUpDiagonal
( UTL, /**/ UTR, U00, U01, /**/ U02,
/**/ U10, U11, /**/ U12,
/*************/ /******************/
UBL, /**/ UBR, U20, U21, /**/ U22 );
RepartitionUp
( xT, x0,
x1,
/**/ /**/
xB, x2 );
x1_MR_STAR.AlignWith( U01 );
z0_MC_STAR.AlignWith( U01 );
z0_MC_STAR.ResizeTo( x0.Height(), 1 );
//----------------------------------------------------------------//
x1_STAR_STAR = x1;
U11_STAR_STAR = U11;
Trsv
( UPPER, NORMAL, diag,
U11_STAR_STAR.LockedLocalMatrix(),
x1_STAR_STAR.LocalMatrix() );
x1 = x1_STAR_STAR;
x1_MR_STAR = x1_STAR_STAR;
Gemv
( NORMAL, (F)-1,
U01.LockedLocalMatrix(),
x1_MR_STAR.LockedLocalMatrix(),
(F)0, z0_MC_STAR.LocalMatrix() );
x0.SumScatterUpdate( (F)1, z0_MC_STAR );
//----------------------------------------------------------------//
x1_MR_STAR.FreeAlignments();
z0_MC_STAR.FreeAlignments();
SlideLockedPartitionUpDiagonal
( UTL, /**/ UTR, U00, /**/ U01, U02,
/*************/ /******************/
/**/ U10, /**/ U11, U12,
UBL, /**/ UBR, U20, /**/ U21, U22 );
SlidePartitionUp
( xT, x0,
/**/ /**/
x1,
xB, x2 );
}
}
else
{
// Matrix views
DistMatrix<F,MC,MR>
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);
DistMatrix<F,MC,MR>
xL(g), xR(g),
x0(g), x1(g), x2(g);
// Temporary distributions
DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
DistMatrix<F,STAR,STAR> x1_STAR_STAR(g);
DistMatrix<F,STAR,MR > x1_STAR_MR(g);
DistMatrix<F,STAR,MC > z0_STAR_MC(g);
DistMatrix<F,MR, MC > z0_MR_MC(g);
DistMatrix<F,MC, MR > z0(g);
// Start the algorithm
LockedPartitionUpDiagonal
( U, UTL, UTR,
UBL, UBR, 0 );
PartitionLeft( x, xL, xR, 0 );
while( xL.Width() > 0 )
{
LockedRepartitionUpDiagonal
( UTL, /**/ UTR, U00, U01, /**/ U02,
/**/ U10, U11, /**/ U12,
/*************/ /******************/
UBL, /**/ UBR, U20, U21, /**/ U22 );
RepartitionLeft
( xL, /**/ xR,
x0, x1, /**/ x2 );
x1_STAR_MR.AlignWith( U01 );
z0_STAR_MC.AlignWith( U01 );
z0.AlignWith( x0 );
z0_STAR_MC.ResizeTo( 1, x0.Width() );
//----------------------------------------------------------------//
x1_STAR_STAR = x1;
U11_STAR_STAR = U11;
Trsv
( UPPER, NORMAL, diag,
U11_STAR_STAR.LockedLocalMatrix(),
x1_STAR_STAR.LocalMatrix() );
x1 = x1_STAR_STAR;
x1_STAR_MR = x1_STAR_STAR;
Gemv
( NORMAL, (F)-1,
U01.LockedLocalMatrix(),
x1_STAR_MR.LockedLocalMatrix(),
(F)0, z0_STAR_MC.LocalMatrix() );
z0_MR_MC.SumScatterFrom( z0_STAR_MC );
z0 = z0_MR_MC;
Axpy( (F)1, z0, x0 );
//----------------------------------------------------------------//
x1_STAR_MR.FreeAlignments();
z0_STAR_MC.FreeAlignments();
z0.FreeAlignments();
SlideLockedPartitionUpDiagonal
( UTL, /**/ UTR, U00, /**/ U01, U02,
/*************/ /******************/
/**/ U10, /**/ U11, U12,
UBL, /**/ UBR, U20, /**/ U21, U22 );
SlidePartitionLeft
( xL, /**/ xR,
x0, /**/ x1, x2 );
}
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
TrsvLT
( Orientation orientation, UnitOrNonUnit diag,
const DistMatrix<F>& L, DistMatrix<F>& x )
{
#ifndef RELEASE
PushCallStack("internal::TrsvLT");
if( L.Grid() != x.Grid() )
throw std::logic_error("{L,x} must be distributed over the same grid");
if( orientation == NORMAL )
throw std::logic_error("TrsvLT expects a (conjugate-)transpose option");
if( L.Height() != L.Width() )
throw std::logic_error("L must be square");
if( x.Width() != 1 && x.Height() != 1 )
throw std::logic_error("x must be a vector");
const int xLength = ( x.Width() == 1 ? x.Height() : x.Width() );
if( L.Width() != xLength )
throw std::logic_error("Nonconformal TrsvLT");
#endif
const Grid& g = L.Grid();
if( x.Width() == 1 )
{
// Matrix views
DistMatrix<F> L10(g), L11(g);
DistMatrix<F>
xT(g), x0(g),
xB(g), x1(g),
x2(g);
// Temporary distributions
DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
DistMatrix<F,STAR,STAR> x1_STAR_STAR(g);
DistMatrix<F,MC, STAR> x1_MC_STAR(g);
DistMatrix<F,MC, MR > z1(g);
DistMatrix<F,MR, MC > z1_MR_MC(g);
DistMatrix<F,MR, STAR> z_MR_STAR(g);
// Views of z[MR,* ]
DistMatrix<F,MR,STAR> z0_MR_STAR(g),
z1_MR_STAR(g);
z_MR_STAR.AlignWith( L );
Zeros( x.Height(), 1, z_MR_STAR );
// Start the algorithm
PartitionUp
( x, xT,
xB, 0 );
while( xT.Height() > 0 )
{
RepartitionUp
( xT, x0,
x1,
/**/ /**/
xB, x2 );
const int n0 = x0.Height();
const int n1 = x1.Height();
LockedView( L10, L, n0, 0, n1, n0 );
LockedView( L11, L, n0, n0, n1, n1 );
View( z0_MR_STAR, z_MR_STAR, 0, 0, n0, 1 );
View( z1_MR_STAR, z_MR_STAR, n0, 0, n1, 1 );
x1_MC_STAR.AlignWith( L10 );
z1.AlignWith( x1 );
//----------------------------------------------------------------//
if( x2.Height() != 0 )
{
z1_MR_MC.SumScatterFrom( z1_MR_STAR );
z1 = z1_MR_MC;
Axpy( F(1), z1, x1 );
}
x1_STAR_STAR = x1;
L11_STAR_STAR = L11;
Trsv
( LOWER, orientation, diag,
L11_STAR_STAR.LockedMatrix(),
x1_STAR_STAR.Matrix() );
x1 = x1_STAR_STAR;
x1_MC_STAR = x1_STAR_STAR;
Gemv
( orientation, F(-1),
L10.LockedMatrix(),
x1_MC_STAR.LockedMatrix(),
F(1), z0_MR_STAR.Matrix() );
//----------------------------------------------------------------//
x1_MC_STAR.FreeAlignments();
z1.FreeAlignments();
SlidePartitionUp
( xT, x0,
/**/ /**/
x1,
xB, x2 );
}
}
else
{
// Matrix views
DistMatrix<F> L10(g), L11(g);
DistMatrix<F>
xL(g), xR(g),
x0(g), x1(g), x2(g);
// Temporary distributions
DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
DistMatrix<F,STAR,STAR> x1_STAR_STAR(g);
DistMatrix<F,STAR,MC > x1_STAR_MC(g);
DistMatrix<F,STAR,MR > z_STAR_MR(g);
// Views of z[* ,MR], which will store updates to x
DistMatrix<F,STAR,MR> z0_STAR_MR(g),
z1_STAR_MR(g);
z_STAR_MR.AlignWith( L );
Zeros( 1, x.Width(), z_STAR_MR );
// Start the algorithm
PartitionLeft( x, xL, xR, 0 );
while( xL.Width() > 0 )
{
RepartitionLeft
( xL, /**/ xR,
x0, x1, /**/ x2 );
const int n0 = x0.Width();
const int n1 = x1.Width();
LockedView( L10, L, n0, 0, n1, n0 );
LockedView( L11, L, n0, n0, n1, n1 );
View( z0_STAR_MR, z_STAR_MR, 0, 0, 1, n0 );
View( z1_STAR_MR, z_STAR_MR, 0, n0, 1, n1 );
x1_STAR_MC.AlignWith( L10 );
//----------------------------------------------------------------//
if( x2.Width() != 0 )
x1.SumScatterUpdate( F(1), z1_STAR_MR );
x1_STAR_STAR = x1;
L11_STAR_STAR = L11;
Trsv
( LOWER, orientation, diag,
L11_STAR_STAR.LockedMatrix(),
x1_STAR_STAR.Matrix() );
x1 = x1_STAR_STAR;
x1_STAR_MC = x1_STAR_STAR;
Gemv
( orientation, F(-1),
L10.LockedMatrix(),
x1_STAR_MC.LockedMatrix(),
F(1), z0_STAR_MR.Matrix() );
//----------------------------------------------------------------//
x1_STAR_MC.FreeAlignments();
SlidePartitionLeft
( xL, /**/ xR,
x0, /**/ x1, x2 );
}
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
internal::TrsvLN
( UnitOrNonUnit diag,
const DistMatrix<F,MC,MR>& L,
DistMatrix<F,MC,MR>& x )
{
#ifndef RELEASE
PushCallStack("internal::TrsvLN");
if( L.Grid() != x.Grid() )
throw std::logic_error("{L,x} must be distributed over the same grid");
if( L.Height() != L.Width() )
throw std::logic_error("L must be square");
if( x.Width() != 1 && x.Height() != 1 )
throw std::logic_error("x must be a vector");
const int xLength = ( x.Width() == 1 ? x.Height() : x.Width() );
if( L.Width() != xLength )
throw std::logic_error("Nonconformal TrsvLN");
#endif
const Grid& g = L.Grid();
if( x.Width() == 1 )
{
// Matrix views
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);
DistMatrix<F,MC,MR>
xT(g), x0(g),
xB(g), x1(g),
x2(g);
// Temporary distributions
DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
DistMatrix<F,STAR,STAR> x1_STAR_STAR(g);
DistMatrix<F,MR, STAR> x1_MR_STAR(g);
DistMatrix<F,MC, STAR> z2_MC_STAR(g);
// Start the algorithm
LockedPartitionDownDiagonal
( L, LTL, LTR,
LBL, LBR, 0 );
PartitionDown
( x, xT,
xB, 0 );
while( xB.Height() > 0 )
{
LockedRepartitionDownDiagonal
( LTL, /**/ LTR, L00, /**/ L01, L02,
/*************/ /******************/
/**/ L10, /**/ L11, L12,
LBL, /**/ LBR, L20, /**/ L21, L22 );
RepartitionDown
( xT, x0,
/**/ /**/
x1,
xB, x2 );
x1_MR_STAR.AlignWith( L21 );
z2_MC_STAR.AlignWith( L21 );
z2_MC_STAR.ResizeTo( x2.Height(), 1 );
//----------------------------------------------------------------//
x1_STAR_STAR = x1;
L11_STAR_STAR = L11;
Trsv
( LOWER, NORMAL, diag,
L11_STAR_STAR.LockedLocalMatrix(),
x1_STAR_STAR.LocalMatrix() );
x1 = x1_STAR_STAR;
x1_MR_STAR = x1_STAR_STAR;
Gemv
( NORMAL, (F)-1,
L21.LockedLocalMatrix(),
x1_MR_STAR.LockedLocalMatrix(),
(F)0, z2_MC_STAR.LocalMatrix() );
x2.SumScatterUpdate( (F)1, z2_MC_STAR );
//----------------------------------------------------------------//
x1_MR_STAR.FreeAlignments();
z2_MC_STAR.FreeAlignments();
SlideLockedPartitionDownDiagonal
( LTL, /**/ LTR, L00, L01, /**/ L02,
/**/ L10, L11, /**/ L12,
/*************/ /******************/
LBL, /**/ LBR, L20, L21, /**/ L22 );
SlidePartitionDown
( xT, x0,
x1,
/**/ /**/
xB, x2 );
}
}
else
{
// Matrix views
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);
DistMatrix<F,MC,MR>
xL(g), xR(g),
x0(g), x1(g), x2(g);
// Temporary distributions
DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
DistMatrix<F,STAR,STAR> x1_STAR_STAR(g);
DistMatrix<F,STAR,MR > x1_STAR_MR(g);
DistMatrix<F,STAR,MC > z2_STAR_MC(g);
DistMatrix<F,MR, MC > z2_MR_MC(g);
DistMatrix<F,MC, MR > z2(g);
// Start the algorithm
LockedPartitionDownDiagonal
( L, LTL, LTR,
LBL, LBR, 0 );
PartitionRight( x, xL, xR, 0 );
while( xR.Width() > 0 )
{
LockedRepartitionDownDiagonal
( LTL, /**/ LTR, L00, /**/ L01, L02,
/*************/ /******************/
/**/ L10, /**/ L11, L12,
LBL, /**/ LBR, L20, /**/ L21, L22 );
RepartitionRight
( xL, /**/ xR,
x0, /**/ x1, x2 );
x1_STAR_MR.AlignWith( L21 );
z2_STAR_MC.AlignWith( L21 );
z2.AlignWith( x2 );
z2_STAR_MC.ResizeTo( 1, x2.Width() );
//----------------------------------------------------------------//
x1_STAR_STAR = x1;
L11_STAR_STAR = L11;
Trsv
( LOWER, NORMAL, diag,
L11_STAR_STAR.LockedLocalMatrix(),
x1_STAR_STAR.LocalMatrix() );
x1 = x1_STAR_STAR;
x1_STAR_MR = x1_STAR_STAR;
Gemv
( NORMAL, (F)-1,
L21.LockedLocalMatrix(),
x1_STAR_MR.LockedLocalMatrix(),
(F)0, z2_STAR_MC.LocalMatrix() );
z2_MR_MC.SumScatterFrom( z2_STAR_MC );
z2 = z2_MR_MC;
Axpy( (F)1, z2, x2 );
//----------------------------------------------------------------//
x1_STAR_MR.FreeAlignments();
z2_STAR_MC.FreeAlignments();
z2.FreeAlignments();
SlideLockedPartitionDownDiagonal
( LTL, /**/ LTR, L00, L01, /**/ L02,
/**/ L10, L11, /**/ L12,
/*************/ /******************/
LBL, /**/ LBR, L20, L21, /**/ L22 );
SlidePartitionRight
( xL, /**/ xR,
x0, x1, /**/ x2 );
}
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
LocalSymvRowAccumulateU
( T alpha,
const DistMatrix<T>& A,
const DistMatrix<T,STAR,MC>& x_STAR_MC,
const DistMatrix<T,STAR,MR>& x_STAR_MR,
DistMatrix<T,STAR,MC>& z_STAR_MC,
DistMatrix<T,STAR,MR>& z_STAR_MR )
{
#ifndef RELEASE
PushCallStack("internal::LocalSymvRowAccumulateU");
if( A.Grid() != x_STAR_MC.Grid() ||
x_STAR_MC.Grid() != x_STAR_MR.Grid() ||
x_STAR_MR.Grid() != z_STAR_MC.Grid() ||
z_STAR_MC.Grid() != z_STAR_MR.Grid() )
throw std::logic_error
("{A,x,z} must be distributed over the same grid");
if( x_STAR_MC.Height() != 1 || x_STAR_MR.Height() != 1 ||
z_STAR_MC.Height() != 1 || z_STAR_MR.Height() != 1 )
throw std::logic_error("Expected x and z to be row vectors");
if( A.Height() != A.Width() ||
A.Height() != x_STAR_MC.Width() ||
A.Height() != x_STAR_MR.Width() ||
A.Height() != z_STAR_MC.Width() ||
A.Height() != z_STAR_MR.Width() )
{
std::ostringstream msg;
msg << "Nonconformal LocalSymvRowAccumulateU: \n"
<< " A ~ " << A.Height() << " x " << A.Width() << "\n"
<< " x[* ,MC] ~ " << x_STAR_MC.Height() << " x "
<< x_STAR_MC.Width() << "\n"
<< " x[* ,MR] ~ " << x_STAR_MR.Height() << " x "
<< x_STAR_MR.Width() << "\n"
<< " z[* ,MC] ~ " << z_STAR_MC.Height() << " x "
<< z_STAR_MC.Width() << "\n"
<< " z[* ,MR] ~ " << z_STAR_MR.Height() << " x "
<< z_STAR_MR.Width() << "\n";
throw std::logic_error( msg.str() );
}
if( x_STAR_MC.RowAlignment() != A.ColAlignment() ||
x_STAR_MR.RowAlignment() != A.RowAlignment() ||
z_STAR_MC.RowAlignment() != A.ColAlignment() ||
z_STAR_MR.RowAlignment() != A.RowAlignment() )
throw std::logic_error("Partial matrix distributions are misaligned");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<T> A11(g), A12(g);
DistMatrix<T> D11(g);
DistMatrix<T,STAR,MC> x1_STAR_MC(g);
DistMatrix<T,STAR,MR>
xL_STAR_MR(g), xR_STAR_MR(g),
x0_STAR_MR(g), x1_STAR_MR(g), x2_STAR_MR(g);
DistMatrix<T,STAR,MC> z1_STAR_MC(g);
DistMatrix<T,STAR,MR> z1_STAR_MR(g), z2_STAR_MR(g);
// We want our local gemvs to be of width blocksize, so we will
// temporarily change to max(r,c) times the current blocksize
const int ratio = std::max( g.Height(), g.Width() );
PushBlocksizeStack( ratio*LocalSymvBlocksize<T>() );
LockedPartitionRight( x_STAR_MR, xL_STAR_MR, xR_STAR_MR, 0 );
while( xL_STAR_MR.Width() < x_STAR_MR.Width() )
{
LockedRepartitionRight
( xL_STAR_MR, /**/ xR_STAR_MR,
x0_STAR_MR, /**/ x1_STAR_MR, x2_STAR_MR );
const int n0 = x0_STAR_MR.Width();
const int n1 = x1_STAR_MR.Width();
const int n2 = x2_STAR_MR.Width();
LockedView( A11, A, n0, n0, n1, n1 );
LockedView( A12, A, n0, n0+n1, n1, n2 );
LockedView( x1_STAR_MC, x_STAR_MC, 0, n0, 1, n1 );
View( z1_STAR_MC, z_STAR_MC, 0, n0, 1, n1 );
View( z1_STAR_MR, z_STAR_MR, 0, n0, 1, n1 );
View( z2_STAR_MR, z_STAR_MR, 0, n0+n1, 1, n2 );
D11.AlignWith( A11 );
//--------------------------------------------------------------------//
// TODO: These diagonal block updates can be greatly improved
D11 = A11;
MakeTrapezoidal( LEFT, UPPER, 0, D11 );
Gemv
( NORMAL,
alpha, D11.LockedLocalMatrix(),
x1_STAR_MR.LockedLocalMatrix(),
T(1), z1_STAR_MC.LocalMatrix() );
MakeTrapezoidal( LEFT, UPPER, 1, D11 );
Gemv
( TRANSPOSE,
alpha, D11.LockedLocalMatrix(),
x1_STAR_MC.LockedLocalMatrix(),
T(1), z1_STAR_MR.LocalMatrix() );
Gemv
( NORMAL,
alpha, A12.LockedLocalMatrix(),
x2_STAR_MR.LockedLocalMatrix(),
T(1), z1_STAR_MC.LocalMatrix() );
Gemv
( TRANSPOSE,
alpha, A12.LockedLocalMatrix(),
x1_STAR_MC.LockedLocalMatrix(),
T(1), z2_STAR_MR.LocalMatrix() );
//--------------------------------------------------------------------//
D11.FreeAlignments();
SlideLockedPartitionRight
( xL_STAR_MR, /**/ xR_STAR_MR,
x0_STAR_MR, x1_STAR_MR, /**/ x2_STAR_MR );
}
PopBlocksizeStack();
#ifndef RELEASE
PopCallStack();
#endif
}
void Flush()
{
if( numQueued_ == 0 )
return;
auto YActive = Y_( ALL, IR(0,numQueued_) );
Matrix<Base<Field>> colNorms;
if( useTranspose_ )
{
// TODO(poulson): Add this as an option
/*
Timer timer;
timer.Start();
BatchTransposedSparseToCoordinates
( NTrans_, YActive, VCand_, blocksize_ );
const double transformTime = timer.Stop();
const double n = YActive.Height();
const double transformGflops =
double(numQueued_)*n*n/(1.e9*transformTime);
Output
(numQueued_," transforms: ",timer.Stop()," seconds (",
transformGflops," GFlop/s");
timer.Start();
colNorms =
BatchTransposedCoordinatesToNorms
( d_, NTrans_, VCand_, insertionBound_ );
const double normTime = timer.Stop();
const double normGflops = double(numQueued_)*n*n/(1.e9*normTime);
Output
(numQueued_," norms: ",timer.Stop()," seconds (",
normGflops," GFlop/s");
*/
BatchTransposedSparseToCoordinates
( NTrans_, YActive, VCand_, blocksize_ );
colNorms =
BatchTransposedCoordinatesToNorms
( d_, NTrans_, VCand_, insertionBound_ );
}
else
{
BatchSparseToCoordinates( N_, YActive, VCand_, blocksize_ );
colNorms =
BatchCoordinatesToNorms( d_, N_, VCand_, insertionBound_ );
}
for( Int j=0; j<numQueued_; ++j )
{
for( Int k=0; k<insertionBound_; ++k )
{
const Base<Field> bNorm = colNorms(j,k);
if( bNorm < normUpperBounds_(k) && bNorm != Base<Field>(0) )
{
const Range<Int> subInd(k,END);
auto y = YActive(subInd,IR(j));
auto vCand = VCand_(subInd,IR(j));
Output
("normUpperBound=",normUpperBounds_(k),
", bNorm=",bNorm,", k=",k);
Print( y, "y" );
// Check that the reverse transformation holds
Matrix<Field> yCheck;
CoordinatesToSparse( N_(subInd,subInd), vCand, yCheck );
yCheck -= y;
if( FrobeniusNorm(yCheck) != Base<Field>(0) )
{
Print( B_(ALL,subInd), "B" );
Print( d_(subInd,ALL), "d" );
Print( N_(subInd,subInd), "N" );
Print( vCand, "vCand" );
Print( yCheck, "eCheck" );
LogicError("Invalid sparse transformation");
}
Copy( vCand, v_ );
Print( v_, "v" );
Matrix<Field> b;
Zeros( b, B_.Height(), 1 );
Gemv( NORMAL, Field(1), B_(ALL,subInd), v_, Field(0), b );
Print( b, "b" );
normUpperBounds_(k) = bNorm;
foundVector_ = true;
insertionBound_ = k+1;
}
// TODO(poulson): Keep track of 'stock' vectors?
}
}
numQueued_ = 0;
Zero( Y_ );
}
Int ADMM
( const Matrix<Real>& A,
const Matrix<Real>& b,
const Matrix<Real>& c,
Matrix<Real>& z,
const ADMMCtrl<Real>& ctrl )
{
EL_DEBUG_CSE
// Cache a custom partially-pivoted LU factorization of
// | rho*I A^H | = | B11 B12 |
// | A 0 | | B21 B22 |
// by (justifiably) avoiding pivoting in the first n steps of
// the factorization, so that
// [I,rho*I] = lu(rho*I).
// The factorization would then proceed with
// B21 := B21 U11^{-1} = A (rho*I)^{-1} = A/rho
// B12 := L11^{-1} B12 = I A^H = A^H.
// The Schur complement would then be
// B22 := B22 - B21 B12 = 0 - (A*A^H)/rho.
// We then factor said matrix with LU with partial pivoting and
// swap the necessary rows of B21 in order to implicitly commute
// the row pivots with the Gauss transforms in the manner standard
// for GEPP. Unless A A' is singular, pivoting should not be needed,
// as Cholesky factorization of the negative matrix should be valid.
//
// The result is the factorization
// | I 0 | | rho*I A^H | = | I 0 | | rho*I U12 |,
// | 0 P22 | | A 0 | | L21 L22 | | 0 U22 |
// where [L22,U22] are stored within B22.
Matrix<Real> U12, L21, B22, bPiv;
Adjoint( A, U12 );
L21 = A;
L21 *= 1/ctrl.rho;
Herk( LOWER, NORMAL, -1/ctrl.rho, A, B22 );
MakeHermitian( LOWER, B22 );
// TODO: Replace with sparse-direct Cholesky version?
Permutation P2;
LU( B22, P2 );
P2.PermuteRows( L21 );
bPiv = b;
P2.PermuteRows( bPiv );
// Possibly form the inverse of L22 U22
Matrix<Real> X22;
if( ctrl.inv )
{
X22 = B22;
MakeTrapezoidal( LOWER, X22 );
FillDiagonal( X22, Real(1) );
TriangularInverse( LOWER, UNIT, X22 );
Trsm( LEFT, UPPER, NORMAL, NON_UNIT, Real(1), B22, X22 );
}
Int numIter=0;
const Int m = A.Height();
const Int n = A.Width();
Matrix<Real> g, xTmp, y, t;
Zeros( g, m+n, 1 );
PartitionDown( g, xTmp, y, n );
Matrix<Real> x, u, zOld, xHat;
Zeros( z, n, 1 );
Zeros( u, n, 1 );
Zeros( t, n, 1 );
while( numIter < ctrl.maxIter )
{
zOld = z;
// Find x from
// | rho*I A^H | | x | = | rho*(z-u)-c |
// | A 0 | | y | | b |
// via our cached custom factorization:
//
// |x| = inv(U) inv(L) P' |rho*(z-u)-c|
// |y| |b |
// = |rho*I U12|^{-1} |I 0 | |I 0 | |rho*(z-u)-c|
// = |0 U22| |L21 L22| |0 P22'| |b |
// = " " |rho*(z-u)-c|
// | P22' b |
xTmp = z;
xTmp -= u;
xTmp *= ctrl.rho;
xTmp -= c;
y = bPiv;
Gemv( NORMAL, Real(-1), L21, xTmp, Real(1), y );
if( ctrl.inv )
{
Gemv( NORMAL, Real(1), X22, y, t );
y = t;
}
else
{
Trsv( LOWER, NORMAL, UNIT, B22, y );
Trsv( UPPER, NORMAL, NON_UNIT, B22, y );
}
Gemv( NORMAL, Real(-1), U12, y, Real(1), xTmp );
xTmp *= 1/ctrl.rho;
// xHat := alpha*x + (1-alpha)*zOld
xHat = xTmp;
xHat *= ctrl.alpha;
Axpy( 1-ctrl.alpha, zOld, xHat );
// z := pos(xHat+u)
z = xHat;
z += u;
LowerClip( z, Real(0) );
// u := u + (xHat-z)
u += xHat;
u -= z;
const Real objective = Dot( c, xTmp );
// rNorm := || x - z ||_2
t = xTmp;
t -= z;
const Real rNorm = FrobeniusNorm( t );
// sNorm := |rho| || z - zOld ||_2
t = z;
t -= zOld;
const Real sNorm = Abs(ctrl.rho)*FrobeniusNorm( t );
const Real epsPri = Sqrt(Real(n))*ctrl.absTol +
ctrl.relTol*Max(FrobeniusNorm(xTmp),FrobeniusNorm(z));
const Real epsDual = Sqrt(Real(n))*ctrl.absTol +
ctrl.relTol*Abs(ctrl.rho)*FrobeniusNorm(u);
if( ctrl.print )
{
t = xTmp;
LowerClip( t, Real(0) );
t -= xTmp;
const Real clipDist = FrobeniusNorm( t );
cout << numIter << ": "
<< "||x-z||_2=" << rNorm << ", "
<< "epsPri=" << epsPri << ", "
<< "|rho| ||z-zOld||_2=" << sNorm << ", "
<< "epsDual=" << epsDual << ", "
<< "||x-Pos(x)||_2=" << clipDist << ", "
<< "c'x=" << objective << endl;
}
if( rNorm < epsPri && sNorm < epsDual )
break;
++numIter;
}
if( ctrl.maxIter == numIter )
cout << "ADMM failed to converge" << endl;
x = xTmp;
return numIter;
}
inline void
PanelLQ( DistMatrix<Real>& A )
{
#ifndef RELEASE
PushCallStack("internal::PanelLQ");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<Real>
ATL(g), ATR(g), A00(g), a01(g), A02(g), aTopRow(g), ABottomPan(g),
ABL(g), ABR(g), a10(g), alpha11(g), a12(g),
A20(g), a21(g), A22(g);
// Temporary distributions
DistMatrix<Real,STAR,MR> aTopRow_STAR_MR(g);
DistMatrix<Real,MC,STAR> z_MC_STAR(g);
PushBlocksizeStack( 1 );
PartitionDownLeftDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
while( ATL.Height() < A.Height() && ATL.Width() < A.Width() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ a01, A02,
/*************/ /**********************/
/**/ a10, /**/ alpha11, a12,
ABL, /**/ ABR, A20, /**/ a21, A22 );
aTopRow.View1x2( alpha11, a12 );
ABottomPan.View1x2( a21, A22 );
aTopRow_STAR_MR.AlignWith( ABottomPan );
z_MC_STAR.AlignWith( ABottomPan );
Zeros( ABottomPan.Height(), 1, z_MC_STAR );
//--------------------------------------------------------------------//
const Real tau = Reflector( alpha11, a12 );
const bool myDiagonalEntry = ( g.Row() == alpha11.ColAlignment() &&
g.Col() == alpha11.RowAlignment() );
Real alpha = 0;
if( myDiagonalEntry )
{
alpha = alpha11.GetLocal(0,0);
alpha11.SetLocal(0,0,1);
}
aTopRow_STAR_MR = aTopRow;
Gemv
( NORMAL,
Real(1), ABottomPan.LockedLocalMatrix(),
aTopRow_STAR_MR.LockedLocalMatrix(),
Real(0), z_MC_STAR.LocalMatrix() );
z_MC_STAR.SumOverRow();
Ger
( -tau,
z_MC_STAR.LockedLocalMatrix(),
aTopRow_STAR_MR.LockedLocalMatrix(),
ABottomPan.LocalMatrix() );
if( myDiagonalEntry )
alpha11.SetLocal(0,0,alpha);
//--------------------------------------------------------------------//
aTopRow_STAR_MR.FreeAlignments();
z_MC_STAR.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, a01, /**/ A02,
/**/ a10, alpha11, /**/ a12,
/*************/ /**********************/
ABL, /**/ ABR, A20, a21, /**/ A22 );
}
PopBlocksizeStack();
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
PanelLQ
( DistMatrix<Complex<Real> >& A,
DistMatrix<Complex<Real>,MD,STAR>& t )
{
#ifndef RELEASE
PushCallStack("internal::PanelLQ");
if( A.Grid() != t.Grid() )
throw std::logic_error("{A,t} must be distributed over the same grid");
if( t.Height() != std::min(A.Height(),A.Width()) || t.Width() != 1 )
throw std::logic_error
("t must be a vector of height equal to the minimum dimension of A");
if( !t.AlignedWithDiagonal( A, 0 ) )
throw std::logic_error("t must be aligned with A's main diagonal");
#endif
typedef Complex<Real> C;
const Grid& g = A.Grid();
// Matrix views
DistMatrix<C>
ATL(g), ATR(g), A00(g), a01(g), A02(g), aTopRow(g), ABottomPan(g),
ABL(g), ABR(g), a10(g), alpha11(g), a12(g),
A20(g), a21(g), A22(g);
DistMatrix<C,MD,STAR>
tT(g), t0(g),
tB(g), tau1(g),
t2(g);
// Temporary distributions
DistMatrix<C> aTopRowConj(g);
DistMatrix<C,STAR,MR > aTopRowConj_STAR_MR(g);
DistMatrix<C,MC, STAR> z_MC_STAR(g);
PushBlocksizeStack( 1 );
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, /**/ alpha11, a12,
ABL, /**/ ABR, A20, /**/ a21, A22 );
RepartitionDown
( tT, t0,
/**/ /****/
tau1,
tB, t2 );
aTopRow.View1x2( alpha11, a12 );
ABottomPan.View1x2( a21, A22 );
aTopRowConj_STAR_MR.AlignWith( ABottomPan );
z_MC_STAR.AlignWith( ABottomPan );
Zeros( ABottomPan.Height(), 1, z_MC_STAR );
//--------------------------------------------------------------------//
const C tau = Reflector( alpha11, a12 );
tau1.Set( 0, 0, tau );
const bool myDiagonalEntry = ( g.Row() == alpha11.ColAlignment() &&
g.Col() == alpha11.RowAlignment() );
C alpha = 0;
if( myDiagonalEntry )
{
alpha = alpha11.GetLocal(0,0);
alpha11.SetLocal(0,0,1);
}
Conjugate( aTopRow, aTopRowConj );
aTopRowConj_STAR_MR = aTopRowConj;
Gemv
( NORMAL,
C(1), ABottomPan.LockedLocalMatrix(),
aTopRowConj_STAR_MR.LockedLocalMatrix(),
C(0), z_MC_STAR.LocalMatrix() );
z_MC_STAR.SumOverRow();
Ger
( -Conj(tau),
z_MC_STAR.LockedLocalMatrix(),
aTopRowConj_STAR_MR.LockedLocalMatrix(),
ABottomPan.LocalMatrix() );
if( myDiagonalEntry )
alpha11.SetLocal(0,0,alpha);
//--------------------------------------------------------------------//
aTopRowConj_STAR_MR.FreeAlignments();
z_MC_STAR.FreeAlignments();
SlidePartitionDown
( tT, t0,
tau1,
/**/ /****/
tB, t2 );
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, a01, /**/ A02,
/**/ a10, alpha11, /**/ a12,
/*************/ /**********************/
ABL, /**/ ABR, A20, a21, /**/ A22 );
}
PopBlocksizeStack();
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
PanelLQ
( Matrix<Complex<Real> >& A,
Matrix<Complex<Real> >& t )
{
#ifndef RELEASE
PushCallStack("internal::PanelLQ");
if( t.Height() != std::min(A.Height(),A.Width()) || t.Width() != 1 )
throw std::logic_error
("t must be a vector of height equal to the minimum dimension of A");
#endif
typedef Complex<Real> C;
Matrix<C>
ATL, ATR, A00, a01, A02, aTopRow, ABottomPan,
ABL, ABR, a10, alpha11, a12,
A20, a21, A22;
Matrix<C>
tT, t0,
tB, tau1,
t2;
Matrix<C> z, aTopRowConj;
PushBlocksizeStack( 1 );
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, /**/ alpha11, a12,
ABL, /**/ ABR, A20, /**/ a21, A22 );
RepartitionDown
( tT, t0,
/**/ /****/
tau1,
tB, t2 );
aTopRow.View1x2( alpha11, a12 );
ABottomPan.View1x2( a21, A22 );
Zeros( ABottomPan.Height(), 1, z );
//--------------------------------------------------------------------//
const C tau = Reflector( alpha11, a12 );
tau1.Set( 0, 0, tau );
const C alpha = alpha11.Get(0,0);
alpha11.Set(0,0,1);
Conjugate( aTopRow, aTopRowConj );
Gemv( NORMAL, C(1), ABottomPan, aTopRowConj, C(0), z );
Ger( -Conj(tau), z, aTopRowConj, ABottomPan );
alpha11.Set(0,0,alpha);
//--------------------------------------------------------------------//
SlidePartitionDown
( tT, t0,
tau1,
/**/ /****/
tB, t2 );
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, a01, /**/ A02,
/**/ a10, alpha11, /**/ a12,
/*************/ /**********************/
ABL, /**/ ABR, A20, a21, /**/ A22 );
}
PopBlocksizeStack();
#ifndef RELEASE
PopCallStack();
#endif
}
