std::unique_ptr<ElDistVector> ElRBFInterpolation::interpolate( const std::unique_ptr<ElDistVector> & values )
{
assert( Phi->Height() > 0 );
assert( H->Height() > 0 );
assert( values->Height() == Phi->Width() );
std::unique_ptr<ElDistVector> result( new ElDistVector( Phi->Grid() ) );
result->AlignRowsWith( *Phi );
El::DistMatrix<double> B = *values;
if ( HCopy.Width() == 0 )
{
HCopy = El::DistMatrix<double> ( *H );
El::DistMatrixReadProxy<double, double, El::MC, El::MR> AProx( HCopy );
auto & A = AProx.Get();
p = El::DistPermutation( A.Grid() );
dSub = El::DistMatrix<double, El::MD, El::STAR> ( A.Grid() );
El::LDL( A, dSub, p, false, El::LDLPivotCtrl<El::Base<double> >() );
}
El::DistMatrixReadProxy<double, double, El::MC, El::MR> AProx( HCopy );
El::DistMatrixReadWriteProxy<double, double, El::MC, El::MR> BProx( B );
auto & A = AProx.Get();
auto & B_LU = BProx.Get();
El::ldl::SolveAfter( A, dSub, p, B_LU, false );
El::Gemm( El::Orientation::NORMAL, El::Orientation::NORMAL, 1.0, *Phi, B, *result );
return result;
}
void ApplyQ
( LeftOrRight side,
Orientation orientation,
const AbstractDistMatrix<F>& APre,
const AbstractDistMatrix<F>& householderScalars,
const AbstractDistMatrix<Base<F>>& signature,
AbstractDistMatrix<F>& BPre )
{
EL_DEBUG_CSE
const bool normal = (orientation==NORMAL);
const bool onLeft = (side==LEFT);
const bool applyDFirst = normal==onLeft;
const Int minDim = Min(APre.Height(),APre.Width());
const ForwardOrBackward direction = ( normal==onLeft ? BACKWARD : FORWARD );
const Conjugation conjugation = ( normal ? CONJUGATED : UNCONJUGATED );
DistMatrixReadProxy<F,F,MC,MR> AProx( APre );
DistMatrixReadWriteProxy<F,F,MC,MR> BProx( BPre );
auto& A = AProx.GetLocked();
auto& B = BProx.Get();
const Int m = B.Height();
const Int n = B.Width();
if( applyDFirst )
{
if( onLeft )
{
auto BTop = B( IR(0,minDim), IR(0,n) );
DiagonalScale( side, orientation, signature, BTop );
}
else
{
auto BLeft = B( IR(0,m), IR(0,minDim) );
DiagonalScale( side, orientation, signature, BLeft );
}
}
ApplyPackedReflectors
( side, LOWER, VERTICAL, direction, conjugation, 0,
A, householderScalars, B );
if( !applyDFirst )
{
if( onLeft )
{
auto BTop = B( IR(0,minDim), IR(0,n) );
DiagonalScale( side, orientation, signature, BTop );
}
else
{
auto BLeft = B( IR(0,m), IR(0,minDim) );
DiagonalScale( side, orientation, signature, BLeft );
}
}
}
void SUMMA_NTDot
( Orientation orientB,
T alpha,
const AbstractDistMatrix<T>& APre,
const AbstractDistMatrix<T>& BPre,
AbstractDistMatrix<T>& CPre,
Int blockSize=2000 )
{
EL_DEBUG_CSE
const Int m = CPre.Height();
const Int n = CPre.Width();
const Grid& g = APre.Grid();
DistMatrixReadProxy<T,T,STAR,VC> AProx( APre );
auto& A = AProx.GetLocked();
ElementalProxyCtrl BCtrl;
BCtrl.rowConstrain = true;
BCtrl.rowAlign = A.RowAlign();
DistMatrixReadProxy<T,T,STAR,VC> BProx( BPre, BCtrl );
auto& B = BProx.GetLocked();
DistMatrixReadWriteProxy<T,T,MC,MR> CProx( CPre );
auto& C = CProx.Get();
DistMatrix<T,STAR,STAR> C11_STAR_STAR(g);
for( Int kOuter=0; kOuter<m; kOuter+=blockSize )
{
const Int nbOuter = Min(blockSize,m-kOuter);
const Range<Int> indOuter( kOuter, kOuter+nbOuter );
auto A1 = A( indOuter, ALL );
for( Int kInner=0; kInner<n; kInner+=blockSize )
{
const Int nbInner = Min(blockSize,n-kInner);
const Range<Int> indInner( kInner, kInner+nbInner );
auto B1 = B( indInner, ALL );
auto C11 = C( indOuter, indInner );
LocalGemm( NORMAL, orientB, alpha, A1, B1, C11_STAR_STAR );
AxpyContract( T(1), C11_STAR_STAR, C11 );
}
}
}
void SUMMA_NTC
( Orientation orientB,
T alpha,
const AbstractDistMatrix<T>& APre,
const AbstractDistMatrix<T>& BPre,
AbstractDistMatrix<T>& CPre )
{
EL_DEBUG_CSE
const Int sumDim = APre.Width();
const Int bsize = Blocksize();
const Grid& g = APre.Grid();
const bool conjugate = ( orientB == ADJOINT );
DistMatrixReadProxy<T,T,MC,MR> AProx( APre );
DistMatrixReadProxy<T,T,MC,MR> BProx( BPre );
DistMatrixReadWriteProxy<T,T,MC,MR> CProx( CPre );
auto& A = AProx.GetLocked();
auto& B = BProx.GetLocked();
auto& C = CProx.Get();
// Temporary distributions
DistMatrix<T,MC,STAR> A1_MC_STAR(g);
DistMatrix<T,VR,STAR> B1_VR_STAR(g);
DistMatrix<T,STAR,MR> B1Trans_STAR_MR(g);
A1_MC_STAR.AlignWith( C );
B1_VR_STAR.AlignWith( C );
B1Trans_STAR_MR.AlignWith( C );
for( Int k=0; k<sumDim; k+=bsize )
{
const Int nb = Min(bsize,sumDim-k);
auto A1 = A( ALL, IR(k,k+nb) );
auto B1 = B( ALL, IR(k,k+nb) );
A1_MC_STAR = A1;
B1_VR_STAR = B1;
Transpose( B1_VR_STAR, B1Trans_STAR_MR, conjugate );
// C[MC,MR] += alpha A1[MC,*] (B1[MR,*])^T
LocalGemm
( NORMAL, NORMAL, alpha, A1_MC_STAR, B1Trans_STAR_MR, T(1), C );
}
}
void L1DistanceMatrix(direction_t dirA, direction_t dirB, T alpha,
const El::ElementalMatrix<T> &APre, const El::ElementalMatrix<T> &BPre,
T beta, El::ElementalMatrix<T> &CPre) {
if (dirA == base::COLUMNS && dirB == base::COLUMNS) {
// Use a SUMMA-like routine, with C as stationary
// Basically an adaptation of Elementals TN case for stationary C.
const El::Int m = CPre.Height();
const El::Int n = CPre.Width();
const El::Int sumDim = BPre.Height();
const El::Int bsize = El::Blocksize();
const El::Grid& g = APre.Grid();
El::DistMatrixReadProxy<T, T, El::MC, El::MR> AProx(APre);
El::DistMatrixReadProxy<T, T, El::MC, El::MR> BProx(BPre);
El::DistMatrixReadWriteProxy<T, T, El::MC, El::MR> CProx(CPre);
auto& A = AProx.GetLocked();
auto& B = BProx.GetLocked();
auto& C = CProx.Get();
// Temporary distributions
El::DistMatrix<T, El::STAR, El::MC> A1_STAR_MC(g);
El::DistMatrix<T, El::STAR, El::MR> B1_STAR_MR(g);
A1_STAR_MC.AlignWith(C);
B1_STAR_MR.AlignWith(C);
El::Scale(beta, C);
for(El::Int k = 0; k < sumDim; k += bsize) {
const El::Int nb = std::min(bsize,sumDim-k);
auto A1 = A(El::IR(k,k+nb), El::IR(0,m));
auto B1 = B(El::IR(k,k+nb), El::IR(0,n));
A1_STAR_MC = A1;
B1_STAR_MR = B1;
L1DistanceMatrix(base::COLUMNS, base::COLUMNS, alpha,
A1_STAR_MC.LockedMatrix(), B1_STAR_MR.LockedMatrix(),
T(1.0), C.Matrix());
}
}
// TODO the rest of the cases.
}
void SUMMA_NTB
( Orientation orientB,
T alpha,
const AbstractDistMatrix<T>& APre,
const AbstractDistMatrix<T>& BPre,
AbstractDistMatrix<T>& CPre )
{
EL_DEBUG_CSE
const Int m = CPre.Height();
const Int bsize = Blocksize();
const Grid& g = APre.Grid();
DistMatrixReadProxy<T,T,MC,MR> AProx( APre );
DistMatrixReadProxy<T,T,MC,MR> BProx( BPre );
DistMatrixReadWriteProxy<T,T,MC,MR> CProx( CPre );
auto& A = AProx.GetLocked();
auto& B = BProx.GetLocked();
auto& C = CProx.Get();
// Temporary distributions
DistMatrix<T,MR,STAR> A1Trans_MR_STAR(g);
DistMatrix<T,STAR,MC> D1_STAR_MC(g);
DistMatrix<T,MR,MC> D1_MR_MC(g);
A1Trans_MR_STAR.AlignWith( B );
D1_STAR_MC.AlignWith( B );
for( Int k=0; k<m; k+=bsize )
{
const Int nb = Min(bsize,m-k);
auto A1 = A( IR(k,k+nb), ALL );
auto C1 = C( IR(k,k+nb), ALL );
// D1[*,MC] := alpha A1[*,MR] (B[MC,MR])^T
// = alpha (A1^T)[MR,*] (B^T)[MR,MC]
Transpose( A1, A1Trans_MR_STAR );
LocalGemm( TRANSPOSE, orientB, alpha, A1Trans_MR_STAR, B, D1_STAR_MC );
// C1[MC,MR] += scattered & transposed D1[*,MC] summed over grid rows
Contract( D1_STAR_MC, D1_MR_MC );
Axpy( T(1), D1_MR_MC, C1 );
}
}
void SUMMA_TNA
( Orientation orientA,
T alpha,
const AbstractDistMatrix<T>& APre,
const AbstractDistMatrix<T>& BPre,
AbstractDistMatrix<T>& CPre )
{
DEBUG_CSE
const Int n = CPre.Width();
const Int bsize = Blocksize();
const Grid& g = APre.Grid();
DistMatrixReadProxy<T,T,MC,MR> AProx( APre );
DistMatrixReadProxy<T,T,MC,MR> BProx( BPre );
DistMatrixReadWriteProxy<T,T,MC,MR> CProx( CPre );
auto& A = AProx.GetLocked();
auto& B = BProx.GetLocked();
auto& C = CProx.Get();
// Temporary distributions
DistMatrix<T,MC,STAR> B1_MC_STAR(g);
DistMatrix<T,MR,STAR> D1_MR_STAR(g);
DistMatrix<T,MR,MC > D1_MR_MC(g);
B1_MC_STAR.AlignWith( A );
D1_MR_STAR.AlignWith( A );
for( Int k=0; k<n; k+=bsize )
{
const Int nb = Min(bsize,n-k);
auto B1 = B( ALL, IR(k,k+nb) );
auto C1 = C( ALL, IR(k,k+nb) );
// D1[MR,*] := alpha (A1[MC,MR])^T B1[MC,*]
// = alpha (A1^T)[MR,MC] B1[MC,*]
B1_MC_STAR = B1;
LocalGemm( orientA, NORMAL, alpha, A, B1_MC_STAR, D1_MR_STAR );
// C1[MC,MR] += scattered & transposed D1[MR,*] summed over grid cols
Contract( D1_MR_STAR, D1_MR_MC );
Axpy( T(1), D1_MR_MC, C1 );
}
}
void SUMMA_NTA
( Orientation orientB,
T alpha,
const AbstractDistMatrix<T>& APre,
const AbstractDistMatrix<T>& BPre,
AbstractDistMatrix<T>& CPre )
{
EL_DEBUG_CSE
const Int n = CPre.Width();
const Int bsize = Blocksize();
const Grid& g = APre.Grid();
const bool conjugate = ( orientB == ADJOINT );
DistMatrixReadProxy<T,T,MC,MR> AProx( APre );
DistMatrixReadProxy<T,T,MC,MR> BProx( BPre );
DistMatrixReadWriteProxy<T,T,MC,MR> CProx( CPre );
auto& A = AProx.GetLocked();
auto& B = BProx.GetLocked();
auto& C = CProx.Get();
// Temporary distributions
DistMatrix<T,MR,STAR> B1Trans_MR_STAR(g);
DistMatrix<T,MC,STAR> D1_MC_STAR(g);
B1Trans_MR_STAR.AlignWith( A );
D1_MC_STAR.AlignWith( A );
for( Int k=0; k<n; k+=bsize )
{
const Int nb = Min(bsize,n-k);
auto B1 = B( IR(k,k+nb), ALL );
auto C1 = C( ALL, IR(k,k+nb) );
// C1[MC,*] := alpha A[MC,MR] (B1^[T/H])[MR,*]
Transpose( B1, B1Trans_MR_STAR, conjugate );
LocalGemm( NORMAL, NORMAL, alpha, A, B1Trans_MR_STAR, D1_MC_STAR );
// C1[MC,MR] += scattered result of D1[MC,*] summed over grid rows
AxpyContract( T(1), D1_MC_STAR, C1 );
}
}
void SUMMA_TNB
( Orientation orientA,
T alpha,
const AbstractDistMatrix<T>& APre,
const AbstractDistMatrix<T>& BPre,
AbstractDistMatrix<T>& CPre )
{
DEBUG_CSE
const Int m = CPre.Height();
const Int bsize = Blocksize();
const Grid& g = APre.Grid();
const bool conjugate = ( orientA == ADJOINT );
DistMatrixReadProxy<T,T,MC,MR> AProx( APre );
DistMatrixReadProxy<T,T,MC,MR> BProx( BPre );
DistMatrixReadWriteProxy<T,T,MC,MR> CProx( CPre );
auto& A = AProx.GetLocked();
auto& B = BProx.GetLocked();
auto& C = CProx.Get();
// Temporary distributions
DistMatrix<T,MC,STAR> A1_MC_STAR(g);
DistMatrix<T,MR,STAR> D1Trans_MR_STAR(g);
A1_MC_STAR.AlignWith( B );
D1Trans_MR_STAR.AlignWith( B );
for( Int k=0; k<m; k+=bsize )
{
const Int nb = Min(bsize,m-k);
auto A1 = A( ALL, IR(k,k+nb) );
auto C1 = C( IR(k,k+nb), ALL );
// D1[*,MR] := alpha (A1[MC,*])^[T/H] B[MC,MR]
// = alpha (A1^[T/H])[*,MC] B[MC,MR]
A1_MC_STAR = A1; // A1[MC,*] <- A1[MC,MR]
LocalGemm( orientA, NORMAL, T(1), B, A1_MC_STAR, D1Trans_MR_STAR );
TransposeAxpyContract( alpha, D1Trans_MR_STAR, C1, conjugate );
}
}
void SUMMA_TNC
( Orientation orientA,
T alpha,
const AbstractDistMatrix<T>& APre,
const AbstractDistMatrix<T>& BPre,
AbstractDistMatrix<T>& CPre )
{
DEBUG_CSE
const Int sumDim = BPre.Height();
const Int bsize = Blocksize();
const Grid& g = APre.Grid();
DistMatrixReadProxy<T,T,MC,MR> AProx( APre );
DistMatrixReadProxy<T,T,MC,MR> BProx( BPre );
DistMatrixReadWriteProxy<T,T,MC,MR> CProx( CPre );
auto& A = AProx.GetLocked();
auto& B = BProx.GetLocked();
auto& C = CProx.Get();
// Temporary distributions
DistMatrix<T,STAR,MC> A1_STAR_MC(g);
DistMatrix<T,MR,STAR> B1Trans_MR_STAR(g);
A1_STAR_MC.AlignWith( C );
B1Trans_MR_STAR.AlignWith( C );
for( Int k=0; k<sumDim; k+=bsize )
{
const Int nb = Min(bsize,sumDim-k);
auto A1 = A( IR(k,k+nb), ALL );
auto B1 = B( IR(k,k+nb), ALL );
// C[MC,MR] += alpha (A1[*,MC])^T B1[*,MR]
// = alpha (A1^T)[MC,*] B1[*,MR]
A1_STAR_MC = A1;
Transpose( B1, B1Trans_MR_STAR );
LocalGemm
( orientA, TRANSPOSE, alpha, A1_STAR_MC, B1Trans_MR_STAR, T(1), C );
}
}
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 Ridge
( Orientation orientation,
const AbstractDistMatrix<Field>& APre,
const AbstractDistMatrix<Field>& BPre,
Base<Field> gamma,
AbstractDistMatrix<Field>& XPre,
RidgeAlg alg )
{
EL_DEBUG_CSE
DistMatrixReadProxy<Field,Field,MC,MR>
AProx( APre ),
BProx( BPre );
DistMatrixWriteProxy<Field,Field,MC,MR>
XProx( XPre );
auto& A = AProx.GetLocked();
auto& B = BProx.GetLocked();
auto& X = XProx.Get();
const bool normal = ( orientation==NORMAL );
const Int m = ( normal ? A.Height() : A.Width() );
const Int n = ( normal ? A.Width() : A.Height() );
if( orientation == TRANSPOSE && IsComplex<Field>::value )
LogicError("Transpose version of complex Ridge not yet supported");
if( m >= n )
{
DistMatrix<Field> Z(A.Grid());
if( alg == RIDGE_CHOLESKY )
{
if( orientation == NORMAL )
Herk( LOWER, ADJOINT, Base<Field>(1), A, Z );
else
Herk( LOWER, NORMAL, Base<Field>(1), A, Z );
ShiftDiagonal( Z, Field(gamma*gamma) );
Cholesky( LOWER, Z );
if( orientation == NORMAL )
Gemm( ADJOINT, NORMAL, Field(1), A, B, X );
else
Gemm( NORMAL, NORMAL, Field(1), A, B, X );
cholesky::SolveAfter( LOWER, NORMAL, Z, X );
}
else if( alg == RIDGE_QR )
{
Zeros( Z, m+n, n );
auto ZT = Z( IR(0,m), IR(0,n) );
auto ZB = Z( IR(m,m+n), IR(0,n) );
if( orientation == NORMAL )
ZT = A;
else
Adjoint( A, ZT );
FillDiagonal( ZB, Field(gamma) );
// NOTE: This QR factorization could exploit the upper-triangular
// structure of the diagonal matrix ZB
qr::ExplicitTriang( Z );
if( orientation == NORMAL )
Gemm( ADJOINT, NORMAL, Field(1), A, B, X );
else
Gemm( NORMAL, NORMAL, Field(1), A, B, X );
cholesky::SolveAfter( LOWER, NORMAL, Z, X );
}
else
{
DistMatrix<Field> U(A.Grid()), V(A.Grid());
DistMatrix<Base<Field>,VR,STAR> s(A.Grid());
if( orientation == NORMAL )
{
SVDCtrl<Base<Field>> ctrl;
ctrl.overwrite = false;
SVD( A, U, s, V, ctrl );
}
else
{
DistMatrix<Field> AAdj(A.Grid());
Adjoint( A, AAdj );
SVDCtrl<Base<Field>> ctrl;
ctrl.overwrite = true;
SVD( AAdj, U, s, V );
}
auto sigmaMap =
[=]( const Base<Field>& sigma )
{ return sigma / (sigma*sigma + gamma*gamma); };
EntrywiseMap( s, MakeFunction(sigmaMap) );
Gemm( ADJOINT, NORMAL, Field(1), U, B, X );
DiagonalScale( LEFT, NORMAL, s, X );
U = X;
Gemm( NORMAL, NORMAL, Field(1), V, U, X );
}
}
else
{
LogicError("This case not yet supported");
}
}
void StackedRuizEquil
( AbstractDistMatrix<Field>& APre,
AbstractDistMatrix<Field>& BPre,
AbstractDistMatrix<Base<Field>>& dRowAPre,
AbstractDistMatrix<Base<Field>>& dRowBPre,
AbstractDistMatrix<Base<Field>>& dColPre,
bool progress )
{
EL_DEBUG_CSE
typedef Base<Field> Real;
ElementalProxyCtrl control;
control.colConstrain = true;
control.rowConstrain = true;
control.colAlign = 0;
control.rowAlign = 0;
DistMatrixReadWriteProxy<Field,Field,MC,MR> AProx( APre, control );
DistMatrixReadWriteProxy<Field,Field,MC,MR> BProx( BPre, control );
DistMatrixWriteProxy<Real,Real,MC,STAR> dRowAProx( dRowAPre, control );
DistMatrixWriteProxy<Real,Real,MC,STAR> dRowBProx( dRowBPre, control );
DistMatrixWriteProxy<Real,Real,MR,STAR> dColProx( dColPre, control );
auto& A = AProx.Get();
auto& B = BProx.Get();
auto& dRowA = dRowAProx.Get();
auto& dRowB = dRowBProx.Get();
auto& dCol = dColProx.Get();
const Int mA = A.Height();
const Int mB = B.Height();
const Int n = A.Width();
const Int nLocal = A.LocalWidth();
Ones( dRowA, mA, 1 );
Ones( dRowB, mB, 1 );
Ones( dCol, n, 1 );
// TODO(poulson): Expose these as control parameters
// For now, simply hard-code the number of iterations
const Int maxIter = 4;
DistMatrix<Real,MC,STAR> rowScale(A.Grid());
DistMatrix<Real,MR,STAR> colScale(A.Grid()), colScaleB(B.Grid());
auto& colScaleLoc = colScale.Matrix();
auto& colScaleBLoc = colScaleB.Matrix();
const Int indent = PushIndent();
for( Int iter=0; iter<maxIter; ++iter )
{
// Rescale the columns
// -------------------
ColumnMaxNorms( A, colScale );
ColumnMaxNorms( B, colScaleB );
for( Int jLoc=0; jLoc<nLocal; ++jLoc )
colScaleLoc(jLoc) =
Max(colScaleLoc(jLoc),colScaleBLoc(jLoc));
EntrywiseMap( colScale, MakeFunction(DampScaling<Real>) );
DiagonalScale( LEFT, NORMAL, colScale, dCol );
DiagonalSolve( RIGHT, NORMAL, colScale, A );
DiagonalSolve( RIGHT, NORMAL, colScale, B );
// Rescale the rows
// ----------------
RowMaxNorms( A, rowScale );
EntrywiseMap( rowScale, MakeFunction(DampScaling<Real>) );
DiagonalScale( LEFT, NORMAL, rowScale, dRowA );
DiagonalSolve( LEFT, NORMAL, rowScale, A );
RowMaxNorms( B, rowScale );
EntrywiseMap( rowScale, MakeFunction(DampScaling<Real>) );
DiagonalScale( LEFT, NORMAL, rowScale, dRowB );
DiagonalSolve( LEFT, NORMAL, rowScale, B );
}
SetIndent( indent );
}
void Tikhonov
( Orientation orientation,
const ElementalMatrix<F>& APre,
const ElementalMatrix<F>& BPre,
const ElementalMatrix<F>& G,
ElementalMatrix<F>& XPre,
TikhonovAlg alg )
{
DEBUG_CSE
DistMatrixReadProxy<F,F,MC,MR>
AProx( APre ),
BProx( BPre );
DistMatrixWriteProxy<F,F,MC,MR>
XProx( XPre );
auto& A = AProx.GetLocked();
auto& B = BProx.GetLocked();
auto& X = XProx.Get();
const bool normal = ( orientation==NORMAL );
const Int m = ( normal ? A.Height() : A.Width() );
const Int n = ( normal ? A.Width() : A.Height() );
if( G.Width() != n )
LogicError("Tikhonov matrix was the wrong width");
if( orientation == TRANSPOSE && IsComplex<F>::value )
LogicError("Transpose version of complex Tikhonov not yet supported");
if( m >= n )
{
DistMatrix<F> Z(A.Grid());
if( alg == TIKHONOV_CHOLESKY )
{
if( orientation == NORMAL )
Herk( LOWER, ADJOINT, Base<F>(1), A, Z );
else
Herk( LOWER, NORMAL, Base<F>(1), A, Z );
Herk( LOWER, ADJOINT, Base<F>(1), G, Base<F>(1), Z );
Cholesky( LOWER, Z );
}
else
{
const Int mG = G.Height();
Zeros( Z, m+mG, n );
auto ZT = Z( IR(0,m), IR(0,n) );
auto ZB = Z( IR(m,m+mG), IR(0,n) );
if( orientation == NORMAL )
ZT = A;
else
Adjoint( A, ZT );
ZB = G;
qr::ExplicitTriang( Z );
}
if( orientation == NORMAL )
Gemm( ADJOINT, NORMAL, F(1), A, B, X );
else
Gemm( NORMAL, NORMAL, F(1), A, B, X );
cholesky::SolveAfter( LOWER, NORMAL, Z, X );
}
else
{
LogicError("This case not yet supported");
}
}
void ApplyQ
( LeftOrRight side,
Orientation orientation,
const ElementalMatrix<F>& APre,
const ElementalMatrix<F>& phasePre,
const ElementalMatrix<Base<F>>& signature,
ElementalMatrix<F>& BPre )
{
DEBUG_CSE
const bool normal = (orientation==NORMAL);
const bool onLeft = (side==LEFT);
const bool applyDFirst = normal!=onLeft;
const Int minDim = Min(APre.Height(),APre.Width());
const ForwardOrBackward direction = ( normal==onLeft ? FORWARD : BACKWARD );
const Conjugation conjugation = ( normal ? CONJUGATED : UNCONJUGATED );
DistMatrixReadProxy<F,F,MC,MR> AProx( APre );
DistMatrixReadWriteProxy<F,F,MC,MR> BProx( BPre );
auto& A = AProx.GetLocked();
auto& B = BProx.Get();
ElementalProxyCtrl phaseCtrl;
phaseCtrl.rootConstrain = true;
phaseCtrl.colConstrain = true;
phaseCtrl.root = A.DiagonalRoot();
phaseCtrl.colAlign = A.DiagonalAlign();
DistMatrixReadProxy<F,F,MD,STAR> phaseProx( phasePre, phaseCtrl );
auto& phase = phaseProx.GetLocked();
const Int m = B.Height();
const Int n = B.Width();
if( applyDFirst )
{
if( onLeft )
{
auto BTop = B( IR(0,minDim), IR(0,n) );
DiagonalScale( side, orientation, signature, BTop );
}
else
{
auto BLeft = B( IR(0,m), IR(0,minDim) );
DiagonalScale( side, orientation, signature, BLeft );
}
}
ApplyPackedReflectors
( side, UPPER, HORIZONTAL, direction, conjugation, 0, A, phase, B );
if( !applyDFirst )
{
if( onLeft )
{
auto BTop = B( IR(0,minDim), IR(0,n) );
DiagonalScale( side, orientation, signature, BTop );
}
else
{
auto BLeft = B( IR(0,m), IR(0,minDim) );
DiagonalScale( side, orientation, signature, BLeft );
}
}
}