void HermitianPseudoinverse
( UpperOrLower uplo, AbstractDistMatrix<Field>& APre, Base<Field> tolerance )
{
EL_DEBUG_CSE
typedef Base<Field> Real;
DistMatrixReadWriteProxy<Field,Field,MC,MR> AProx( APre );
auto& A = AProx.Get();
const Grid& g = A.Grid();
// Get the EVD of A
// TODO(poulson): Use a relative eigenvalue lower-bound
DistMatrix<Real,VR,STAR> w(g);
DistMatrix<Field> Z(g);
HermitianEig( uplo, A, w, Z );
if( tolerance == Real(0) )
{
// Set the tolerance equal to n ||A||_2 eps
const Int n = Z.Height();
const Real eps = limits::Epsilon<Real>();
const Real twoNorm = MaxNorm( w );
tolerance = n*twoNorm*eps;
}
// Invert above the tolerance
auto omegaMap =
[=]( const Real& omega )
{ return ( omega < tolerance ? Real(0) : 1/omega ); };
EntrywiseMap( w, MakeFunction(omegaMap) );
// Form the pseudoinverse
HermitianFromEVD( uplo, A, w, Z );
}
void HingeLossProx( AbstractDistMatrix<Real>& A, Real tau )
{
DEBUG_CSE
auto hingeProx =
[=]( Real alpha ) -> Real
{ if( alpha < 1 ) { return Min(alpha+1/tau,Real(1)); }
else { return alpha; } };
EntrywiseMap( A, function<Real(Real)>(hingeProx) );
}
inline void
FinalSnapshot
( const Matrix<Real>& estimates,
const Matrix<Int>& itCounts,
SnapshotCtrl& snapCtrl )
{
DEBUG_ONLY(CSE cse("pspec::FinalSnapshot"));
auto logMap = []( Real alpha ) { return Log(alpha); };
if( snapCtrl.realSize != 0 && snapCtrl.imagSize != 0 )
{
const bool numSave = ( snapCtrl.numSaveFreq >= 0 );
const bool imgSave = ( snapCtrl.imgSaveFreq >= 0 );
const bool imgDisp = ( snapCtrl.imgDispFreq >= 0 );
Matrix<Real> estMap;
Matrix<Int> itCountMap;
if( numSave || imgSave || imgDisp )
{
ReshapeIntoGrid
( snapCtrl.realSize, snapCtrl.imagSize, estimates, estMap );
if( snapCtrl.itCounts )
ReshapeIntoGrid
( snapCtrl.realSize, snapCtrl.imagSize, itCounts, itCountMap );
}
if( numSave )
{
string base = snapCtrl.numBase;
Write( estMap, base, snapCtrl.numFormat );
if( snapCtrl.itCounts )
Write( itCountMap, base+"_counts", snapCtrl.numFormat );
}
if( imgSave || imgDisp )
EntrywiseMap( estMap, function<Real(Real)>(logMap) );
if( imgSave )
{
string base = snapCtrl.imgBase;
Write( estMap, base, snapCtrl.imgFormat );
if( snapCtrl.itCounts )
Write( itCountMap, base+"_counts", snapCtrl.imgFormat );
auto colorMap = GetColorMap();
SetColorMap( GRAYSCALE_DISCRETE );
Write( estMap, base+"_discrete", snapCtrl.imgFormat );
SetColorMap( colorMap );
}
if( imgDisp )
{
string base = snapCtrl.imgBase;
Display( estMap, base );
if( snapCtrl.itCounts )
Display( itCountMap, base+"_counts" );
auto colorMap = GetColorMap();
SetColorMap( GRAYSCALE_DISCRETE );
Display( estMap, base+"_discrete" );
SetColorMap( colorMap );
}
}
}
void EntrywiseMap
( const DistMultiVec<S>& A,
DistMultiVec<T>& B,
function<T(S)> func )
{
DEBUG_CSE
B.SetComm( A.Comm() );
B.Resize( A.Height(), A.Width() );
EntrywiseMap( A.LockedMatrix(), B.Matrix(), func );
}
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 );
}
void FinalSnapshot
( const DistMatrix<Real,VR,STAR>& estimates,
const DistMatrix<Int, VR,STAR>& itCounts,
SnapshotCtrl& snapCtrl )
{
EL_DEBUG_CSE
auto logMap = []( const Real& alpha ) { return Log(alpha); };
if( snapCtrl.realSize != 0 && snapCtrl.imagSize != 0 )
{
const bool numSave = ( snapCtrl.numSaveFreq >= 0 );
const bool imgSave = ( snapCtrl.imgSaveFreq >= 0 );
const bool imgDisp = ( snapCtrl.imgDispFreq >= 0 );
DistMatrix<Real> estMap(estimates.Grid());
DistMatrix<Int> itCountMap(itCounts.Grid());
if( numSave || imgSave || imgDisp )
{
ReshapeIntoGrid
( snapCtrl.realSize, snapCtrl.imagSize, estimates, estMap );
if( snapCtrl.itCounts )
ReshapeIntoGrid
( snapCtrl.realSize, snapCtrl.imagSize, itCounts, itCountMap );
}
if( numSave )
{
string base = snapCtrl.numBase;
Write( estMap, base, snapCtrl.numFormat );
if( snapCtrl.itCounts )
Write( itCountMap, base+"_counts", snapCtrl.numFormat );
}
if( imgSave || imgDisp )
EntrywiseMap( estMap, MakeFunction(logMap) );
if( imgSave )
{
string base = snapCtrl.imgBase;
Write( estMap, base, snapCtrl.imgFormat );
if( snapCtrl.itCounts )
Write( itCountMap, base+"_counts", snapCtrl.imgFormat );
auto colorMap = GetColorMap();
SetColorMap( GRAYSCALE_DISCRETE );
Write( estMap, base+"_discrete", snapCtrl.imgFormat );
SetColorMap( colorMap );
}
if( imgDisp )
{
string base = snapCtrl.imgBase;
Display( estMap, base );
if( snapCtrl.itCounts )
Display( itCountMap, base+"_counts" );
auto colorMap = GetColorMap();
SetColorMap( GRAYSCALE_DISCRETE );
Display( estMap, base+"_discrete" );
SetColorMap( colorMap );
}
}
}
void RuizEquil
( DistSparseMatrix<Field>& A,
DistMultiVec<Base<Field>>& dRow,
DistMultiVec<Base<Field>>& dCol,
bool progress )
{
EL_DEBUG_CSE
typedef Base<Field> Real;
const Int m = A.Height();
const Int n = A.Width();
mpi::Comm comm = A.Comm();
dRow.SetComm( comm );
dCol.SetComm( comm );
Ones( dRow, m, 1 );
Ones( dCol, n, 1 );
// TODO(poulson): Expose to control structure
// For, simply hard-code a small number of iterations
const Int maxIter = 4;
DistMultiVec<Real> scales(comm);
const Int indent = PushIndent();
for( Int iter=0; iter<maxIter; ++iter )
{
// Rescale the columns
// -------------------
ColumnMaxNorms( A, scales );
EntrywiseMap( scales, MakeFunction(DampScaling<Real>) );
DiagonalScale( LEFT, NORMAL, scales, dCol );
DiagonalSolve( RIGHT, NORMAL, scales, A );
// Rescale the rows
// ----------------
RowMaxNorms( A, scales );
EntrywiseMap( scales, MakeFunction(DampScaling<Real>) );
DiagonalScale( LEFT, NORMAL, scales, dRow );
DiagonalSolve( LEFT, NORMAL, scales, A );
}
SetIndent( indent );
}
void SymmetricRuizEquil
( ElementalMatrix<F>& APre,
ElementalMatrix<Base<F>>& dPre,
Int maxIter, bool progress )
{
DEBUG_CSE
typedef Base<F> Real;
ElementalProxyCtrl control;
control.colConstrain = true;
control.rowConstrain = true;
control.colAlign = 0;
control.rowAlign = 0;
DistMatrixReadWriteProxy<F,F,MC,MR> AProx( APre, control );
DistMatrixWriteProxy<Real,Real,MC,STAR> dProx( dPre, control );
auto& A = AProx.Get();
auto& d = dProx.Get();
const Int n = A.Height();
Ones( d, n, 1 );
DistMatrix<Real,MR,STAR> scales(A.Grid());
const Int indent = PushIndent();
for( Int iter=0; iter<maxIter; ++iter )
{
// Rescale the columns (and rows)
// ------------------------------
ColumnMaxNorms( A, scales );
EntrywiseMap( scales, function<Real(Real)>(DampScaling<Real>) );
EntrywiseMap( scales, function<Real(Real)>(SquareRootScaling<Real>) );
DiagonalScale( LEFT, NORMAL, scales, d );
// TODO: Replace with SymmetricDiagonalSolve
DiagonalSolve( RIGHT, NORMAL, scales, A );
DiagonalSolve( LEFT, NORMAL, scales, A );
}
SetIndent( indent );
}
void HermitianSVD
( UpperOrLower uplo, AbstractDistMatrix<F>& A, AbstractDistMatrix<Base<F>>& s,
AbstractDistMatrix<F>& U, AbstractDistMatrix<F>& V )
{
DEBUG_ONLY(CallStackEntry cse("HermitianSVD"))
// Grab an eigenvalue decomposition of A
HermitianEig( uplo, A, s, V );
// Copy V into U (flipping the sign as necessary)
Copy( U, V );
typedef Base<F> Real;
DistMatrix<Real,VR,STAR> sSgn( s );
auto sgnLambda = []( Real sigma ) { return Sgn(sigma,false); };
EntrywiseMap( sSgn, function<Real(Real)>(sgnLambda) );
DiagonalScale( RIGHT, NORMAL, sSgn, U );
// Set the singular values to the absolute value of the eigenvalues
auto absLambda = []( Real sigma ) { return Abs(sigma); };
EntrywiseMap( s, function<Real(Real)>(absLambda) );
// TODO: Descending sort of triplets
}
void RuizEquil
( Matrix<Field>& A,
Matrix<Base<Field>>& dRow,
Matrix<Base<Field>>& dCol,
bool progress )
{
EL_DEBUG_CSE
typedef Base<Field> Real;
const Int m = A.Height();
const Int n = A.Width();
Ones( dRow, m, 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;
Matrix<Real> rowScale, colScale;
const Int indent = PushIndent();
for( Int iter=0; iter<maxIter; ++iter )
{
// Rescale the columns
// -------------------
ColumnMaxNorms( A, colScale );
EntrywiseMap( colScale, MakeFunction(DampScaling<Real>) );
DiagonalScale( LEFT, NORMAL, colScale, dCol );
DiagonalSolve( RIGHT, NORMAL, colScale, A );
// Rescale the rows
// ----------------
RowMaxNorms( A, rowScale );
EntrywiseMap( rowScale, MakeFunction(DampScaling<Real>) );
DiagonalScale( LEFT, NORMAL, rowScale, dRow );
DiagonalSolve( LEFT, NORMAL, rowScale, A );
}
SetIndent( indent );
}
void SymmetricRuizEquil
( SparseMatrix<F>& A,
Matrix<Base<F>>& d,
Int maxIter, bool progress )
{
DEBUG_CSE
typedef Base<F> Real;
const Int n = A.Height();
Ones( d, n, 1 );
Matrix<Real> scales;
const Int indent = PushIndent();
for( Int iter=0; iter<maxIter; ++iter )
{
// Rescale the columns (and rows)
// ------------------------------
ColumnMaxNorms( A, scales );
EntrywiseMap( scales, function<Real(Real)>(DampScaling<Real>) );
EntrywiseMap( scales, function<Real(Real)>(SquareRootScaling<Real>) );
DiagonalScale( LEFT, NORMAL, scales, d );
SymmetricDiagonalSolve( scales, A );
}
SetIndent( indent );
}
void Inverse
( const Matrix<Real>& x,
Matrix<Real>& xInv,
const Matrix<Int>& orders,
const Matrix<Int>& firstInds )
{
DEBUG_CSE
Matrix<Real> dInv;
soc::Dets( x, dInv, orders, firstInds );
cone::Broadcast( dInv, orders, firstInds );
auto entryInv = [=]( Real alpha ) { return Real(1)/alpha; };
EntrywiseMap( dInv, function<Real(Real)>(entryInv) );
auto Rx = x;
soc::Reflect( Rx, orders, firstInds );
Hadamard( dInv, Rx, xInv );
}
void Inverse
( const DistMultiVec<Real>& x,
DistMultiVec<Real>& xInv,
const DistMultiVec<Int>& orders,
const DistMultiVec<Int>& firstInds,
Int cutoff )
{
DEBUG_CSE
DistMultiVec<Real> dInv(x.Comm());
soc::Dets( x, dInv, orders, firstInds, cutoff );
cone::Broadcast( dInv, orders, firstInds );
auto entryInv = [=]( Real alpha ) { return Real(1)/alpha; };
EntrywiseMap( dInv, function<Real(Real)>(entryInv) );
auto Rx = x;
soc::Reflect( Rx, orders, firstInds );
Hadamard( dInv, Rx, xInv );
}
void Inverse
( const ElementalMatrix<Real>& xPre,
ElementalMatrix<Real>& xInvPre,
const ElementalMatrix<Int>& ordersPre,
const ElementalMatrix<Int>& firstIndsPre,
Int cutoff )
{
DEBUG_CSE
AssertSameGrids( xPre, xInvPre, ordersPre, firstIndsPre );
ElementalProxyCtrl ctrl;
ctrl.colConstrain = true;
ctrl.colAlign = 0;
DistMatrixReadProxy<Real,Real,VC,STAR>
xProx( xPre, ctrl );
DistMatrixWriteProxy<Real,Real,VC,STAR>
xInvProx( xInvPre, ctrl );
DistMatrixReadProxy<Int,Int,VC,STAR>
ordersProx( ordersPre, ctrl ),
firstIndsProx( firstIndsPre, ctrl );
auto& x = xProx.GetLocked();
auto& xInv = xInvProx.Get();
auto& orders = ordersProx.GetLocked();
auto& firstInds = firstIndsProx.GetLocked();
DistMatrix<Real,VC,STAR> dInv(x.Grid());
soc::Dets( x, dInv, orders, firstInds, cutoff );
cone::Broadcast( dInv, orders, firstInds );
auto entryInv = [=]( Real alpha ) { return Real(1)/alpha; };
EntrywiseMap( dInv, function<Real(Real)>(entryInv) );
auto Rx = x;
soc::Reflect( Rx, orders, firstInds );
Hadamard( dInv, Rx, xInv );
}
void Ridge
( Orientation orientation,
const Matrix<Field>& A,
const Matrix<Field>& B,
Base<Field> gamma,
Matrix<Field>& X,
RidgeAlg alg )
{
EL_DEBUG_CSE
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 )
{
Matrix<Field> Z;
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
{
Matrix<Field> U, V;
Matrix<Base<Field>> s;
if( orientation == NORMAL )
{
SVDCtrl<Base<Field>> ctrl;
ctrl.overwrite = false;
SVD( A, U, s, V, ctrl );
}
else
{
Matrix<Field> AAdj;
Adjoint( A, AAdj );
SVDCtrl<Base<Field>> ctrl;
ctrl.overwrite = true;
SVD( AAdj, U, s, V, ctrl );
}
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 Snapshot
( const Matrix<Int>& preimage,
const Matrix<Real>& estimates,
const Matrix<Int>& itCounts,
Int numIts,
bool deflate,
SnapshotCtrl& snapCtrl )
{
EL_DEBUG_CSE
auto logMap = []( const Real& alpha ) { return Log(alpha); };
if( snapCtrl.realSize != 0 && snapCtrl.imagSize != 0 )
{
const bool numSave =
( snapCtrl.numSaveFreq > 0 &&
snapCtrl.numSaveCount >= snapCtrl.numSaveFreq );
const bool imgSave =
( snapCtrl.imgSaveFreq > 0 &&
snapCtrl.imgSaveCount >= snapCtrl.imgSaveFreq );
const bool imgDisp =
( snapCtrl.imgDispFreq > 0 &&
snapCtrl.imgDispCount >= snapCtrl.imgDispFreq );
Matrix<Real> invNorms, estMap;
Matrix<Int> itCountsReord, itCountMap;
if( numSave || imgSave || imgDisp )
{
invNorms = estimates;
if( deflate )
RestoreOrdering( preimage, invNorms );
ReshapeIntoGrid
( snapCtrl.realSize, snapCtrl.imagSize, invNorms, estMap );
if( snapCtrl.itCounts )
{
itCountsReord = itCounts;
if( deflate )
RestoreOrdering( preimage, itCountsReord );
ReshapeIntoGrid
( snapCtrl.realSize, snapCtrl.imagSize, itCountsReord,
itCountMap );
}
}
if( numSave )
{
auto title = BuildString( snapCtrl.numBase, "_", numIts );
Write( estMap, title, snapCtrl.numFormat );
if( snapCtrl.itCounts )
Write( itCountMap, title+"_counts", snapCtrl.numFormat );
snapCtrl.numSaveCount = 0;
}
if( imgSave || imgDisp )
EntrywiseMap( estMap, MakeFunction(logMap) );
if( imgSave )
{
auto title = BuildString( snapCtrl.imgBase, "_", numIts );
Write( estMap, title, snapCtrl.imgFormat );
if( snapCtrl.itCounts )
Write( itCountMap, title+"_counts", snapCtrl.imgFormat );
auto colorMap = GetColorMap();
SetColorMap( GRAYSCALE_DISCRETE );
Write( estMap, title+"_discrete", snapCtrl.imgFormat );
SetColorMap( colorMap );
snapCtrl.imgSaveCount = 0;
}
if( imgDisp )
{
auto title = BuildString( snapCtrl.imgBase, "_", numIts );
Display( estMap, title );
if( snapCtrl.itCounts )
Display( itCountMap, title+"_counts" );
auto colorMap = GetColorMap();
SetColorMap( GRAYSCALE_DISCRETE );
Display( estMap, title+"_discrete" );
SetColorMap( colorMap );
snapCtrl.imgDispCount = 0;
}
}
}
inline void
Snapshot
( const Matrix<Int>& preimage, const Matrix<Real>& estimates,
const Matrix<Int>& itCounts,
Int numIts, bool deflate, SnapshotCtrl& snapCtrl )
{
DEBUG_ONLY(CallStackEntry cse("pspec::Snapshot"));
if( snapCtrl.realSize != 0 && snapCtrl.imagSize != 0 )
{
const bool numSave =
( snapCtrl.numSaveFreq > 0 &&
snapCtrl.numSaveCount >= snapCtrl.numSaveFreq );
const bool imgSave =
( snapCtrl.imgSaveFreq > 0 &&
snapCtrl.imgSaveCount >= snapCtrl.imgSaveFreq );
const bool imgDisp =
( snapCtrl.imgDispFreq > 0 &&
snapCtrl.imgDispCount >= snapCtrl.imgDispFreq );
Matrix<Real> invNorms, estMap;
Matrix<Int> itCountsReord, itCountMap;
if( numSave || imgSave || imgDisp )
{
invNorms = estimates;
if( deflate )
RestoreOrdering( preimage, invNorms );
ReshapeIntoGrid
( snapCtrl.realSize, snapCtrl.imagSize, invNorms, estMap );
if( snapCtrl.itCounts )
{
itCountsReord = itCounts;
if( deflate )
RestoreOrdering( preimage, itCountsReord );
ReshapeIntoGrid
( snapCtrl.realSize, snapCtrl.imagSize, itCountsReord,
itCountMap );
}
}
if( numSave )
{
std::ostringstream os;
os << snapCtrl.numBase << "-" << numIts;
Write( estMap, os.str(), snapCtrl.numFormat );
if( snapCtrl.itCounts )
Write( itCountMap, os.str()+"-counts", snapCtrl.numFormat );
snapCtrl.numSaveCount = 0;
}
if( imgSave || imgDisp )
EntrywiseMap( estMap, []( Real alpha ) { return Log(alpha); } );
if( imgSave )
{
std::ostringstream os;
os << snapCtrl.imgBase << "-" << numIts;
Write( estMap, os.str(), snapCtrl.imgFormat );
if( snapCtrl.itCounts )
Write( itCountMap, os.str()+"-counts", snapCtrl.imgFormat );
auto colorMap = GetColorMap();
SetColorMap( GRAYSCALE_DISCRETE );
Write( estMap, os.str()+"-discrete", snapCtrl.imgFormat );
SetColorMap( colorMap );
snapCtrl.imgSaveCount = 0;
}
if( imgDisp )
{
std::ostringstream os;
os << snapCtrl.imgBase << "-" << numIts;
Display( estMap, os.str() );
if( snapCtrl.itCounts )
Display( itCountMap, os.str()+"-counts" );
auto colorMap = GetColorMap();
SetColorMap( GRAYSCALE_DISCRETE );
Display( estMap, os.str()+"-discrete" );
SetColorMap( colorMap );
snapCtrl.imgDispCount = 0;
}
}
}
void EntrywiseMap( AbstractDistMatrix<T>& A, function<T(T)> func )
{ EntrywiseMap( A.Matrix(), func ); }
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 EntrywiseMap( DistMultiVec<T>& A, function<T(T)> func )
{ EntrywiseMap( A.Matrix(), func ); }
void ImagPart
( const AbstractDistMatrix<T>& A, AbstractDistMatrix<Base<T>>& AImag )
{
auto imagPart = []( const T& alpha ) { return ImagPart(alpha); };
EntrywiseMap( A, AImag, MakeFunction(imagPart) );
}
inline void NormalizeEntries( ElementalMatrix<F>& A )
{
auto unitMap = []( F alpha )
{ return alpha==F(0) ? F(1) : alpha/Abs(alpha); };
EntrywiseMap( A, function<F(F)>(unitMap) );
}