void ConsistentlyComputeDecomposition
( DistMatrix<Field,MC,MR,BLOCK>& H,
DistMatrix<Complex<Base<Field>>,STAR,STAR>& w,
Matrix<Field>& Z,
const HessenbergSchurCtrl& ctrl=HessenbergSchurCtrl() )
{
EL_DEBUG_CSE
// Because double-precision floating-point computation is often
// non-deterministic due to extra-precision computation being frequent but
// not guaranteed, we must be careful to not allow this non-determinism to
// be amplified by the forward instability of Francis sweeps.
const Grid& grid = H.Grid();
const int owner = H.Owner(0,0);
DistMatrix<Field,CIRC,CIRC> H_CIRC_CIRC( grid, owner );
H_CIRC_CIRC = H;
w.Resize( H.Height(), 1 );
if( H_CIRC_CIRC.CrossRank() == H_CIRC_CIRC.Root() )
HessenbergSchur( H_CIRC_CIRC.Matrix(), w.Matrix(), Z, ctrl );
else
Z.Resize( H.Height(), H.Height() );
H = H_CIRC_CIRC;
El::Broadcast( w.Matrix(), H_CIRC_CIRC.CrossComm(), H_CIRC_CIRC.Root() );
El::Broadcast( Z, H_CIRC_CIRC.CrossComm(), H_CIRC_CIRC.Root() );
}
AEDInfo NibbleHelper
( Matrix<Real>& H,
Real& spikeValue,
Matrix<Complex<Real>>& w,
Matrix<Real>& V,
const HessenbergSchurCtrl& ctrl )
{
EL_DEBUG_CSE
const Int n = H.Height();
AEDInfo info;
const Real zero(0);
const Real ulp = limits::Precision<Real>();
const Real safeMin = limits::SafeMin<Real>();
const Real smallNum = safeMin*(Real(n)/ulp);
Zeros( V, 0, 0 );
if( n == 1 )
{
w(0) = H(0,0);
if( Abs(spikeValue) <= Max( smallNum, ulp*Abs(w(0).real()) ) )
{
// The offdiagonal entry was small enough to deflate
info.numDeflated = 1;
spikeValue = zero;
}
else
{
// The offdiagonal entry was too large to deflate
info.numShiftCandidates = 1;
}
return info;
}
// NOTE(poulson): We could only copy the upper-Hessenberg portion of H
auto T( H ); // TODO(poulson): Reuse this matrix?
Identity( V, n, n );
auto ctrlSub( ctrl );
ctrlSub.winBeg = 0;
ctrlSub.winEnd = n;
ctrlSub.fullTriangle = true;
ctrlSub.wantSchurVecs = true;
ctrlSub.demandConverged = false;
ctrlSub.alg = ( ctrl.recursiveAED ? HESSENBERG_SCHUR_AED
: HESSENBERG_SCHUR_MULTIBULGE );
auto infoSub = HessenbergSchur( T, w, V, ctrlSub );
EL_DEBUG_ONLY(
if( infoSub.numUnconverged != 0 )
Output(infoSub.numUnconverged," eigenvalues did not converge");
)
AEDInfo Nibble
( Matrix<Real>& H,
Int deflationSize,
Matrix<Complex<Real>>& w,
Matrix<Real>& Z,
const HessenbergSchurCtrl& ctrl )
{
DEBUG_CSE
const Int n = H.Height();
Int winBeg = ( ctrl.winBeg==END ? n : ctrl.winBeg );
Int winEnd = ( ctrl.winEnd==END ? n : ctrl.winEnd );
AEDInfo info;
const Real zero(0);
const Real ulp = limits::Precision<Real>();
const Real safeMin = limits::SafeMin<Real>();
const Real smallNum = safeMin*(Real(n)/ulp);
if( winBeg > winEnd )
return info;
if( deflationSize < 1 )
return info;
Int blockSize = Min( deflationSize, winEnd-winBeg );
const Int deflateBeg = winEnd-blockSize;
// If the deflation window touches the beginning of the full window,
// then there is no spike
Real spikeValue =
( deflateBeg==winBeg ? zero : H(deflateBeg,deflateBeg-1) );
if( blockSize == 1 )
{
w(deflateBeg) = H(deflateBeg,deflateBeg);
if( Abs(spikeValue) <= Max( smallNum, ulp*Abs(w(deflateBeg).real()) ) )
{
// The offdiagonal entry was small enough to deflate
info.numDeflated = 1;
if( deflateBeg > winBeg )
{
// Explicitly deflate by zeroing the offdiagonal entry
H(deflateBeg,deflateBeg-1) = zero;
}
}
else
{
// The offdiagonal entry was too large to deflate
info.numShiftCandidates = 1;
}
return info;
}
auto deflateInd = IR(deflateBeg,winEnd);
auto H11 = H( deflateInd, deflateInd );
// NOTE(poulson): We could only copy the upper-Hessenberg portion of H11
auto T( H11 ); // TODO(poulson): Reuse this matrix?
auto w1 = w( deflateInd, ALL );
Matrix<Real> V;
Identity( V, blockSize, blockSize );
auto ctrlSub( ctrl );
ctrlSub.winBeg = 0;
ctrlSub.winEnd = blockSize;
ctrlSub.fullTriangle = true;
ctrlSub.wantSchurVecs = true;
ctrlSub.demandConverged = false;
ctrlSub.alg = ( ctrl.recursiveAED ? HESSENBERG_SCHUR_AED
: HESSENBERG_SCHUR_MULTIBULGE );
auto infoSub = HessenbergSchur( T, w1, V, ctrlSub );
DEBUG_ONLY(
if( infoSub.numUnconverged != 0 )
Output(infoSub.numUnconverged," eigenvalues did not converge");
)
