void GetMappedDiagonal
( const DistMatrix<T,U,V>& A,
AbstractDistMatrix<S>& dPre,
function<S(const T&)> func,
Int offset )
{
EL_DEBUG_CSE
EL_DEBUG_ONLY(AssertSameGrids( A, dPre ))
ElementalProxyCtrl ctrl;
ctrl.colConstrain = true;
ctrl.colAlign = A.DiagonalAlign(offset);
ctrl.rootConstrain = true;
ctrl.root = A.DiagonalRoot(offset);
DistMatrixWriteProxy<S,S,DiagCol<U,V>(),DiagRow<U,V>()> dProx( dPre, ctrl );
auto& d = dProx.Get();
d.Resize( A.DiagonalLength(offset), 1 );
if( d.Participating() )
{
const Int diagShift = d.ColShift();
const Int iStart = diagShift + Max(-offset,0);
const Int jStart = diagShift + Max( offset,0);
const Int colStride = A.ColStride();
const Int rowStride = A.RowStride();
const Int iLocStart = (iStart-A.ColShift()) / colStride;
const Int jLocStart = (jStart-A.RowShift()) / rowStride;
const Int iLocStride = d.ColStride() / colStride;
const Int jLocStride = d.ColStride() / rowStride;
const Int localDiagLength = d.LocalHeight();
S* dBuf = d.Buffer();
const T* ABuf = A.LockedBuffer();
const Int ldim = A.LDim();
EL_PARALLEL_FOR
for( Int k=0; k<localDiagLength; ++k )
{
const Int iLoc = iLocStart + k*iLocStride;
const Int jLoc = jLocStart + k*jLocStride;
dBuf[k] = func(ABuf[iLoc+jLoc*ldim]);
}
}
}
void TestCorrectness
( UpperOrLower uplo,
const DistMatrix<F>& A,
const DistMatrix<F,STAR,STAR>& t,
DistMatrix<F>& AOrig,
bool print, bool display )
{
typedef Base<F> Real;
const Grid& g = A.Grid();
const Int m = AOrig.Height();
const Real infNormAOrig = HermitianInfinityNorm( uplo, AOrig );
const Real frobNormAOrig = HermitianFrobeniusNorm( uplo, AOrig );
if( g.Rank() == 0 )
cout << "Testing error..." << endl;
// Grab the diagonal and subdiagonal of the symmetric tridiagonal matrix
Int subdiagonal = ( uplo==LOWER ? -1 : +1 );
auto d = GetRealPartOfDiagonal(A);
auto e = GetRealPartOfDiagonal(A,subdiagonal);
// Grab a full copy of e so that we may fill the opposite subdiagonal
DistMatrix<Real,STAR,STAR> e_STAR_STAR( e );
DistMatrix<Real,MD,STAR> eOpposite(g);
eOpposite.SetRoot( A.DiagonalRoot(-subdiagonal) );
eOpposite.AlignCols( A.DiagonalAlign(-subdiagonal) );
eOpposite = e_STAR_STAR;
// Zero B and then fill its tridiagonal
DistMatrix<F> B(g);
B.AlignWith( A );
Zeros( B, m, m );
SetRealPartOfDiagonal( B, d );
SetRealPartOfDiagonal( B, e, subdiagonal );
SetRealPartOfDiagonal( B, eOpposite, -subdiagonal );
if( print )
Print( B, "Tridiagonal" );
if( display )
Display( B, "Tridiagonal" );
// Reverse the accumulated Householder transforms, ignoring symmetry
herm_tridiag::ApplyQ( LEFT, uplo, NORMAL, A, t, B );
herm_tridiag::ApplyQ( RIGHT, uplo, ADJOINT, A, t, B );
if( print )
Print( B, "Rotated tridiagonal" );
if( display )
Display( B, "Rotated tridiagonal" );
// Compare the appropriate triangle of AOrig and B
MakeTrapezoidal( uplo, AOrig );
MakeTrapezoidal( uplo, B );
B -= AOrig;
if( print )
Print( B, "Error in rotated tridiagonal" );
if( display )
Display( B, "Error in rotated tridiagonal" );
const Real infNormError = HermitianInfinityNorm( uplo, B );
const Real frobNormError = HermitianFrobeniusNorm( uplo, B );
// Compute || I - Q Q^H ||
MakeIdentity( B );
herm_tridiag::ApplyQ( RIGHT, uplo, ADJOINT, A, t, B );
DistMatrix<F> QHAdj( g );
Adjoint( B, QHAdj );
MakeIdentity( B );
herm_tridiag::ApplyQ( LEFT, uplo, NORMAL, A, t, B );
QHAdj -= B;
herm_tridiag::ApplyQ( RIGHT, uplo, ADJOINT, A, t, B );
ShiftDiagonal( B, F(-1) );
const Real infNormQError = InfinityNorm( B );
const Real frobNormQError = FrobeniusNorm( B );
if( g.Rank() == 0 )
{
cout << " ||A||_oo = " << infNormAOrig << "\n"
<< " ||A||_F = " << frobNormAOrig << "\n"
<< " || I - Q^H Q ||_oo = " << infNormQError << "\n"
<< " || I - Q^H Q ||_F = " << frobNormQError << "\n"
<< " ||A - Q T Q^H||_oo = " << infNormError << "\n"
<< " ||A - Q T Q^H||_F = " << frobNormError << endl;
}
}