void NormalUniformSpectrum
( ElementalMatrix<Complex<Real>>& APre, Int n,
Complex<Real> center, Real radius )
{
EL_DEBUG_CSE
typedef Complex<Real> C;
DistMatrixWriteProxy<C,C,MC,MR> AProx( APre );
auto& A = AProx.Get();
const Grid& grid = A.Grid();
A.Resize( n, n );
// Form d and D
vector<C> d( n );
if( grid.Rank() == 0 )
for( Int j=0; j<n; ++j )
d[j] = SampleBall<C>( center, radius );
mpi::Broadcast( d.data(), n, 0, grid.Comm() );
Diagonal( A, d );
// Apply a Haar matrix from both sides
DistMatrix<C> Q(grid);
DistMatrix<C,MD,STAR> t(grid);
DistMatrix<Real,MD,STAR> s(grid);
ImplicitHaar( Q, t, s, n );
// Copy the result into the correct distribution
qr::ApplyQ( LEFT, NORMAL, Q, t, s, A );
qr::ApplyQ( RIGHT, ADJOINT, Q, t, s, A );
}
void HermitianUniformSpectrum
( Matrix<F>& A, Int n, Base<F> lower, Base<F> upper )
{
DEBUG_ONLY(CallStackEntry cse("HermitianUniformSpectrum"))
A.Resize( n, n );
typedef Base<F> Real;
const bool isComplex = IsComplex<F>::val;
// Form d and D
std::vector<F> d( n );
for( Int j=0; j<n; ++j )
d[j] = SampleUniform<Real>( lower, upper );
Diagonal( A, d );
// Apply a Haar matrix from both sides
Matrix<F> Q, t;
Matrix<Real> s;
ImplicitHaar( Q, t, s, n );
qr::ApplyQ( LEFT, NORMAL, Q, t, s, A );
qr::ApplyQ( RIGHT, ADJOINT, Q, t, s, A );
if( isComplex )
{
const Int height = A.Height();
for( Int j=0; j<height; ++j )
A.SetImagPart( j, j, Real(0) );
}
}
void HermitianUniformSpectrum
( DistMatrix<F,U,V>& A, Int n, Base<F> lower, Base<F> upper )
{
DEBUG_ONLY(CallStackEntry cse("HermitianUniformSpectrum"))
A.Resize( n, n );
const Grid& grid = A.Grid();
typedef Base<F> Real;
const bool isComplex = IsComplex<F>::val;
const bool standardDist = ( U == MC && V == MR );
// Form d and D
std::vector<F> d( n );
if( grid.Rank() == 0 )
for( Int j=0; j<n; ++j )
d[j] = SampleUniform<Real>( lower, upper );
mpi::Broadcast( d.data(), n, 0, grid.Comm() );
DistMatrix<F> ABackup( grid );
ABackup.AlignWith( A );
Diagonal( ABackup, d );
// Apply a Haar matrix from both sides
DistMatrix<F> Q(grid);
DistMatrix<F,MD,STAR> t(grid);
DistMatrix<Real,MD,STAR> s(grid);
ImplicitHaar( Q, t, s, n );
// Copy the result into the correct distribution
qr::ApplyQ( LEFT, NORMAL, Q, t, s, ABackup );
qr::ApplyQ( RIGHT, ADJOINT, Q, t, s, ABackup );
A = ABackup;
// Force the diagonal to be real-valued
if( isComplex )
{
const Int localHeight = A.LocalHeight();
const Int localWidth = A.LocalWidth();
for( Int jLoc=0; jLoc<localWidth; ++jLoc )
{
const Int j = A.GlobalCol(jLoc);
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
{
const Int i = A.GlobalRow(iLoc);
if( i == j )
A.SetLocalImagPart( iLoc, jLoc, Real(0) );
}
}
}
}
void NormalUniformSpectrum
( Matrix<Complex<Real>>& A, Int n, Complex<Real> center, Real radius )
{
EL_DEBUG_CSE
typedef Complex<Real> C;
A.Resize( n, n );
// Form d and D
vector<C> d( n );
for( Int j=0; j<n; ++j )
d[j] = SampleBall<C>( center, radius );
Diagonal( A, d );
// Apply a Haar matrix from both sides
Matrix<C> Q, t;
Matrix<Real> s;
ImplicitHaar( Q, t, s, n );
qr::ApplyQ( LEFT, NORMAL, Q, t, s, A );
qr::ApplyQ( RIGHT, ADJOINT, Q, t, s, A );
}
