inline void
Hanowa( DistMatrix<T,U,V>& A, int n, T mu )
{
#ifndef RELEASE
CallStackEntry entry("Hanowa");
#endif
if( n % 2 != 0 )
throw std::logic_error("n must be an even integer");
A.ResizeTo( n, n );
const int m = n/2;
std::vector<T> d(m);
DistMatrix<T,U,V> ABlock( A.Grid() );
for( int j=0; j<m; ++j )
d[j] = mu;
View( ABlock, A, 0, 0, m, m );
Diagonal( ABlock, d );
View( ABlock, A, m, m, m, m );
Diagonal( ABlock, d );
for( int j=0; j<m; ++j )
d[j] = -(j+1);
View( ABlock, A, 0, m, m, m );
Diagonal( ABlock, d );
for( int j=0; j<m; ++j )
d[j] = j+1;
View( ABlock, A, m, 0, m, m );
Diagonal( ABlock, d );
}
void MakeExtendedKahan
( ElementalMatrix<F>& A, Base<F> phi, Base<F> mu )
{
EL_DEBUG_CSE
typedef Base<F> Real;
if( A.Height() != A.Width() )
LogicError("Extended Kahan matrices must be square");
const Int n = A.Height();
if( n % 3 != 0 )
LogicError("Dimension must be an integer multiple of 3");
const Int l = n / 3;
if( !l || (l & (l-1)) )
LogicError("n/3 is not a power of two");
Int k=0;
while( Int(1u<<k) < l )
++k;
if( phi <= Real(0) || phi >= Real(1) )
LogicError("phi must be in (0,1)");
if( mu <= Real(0) || mu >= Real(1) )
LogicError("mu must be in (0,1)");
// Start by setting A to the identity, and then modify the necessary
// l x l blocks of its 3 x 3 partitioning.
MakeIdentity( A );
unique_ptr<ElementalMatrix<F>> ABlock( A.Construct(A.Grid(),A.Root()) );
View( *ABlock, A, IR(2*l,3*l), IR(2*l,3*l) );
*ABlock *= mu;
View( *ABlock, A, IR(0,l), IR(l,2*l) );
Walsh( *ABlock, k );
*ABlock *= -phi;
View( *ABlock, A, IR(l,2*l), IR(2*l,3*l) );
Walsh( *ABlock, k );
*ABlock *= phi;
// Now scale A by S
const Real zeta = Sqrt(Real(1)-phi*phi);
auto& ALoc = A.Matrix();
for( Int iLoc=0; iLoc<A.LocalHeight(); ++iLoc )
{
const Int i = A.GlobalRow(iLoc);
const Real gamma = Pow(zeta,Real(i));
for( Int jLoc=0; jLoc<A.LocalWidth(); ++jLoc )
ALoc(iLoc,jLoc) *= gamma;
}
}
