void Lotkin( AbstractBlockDistMatrix<F>& A, Int n )
{
DEBUG_ONLY(CallStackEntry cse("Lotkin"))
Hilbert( A, n );
// Set first row to all ones
if( A.ColShift() == 0 )
{
const Int localWidth = A.LocalWidth();
for( Int jLoc=0; jLoc<localWidth; ++jLoc )
A.SetLocal( 0, jLoc, F(1) );
}
}
void Hilbert( AbstractBlockDistMatrix<F>& A, Int n )
{
DEBUG_ONLY(CSE cse("Hilbert"))
A.Resize( n, n );
auto hilbertFill = []( Int i, Int j ) { return F(1)/F(i+j+1); };
IndexDependentFill( A, function<F(Int,Int)>(hilbertFill) );
}
void Ris( AbstractBlockDistMatrix<F>& R, Int n )
{
DEBUG_ONLY(CallStackEntry cse("Ris"))
R.Resize( n, n );
const F oneHalf = F(1)/F(2);
auto risFill = [=]( Int i, Int j ) { return oneHalf/(F(n-i-j)-oneHalf); };
IndexDependentFill( R, function<F(Int,Int)>(risFill) );
}
void Parter( AbstractBlockDistMatrix<F>& P, Int n )
{
DEBUG_ONLY(CallStackEntry cse("Parter"))
P.Resize( n, n );
const F oneHalf = F(1)/F(2);
auto parterFill = [=]( Int i, Int j ) { return F(1)/(F(i)-F(j)+oneHalf); };
IndexDependentFill( P, function<F(Int,Int)>(parterFill) );
}
void KMS( AbstractBlockDistMatrix<T>& K, Int n, T rho )
{
DEBUG_ONLY(CallStackEntry cse("KMS"))
K.Resize( n, n );
auto kmsFill =
[=]( Int i, Int j ) -> T
{ if( i < j ) { return Pow(rho,T(j-i)); }
else { return Conj(Pow(rho,T(i-j))); } };
IndexDependentFill( K, function<T(Int,Int)>(kmsFill) );
}
void Redheffer( AbstractBlockDistMatrix<T>& R, Int n )
{
DEBUG_ONLY(CSE cse("Redheffer"))
R.Resize( n, n );
auto redhefferFill =
[]( Int i, Int j ) -> T
{ if( j == 0 || ((j+1)%(i+1))==0 ) { return T(1); }
else { return T(0); } };
IndexDependentFill( R, function<T(Int,Int)>(redhefferFill) );
}
void GKS( AbstractBlockDistMatrix<F>& A, Int n )
{
DEBUG_ONLY(CallStackEntry cse("GKS"))
A.Resize( n, n );
auto gksFill =
[]( Int i, Int j ) -> F
{ if( i < j ) { return -F(1)/Sqrt(F(j+1)); }
else if( i == j ) { return F(1)/Sqrt(F(j+1)); }
else { return F(0); } };
IndexDependentFill( A, function<F(Int,Int)>(gksFill) );
}
void Fourier( AbstractBlockDistMatrix<Complex<Real>>& A, Int n )
{
DEBUG_ONLY(CallStackEntry cse("Fourier"))
A.Resize( n, n );
const Real pi = 4*Atan( Real(1) );
const Real nSqrt = Sqrt( Real(n) );
auto fourierFill =
[=]( Int i, Int j ) -> Complex<Real>
{ const Real theta = -2*pi*i*j/n;
return Complex<Real>(Cos(theta),Sin(theta))/nSqrt; };
IndexDependentFill( A, function<Complex<Real>(Int,Int)>(fourierFill) );
}
void Egorov
( AbstractBlockDistMatrix<Complex<Real>>& A,
std::function<Real(Int,Int)> phase, Int n )
{
DEBUG_ONLY(CallStackEntry cse("Egorov"))
A.Resize( n, n );
auto egorovFill =
[&]( Int i, Int j )
{ const Real theta = phase(i,j);
return Complex<Real>(Cos(theta),Sin(theta)); };
IndexDependentFill( A, std::function<Complex<Real>(Int,Int)>(egorovFill) );
}
void Kahan( AbstractBlockDistMatrix<F>& A, Int n, F phi )
{
DEBUG_ONLY(CSE cse("Kahan"))
A.Resize( n, n );
const F zeta = Sqrt(F(1)-phi*Conj(phi));
typedef Base<F> Real;
auto kahanFill =
[=]( Int i, Int j ) -> F
{ if( i == j ) { return Pow(zeta,Real(i)); }
else if( i < j ) { return -phi*Pow(zeta,Real(i)); }
else { return F(0); } };
IndexDependentFill( A, function<F(Int,Int)>(kahanFill) );
}
void ThreeValued( AbstractBlockDistMatrix<T>& A, Int m, Int n, double p )
{
DEBUG_ONLY(CSE cse("ThreeValued"))
A.Resize( m, n );
if( A.RedundantRank() == 0 )
ThreeValued( A.Matrix(), A.LocalHeight(), A.LocalWidth(), p );
Broadcast( A, A.RedundantComm(), 0 );
}
void Identity( AbstractBlockDistMatrix<T>& I, Int m, Int n )
{
DEBUG_ONLY(CallStackEntry cse("Identity"))
I.Resize( m, n );
MakeIdentity( I );
}
void Zeros( AbstractBlockDistMatrix<T>& A, Int m, Int n )
{
DEBUG_ONLY(CallStackEntry cse("Zeros"))
A.Resize( m, n );
Zero( A );
}
