void GCDMatrix( AbstractDistMatrix<T>& G, Int m, Int n )
{
DEBUG_ONLY(CSE cse("GCDMatrix"))
G.Resize( m, n );
auto gcdFill = []( Int i, Int j ) { return T(GCD(i+1,j+1)); };
IndexDependentFill( G, function<T(Int,Int)>(gcdFill) );
}
void MinIJ( AbstractDistMatrix<T>& M, Int n )
{
DEBUG_ONLY(CSE cse("MinIJ"))
M.Resize( n, n );
auto minIJFill = []( Int i, Int j ) { return T(Min(i+1,j+1)); };
IndexDependentFill( M, function<T(Int,Int)>(minIJFill) );
}
void Hilbert( AbstractDistMatrix<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 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 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 Ris( AbstractDistMatrix<F>& R, Int n )
{
DEBUG_CSE
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( AbstractDistMatrix<F>& P, Int n )
{
EL_DEBUG_CSE
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 Lehmer( AbstractDistMatrix<F>& L, Int n )
{
DEBUG_ONLY(CSE cse("Lehmer"))
L.Resize( n, n );
auto lehmerFill =
[]( Int i, Int j ) -> F
{ if( i < j ) { return F(i+1)/F(j+1); }
else { return F(j+1)/F(i+1); } };
IndexDependentFill( L, function<F(Int,Int)>(lehmerFill) );
}
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 Toeplitz( AbstractDistMatrix<S>& A, Int m, Int n, const vector<T>& a )
{
EL_DEBUG_CSE
const Int length = m+n-1;
if( a.size() != Unsigned(length) )
LogicError("a was the wrong size");
A.Resize( m, n );
auto toeplitzFill = [&]( Int i, Int j ) { return a[i-j+(n-1)]; };
IndexDependentFill( A, function<S(Int,Int)>(toeplitzFill) );
}
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 Egorov
( Matrix<Complex<Real>>& A, function<Real(Int,Int)> phase, Int n )
{
DEBUG_ONLY(CSE cse("Egorov"))
A.Resize( n, n );
auto egorovFill =
[&]( Int i, Int j ) -> Complex<Real>
{ const Real theta = phase(i,j);
return Complex<Real>(Cos(theta),Sin(theta)); };
IndexDependentFill( A, function<Complex<Real>(Int,Int)>(egorovFill) );
}
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 KMS( AbstractDistMatrix<T>& K, Int n, T rho )
{
EL_DEBUG_CSE
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 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 Fourier( Matrix<Complex<Real>>& A, Int n )
{
EL_DEBUG_CSE
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( AbstractDistMatrix<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 Riffle( AbstractDistMatrix<F>& P, Int n )
{
DEBUG_CSE
typedef Base<F> Real;
auto logBinom = LogBinomial<Real>( n+1 );
auto logEuler = LogEulerian<Real>( n );
const Real gamma = n*Log(Real(2));
P.Resize( n, n );
auto riffleFill =
[&]( Int i, Int j ) -> F
{ const Int k = 2*i - j + 1;
if( k >= 0 && k <= n+1 )
return Exp(logBinom[k]-gamma+logEuler[j]-logEuler[i]);
else
return Base<F>(0);
};
IndexDependentFill( P, function<F(Int,Int)>(riffleFill) );
}
void RiffleStationary( AbstractDistMatrix<F>& PInf, Int n )
{
DEBUG_CSE
typedef Base<F> Real;
// NOTE: This currently requires quadratic time
vector<Real> sigma(n,0), sigmaTmp(n,0);
sigma[0] = sigmaTmp[0] = 1;
for( Int j=1; j<n; ++j )
{
sigmaTmp[0] = sigma[0];
for( Int k=1; k<=j; ++k )
sigmaTmp[k] = (k+1)*sigma[k] + (j-k+1)*sigma[k-1];
for( Int k=0; k<n; ++k )
sigma[k] = sigmaTmp[k]/(j+1);
}
SwapClear( sigmaTmp );
PInf.Resize( n, n );
auto riffleStatFill = [&]( Int i, Int j ) { return sigma[j]; };
IndexDependentFill( PInf, function<F(Int,Int)>(riffleStatFill) );
}