void UniformHelmholtzGreens
( ElementalMatrix<Complex<Real>>& A, Int n, Real lambda )
{
EL_DEBUG_CSE
typedef Complex<Real> C;
const Real pi = 4*Atan( Real(1) );
const Real k0 = 2*pi/lambda;
const Grid& g = A.Grid();
// Generate a list of n uniform samples from the 3D unit ball
DistMatrix<Real,STAR,VR> X_STAR_VR(3,n,g);
for( Int jLoc=0; jLoc<X_STAR_VR.LocalWidth(); ++jLoc )
{
Real x0, x1, x2;
// Sample uniformly from [-1,+1]^3 until a point is drawn from the ball
while( true )
{
x0 = SampleUniform( Real(-1), Real(1) );
x1 = SampleUniform( Real(-1), Real(1) );
x2 = SampleUniform( Real(-1), Real(1) );
const Real radiusSq = x0*x0 + x1*x1 + x2*x2;
if( radiusSq > 0 && radiusSq <= 1 )
break;
}
X_STAR_VR.SetLocal( 0, jLoc, x0 );
X_STAR_VR.SetLocal( 1, jLoc, x1 );
X_STAR_VR.SetLocal( 2, jLoc, x2 );
}
DistMatrix<Real,STAR,STAR> X_STAR_STAR( X_STAR_VR );
A.Resize( n, n );
for( Int jLoc=0; jLoc<A.LocalWidth(); ++jLoc )
{
const Int j = A.GlobalCol(jLoc);
const Real xj0 = X_STAR_STAR.GetLocal(0,j);
const Real xj1 = X_STAR_STAR.GetLocal(1,j);
const Real xj2 = X_STAR_STAR.GetLocal(2,j);
for( Int iLoc=0; iLoc<A.LocalHeight(); ++iLoc )
{
const Int i = A.GlobalRow(iLoc);
if( i == j )
{
A.SetLocal( iLoc, jLoc, 0 );
}
else
{
const Real d0 = X_STAR_STAR.GetLocal(0,i)-xj0;
const Real d1 = X_STAR_STAR.GetLocal(1,i)-xj1;
const Real d2 = X_STAR_STAR.GetLocal(2,i)-xj2;
const Real gamma = k0*Sqrt(d0*d0+d1*d1+d2*d2);
const Real realPart = Cos(gamma)/gamma;
const Real imagPart = Sin(gamma)/gamma;
A.SetLocal( iLoc, jLoc, C(realPart,imagPart) );
}
}
}
}
