inline void
MakeNormalUniformSpectrum
( Matrix<Complex<R> >& A, Complex<R> center, R radius )
{
#ifndef RELEASE
PushCallStack("MakeNormalUniformSpectrum");
#endif
typedef Complex<R> C;
if( A.Height() != A.Width() )
throw std::logic_error("Cannot make a non-square matrix normal");
// Sample the diagonal matrix D from the ball B_radius(center)
// and then rotate it with a random Householder similarity transformation:
//
// (I-2uu^H) D (I-2uu^H)^H = D - 2(u (conj(D) u)^H + (D u) u^H) +
// (4 u^H D u) u u^H
//
// Form d and D
const int n = A.Height();
std::vector<C> d( n );
for( int j=0; j<n; ++j )
d[j] = center + radius*SampleUnitBall<C>();
Diagonal( d, A );
// Form u
Matrix<C> u( n, 1 );
MakeUniform( u );
const R origNorm = Nrm2( u );
Scale( 1/origNorm, u );
// Form v := D u
Matrix<C> v( n, 1 );
for( int i=0; i<n; ++i )
v.Set( i, 0, d[i]*u.Get(i,0) );
// Form w := conj(D) u
Matrix<C> w( n, 1 );
for( int i=0; i<n; ++i )
w.Set( i, 0, Conj(d[i])*u.Get(i,0) );
// Update A := A - 2(u w^H + v u^H)
Ger( C(-2), u, w, A );
Ger( C(-2), v, u, A );
// Form \gamma := 4 u^H (D u) = 4 (u,Du)
const C gamma = 4*Dot(u,v);
// Update A := A + gamma u u^H
Ger( gamma, u, u, A );
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
Uniform( int m, int n, Matrix<T>& A, T center, typename Base<T>::type radius )
{
#ifndef RELEASE
PushCallStack("Uniform");
#endif
A.ResizeTo( m, n );
MakeUniform( A, center, radius );
#ifndef RELEASE
PopCallStack();
#endif
}
void Uniform( Matrix<T>& A, Int m, Int n, T center, Base<T> radius )
{
EL_DEBUG_CSE
A.Resize( m, n );
MakeUniform( A, center, radius );
}
