public static double MaxAbsoluteEigenvalue2(Matrix D, double accuracy, int N)
{
int m = D.Height;
if (m!=D.Width)
throw new Exception("Dimensions do not match");
ASampler Sampler = new ASampler();
Vector x = new Vector(m);
Sampler.FillWithNormals(ref x);
x /= Math.Sqrt(x*x);
double eigenval = Math.Abs(x*D*x);
int n = 0;
while (true)
{
Vector y = new Vector(m);
Sampler.FillWithNormals(ref y);
y = y - x*(x*y);
y /= Math.Sqrt(y*y);
double xy = x*y;
double yy = y*y;
double xDx = x*D*x;
double xDy = x*D*y;
double yDx = y*D*x;
double yDy = y*D*y;
double M = Math.Sqrt(Sq(xDy + yDx) + Sq(xDx - yDy));
double sin_tau = (xDy+yDx)/M;
double cos_tau = (xDx-yDy)/M;
double sin_arc1 = 0;
double cos_arc1 = 1;
if (cos_tau>0)
{
cos_arc1 = Math.Sqrt(0.5*(1.0+cos_tau));
sin_arc1 = sin_tau/2/cos_arc1;
}
else
{
sin_arc1 = Math.Sqrt(0.5*(1.0-cos_tau));
cos_arc1 = sin_tau/2/sin_arc1;
}
double cos_arc2 = -sin_arc1;
double sin_arc2 = cos_arc1;
Vector x1 = x*cos_arc1 + y*sin_arc1;
Vector x2 = x*cos_arc2 + y*sin_arc2;
y =(Math.Abs(x1*D*x1)>Math.Abs(x2*D*x2)) ? x1 : x2;
double dlug = Math.Sqrt(y*y);
y /= dlug;
double eig = Math.Abs(y*D*y);
n = (eig-eigenval<accuracy) ? n+1 : 0;
x = y;
eigenval = eig;
if (n>=N)
{
Vector t1 = D*x;
return eigenval;
}
}
}
public static double MaxAbsoluteEigenvalue(Matrix D, double accuracy, int N)
{
int m = D.Height;
if (m!=D.Width)
throw new Exception("Dimensions do not match");
ASampler Sampler = new ASampler();
Matrix DD = D*D;
Vector x = new Vector(m);
Sampler.FillWithNormals(ref x);
x /= Math.Sqrt(x*x);
double eigenval = Math.Abs(x*D*x);
int n = 0;
for (int i=0; true; i++)
{
Vector y = DD*x;
x = y/Math.Sqrt(y*y);
double eig = Math.Abs(x*D*x);
n = (Math.Abs(eig-eigenval)<accuracy) ? n+1 : 0;
eigenval = eig;
if (i>=m*2 && n>=N)
return (eigenval);
}
}
