public static bool IsNearlyEigenpair(AnySquareMatrix A, Complex[] v, Complex a)
{
int d = A.Dimension;
// compute products
Complex[] Av = new Complex[d];
for (int i = 0; i < d; i++)
{
Av[i] = 0.0;
for (int j = 0; j < d; j++)
{
Av[i] += A[i, j] * v[j];
}
}
Complex[] av = new Complex[d];
for (int i = 0; i < d; i++)
{
av[i] = a * v[i];
}
// compute tolorance
double N = MatrixNorm(A);
double n = 0.0;
for (int i = 0; i < d; i++)
{
n += ComplexMath.Abs(v[i]);
}
double ep = TargetPrecision * (N * n / d + ComplexMath.Abs(a) * n);
// compare elements within tollerance
for (int i = 0; i < d; i++)
{
if (ComplexMath.Abs(Av[i] - av[i]) > ep)
{
return(false);
}
}
return(true);
}
public static bool IsNearlyEigenpair(AnySquareMatrix A, ColumnVector v, double a)
{
// compute products
ColumnVector Av = A * v;
ColumnVector av = a * v;
// compute tolorance
int d = v.Dimension;
double N = MatrixNorm(A);
double n = MatrixNorm(v);
double ep = TargetPrecision * (Math.Abs(N * n) / d + Math.Abs(a * n));
// compare elements within tolorance
for (int i = 0; i < d; i++)
{
if (Math.Abs(Av[i] - av[i]) > ep)
{
return(false);
}
}
return(true);
}
public static bool IsNearlyEigenpair(AnySquareMatrix A, ComplexColumnVector v, Complex a)
{
int d = A.Dimension;
// compute products
/*
* Complex[] Av = new Complex[d];
* for (int i=0; i<d; i++) {
* Av[i] = 0.0;
* for (int j=0; j<d; j++) {
* Av[i] += A[i,j]*v[j];
* }
* }
*/
ComplexColumnVector Av = A * v;
ComplexColumnVector av = a * v;
// compute tolerance
double N = A.MaxNorm();
double n = 0.0;
for (int i = 0; i < d; i++)
{
n += ComplexMath.Abs(v[i]);
}
double ep = TargetPrecision * (N * n / d + ComplexMath.Abs(a) * n);
// compare elements within tolerance
for (int i = 0; i < d; i++)
{
if (ComplexMath.Abs(Av[i] - av[i]) > ep)
{
return(false);
}
}
return(true);
}
