public VectorR GaussSeidel(MatrixR A, VectorR b, int MaxIterations, double tolerance)
{
int n = b.GetSize();
VectorR x = new VectorR(n);
for (int nIteration = 0; nIteration < MaxIterations; nIteration++)
{
VectorR xOld = x.Clone();
for (int i = 0; i < n; i++)
{
double db = b[i];
double da = A[i, i];
if (Math.Abs(da) < epsilon)
{
throw new ArgumentException("Diagonal element is too small!");
}
for (int j = 0; j < i; j++)
{
db -= A[i, j] * x[j];
}
for (int j = i + 1; j < n; j++)
{
db -= A[i, j] * xOld[j];
}
x[i] = db / da;
}
VectorR dx = x - xOld;
if (dx.GetNorm() < tolerance)
{
//MessageBox.Show(nIteration.ToString());
return(x);
}
}
return(x);
}
private static MatrixR Jacobian(MFunction f, VectorR x)
{
double h = 0.0001;
int n = x.GetSize();
MatrixR jacobian = new MatrixR(n, n);
VectorR x1 = x.Clone();
for (int j = 0; j < n; j++)
{
x1[j] = x[j] + h;
for (int i = 0; i < n; i++)
{
jacobian[i, j] = (f(x1)[i] - f(x)[i]) / h;
}
}
return(jacobian);
}
public static VectorR TridiagonalEigenvector(double s, double tolerance, out double lambda)
{
int n = Alpha.GetLength(0);
double[] gamma = (double[])Beta.Clone();
double[] beta = (double[])Beta.Clone();
double[] alpha = new double[n];
for (int i = 0; i < n; i++)
{
alpha[i] = Alpha[i] - s;
}
double[] gamma1, alpha1, beta1;
LUDecomposition(gamma, alpha, beta, out gamma1, out alpha1, out beta1);
VectorR x = new VectorR(n);
Random random = new Random();
for (int i = 0; i < n; i++)
{
x[i] = random.NextDouble();
}
x.Normalize();
VectorR x1 = new VectorR(n);;
double sign;
do
{
x1 = x.Clone();
LUSolver(gamma1, alpha1, beta1, x);
x.Normalize();
if (VectorR.DotProduct(x1, x) < 0.0)
{
sign = -1.0;
x = -x;
}
else
{
sign = 1.0;
}
}while ((x - x1).GetNorm() > tolerance);
lambda = s + sign / x.GetNorm();
return(x);
}
