static void RelaxationMethodCheckConvergence_SpecialMatrix(SpecialMatrix M, double w)
{
double left_upper = 1 - w;
double left_lower = ((-w * M.B) / M.A) * (1 - w);
double right_upper = (1 / M.A) * (-w * M.B);
double right_lower = Math.Pow((w * M.B) / M.A, 2) + 1 - w;
double max_column_sum = Math.Max
(
Math.Abs(Math.Abs(left_upper) + Math.Abs(left_lower)),
Math.Abs(Math.Abs(right_upper) + Math.Abs(right_lower))
);
double max_row_sum = Math.Max
(
Math.Abs(Math.Abs(left_upper) + Math.Abs(right_upper)),
Math.Abs(Math.Abs(left_lower) + Math.Abs(right_lower))
);
if (max_row_sum >= 1 && max_column_sum >= 1)
{
throw new ArgumentException("Метод не сходится");
}
}
static Matrix <double> ToFullMatrix(SpecialMatrix M)
{
var M_Full = MatrixBuilder.Dense(M.N, M.N);
for (int i = 0; i < M.N; i++)
{
M_Full[i, i] = M.A;
M_Full[i, M.N - i - 1] = M.B;
}
return(M_Full);
}
static Vector <double> RelaxationMethod_SpecialMatrix(SpecialMatrix A, Vector <double> b, Vector <double> x_0, double w, int K)
{
RelaxationMethodCheckConvergence_SpecialMatrix(A, w);
Vector <double> x = x_0.Clone();
for (int k = 0; k < K; k++)
{
x = RelaxationMethodIteration_SpecialMatrix(A, b, x, w);
}
return(x);
}
static double SpecialMatrix_L2Norm(SpecialMatrix M, Vector <double> x, Vector <double> b)
{
int n = b.Count();
double A = M.A;
double B = M.B;
double sum = 0;
for (int i = 0; i < n; i++)
{
sum += Math.Pow(A * x[i] + B * x[n - i - 1] - b[i], 2);
}
return(Math.Sqrt(sum));
}
static Vector <double> RelaxationMethodIteration_SpecialMatrix(SpecialMatrix M, Vector <double> b, Vector <double> x_k, double w)
{
int n = b.Count();
double A = M.A;
double B = M.B;
double w_inv = 1 - w;
double w_divided = w / A;
for (int i = 0; i < n; i++)
{
x_k[i] = w_inv * x_k[i] + w_divided * (b[i] - x_k[n - i - 1] * B);
}
return(x_k);
}
static Vector <double> RelaxationMethod_SpecialMatrix(SpecialMatrix A, Vector <double> b, Vector <double> x_0, double w, double e, out int iterations, out List <Tuple <int, double> > residuals)
{
RelaxationMethodCheckConvergence_SpecialMatrix(A, w);
Vector <double> x = x_0.Clone();
iterations = 0;
residuals = new List <Tuple <int, double> >();
while (e < SpecialMatrix_L2Norm(A, x, b))
{
residuals.Add(new Tuple <int, double>(iterations, SpecialMatrix_L2Norm(A, x, b)));
x = RelaxationMethodIteration_SpecialMatrix(A, b, x, w);
iterations++;
}
return(x);
}
