static (int, double, double[]) PM_Method(double [,] A, double [] y, double [] l, double delta, double eps)
{
double ynorm = Math.Sqrt(Enumerable.Range(0, y.Length).Select(i => Math.Pow(y[i], 2)).Sum()); // ||y^(i)||
double [] x = Enumerable.Range(0, y.Length).Select(i => y[i] / ynorm).ToArray(); //x^(0) and x^(k)
int[] S = Enumerable.Range(0, x.Length).Where(i => Math.Abs(x[i]) > delta).ToArray(); //S^(0) and S^(k)
double[] x_ = new double[x.Length]; //x^(k-1)
int[] S_ = new int[S.Length]; //S^(k-1)
double[] l_ = new double[l.Length]; //λ^(0) and λ^(k)
for (int k = 1;; k++)
{
Array.Copy(x, x_, x.Length); //x^(k) -> x^(k-1)
Array.Copy(S, S_, S.Length); //S^(k) -> S^(k-1)
Array.Copy(l, l_, l.Length); //λ^(k) -> λ^(k-1)
y = MatrixTools.MatToVec(MatrixTools.MatrixMult(A, x_));
l = Enumerable.Range(0, l.Length).Select(i => S_.Contains(i) ? y[i] / x_[i] : 0).ToArray();
ynorm = Math.Sqrt(Enumerable.Range(0, y.Length).Select(i => Math.Pow(y[i], 2)).Sum());
x = Enumerable.Range(0, x.Length).Select(i => y[i] / ynorm).ToArray();
S = Enumerable.Range(0, S.Length).Where(i => Math.Abs(x[i]) > delta).ToArray();
if (S_.All(i => Math.Abs(l[i] - l_[i]) <= eps) || MatrixTools.SubVecs(x, x_).Max() <= eps)
{
return(k, S_.Select(i => l[i]).Sum() / S_.Length, x);
}
}
}
static void Main(string[] args)
{
//Inpute
Console.Write("n : "); int n = int.Parse(Console.ReadLine());
Console.Write("Enter n (δ = 10^(-n)) : "); double delta = Math.Pow(10, -double.Parse(Console.ReadLine()));
//Console.Write("Enter δ : "); double delta = double.Parse(Console.ReadLine());
Console.Write("Enter n (ε = 10^(-n)) : "); double eps = Math.Pow(10, -double.Parse(Console.ReadLine()));
//Console.Write("Enter ε : "); double eps = double.Parse(Console.ReadLine());
double[,] A = IOMatrix.InputSquareMatrix(n, "A");
double[] y0 = IOMatrix.InputVector(n, "y_0");
double[] l0 = IOMatrix.InputVector(n, "l_0");
//Compute
var res = PM_Method(A, y0, l0, delta, eps);
//Output
Console.WriteLine($"k : {res.Item1}");
Console.WriteLine($"l_1 : {res.Item2}");
Console.WriteLine("x^(k) : ");
IOMatrix.OutputVector(res.Item3);
Console.WriteLine(new string('-', 60));
Console.WriteLine($"Ax : ");
IOMatrix.OutputVector(MatrixTools.MatToVec(MatrixTools.MatrixMult(A, res.Item3)));
Console.WriteLine($"lx : ");
IOMatrix.OutputVector(res.Item3.Select(e => e * res.Item2).ToArray());
Console.WriteLine(new string('-', 60));
Console.WriteLine("A : ");
IOMatrix.OutputMatrix(A);
Console.WriteLine("y_0 : ");
IOMatrix.OutputVector(y0);
Console.WriteLine("l_0 : ");
IOMatrix.OutputVector(l0);
Console.WriteLine($"δ : {eps}");
Console.WriteLine($"ε : {eps}");
}
static (double[], double, int) JacobiMethod(double[,] A, double[] b, double e, int max_k = -1)
{
double step = 0;
double [] x = new double [b.Length], _x = new double[b.Length];
for (int k = 1;; k++)
{
for (int n = 0; n < x.Length; n++)
{
x[n] = _x[n];
}
for (int i = 0; i < b.Length; i++)
{
_x[i] = -(Enumerable.Range(0, x.Length).Where(j => j != i).Select(j => A[i, j] * x[j]).Sum() - b[i]) / A[i, i];
}
step = MatrixTools.SubVecs(_x, x).Select(x => Math.Abs(x)).Max();
if (step < e || k == max_k + 1)
{
double r = MatrixTools.SubVecs(MatrixTools.MatToVec(MatrixTools.MatrixMult(A, _x)), b).Select(x => Math.Abs(x)).Max();
return(_x, r, k);
}
}
}