public static Vector operator +(Vector a, Vector b)
{
int n = a.GetLength();
Vector c = new Vector(n);
for (int i = 0; i < n; ++i)
c[i] = a[i] + b[i];
return c;
}
public static Vector operator *(Matrix a, Vector b)
{
int n = a.GetLength(0);
Vector c = new Vector(n);
for (int i = 0; i < n; ++i)
{
double sum = 0;
for (int j = 0; j < n; ++j)
sum += a[i, j] * b[j];
c[i] = sum;
}
return c;
}
public Vector(Vector a)
{
this.a = new double[a.GetLength()];
for (int i = 0; i < a.GetLength(); ++i)
this.a[i] = a[i];
}
static void Main(string[] args)
{
Console.Clear();
System.IO.StreamReader file = new System.IO.StreamReader(@"C:\Users\sema7\Desktop\Eigenvalues2\input.txt");
string line;
line = file.ReadLine();
int n = int.Parse(line);
Matrix A = new Matrix(n, n);
Matrix B = new Matrix(n, n);
for (int i = 0; i < n; i++)
{
string enterString = file.ReadLine();
string[] massiveString = enterString.Split(new Char[] { ' ' });
for (int j = 0; j < massiveString.Length; j++)
{
A[i, j] = double.Parse(massiveString[j]);
B[i, j] = A[i, j];
}
}
Console.WriteLine("Matrix A of size {0}:", n);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
Console.Write("{0:f5} ", A[i, j]);
Console.WriteLine();
}
Console.WriteLine();
file.Close();
double eps = Math.Pow(10, -6);
Matrix X1 = new Matrix(n, n, 1);
Matrix.Eigenvalue(ref B, ref X1, eps, n);
Console.WriteLine("Eigenvalue matrix A: ");
for (int i = 0; i < n; i++)
Console.Write("{0:f15} ", B[i, i]);
Console.WriteLine();
Console.WriteLine();
Console.WriteLine("Matrix X of size {0}:", n);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
Console.Write("{0:f15} ", X1[i, j]);
Console.WriteLine();
}
Console.WriteLine();
Console.WriteLine("____________ Power Method ___________________");
Vector X2 = new Vector(n);
int k = 0;
double l1 = Matrix.PowMethod(A, ref X2, false, ref k);
Console.WriteLine("Number step: {0}", k);
Console.WriteLine("Eigenvalue l1 of Matrix A: {0:f15}", l1);
Console.WriteLine();
Console.WriteLine("Vector X1 for eigenvalue l1");
for (int i = 0; i < n; i++)
Console.WriteLine("X[{0}] = {1:f15}", i + 1, X2[i]);
double R = 0;
Vector P = new Vector(n);
P = A * X2;
for (int i=0; i< n; ++i)
R += Math.Abs(P[i] - l1 * X2[i]);
Console.WriteLine("R = {0:f15}", R);
Console.WriteLine("||X1|| = {0:f15}", X2.Norma2());
Console.WriteLine();
Console.WriteLine("____________ Scalyar Method ___________________");
Vector X3 = new Vector(n);
k = 0;
double l2 = Matrix.ScalyarMethod(A, ref X3, ref k);
Console.WriteLine("Number step: {0}", k);
Console.WriteLine("Eigenvalue l1 of Matrix A: {0:f15}", l2);
Console.WriteLine();
Console.WriteLine("Vector X1 for eigenvalue l1");
for (int i = 0; i < n; i++)
Console.WriteLine("X[{0}] = {1:f15}", i + 1, X3[i]);
R = 0;
P = new Vector(n);
P = A * X3;
for (int i = 0; i < n; ++i)
R += Math.Abs(P[i] - l2 * X3[i]);
Console.WriteLine("R = {0:f15}", R);
Console.WriteLine("||X1|| = {0:f15}", X3.Norma2());
Console.WriteLine();
Vector X4 = new Vector(n);
k = 0;
double l3 = Matrix.OppositeEndSpectrum(A, ref X4, l1, ref k);
Console.WriteLine("Number step: {0}", k);
Console.WriteLine("The opposite end of the spectrum matrix A: {0:f15}", l3);
Console.WriteLine("Vector X:");
for (int i = 0; i < n; i++)
Console.WriteLine("X[{0}] = {1:f15}", i + 1, X4[i]);
Console.WriteLine();
Vector X5 = new Vector(n);
k = 0;
double l4 = Matrix.MethodVilanda(A, ref X5, l1, ref k);
Console.WriteLine("Number step: {0}", k);
Console.WriteLine("The eigenvalue of method Vilanda matrix A: {0:f15}", l4);
Console.WriteLine("Vector X:");
for (int i = 0; i < n; i++)
Console.WriteLine("X[{0}] = {1:f15}", i + 1, X5[i]);
R = 0;
P = new Vector(n);
P = A * X5;
for (int i = 0; i < n; ++i)
R += Math.Abs(P[i] - l4 * X5[i]);
Console.WriteLine("R = {0:f15}", R);
Console.ReadLine();
}