Matrix GetEigenSpace(Complex eigenValue, int dimensions)
{
Matrix m = (this - eigenValue * DiagonalMatrix.IdentityMatrix(Width));
m = m.RowReducedEchelonForm();
Matrix eigenSpace = new Matrix(dimensions, Height);
int basis = 0;
for (int i = 0; i + basis < Width; i++)
{
if (m[i + basis, i] != 1)
{
int j = 0;
for (; j < i + basis; j++)
{
eigenSpace[i, j] = -m[i, j];
}
eigenSpace[i, j++] = (Complex)1;
for (; j < Height; j++)
{
eigenSpace[i, j] = -m[i, j];
}
basis++;
}
}
return(eigenSpace);
}
/// <summary>
/// Throws exception if not a square matrix.
/// </summary>
/// <returns></returns>
public Polynomial FindCharacteristicPolynomial()
{
if (Width != Height)
{
throw new Exception("Must be square matrix.");
}
//Method can be found at: https://en.wikipedia.org/wiki/Faddeev%E2%80%93LeVerrier_algorithm
Complex[] c = new Complex[Width + 1];
c[0] = (Complex)1;
var I = DiagonalMatrix.IdentityMatrix(Width);
var M = (Matrix)I;
for (int i = 1; i < c.Length; i++)
{
//Console.WriteLine();
//Console.WriteLine(M);
M = this * M;
c[i] = -1.0 / i * M.Trace();
//Console.WriteLine(M);
//Console.WriteLine(c[i]);
if (i + 1 < c.Length)
{
M += c[i] * I;
}
}
Polynomial poly = new Polynomial(c.Length);
for (int i = 0; i < c.Length; i++)
{
poly[i] = c[c.Length - i - 1];
}
return(poly);
}
static void Main(string[] args)
{
DateTime t0 = DateTime.Now;
Console.WriteLine("Start Time: {0}", t0);
List <string> str = new List <string>();
File.WriteAllLines("Test.txt",
PolynomialGeneratorX.GenerateAndBuild("eccentricemery", PolynomialGeneratorX.InputTypes.Primes, TextFormat.PlainText, 'x', "f", 47, true)
);
DateTime t1 = DateTime.Now;
Console.WriteLine("End Time: {0}", t1);
Console.WriteLine("Total Time: {0}", t1 - t0);
Console.WriteLine("Press enter to exit.");
Console.ReadLine();
return;
//Matrix m = new Matrix(3, 3);
//m[0, 0] = (Complex)3;
//m[1, 0] = (Complex)1;
//m[2, 0] = (Complex)5;
//m[0, 1] = (Complex)3;
//m[1, 1] = (Complex)3;
//m[2, 1] = (Complex)1;
//m[0, 2] = (Complex)4;
//m[1, 2] = (Complex)6;
//m[2, 2] = (Complex)4;
Matrix m = new Matrix(3, 3);
Random ran = new Random(465165313);
for (int i = 0; i < m.Width; i++)
{
for (int j = 0; j < m.Height; j++)
{
m[i, j] = new Complex(ran.Next() / 100.0, ran.Next() / 100.0 * 0);
}
}
Console.WriteLine(m);
Polynomial poly = m.FindCharacteristicPolynomial();
Console.WriteLine("f(x) = {0}", poly);
////poly[0] = (Complex)(3);
////poly[1] = (Complex)(47);
////poly[2] = (Complex)(182);
////poly[3] = (Complex)(327);
////poly[4] = (Complex)(1027);
foreach (var root in poly.FindAllRoots())
{
Console.WriteLine("Root: {0}, Approx: {1}", root, poly.F(root));
}
Console.ReadLine();
Console.WriteLine("SBS^(-1) = ");
m.Diagonalize(out Matrix S, out DiagonalMatrix B);
var S1 = S.Invert();
//S.Round(5);
//S1.Round(5);
//B.Round(5);
string[] M1 = S.ToStringArray(), M2 = ((Matrix)B).ToStringArray(), M3 = S1.ToStringArray();
for (int i = 0; i < B.Height; i++)
{
Console.WriteLine(M1[i] + M2[i] + M3[i]);
}
Console.WriteLine("=");
Console.WriteLine(S * B * S1);
Console.WriteLine("M^20 = ");
Console.WriteLine(S * DiagonalMatrix.Pow(B, 20) * S1);
Matrix m20 = (Matrix)DiagonalMatrix.IdentityMatrix(2);
for (int i = 0; i < 20; i++)
{
m20 *= m;
}
Console.WriteLine("?=");
Console.WriteLine(m20);
Console.WriteLine("(M^(1/3))^3 = ");
var cubeRt = S * DiagonalMatrix.Pow(B, 1.0 / 3) * S1;
Console.WriteLine(cubeRt * cubeRt * cubeRt);
Console.WriteLine("END");
Console.ReadLine();
//Matrix m = GetSquareMatrixFromUser();
//Console.WriteLine("\nInput Matrix: \n" + m);
//Matrix inverse = m.Invert();
//if (inverse == null)
// Console.WriteLine("Matrix is not invertable");
//else
//{
// Console.WriteLine("\nInverse Matrix: \n" + inverse);
// Matrix product = inverse * m;
// Console.WriteLine("\nProduct: \n" + product);
// product.Round(10);
// Console.WriteLine("\nProduct (rounded to 10 decimel places): \n" + product);
// Console.WriteLine("\nPress Enter to exit");
// Console.ReadLine();
//}
}