/// <summary>
/// returns the eigen values and eigen vectors of a matrix
/// IMPORTANT: THIS METHOD NEEDS DEBUGGING.
/// IT RETURNS THE NEGATIVE VALUES OF THE EIGEN VECTORS ON A TOY EXMAPLE
/// double[,] matrix = {
/// { 3.0, -1.0 },
/// { -1.0, 3.0 }
/// };
/// eigen values are correct ie, 2.0, 4.0; but in the wrong order.
/// </summary>
public static Tuple <double[], double[, ]> EigenVectors(double[,] matrix)
{
Evd <double> eigen = DenseMatrix.OfArray(matrix).Evd();
Vector <System.Numerics.Complex> eigenvaluesComplex = eigen.EigenValues;
//WriteArrayOfComplexNumbers(eigenvalues);
double[] eigenvaluesReal = new double[eigenvaluesComplex.Count];
for (int i = 0; i < eigenvaluesComplex.Count; i++)
{
System.Numerics.Complex c = eigenvaluesComplex[i];
double magnitude = c.Magnitude;
Console.WriteLine("eigen value[{0}] {1} Magnitude={2}", i, c.ToString(), magnitude);
}
Matrix <double> eigenvectorsComplex = eigen.EigenVectors;
double[,] eigenvectorsReal = new double[eigenvaluesComplex.Count, matrix.GetLength(0)];
for (int col = 0; col < eigenvectorsComplex.RowCount; col++)
{
Vector <double> ev = eigenvectorsComplex.Column(col);
for (int i = 0; i < ev.Count; i++)
{
eigenvectorsReal[col, i] = ev[i];
Console.WriteLine("eigen vector {0}, value {1} = {2}", col, i, ev[i]);
}
}
return(Tuple.Create(eigenvaluesReal, eigenvectorsReal));
}
public QA GetImaginaryDivideQA()
{
System.Numerics.Complex z1 = new System.Numerics.Complex(ran.Next(1, 5), ran.Next(1, 5)), z2 = new System.Numerics.Complex(ran.Next(1, 5), ran.Next(1, 5));
QA result;
result.Q = z1.ToString() + "/" + z2.ToString();
result.A = (z1 / z2).ToString();
return(result);
}
public static string ToMathString(this System.Numerics.Complex z)
{
//if (double.IsNaN(z.Real) && double.IsNaN(z.Imaginary))
//return "NaN";
switch (Properties.Settings.Default.NumericalOutputNotation)
{
case Computator.NET.DataTypes.SettingsTypes.NumericalOutputNotationType.MathematicalNotation:
if (z.Real == 0)
{
if (z.Imaginary == 1.0)
{
return("i");
}
if (z.Imaginary == -1.0)
{
return("-i");
}
return(z.Imaginary != 0
? string.Format("{0}{1}i", z.Imaginary.ToMathString(), Computator.NET.DataTypes.Text.SpecialSymbols.DotSymbol)
: "0");
}
if (z.Imaginary == 0)
{
return(z.Real.ToMathString());
}
return((z.Imaginary > 0 || double.IsNaN(z.Imaginary))
? string.Format("{0}+{1}{2}i", z.Real.ToMathString(), z.Imaginary.ToMathString(),
Computator.NET.DataTypes.Text.SpecialSymbols.DotSymbol)
: string.Format("{0}{1}{2}i", z.Real.ToMathString(), z.Imaginary.ToMathString(),
Computator.NET.DataTypes.Text.SpecialSymbols.DotSymbol));
default:
//case NumericalOutputNotationType.EngineeringNotation:
return(z.ToString(System.Globalization.CultureInfo.InvariantCulture));
}
}
