?? example.cs
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using System;
using Mapack;
class Example
{
public static void Main(String[] args)
{
Matrix A = new Matrix(3, 3);
A[0,0] = 2.0; A[0,1] = 1.0; A[0,2] = 2.0;
A[1,0] = 1.0; A[1,1] = 4.0; A[1,2] = 0.0;
A[2,0] = 2.0; A[2,1] = 0.0; A[2,2] = 8.0;
Console.WriteLine("A = ");
Console.WriteLine(A.ToString());
Console.WriteLine("A.Determinant = " + A.Determinant);
Console.WriteLine("A.Trace = " + A.Trace);
Console.WriteLine("A.Norm1 = " + A.Norm1);
Console.WriteLine("A.NormInfinite = " + A.InfinityNorm);
Console.WriteLine("A.NormFrobenius = " + A.FrobeniusNorm);
SingularValueDecomposition svg = new SingularValueDecomposition(A);
Console.WriteLine("A.Norm2 = " + svg.Norm2);
Console.WriteLine("A.Condition = " + svg.Condition);
Console.WriteLine("A.Rank = " + svg.Rank);
Console.WriteLine();
Console.WriteLine("A.Transpose = ");
Console.WriteLine(A.Transpose().ToString());
Console.WriteLine("A.Inverse = ");
Console.WriteLine(A.Inverse.ToString());
Matrix I = A * A.Inverse;
Console.WriteLine("I = A * A.Inverse = ");
Console.WriteLine(I.ToString());
Matrix B = new Matrix(3, 3);
Console.WriteLine("B = ");
B[0, 0] = 2.0; B[0, 1] = 0.0; B[0, 2] = 0.0;
B[1, 0] = 1.0; B[1, 1] = 0.0; B[1, 2] = 0.0;
B[2, 0] = 2.0; B[2, 1] = 0.0; B[2, 2] = 0.0;
Console.WriteLine(B.ToString());
Matrix X = A.Solve(B);
Console.WriteLine("A.Solve(B)");
Console.WriteLine(X.ToString());
Matrix T = A * X;
Console.WriteLine("A * A.Solve(B) = B = ");
Console.WriteLine(T.ToString());
Console.WriteLine("A = V * D * V");
EigenvalueDecomposition eigen = new EigenvalueDecomposition(A);
Console.WriteLine("D = ");
Console.WriteLine(eigen.DiagonalMatrix.ToString());
Console.WriteLine("lambda = ");
foreach (double eigenvalue in eigen.RealEigenvalues)
{
Console.WriteLine(eigenvalue.ToString());
}
Console.WriteLine();
Console.WriteLine("V = ");
Console.WriteLine(eigen.EigenvectorMatrix);
Console.WriteLine("V * D * V' = ");
Console.WriteLine(eigen.EigenvectorMatrix * (eigen.DiagonalMatrix * eigen.EigenvectorMatrix.Transpose()));
Console.WriteLine("A * V = ");
Console.WriteLine(A * eigen.EigenvectorMatrix);
Console.WriteLine("V * D = ");
Console.WriteLine(eigen.EigenvectorMatrix * eigen.DiagonalMatrix);
}
}
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