/// <summary>Initializes a new instance of the <see cref="LapackEigenvalues"/> class.
/// </summary>
/// <param name="generalizedNonsymmetricEigenvalueProblems">The generalized nonsymmetric eigenvalue problems.</param>
/// <param name="generalizedSymmetricEigenvalueProblems">The generalized symmetric eigenvalue problems.</param>
/// <param name="nonSymmetricEigenvalueProblems">The non symmetric eigenvalue problems.</param>
/// <param name="symmetricEigenvalueProblems">The symmetric eigenvalue problems.</param>
/// <param name="singularValueDecomposition">The singular value decomposition.</param>
/// <param name="generalizedSingularValueDecomposition">The generalized singular value decomposition.</param>
/// <param name="linearLeastSquaresProblems">The linear least squares problems.</param>
public LapackEigenvalues(
IGeneralizedNonsymmetricEigenvalueProblems generalizedNonsymmetricEigenvalueProblems,
IGeneralizedSymmetricEigenvalueProblems generalizedSymmetricEigenvalueProblems,
INonSymmetricEigenvalueProblems nonSymmetricEigenvalueProblems,
ISymmetricEigenvalueProblems symmetricEigenvalueProblems,
ISingularValueDecomposition singularValueDecomposition,
IGeneralizedSingularValueDecomposition generalizedSingularValueDecomposition,
ILinearLeastSquaresProblems linearLeastSquaresProblems)
{
GeneralizedNonSymmetric = generalizedNonsymmetricEigenvalueProblems;
GeneralizedSymmetric = generalizedSymmetricEigenvalueProblems;
NonSymmetric = nonSymmetricEigenvalueProblems;
Symmetric = symmetricEigenvalueProblems;
SingularValueDecomposition = singularValueDecomposition;
GeneralizedSingularValueDecomposition = generalizedSingularValueDecomposition;
LinearLeastSquaresProblem = linearLeastSquaresProblems;
}
public static void Main(String[] args)
{
IMatrix 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);
ISingularValueDecomposition svg = A.GetSingularValueDecomposition();
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());
IMatrix I = A.Multiply(A.Inverse);
Console.WriteLine("I = A * A.Inverse = ");
Console.WriteLine(I.ToString());
IMatrix 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());
IMatrix X = A.Solve(B);
Console.WriteLine("A.Solve(B)");
Console.WriteLine(X.ToString());
IMatrix T = A.Multiply(X);
Console.WriteLine("A * A.Solve(B) = B = ");
Console.WriteLine(T.ToString());
Console.WriteLine("A = V * D * V");
IEigenvalueDecomposition eigen = A.GetEigenvalueDecomposition();
Console.WriteLine("D = ");
Console.WriteLine(eigen.DiagonalMatrix.ToString());
Console.WriteLine("lambda = ");
foreach (double eigenvalue in eigen.RealEigenvalues)
{
Console.WriteLine(eigenvalue);
}
Console.WriteLine();
Console.WriteLine("V = ");
Console.WriteLine(eigen.EigenvectorMatrix);
Console.WriteLine("V * D * V' = ");
Console.WriteLine(eigen.EigenvectorMatrix.Multiply(eigen.DiagonalMatrix).Multiply(eigen.EigenvectorMatrix.Transpose()));
Console.WriteLine("A * V = ");
Console.WriteLine(A.Multiply(eigen.EigenvectorMatrix));
Console.WriteLine("V * D = ");
Console.WriteLine(eigen.EigenvectorMatrix.Multiply(eigen.DiagonalMatrix));
}
