public static Eigendecomp Eigendecomposition(Matrix matrix, double eps)
{
Eigendecomp result = new Eigendecomp();
result.Compute(matrix, eps);
return(result);
}
private void Swap(Eigendecomp eigendecomp, int first, int second)
{
double b = eigendecomp.Eigenvalues[first];
eigendecomp.Eigenvalues[first] = eigendecomp.Eigenvalues[second];
eigendecomp.Eigenvalues[second] = b;
Vector vec = eigendecomp.Eigenvectors[first].Copy();
eigendecomp.Eigenvectors[first] = eigendecomp.Eigenvectors[second].Copy();
eigendecomp.Eigenvectors[second] = vec;
}
private void SortEigen(Eigendecomp eigendecomp)
{
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3 - i - 1; j++)
{
if (eigendecomp.Eigenvalues[j] < eigendecomp.Eigenvalues[j + 1])
{
Swap(eigendecomp, j, j + 1);
}
}
}
}
public void Compute(Matrix matrix, double eps)
{
Matrix g = matrix.Transpose() * matrix;
Eigendecomp eigendecomp = MatrixOperations.Eigendecomposition(g, eps);
SortEigen(eigendecomp);
Vector sigma = new Vector();
for (int i = 0; i < matrix.N; i++)
{
sigma[i] = Math.Sqrt(Math.Abs(eigendecomp.Eigenvalues[i]));
}
V = new Matrix();
S = Matrix.ZeroMatrix();
U = new Matrix(eigendecomp.Eigenvectors);
List <Vector> v = new List <Vector>();
for (int i = 0; i < matrix.N; i++)
{
S[i, i] = sigma[i];
v.Add(matrix * U.GetColumn(i) / sigma[i]);
}
V = new Matrix(v);
}
