/// <returns>true if 'm' is symmetric up to a small epsilon constant</returns>
public static bool IsSymmetric(DotNetMatrix.GeneralMatrix m)
{
const double EPS = 1e-6;
DotNetMatrix.GeneralMatrix Z = m.Transpose();
Z = Z.Subtract(m);
return (Z.NormInf() < EPS);
}
public static String ToString(DotNetMatrix.GeneralMatrix m)
{
System.Text.StringBuilder result = new System.Text.StringBuilder();
for (int i = 0; i < m.RowDimension; i++) {
for (int j = 0; j < m.ColumnDimension; j++) {
result.Append(m.GetElement(i, j));
result.Append(" ");
}
result.Append("\n");
}
return result.ToString();
}
public static bool IsDiagonal(DotNetMatrix.GeneralMatrix m)
{
const double EPS = 1e-6;
for (int i = 0; i < m.RowDimension; i++)
for (int j = 0; j < m.ColumnDimension; j++)
if ((i != j) && (Math.Abs(m.GetElement(i, j)) > EPS))
return false;
return true;
}
/// <summary>
/// Returns true when the matrix is diagonal and has only exact 0, +1 and/or -1 entries on the diagonal.
/// </summary>
/// <param name="m">the (square) matrix</param>
/// <returns></returns>
public static bool IsSimpleDiagonal(DotNetMatrix.GeneralMatrix m)
{
for (int i = 0; i < m.RowDimension; i++)
for (int j = 0; j < m.ColumnDimension; j++)
{
double v = m.GetElement(i, j);
if ((i != j) && (v != 0.0))
return false;
else if (i == j) {
if (!((v == 0.0) || (v == 1.0) || (v == -1.0)))
return false;
}
}
return true;
}
/// <returns>true when exact 'value' is anywhere on the diagonal.</returns>
public static bool HasValueOnDiagonal(DotNetMatrix.GeneralMatrix m, double value)
{
for (int i = 0; i < Math.Min(m.RowDimension, m.ColumnDimension); i++)
{
if (m.GetElement(i, i) == value) return true;
}
return false;
}
/// <summary>Creates a new instance of Metric</summary>
/// <param name="m">The NxN metric matrix</param>
public Metric(DotNetMatrix.GeneralMatrix m)
{
init(m); // forward call to init()
}
/// <summary>Initializes this Metric object from metric matrix (called by constructor) </summary>
/// <param name="m">The NxN metric matrix</param>
private void init(DotNetMatrix.GeneralMatrix m)
{
if (!Util.IsSymmetric(m))
throw new Exception("The metric matrix must be symmetric");
m_matrix = m.Copy();
// System.Console.WriteLine("m_matrix: " + Util.ToString(m_matrix));
// compute eigen value decomposition
m_eig = new DotNetMatrix.EigenvalueDecomposition(m_matrix);
// System.Console.WriteLine("m_eig: " + Util.ToString(m_eig.GetV()));
m_invEigMatrix = m_eig.GetV().Transpose();
m_eigenMetric = m_eig.RealEigenvalues;
// {
// DotNetMatrix.GeneralMatrix D = Util.Diagonal(m_eigenMetric);
// DotNetMatrix.GeneralMatrix tmp = m_eig.GetV().Multiply(D).Multiply(m_invEigMatrix);
// System.Console.WriteLine("input_matrix = " + Util.ToString(tmp));
// }
m_isDiagonal = Util.IsDiagonal(m_matrix);
if (!m_isDiagonal)
{
m_isEuclidean = m_isAntiEuclidean = false;
}
else
{
m_isEuclidean = m_isAntiEuclidean = true;
for (int i = 0; i < m.RowDimension; i++)
{
if (m_matrix.GetElement(i, i) != 1.0)
m_isEuclidean = false;
if (m_matrix.GetElement(i, i) != -1.0)
m_isAntiEuclidean = false;
}
}
}
/// <summary>
/// Transforms a basis blade to another basis which is represented by the columns of M.
/// </summary>
/// <param name="a">The basis blade to transform according to <paramref name="M"/>.</param>
/// <param name="M">The matrix to use to transform <paramref name="a"/>.</param>
/// <returns>a list of BasisBlade whose sum represents <paramref name="a"/> on the new basis.</returns>
public static ArrayList Transform(BasisBlade a, DotNetMatrix.GeneralMatrix M)
{
ArrayList A = new ArrayList();
A.Add(new BasisBlade(0, a.scale, a.symScale)); // start with just the scalar part;
int dim = M.RowDimension;
// for each 1 bit: convert to list of blades
int i = 0;
uint b = a.bitmap;
while (b != 0) {
if ((b & 1) != 0) {
// take column 'i' out of the matrix, wedge it to 'A'
ArrayList tmp = new ArrayList();
for (int j = 0; j < dim; j++) {
double m = M.GetElement(j, i);
if (m != 0.0) {
for (int k = 0; k < A.Count; k++)
{
BasisBlade o = BasisBlade.op((BasisBlade)A[k], new BasisBlade((uint)(1 << j), m));
if (o.scale != 0.0) tmp.Add(o);
}
}
}
A = tmp;
}
b >>= 1;
i++;
}
return A;
}
/// <summary>
/// Constructor where caller determines the value of all fields (used internally by RoundEigenMetric())
/// </summary>
protected Metric(DotNetMatrix.GeneralMatrix matrix,
DotNetMatrix.EigenvalueDecomposition eig, double[] eigenMetric,
DotNetMatrix.GeneralMatrix invEigMatrix, bool isDiagonal,
bool isEuclidean, bool isAntiEuclidean)
{
m_eigenMetric = eigenMetric;
m_matrix = matrix;
m_eig = eig;
m_eigenMetric = eigenMetric;
m_invEigMatrix = invEigMatrix;
m_isDiagonal = isDiagonal;
m_isEuclidean = isEuclidean;
m_isAntiEuclidean = isAntiEuclidean;
}
