/// <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;
}
/// <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;
}
}
}
}
public static void Main(System.String[] argv)
{
/*
| Tests LU, QR, SVD and symmetric Eig decompositions.
|
| n = order of magic square.
| trace = diagonal sum, should be the magic sum, (n^3 + n)/2.
| max_eig = maximum eigenvalue of (A + A')/2, should equal trace.
| rank = linear algebraic rank,
| should equal n if n is odd, be less than n if n is even.
| cond = L_2 condition number, ratio of singular values.
| lu_res = test of LU factorization, norm1(L*U-A(p,:))/(n*eps).
| qr_res = test of QR factorization, norm1(Q*R-A)/(n*eps).
*/
print("\n Test of GeneralMatrix Class, using magic squares.\n");
print(" See MagicSquareExample.main() for an explanation.\n");
print("\n n trace max_eig rank cond lu_res qr_res\n\n");
System.DateTime start_time = System.DateTime.Now;
double eps = System.Math.Pow(2.0, - 52.0);
for (int n = 3; n <= 32; n++)
{
print(fixedWidthIntegertoString(n, 7));
GeneralMatrix M = magic(n);
//UPGRADE_WARNING: Narrowing conversions may produce unexpected results in C#. 'ms-help://MS.VSCC.2003/commoner/redir/redirect.htm?keyword="jlca1042"'
int t = (int) M.Trace();
print(fixedWidthIntegertoString(t, 10));
EigenvalueDecomposition E = new EigenvalueDecomposition(M.Add(M.Transpose()).Multiply(0.5));
double[] d = E.RealEigenvalues;
print(fixedWidthDoubletoString(d[n - 1], 14, 3));
int r = M.Rank();
print(fixedWidthIntegertoString(r, 7));
double c = M.Condition();
print(c < 1 / eps ? fixedWidthDoubletoString(c, 12, 3):" Inf");
LUDecomposition LU = new LUDecomposition(M);
GeneralMatrix L = LU.L;
GeneralMatrix U = LU.U;
int[] p = LU.Pivot;
GeneralMatrix R = L.Multiply(U).Subtract(M.GetMatrix(p, 0, n - 1));
double res = R.Norm1() / (n * eps);
print(fixedWidthDoubletoString(res, 12, 3));
QRDecomposition QR = new QRDecomposition(M);
GeneralMatrix Q = QR.Q;
R = QR.R;
R = Q.Multiply(R).Subtract(M);
res = R.Norm1() / (n * eps);
print(fixedWidthDoubletoString(res, 12, 3));
print("\n");
}
System.DateTime stop_time = System.DateTime.Now;
double etime = (stop_time.Ticks - start_time.Ticks) / 1000.0;
print("\nElapsed Time = " + fixedWidthDoubletoString(etime, 12, 3) + " seconds\n");
print("Adios\n");
}
private void UseGeneralMatrix(out Matrix eigenvals, out Matrix eigenvecs)
{
if (AllElementsReal == false)
throw new Exception("All matrix elements must be real to diagonalize.");
double[][] eles = new double[Rows][];
for (int i = 0; i < Rows; i++)
eles[i] = new double[Columns];
for (int i = 0; i < Rows; i++)
{
for (int j = 0; j < Columns; j++)
{
eles[i][j] = this[i, j].RealPart;
}
}
GeneralMatrix matrix = new GeneralMatrix(eles);
EigenvalueDecomposition evs = new EigenvalueDecomposition(matrix);
GeneralMatrix vectors = evs.GetV();
eigenvecs = new Matrix(Rows, Columns);
for (int i = 0; i < Rows; i++)
{
for (int j = 0; j < Columns; j++)
{
eigenvecs[i, j] = vectors.GetElement(i, j);
}
}
double[] values = evs.RealEigenvalues;
double[] valimag = evs.ImagEigenvalues;
eigenvals = new Matrix(Rows, 1);
for (int i = 0; i < Rows; i++)
{
eigenvals[i, 0] = new Complex(values[i], valimag[i]);
}
}
/// <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>
/// 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;
}
