public static Matrix DMD(Vector diagmat1, Matrix mat, Vector diagmat2)
{
if (DMD_selftest)
#region selftest
{
HDebug.ToDo("check");
DMD_selftest = false;
Vector td1 = new double[] { 1, 2, 3 };
Vector td2 = new double[] { 4, 5, 6 };
Matrix tm = new double[, ] {
{ 1, 2, 3 }, { 4, 5, 6 }, { 7, 8, 9 }
};
Matrix dmd0 = LinAlg.Diag(td1) * tm * LinAlg.Diag(td2);
Matrix dmd1 = LinAlg.DMD(td1, tm, td2);
double err = (dmd0 - dmd1).HAbsMax();
HDebug.Assert(err == 0);
}
#endregion
Matrix DMD = mat.Clone();
for (int c = 0; c < mat.ColSize; c++)
{
for (int r = 0; r < mat.RowSize; r++)
{
double v0 = mat[c, r];
double v1 = diagmat1[c] * v0 * diagmat2[r];
if (v0 == v1)
{
continue;
}
DMD[c, r] = v1;
}
}
return(DMD);
}
public static Tuple <MatrixByArr, Vector> Eig(MatrixByArr A)
{
if (HDebug.Selftest())
{
MatrixByArr tA = new double[, ] {
{ 1, 2, 3 },
{ 2, 9, 5 },
{ 3, 5, 6 }
};
MatrixByArr tV = new double[, ] {
{ -0.8879, 0.3782, 0.2618 },
{ -0.0539, -0.6508, 0.7573 },
{ 0.4568, 0.6583, 0.5983 }
};
Vector tD = new double[] { -0.4219, 2.7803, 13.6416 };
Tuple <MatrixByArr, Vector> tVD = Eig(tA);
Vector tV0 = tVD.Item1.GetColVector(0); double tD0 = tVD.Item2[0];
Vector tV1 = tVD.Item1.GetColVector(1); double tD1 = tVD.Item2[1];
Vector tV2 = tVD.Item1.GetColVector(2); double tD2 = tVD.Item2[2];
HDebug.AssertTolerance(0.00000001, 1 - LinAlg.VtV(tV0, tV0));
HDebug.AssertTolerance(0.00000001, 1 - LinAlg.VtV(tV1, tV1));
HDebug.AssertTolerance(0.00000001, 1 - LinAlg.VtV(tV2, tV2));
MatrixByArr tAA = tVD.Item1 * LinAlg.Diag(tVD.Item2) * tVD.Item1.Tr();
HDebug.AssertTolerance(0.00000001, tA - tAA);
//HDebug.AssertTolerance(0.0001, VD.Item1-tV);
HDebug.AssertTolerance(0.0001, tVD.Item2 - tD);
}
HDebug.Assert(A.ColSize == A.RowSize);
double[] eigval;
double[,] eigvec;
#region bool alglib.smatrixevd(double[,] a, int n, int zneeded, bool isupper, out double[] d, out double[,] z)
/// Finding the eigenvalues and eigenvectors of a symmetric matrix
///
/// The algorithm finds eigen pairs of a symmetric matrix by reducing it to
/// tridiagonal form and using the QL/QR algorithm.
///
/// Input parameters:
/// A - symmetric matrix which is given by its upper or lower
/// triangular part.
/// Array whose indexes range within [0..N-1, 0..N-1].
/// N - size of matrix A.
/// ZNeeded - flag controlling whether the eigenvectors are needed or not.
/// If ZNeeded is equal to:
/// * 0, the eigenvectors are not returned;
/// * 1, the eigenvectors are returned.
/// IsUpper - storage format.
///
/// Output parameters:
/// D - eigenvalues in ascending order.
/// Array whose index ranges within [0..N-1].
/// Z - if ZNeeded is equal to:
/// * 0, Z hasn’t changed;
/// * 1, Z contains the eigenvectors.
/// Array whose indexes range within [0..N-1, 0..N-1].
/// The eigenvectors are stored in the matrix columns.
///
/// Result:
/// True, if the algorithm has converged.
/// False, if the algorithm hasn't converged (rare case).
///
/// -- ALGLIB --
/// Copyright 2005-2008 by Bochkanov Sergey
///
/// public static bool alglib.smatrixevd(
/// double[,] a,
/// int n,
/// int zneeded,
/// bool isupper,
/// out double[] d,
/// out double[,] z)
#endregion
bool success = alglib.smatrixevd(A, A.ColSize, 1, false, out eigval, out eigvec);
if (success == false)
{
HDebug.Assert(false);
return(null);
}
return(new Tuple <MatrixByArr, Vector>(eigvec, eigval));
}