public static double Corr(Vector bfactor1, Vector bfactor2, bool ignore_nan = false)
{
double hcorr = HMath.HCorr(bfactor1, bfactor2, ignore_nan);
if (HDebug.IsDebuggerAttached)
{
double corr = double.NaN;
using (new Matlab.NamedLock("CORR"))
{
Matlab.Clear("CORR");
Matlab.PutVector("CORR.bfactor1", bfactor1);
Matlab.PutVector("CORR.bfactor2", bfactor2);
if (ignore_nan)
{
Matlab.Execute("CORR.idxnan = isnan(CORR.bfactor1) | isnan(CORR.bfactor2);");
Matlab.Execute("CORR.bfactor1 = CORR.bfactor1(~CORR.idxnan);");
Matlab.Execute("CORR.bfactor2 = CORR.bfactor2(~CORR.idxnan);");
}
if (Matlab.GetValueInt("min(size(CORR.bfactor1))") != 0)
{
corr = Matlab.GetValue("corr(CORR.bfactor1, CORR.bfactor2)");
}
Matlab.Clear("CORR");
}
if ((double.IsNaN(hcorr) && double.IsNaN(corr)) == false)
{
HDebug.AssertTolerance(0.00000001, hcorr - corr);
}
//HDebug.ToDo("use HMath.HCorr(...) instead");
}
return(hcorr);
}
public bool CheckModeWithHess(MatrixByArr hess, double[] masses, ILinAlg la, Mode[] modes = null, double tolerance = 0.00001)
{
if (modes == null)
{
modes = ToModes(masses);
}
HessMatrix ohess = new HessMatrixDense
{
hess = modes.GetHessian(masses, la),
};
double corr = HMath.HCorr(hess.ToArray().HToArray1D(), ohess.ToArray().HToArray1D());
System.Console.Write("corr(TestHess,HessVibr:{0} ", corr);
{
HDebug.Assert(hess.ColSize == ohess.ColSize);
HDebug.Assert(hess.RowSize == ohess.RowSize);
double ltolerance = hess.ToArray().HAbs().HMax() * tolerance;
ltolerance = tolerance;
for (int c = 0; c < ohess.ColSize; c++)
{
for (int r = 0; r < ohess.RowSize; r++)
{
double v = hess[c, r];
double mwv = ohess[c, r];
double diff = Math.Abs(v - mwv);
if (diff >= ltolerance)
{
return(false);
}
}
}
}
//{
// Matrix vhess = hess / hess.ToArray().HToArray1D().HVar();
// Matrix vohess = ohess / ohess.ToArray().HToArray1D().HVar();
//
// HDebug.Assert(hess.ColSize == ohess.ColSize);
// HDebug.Assert(hess.RowSize == ohess.RowSize);
// HDebug.Assert(vhess.Size == vohess.Size);
// for(int c=0; c<vhess.ColSize; c++)
// for(int r=0; r<vhess.RowSize; r++)
// {
// double v = vhess[c,r];
// double vo = vohess[c,r];
// double diff = Math.Abs(v - vo);
// if(diff >= tolerance)
// {
// HDebug.Assert(false);
// return false;
// }
// }
//}
return(true);
}
public static double[,] ModeContribToBFactorCorr(IList <Mode> modes1, IList <Mode> modes2)
{
/// Similar to "double[] ModeContribToBFactorCorr(bfactor1, modes2)",
/// the correlation between bfactor1 and bfactor 2 can be decomposed as
/// the list of correlation contributions by "normalized bfactor by modes1.m_i"
/// and "normalized bfactor by modes2.m_j"
/// in a matrix form.
///
/// therefore, the correlation of bfactor1 and bfactor(modes2) is determined as their normalized dot-product:
/// corr = dot(nbfactor1, nbfactor2) / (n-1)
/// = 1/(n-1) * dot(nbfactor1, nmwbfactor(modes2.m1) + nmwbfactor(modes2.m2) + ... )
/// = 1/(n-1) * ( dot(nbfactor1, nmwbfactor(modes2.m1)) + dot(nbfactor1, nmwbfactor(modes2.m2)) + ... )
/// = 1/(n-1) * ( dot(nmwbfactor(modes1.m1), nmwbfactor(modes2.m1)) + dot(nmwbfactor(modes1.m1), nmwbfactor(modes2.m2)) + ...
/// dot(nmwbfactor(modes1.m2), nmwbfactor(modes2.m1)) + dot(nmwbfactor(modes1.m2), nmwbfactor(modes2.m2)) + ... )
/// = 1/(n-1) * sum_{ i1=1..m1, i2=1..m2 } dot(nmwbfactor(modes1.m_i), nmwbfactor(modes2.m_j))
/// = sum_{ i1=1..m1, i2=1..m2 } dot(nmwbfactor(modes1.m_i), nmwbfactor(modes2.m_j))/(n-1)
/// = sum_{ i1=1..m1, i2=1..m2 } "correlation contribution by modes1.m_i and modes2.m_j"
///
Vector[] nbfactor1mw = GetBFactorModewiseNormalized(modes1);
Vector[] nbfactor2mw = GetBFactorModewiseNormalized(modes2);
int n = nbfactor1mw[0].Size;
int m1 = modes1.Count; HDebug.Assert(nbfactor1mw.Length == m1);
int m2 = modes2.Count; HDebug.Assert(nbfactor2mw.Length == m2);
MatrixByArr contrib = new double[m1, m2];
for (int i1 = 0; i1 < m1; i1++)
{
for (int i2 = 0; i2 < m2; i2++)
{
HDebug.Assert(nbfactor1mw[i1].Size == n);
HDebug.Assert(nbfactor2mw[i2].Size == n);
contrib[i1, i2] = LinAlg.VtV(nbfactor1mw[i1], nbfactor2mw[i2]) / (n - 1);
}
}
if (HDebug.IsDebuggerAttached)
{
Vector bfactor1 = modes1.GetBFactor().ToArray();
Vector nbfactor1 = GetBFactorNormalized(bfactor1);
Vector bfactor2 = modes2.GetBFactor().ToArray();
Vector nbfactor2 = GetBFactorNormalized(bfactor2);
double corr0 = HMath.HCorr(bfactor1, bfactor2);
double corr1 = LinAlg.VtV(nbfactor1, nbfactor2) / (n - 1);
double corr2 = contrib.ToArray().HSum();
HDebug.AssertTolerance(0.00000001, corr0 - corr1, corr0 - corr2, corr1 - corr2);
}
return(contrib);
}
public static double[] ModeContribToBFactorCorr(Vector bfactor1, IList <Mode> modes2)
{
/// the correlation(corr) of two bfactors (bfactor1, bfactor 2) is the same to
/// the dot product of their normalizeds (mean 0, variance 1):
/// corr = Math.HCorr( bfactor1, bfactor2)
/// = Math.HCorr(nbfactor1, nbfactor2)
/// = LinAlg.VtV(nbfactor1, nbfactor2) (for biased estimation)
/// = LinAlg.VtV(nbfactor1, nbfactor2) / (n-1) (for unbiased estimation)
///
/// bfactor of mode(m1,m2,...) can be determined by the sum of bfactors of each mode:
/// bfactor(mode) = bfactor(m1) + bfactor(m2) + ...
///
/// in the similar manner, the normalized bfactor of mode(m1,m2,...) is determined by
/// sum of normalized-modewise-bfactor (GetBFactorModewiseNormalized):
/// normal-bfactor(mode) = nmwbfactor(m1) + nmwbfactor(m2) + ...
///
/// therefore, the correlation of bfactor1 and bfactor(modes2) is determined as their normalized dot-product:
/// corr = dot(nbfactor1, nbfactor2) / (n-1)
/// = dot(nbfactor1, nmwbfactor(modes2.m1) + nmwbfactor(modes2.m2) + ... ) / (n-1)
/// = dot(nbfactor1, nmwbfactor(modes2.m1))/(n-1) + dot(nbfactor1, nmwbfactor(modes2.m2)) / (n-1) + ...
///
Vector nbfactor1 = GetBFactorNormalized(bfactor1);
Vector[] nbfactor2mw = GetBFactorModewiseNormalized(modes2);
int n = bfactor1.Size;
int m = modes2.Count;
HDebug.Assert(nbfactor2mw.Length == m);
Vector contrib = new double[m];
for (int i = 0; i < m; i++)
{
contrib[i] = LinAlg.VtV(nbfactor1, nbfactor2mw[i]) / (n - 1);
}
if (HDebug.IsDebuggerAttached)
{
Vector bfactor2 = modes2.GetBFactor().ToArray();
Vector nbfactor2 = GetBFactorNormalized(bfactor2);
double corr0 = HMath.HCorr(bfactor1, bfactor2);
double corr1 = LinAlg.VtV(nbfactor1, nbfactor2) / (n - 1);
double corr2 = contrib.Sum();
HDebug.AssertTolerance(0.00000001, corr0 - corr1, corr0 - corr2, corr1 - corr2);
}
return(contrib);
}