private static double EstimateDensity(double x, double y, double[,] data, double[,] hinv)
{
double result = 0;
for (int i = 0; i < data.GetLength(0); i++)
{
double[] w = new double[] { x - data[i, 0], y - data[i, 1] };
double[] b = NumUtil.MatrixTimesVector(hinv, w);
result += NumUtil.StandardGaussian(b);
}
result *= NumUtil.Determinant2x2(hinv) / data.Length;
return(result);
}
private static void Invert(double[,] falseData, double[,] trueData, double falseP, out double[] xRes,
out double[] yRes, out double[,] zRes, out double[,] forwardOut, out double[,] reverseOut,
bool debug)
{
double xmin = double.MaxValue;
double xmax = -double.MaxValue;
double ymin = double.MaxValue;
double ymax = -double.MaxValue;
for (int i = 0; i < falseData.GetLength(0); i++)
{
double xx = falseData[i, 0];
double yy = falseData[i, 1];
if (xx < xmin)
{
xmin = xx;
}
if (xx > xmax)
{
xmax = xx;
}
if (yy < ymin)
{
ymin = yy;
}
if (yy > ymax)
{
ymax = yy;
}
}
for (int i = 0; i < trueData.GetLength(0); i++)
{
double xx = trueData[i, 0];
double yy = trueData[i, 1];
if (xx < xmin)
{
xmin = xx;
}
if (xx > xmax)
{
xmax = xx;
}
if (yy < ymin)
{
ymin = yy;
}
if (yy > ymax)
{
ymax = yy;
}
}
double dx = xmax - xmin;
xmin -= 0.1 * dx;
xmax += 0.1 * dx;
double dy = ymax - ymin;
ymin -= 0.1 * dy;
ymax += 0.1 * dy;
double[] falseX;
double[] falseY;
double[,] falseZ;
int n = trueData.GetLength(0);
double[,] cov = NumUtil.CalcCovariance(trueData);
double fact = Math.Pow(n, 1.0 / 6.0);
double[,] hinv = null;
try {
hinv = NumUtil.ApplyFunction(cov, delegate(double w) { return(fact / Math.Sqrt(w)); });
} catch {
}
if (hinv == null || !IsValidMatrix(hinv))
{
xRes = null;
yRes = null;
zRes = null;
forwardOut = null;
reverseOut = null;
return;
}
EstimateBivariateDensity(falseData, out falseX, out falseY, out falseZ, xmin, xmax, ymin, ymax, hinv);
double[] trueX;
double[] trueY;
double[,] trueZ;
EstimateBivariateDensity(trueData, out trueX, out trueY, out trueZ, xmin, xmax, ymin, ymax, hinv);
double[] x = UnifySupport(falseX, trueX);
double[] y = UnifySupport(falseY, trueY);
falseZ = Interpolate(x, y, falseX, falseY, falseZ);
trueZ = Interpolate(x, y, trueX, trueY, trueZ);
double[,] inverse = new double[x.Length, y.Length];
for (int i = 0; i < x.Length; i++)
{
for (int j = 0; j < y.Length; j++)
{
inverse[i, j] = falseZ[i, j] <= 0 ? double.Epsilon : Math.Max((falseZ[i, j] * 0.5) / trueZ[i, j], double.Epsilon);
}
}
for (int j = 0; j < y.Length; j++)
{
double maxVal = double.MinValue;
int maxInd = -1;
for (int i = 0; i < x.Length; i++)
{
if (inverse[i, j] > maxVal)
{
maxVal = inverse[i, j];
maxInd = i;
}
}
for (int i = 0; i < maxInd; i++)
{
inverse[i, j] = maxVal;
}
}
xRes = x;
yRes = y;
zRes = inverse;
if (debug)
{
forwardOut = trueZ;
reverseOut = falseZ;
}
else
{
forwardOut = null;
reverseOut = null;
}
}