public static void Calculate_YGradient(Vector[] X, double[] Y, out Vector Center_X, out Vector[] DX, out double Center_Y, out Vector Gradient)
{
int N = X.Length;
Vector X_c = Vector.Average(X);
Vector Sum_DX = new Vector(2);
double Sum_Y = 0.0D;
Vector Sum_YDX = new Vector(2);
DX = new Vector[N];
for (int i = 0; i < N; i++)
{
DX[i] = new Vector(2);
DX[i] = X[i] - X_c;
Sum_DX += DX[i];
}
OOPTools_Math.Matrix_Jagged M = new OOPTools_Math.Matrix_Jagged(2, 2);
for (int i = 0; i < N; i++)
{
M += OOPTools_Math.Matrix_Jagged.TensorProduct(DX[i], DX[i]);
}
Matrix_Jagged A = new Matrix_Jagged(3, 3);
A.Values[0][0] = Convert.ToDouble(N);
A.Values[0][1] = Sum_DX.Values[0];
A.Values[0][2] = Sum_DX.Values[1];
A.Values[1][0] = Sum_DX.Values[0];
A.Values[1][1] = M.Values[0][0];
A.Values[1][2] = M.Values[0][1];
A.Values[2][0] = Sum_DX.Values[1];
A.Values[2][1] = M.Values[1][0];
A.Values[2][2] = M.Values[1][1];
double DetA;
A.SolveLinearSystem_LUDecomp(out DetA);
Gradient = new Vector(2);
if (DetA < 1.0E-20)
{
Center_Y = ArrayTools.Average(Y);
}
else
{
for (int i = 0; i < N; i++)
{
Sum_Y += Y[i];
Sum_YDX += Y[i] * DX[i];
}
Vector b = new Vector(3);
b.Values[0] = Sum_Y;
b.Values[1] = Sum_YDX.Values[0];
b.Values[2] = Sum_YDX.Values[1];
Vector x = A.SolveLinearSystem_BackSub(b);
Center_Y = x.Values[0];
Gradient.Values[0] = x.Values[1];
Gradient.Values[1] = x.Values[2];
}
Center_X = X_c;
}
public double Average(Vector u)
{
return(ArrayTools.Average(u.Values));
}
public double Average()
{
return(ArrayTools.Average(Values));
}
/// <summary>
/// Return the average of the components in the vector (or this vector)
/// </summary>
/// <param name="u"></param>
/// <returns></returns>
public double Average(double[] u)
{
return(ArrayTools.Average(u));
}
