/// <summary>
/// 回傳數列中最明顯的 Change Point。
/// </summary>
/// <param name="d">The numeric array which use to run change point procedure. Missing value (1.23456E+30) element is not allow in the array.</param>
/// <param name="conf">The confidence level used to test whether it is a significant change point</param>
/// <param name="N">Number of boostrap</param>
/// <returns></returns>
public static ChangePointInfo ChangePointOnSingleCase(double[] d, double conf = 0.9, int N = 1000)
{
if (d.Length < 7)
{
return new ChangePointInfo()
{
Index = -1
}
}
;
if (d.Any(x => x >= MtbTools.MISSINGVALUE))
{
throw new ArgumentException("數列中包含遺失值");
}
LinearAlgebra.Vector <double> xs = LinearAlgebra.Vector <double> .Build.DenseOfArray(d);
double xbar = xs.Average();
xs = xs - xbar; //Xi-Xbar
LinearAlgebra.Vector <double> si
= LinearAlgebra.Vector <double> .Build.DenseOfArray(MathTool.PartialSum(xs.ToArray()));
int changepointindex = si.AbsoluteMaximumIndex();
double sdiff = si.Maximum() - si.Minimum();
double[] Sdiff_boostrap = new double[N];
for (int i = 0; i < N; i++)
{
double[] si_boostrap = MathTool.PartialSum(MathTool.RandomSample(xs.ToArray()).Cast <double>().ToArray());
Sdiff_boostrap[i] = si_boostrap.Max() - si_boostrap.Min();
}
double confLv = (double)Sdiff_boostrap.Where(x => x < sdiff).Count() / N;
if (confLv < conf)
{
return new ChangePointInfo()
{
Index = -1
}
}
; //Not significant
return(new ChangePointInfo()
{
Index = changepointindex, Sdiff = sdiff, ConfidenceLevel = confLv
});
}
/// <summary>
/// 計算數列各元素的累積和
/// </summary>
/// <param name="x">要處理的陣列，合法的輸入是 double[]</param>
/// <returns></returns>
public static double[] PartialSum(double[] x)
{
LinearAlgebra.Vector <double> vx
= LinearAlgebra.Double.DenseVector.OfArray(x);
int row = vx.Count;
int col = row;
LinearAlgebra.Matrix <double> lmat
= LinearAlgebra.Matrix <double> .Build.Dense(row, col, 1);
lmat = lmat.LowerTriangle();
LinearAlgebra.Vector <double> result
= lmat.Multiply(vx);
return(result.ToArray());
}