/// <summary>
/// 各要素の標準偏差を計算する
/// </summary>
/// <param name="design_Matrix"></param>
/// <returns></returns>
public static double[,] Standard_Deviation(double[,] design_Matrix)
{
double[,] average = Design_Matrix.Average(design_Matrix);
double[,] average_square = new double[1, design_Matrix.GetLength(1)];
for (int k = 0; k < design_Matrix.GetLength(1); k++)
{
for (int j = 0; j < design_Matrix.GetLength(0); j++)
{
average_square[0, k] += design_Matrix[j, k] * design_Matrix[j, k];
}
average_square[0, k] /= design_Matrix.GetLength(0);
}
double[,] result = new double[1, design_Matrix.GetLength(1)];
for (int k = 0; k < design_Matrix.GetLength(1); k++)
{
result[0, k] = Math.Sqrt(average_square[0, k] - average[0, k] * average[0, k]);
}
return(result);
}
/// <summary>
/// 相関係数の行列を得る
/// </summary>
/// <param name="design_Matrix"></param>
/// <returns></returns>
public static double[,] Corelation_Matrix(double[,] design_Matrix)
{
double[,] average = Design_Matrix.Average(design_Matrix);
double[,] corelation_Matrix
= new double[design_Matrix.GetLength(1), design_Matrix.GetLength(1)];
//分散・共分散行列の要素[j,k]を計算する。
for (int j = 0; j < design_Matrix.GetLength(1); j++)
{
for (int k = j; k < design_Matrix.GetLength(1); k++)
{
//j次元目とk次元目の積の平均値を計算する。 E[XY]
for (int n = 0; n < design_Matrix.GetLength(0); n++)
{
corelation_Matrix[j, k] += design_Matrix[n, j] * design_Matrix[n, k];
}
corelation_Matrix[j, k] /= design_Matrix.GetLength(0);
//j次元目の平均値とk次元目の平均値の積を引く。-E[X]E[Y]
corelation_Matrix[j, k] -= average[0, j] * average[0, k];
//j , kを入れ替えても値は同じ
corelation_Matrix[k, j] = corelation_Matrix[j, k];
}
}
//対角成分は正の数
bool minus = false;
for (int j = 0; j < corelation_Matrix.GetLength(0); j++)
{
if (corelation_Matrix[j, j] < 0)
{
minus = true; break;
}
}
if (minus)
{
for (int j = 0; j < corelation_Matrix.GetLength(0); j++)
{
for (int k = 0; k < corelation_Matrix.GetLength(1); k++)
{
corelation_Matrix[j, k] *= -1;
}
}
}
double[] std = new double[corelation_Matrix.GetLength(0)];
for (int j = 0; j < corelation_Matrix.GetLength(0); j++)
{
std[j] = Math.Sqrt(corelation_Matrix[j, j]);
}
for (int j = 0; j < corelation_Matrix.GetLength(0); j++)
{
for (int k = 0; k < corelation_Matrix.GetLength(1); k++)
{
corelation_Matrix[j, k] /= std[j] * std[k];
}
}
return(corelation_Matrix);
}
/// <summary>
/// 共分散行列の逆行列
/// Calculate Inverse of the covariance matrix.
/// </summary>
/// <param name="design_Matrix"></param>
/// <returns></returns>
public static double[,] Inverse_Variance_Covariance_Matrix(double[,] design_Matrix)
{
return(Matrix.Inverse_of_a_Matrix(Design_Matrix.Variance_Covariance_Matrix(design_Matrix)));
}
/// <summary>
/// 共分散行列を計算する。
/// Calculate the covariance matrix.
/// </summary>
/// <param name="design_Matrix"></param>
/// <returns></returns>
public static double[,] Variance_Covariance_Matrix(double[,] design_Matrix)
{
/*
* double[,] average = Design_Matrix.Average(design_Matrix);
*
* double[,] variance_Covariance_Matrix
* = new double[design_Matrix.GetLength(1), design_Matrix.GetLength(1)];
*
* double[,] row_Vector = new double[1, design_Matrix.GetLength(1)];
*
* double squar = 0;
*
* for (int i = 0; i < design_Matrix.GetLength(0); i++)
* {
* //i行目のベクトルと平均値ベクトルとの差分ベクトルを求め、j列目とk列目との積を、共分散行列の要素[j,k]に加える。
* for (int j = 0; j < row_Vector.GetLength(1); j++)
* {
* row_Vector[0, j] = design_Matrix[i, j] - average[0, j];
* }
* //row_Vector = Matrix.Subtraction(Matrix.Pick_Up_Row_Vector(design_Matrix, i), average);
*
* for (int j = 0; j < row_Vector.GetLength(1); j++)
* {
* for (int k = j; k < row_Vector.GetLength(1); k++)
* {
* squar = row_Vector[0, j] * row_Vector[0, k];
* variance_Covariance_Matrix[j, k] += squar;
* if (j != k)
* {
* variance_Covariance_Matrix[k, j] += squar;
* }
* }
* }
* }
*
* //ベクトルの数で割る
* for (int j = 0; j < variance_Covariance_Matrix.GetLength(0); j++)
* {
* for (int k = 0; k < variance_Covariance_Matrix.GetLength(1); k++)
* {
* variance_Covariance_Matrix[j, k] /= design_Matrix.GetLength(0);
* }
* }
*
* return variance_Covariance_Matrix;
*/
double[,] average = Design_Matrix.Average(design_Matrix);
double[,] variance_Covariance_Matrix
= new double[design_Matrix.GetLength(1), design_Matrix.GetLength(1)];
//分散・共分散行列の要素[j,k]を計算する。
for (int j = 0; j < design_Matrix.GetLength(1); j++)
{
for (int k = j; k < design_Matrix.GetLength(1); k++)
{
//j次元目とk次元目の積の平均値を計算する。 E[XY]
for (int n = 0; n < design_Matrix.GetLength(0); n++)
{
variance_Covariance_Matrix[j, k] += design_Matrix[n, j] * design_Matrix[n, k];
}
variance_Covariance_Matrix[j, k] /= design_Matrix.GetLength(0);
//j次元目の平均値とk次元目の平均値の積を引く。-E[X]E[Y]
variance_Covariance_Matrix[j, k] -= average[0, j] * average[0, k];
//j , kを入れ替えても値は同じ
variance_Covariance_Matrix[k, j] = variance_Covariance_Matrix[j, k];
}
}
return(variance_Covariance_Matrix);
}