/// <summary>
/// 共分散行列を計算する。
/// Calculate the covariance matrix.
/// </summary>
/// <param name="designMatrix"></param>
/// <returns></returns>
public static double[,] Variance_Covariance_Matrix(double[,] designMatrix)
{
double[,] average = DesignMatrix.Average(designMatrix);
double[,] variance_Covariance_Matrix
= new double[designMatrix.GetLength(1), designMatrix.GetLength(1)];
//分散・共分散行列の要素[j,k]を計算する。
for (int j = 0; j < designMatrix.GetLength(1); j++)
{
for (int k = j; k < designMatrix.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 < designMatrix.GetLength(0); n++)
{
variance_Covariance_Matrix[j, k] += designMatrix[n, j] * designMatrix[n, k];
}
variance_Covariance_Matrix[j, k] /= designMatrix.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);
}
/// <summary>
/// 各要素の標準偏差を計算する
/// </summary>
/// <param name="designMatrix"></param>
/// <returns></returns>
public static double[,] StandardDeviation(double[,] designMatrix)
{
double[,] average = DesignMatrix.Average(designMatrix);
double[,] average_square = new double[1, designMatrix.GetLength(1)];
for (int k = 0; k < designMatrix.GetLength(1); k++)
{
for (int j = 0; j < designMatrix.GetLength(0); j++)
{
average_square[0, k] += designMatrix[j, k] * designMatrix[j, k];
}
average_square[0, k] /= designMatrix.GetLength(0);
}
double[,] result = new double[1, designMatrix.GetLength(1)];
for (int k = 0; k < designMatrix.GetLength(1); k++)
{
result[0, k] = Math.Sqrt(average_square[0, k] - average[0, k] * average[0, k]);
}
return(result);
}
/// <summary>
/// 共分散行列の逆行列
/// Calculate Inverse of the covariance matrix.
/// </summary>
/// <param name="designMatrix"></param>
/// <returns></returns>
public static double[,] Inverse_Variance_Covariance_Matrix(double[,] designMatrix)
{
return(Matrix.Inverse_of_a_Matrix(DesignMatrix.Variance_Covariance_Matrix(designMatrix)));
}
/// <summary>
/// 相関係数の行列を得る
/// </summary>
/// <param name="designMatrix"></param>
/// <returns></returns>
public static double[,] CorelationMatrix(double[,] designMatrix)
{
double[,] average = DesignMatrix.Average(designMatrix);
double[,] corelationMatrix
= new double[designMatrix.GetLength(1), designMatrix.GetLength(1)];
//分散・共分散行列の要素[j,k]を計算する。
for (int j = 0; j < designMatrix.GetLength(1); j++)
{
for (int k = j; k < designMatrix.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 < designMatrix.GetLength(0); n++)
{
corelationMatrix[j, k] += designMatrix[n, j] * designMatrix[n, k];
}
corelationMatrix[j, k] /= designMatrix.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]
corelationMatrix[j, k] -= average[0, j] * average[0, k];
//j , kを入れ替えても値は同じ
corelationMatrix[k, j] = corelationMatrix[j, k];
}
}
//対角成分は正の数
bool minus = false;
for (int j = 0; j < corelationMatrix.GetLength(0); j++)
{
if (corelationMatrix[j, j] < 0)
{
minus = true; break;
}
}
if (minus)
{
for (int j = 0; j < corelationMatrix.GetLength(0); j++)
{
for (int k = 0; k < corelationMatrix.GetLength(1); k++)
{
corelationMatrix[j, k] *= -1;
}
}
}
double[] std = new double[corelationMatrix.GetLength(0)];
for (int j = 0; j < corelationMatrix.GetLength(0); j++)
{
std[j] = Math.Sqrt(corelationMatrix[j, j]);
}
for (int j = 0; j < corelationMatrix.GetLength(0); j++)
{
for (int k = 0; k < corelationMatrix.GetLength(1); k++)
{
corelationMatrix[j, k] /= std[j] * std[k];
}
}
return(corelationMatrix);
}