/// <summary>
/// 四分位数を計算する。
/// </summary>
/// <param name="designMatrix"></param>
/// <returns></returns>
public static double[,] Lower_Quartile_Sample(double[,] designMatrix)
{
//配列を昇順に並べ替える。
double[,] sorted = InferentialStatistics.Sorted_in_Ascending_Order(designMatrix);
double[,] lowerQuartile = new double[1, sorted.GetLength(1)];
//四分位数は、要素数を4で割ったときのあまりで計算が異なる。
int lower_quartile_point = sorted.GetLength(0) / 4;
if (sorted.GetLength(0) % 4 < 2)
{
for (int j = 0; j < sorted.GetLength(1); j++)
{
lowerQuartile[0, j] = (sorted[lower_quartile_point, j] + sorted[Math.Max(lower_quartile_point - 1, 0), j]) / 2;
}
}
else
{
for (int j = 0; j < sorted.GetLength(1); j++)
{
lowerQuartile[0, j] = sorted[lower_quartile_point, j];
}
}
return(lowerQuartile);
}
/// <summary>
/// 中央値を計算する
/// </summary>
/// <param name="designMatrix"></param>
/// <returns></returns>
public static double[,] Median(double[,] designMatrix)
{
//配列を昇順に並べ替える。
double[,] sorted = InferentialStatistics.Sorted_in_Ascending_Order(designMatrix);
double[,] median = new double[1, sorted.GetLength(1)];
//中央値は、要素数を2で割ったときのあまりで計算が異なる。
int median_point = sorted.GetLength(0) / 2;
if (sorted.GetLength(0) % 2 == 0)
{
for (int j = 0; j < sorted.GetLength(1); j++)
{
median[0, j] = (sorted[median_point, j] + sorted[Math.Max(median_point - 1, 0), j]) / 2;
}
}
else
{
for (int j = 0; j < sorted.GetLength(1); j++)
{
median[0, j] = sorted[median_point, j];
}
}
return(median);
}
/// <summary>
/// 相関係数を計算する。
/// </summary>
/// <param name="designMatrix"></param>
/// <returns></returns>
public static double[,] Correlation_Matrix_Sample(double[,] designMatrix)
{
//分散共分散行列
double[,] variance_Covariance_Matrix = InferentialStatistics.Variance_Covariance_Matrix_Nonbias(designMatrix);
//標準偏差を計算する
double[] std = new double[designMatrix.GetLength(1)];
for (int j = 0; j < variance_Covariance_Matrix.GetLength(0); j++)
{
std[j] = Math.Sqrt(variance_Covariance_Matrix[j, j]);
}
//相関係数行列
double[,] CorrelationMatrix
= new double[designMatrix.GetLength(1), designMatrix.GetLength(1)];
//相関係数を計算する。
for (int i = 0; i < CorrelationMatrix.GetLength(0); i++)
{
for (int j = 0; j < CorrelationMatrix.GetLength(1); j++)
{
CorrelationMatrix[i, j] = variance_Covariance_Matrix[i, j] / std[i] / std[j];
}
}
return(CorrelationMatrix);
}
/// <summary>
/// [0,*] 最小値
/// [1,*] 第一四分位数
/// [2,*] 中央値
/// [3,*] 平均値
/// [4,*] 第三四分位数
/// [5,*] 最大値
/// [6,*] 偏差平方和
/// [7,*] 不偏分散
/// [8,*] 不偏標準偏差
/// </summary>
/// <param name="design_Matrix"></param>
/// <returns></returns>
public static double[,] Summary(double[,] designMatrix)
{
//配列を昇順に並べ替える。
double[,] sorted = InferentialStatistics.Sorted_in_Ascending_Order(designMatrix);
double[,] summary = new double[9, sorted.GetLength(1)];
//[0,*] 最小値 and [5,*] 最大値
for (int j = 0; j < summary.GetLength(1); j++)
{
summary[0, j] = sorted[0, j];
summary[5, j] = sorted[sorted.GetLength(0) - 1, j];
}
//[3,*] 平均値
for (int j = 0; j < sorted.GetLength(1); j++)
{
for (int i = 0; i < sorted.GetLength(0); i++)
{
summary[3, j] += sorted[i, j];
}
summary[3, j] /= sorted.GetLength(0);
}
//[2,*] 中央値
int median_point = sorted.GetLength(0) / 2;
if (sorted.GetLength(0) % 2 == 0)
{
for (int j = 0; j < sorted.GetLength(1); j++)
{
summary[2, j] = (sorted[median_point, j] + sorted[Math.Max(median_point - 1, 0), j]) / 2;
}
}
else
{
for (int j = 0; j < sorted.GetLength(1); j++)
{
summary[2, j] = sorted[median_point, j];
}
}
//[1,*] 第一四分位数
//[4,*] 第三四分位数
int lower_quartile_point = sorted.GetLength(0) / 4;
int upper_quartile_point = Math.Max(sorted.GetLength(0) - sorted.GetLength(0) / 4, 0);
if (sorted.GetLength(0) % 4 < 2)
{
for (int j = 0; j < sorted.GetLength(1); j++)
{
summary[1, j] = (sorted[lower_quartile_point, j] + sorted[Math.Max(lower_quartile_point - 1, 0), j]) / 2;
summary[4, j] = (sorted[upper_quartile_point, j] + sorted[Math.Max(upper_quartile_point - 1, 0), j]) / 2;
}
}
else
{
upper_quartile_point = Math.Max(upper_quartile_point - 1, 0);
for (int j = 0; j < sorted.GetLength(1); j++)
{
summary[1, j] = sorted[lower_quartile_point, j];
summary[4, j] = sorted[upper_quartile_point, j];
}
}
//[6,*] 偏差平方和
for (int i = 0; i < designMatrix.GetLength(0); i++)
{
for (int j = 0; j < designMatrix.GetLength(1); j++)
{
summary[6, j] += (designMatrix[i, j] - summary[3, j]) * (designMatrix[i, j] - summary[3, j]);
}
}
//[7,*] 不偏分散
//[8,*] 不偏標準偏差
for (int j = 0; j < designMatrix.GetLength(1); j++)
{
summary[7, j] = summary[6, j] / (designMatrix.GetLength(0) - 1);
summary[8, j] = Math.Sqrt(summary[7, j]);
}
return(summary);
}