public static BigNumber[,] MatPlus(BigNumber[,] mat1, BigNumber[,] mat2)
{//矩阵加法
int len11 = mat1.GetLength(0);
int len12 = mat1.GetLength(1);
int len21 = mat2.GetLength(0);
int len22 = mat2.GetLength(1);
if (len11 == len21 && len12 == len22)
{
BigNumber[,] a = new BigNumber[len11, len12];
for (int i = 0; i < len11; i++)
{
for (int j = 0; j < len12; j++)
{
a[i, j] = mat1[i, j] + mat2[i, j];
}
}
return a;
}
else
{
return null;
}
}
public static BigNumber[,] MatTrans(BigNumber[,] mat)
{
//矩阵转置
int len1 = mat.GetLength(0);
int len2 = mat.GetLength(1);
BigNumber[,] a = new BigNumber[len2, len1];
for (int i = 0; i < len1; i++)
{
for (int j = 0; j < len2; j++)
{
a[j, i] = mat[i, j];
}
}
return a;
}
public static BigNumber[,] MatCorr(BigNumber[,] matrix)
{
int len1 = matrix.GetLength(0);
int len2 = matrix.GetLength(1);
BigNumber[] a1 = new BigNumber[len1 * len2];
for (int j = 0; j < len2; j++)
{
for (int i = 0; i < len1; i++)
{
a1[j * len1 + i] = matrix[i, j];
}
}
BigNumber[] a2 = new BigNumber[len1];
BigNumber[] a3 = new BigNumber[len1];
BigNumber[,] corr = new BigNumber[len2, len2];
for (int c = 1; c < len2 ;c++ )
{
for (int j = 0; j < len2 -1; j++)
{
for (int i = 0; i < len1; i++)
{
a2[i] = a1[j * len1 + i];
}
for (int i = 0; i < len1; i++)
{
a3[i] = a1[(j +1)* len1 + i];
}
try
{
corr[j, j + c] = Corr(a2, a3);
corr[j + c, j] = Corr(a2, a3);
}
catch (Exception ex)
{
}
}
}
for (int i = 0; i < len2;i ++ )
{
corr[i, i] = new BigNumber("1");
}
return corr;
}
public static BigNumber[,] MatTimes(BigNumber[,] mat1, BigNumber[,] mat2)
{ //矩阵乘法
int len11 = mat1.GetLength(0);
int len12 = mat1.GetLength(1);
int len21 = mat2.GetLength(0);
int len22 = mat2.GetLength(1);
if (len12 == len21)
{
BigNumber[,] a = new BigNumber[len11, len22];
for (int i = 0; i < len11; i++)
{
for (int j = 0; j < len22; j++)
{
for (int u = 0; u < len12; u++)
{
a[i, j] += mat1[i, u] * mat2[u, j];
}
}
}
return a;
}
else
{
return null;
}
}
public static string MutiRegR(BigNumber[,] x, BigNumber[,] y)
{ //返回多元回归拟合优度R^2 and adj_R^2
int len11 = x.GetLength(0);//x行数
int len12 = x.GetLength(1);//x列数
int len21 = y.GetLength(1);//y列数
int len22 = y.GetLength(0);//y列数
if (len21 != 1)
{
return null;
}
BigNumber ysum = new BigNumber("0");
for (int i = 0; i < len11;i++ )
{
ysum += y[i,1];
}
BigNumber ybar = ysum / (new BigNumber(len11.ToString()));
BigNumber TSS = new BigNumber("0");
for (int i = 0; i < len11; i++)
{
TSS += (y[i, 1] - ybar).Power(new BigNumber("2"));
}
BigNumber[,] b1 = MathV.MatTrans(x);
BigNumber[,] b2 = MathV.MatTimes(b1, x);
BigNumber[,] b3 = Stat.MatInv(b2, len12);
BigNumber[,] b4 = MathV.MatTimes(b3, b1);
BigNumber[,] bhat = MathV.MatTimes(b4, y);
BigNumber[,] b5 = MathV.MatTimes(x, bhat);
BigNumber[,] epsilon = MathV.MatMinu(y, b5);
BigNumber ESS = new BigNumber("0");
for (int i = 0; i < len11; i++)
{
ESS += (epsilon[i, 1]).Power(new BigNumber("2"));
}
BigNumber MSS = TSS - ESS;
BigNumber Rsquare = MSS / TSS;
BigNumber Adj_Rsquare = new BigNumber("1") - (new BigNumber("1")- Rsquare)*(new BigNumber(len11.ToString()) -new BigNumber("1") / (new BigNumber(len11.ToString()) -new BigNumber(len12.ToString()) -new BigNumber("1")));
BigNumber Fvalue = (MSS/new BigNumber(len12.ToString()))/(ESS/( new BigNumber(len11.ToString())- new BigNumber(len12.ToString()) - new BigNumber("1") ));
return Rsquare.ToString() + "," + Adj_Rsquare.ToString() + ","+ Fvalue.ToString();
}
public static BigNumber[] MutiRegP(BigNumber[,] x, BigNumber[,] y)
{ //返回多元回归P值
int len11 = x.GetLength(0);//行数
int len12 = x.GetLength(1);//列数
int len21 = y.GetLength(1);//y列数
if (len21 != 1)
{
return null;
}
BigNumber[,] b1 = MathV.MatTrans(x);
BigNumber[,] b2 = MathV.MatTimes(b1, x);
BigNumber[,] b3 = Stat.MatInv(b2, len12);
BigNumber[,] b4 = MathV.MatTimes(b3, b1);
BigNumber[,] bhat = MathV.MatTimes(b4, y);
BigNumber[,] b5 = MathV.MatTimes(x, bhat);
BigNumber[,] epsilon = MathV.MatMinu(y, b5);
BigNumber[] variance = new BigNumber[len12];
for (int i = 1; i < len11; i++)
{
variance[i] = epsilon[i, 1];
}
BigNumber sigma2 = Variance(variance) * new BigNumber(((len11 - 1) / len11).ToString());
BigNumber[,] b6 = new BigNumber[len12, len12]; //sigma^2*(C^T C)^{-1} 参数方差
for (int i = 0; i < len12; i++)
{
for (int j = 0; j < len12; j++)
{
b6[i, j] = sigma2 * b3[i, j];
}
}
BigNumber[] std_b = new BigNumber[len12];
for (int i = 0; i < len12; i++)
{
std_b[i] = b6[i, i].Power(new BigNumber("0.5"));
}
BigNumber[] tvalue_b = new BigNumber[len12];
for (int i = 0; i < len12; i++)
{
tvalue_b[i] = bhat[i, 1] / std_b[i];
}
BigNumber[] pvalue_b = new BigNumber[len12];
for (int i = 0; i < len12; i++)
{
pvalue_b[i] = new BigNumber(Stat.NORMSDIST(Convert.ToDouble(tvalue_b[i].ToString())).ToString());
}
return pvalue_b;
}
/* static void Main(string[] args)
{
BigNumber[,] dMatrix = new BigNumber[2, 2] { { new BigNumber("0"), new BigNumber("1") }, { new BigNumber("2"), new BigNumber("2") } };
BigNumber[,] dReturn = MatInv(dMatrix,2);
if (dReturn != null)
{
for (int i = 0; i < 2; i++)
Console.WriteLine(string.Format("{0} {1} ", dReturn[i, 0], dReturn[i, 1])); //输出
Console.ReadKey();
}
}*/
public static BigNumber[,] MutiRegB(BigNumber[,] x,BigNumber[,] y)
{ //返回多元回归参数估计值**************************************注意：x第一列为1*******************
int len11 = x.GetLength(0);//行数
int len12 = x.GetLength(1);//列数
BigNumber[,] b1 = MathV.MatTrans(x);
BigNumber[,] b2 = MathV.MatTimes(b1, x);
BigNumber[,] b3 = Stat.MatInv(b2, len12);
BigNumber[,] b4 = MathV.MatTimes(b3,b1);
BigNumber[,] bhat = MathV.MatTimes(b4, y);
return bhat;
}
public static string OneWayANOVA(BigNumber[,] Numberseies)
{ // 单因素方差分析
int weidu = Numberseies.Rank;
int x = Numberseies.GetLength(0);
int y = Numberseies.GetLength(1);
int z = Numberseies.Length;
BigNumber SST = new BigNumber("0");
BigNumber SSA = new BigNumber("0");
BigNumber SSW = new BigNumber("0");
BigNumber sum1 = new BigNumber("0");
BigNumber[] sum2 = new BigNumber[y];
for (int j = 0; j < y; j++)
{
for (int i = 0; i < x; i++)
{
sum1 += Numberseies[i, j];
sum2[j] += Numberseies[i, j];
}
}
BigNumber Txbar = sum1 / new BigNumber(z.ToString());
BigNumber[] Axbar = new BigNumber[y];
for (int j = 0; j < y; j++)
{
Axbar[j] = sum2[j] / new BigNumber(y.ToString());
}
for (int j = 0; j < y; j++)
{
SSA += new BigNumber(y.ToString()) * (Axbar[j] - Txbar).Power(new BigNumber("0.5"), 30);
}
for (int j = 0; j < y; j++)
{
for (int i = 0; i < x; i++)
{
SST += (Numberseies[i, j] - Txbar).Power(new BigNumber("0.5"), 30);
SSW += (Numberseies[i, j] - Axbar[j]).Power(new BigNumber("0.5"), 30);
}
}
BigNumber MSA = SSA / (new BigNumber(y.ToString()) - new BigNumber("1"));
BigNumber MSW = SSW / (new BigNumber(z.ToString()) - new BigNumber(y.ToString()));
BigNumber MST = SST / (new BigNumber(z.ToString()) - new BigNumber("1"));
BigNumber Fvalue = MSA / MSW;
return Fvalue.ToString();
}
public static string contingency(BigNumber[,] table)
{
int len11 = table.GetLength(0);//x行数
int len12 = table.GetLength(1);//x列数
BigNumber[,] fe = new BigNumber[len11, len12];//给定单元中的频数期望值
BigNumber chisq_value = new BigNumber("0");
BigNumber sum = new BigNumber("0");
BigNumber[] sum_c = new BigNumber[len12];
BigNumber[] sum_r = new BigNumber[len11];
for (int i = 0; i < len11; i++)
{
for (int j = 0; j < len12; j++)
{
sum = sum + table[i, j];
}
}
for (int j = 0; j < len12;j++ )
{
sum_c[j] = new BigNumber("0");
for(int i =0; i<len11; i++)
{
sum_c[j] += table[i,j];
}
}//对每一列求和
for (int i = 0; i < len12; i++)
{
sum_r[i] = new BigNumber("0");
for (int j = 0; j < len11; j++)
{
sum_r[i] += table[i, j];
}
}//对每行求和
for (int i = 0; i < len11;i++ )
{
for(int j = 0; j < len12;j++)
{
fe[i, j] = sum_r[i] * sum_c[j] / sum;
}
}//计算给定单元的频数期望值
for (int i = 0; i < len11;i++ )
{
for(int j = 0; j < len12;j++)
{
chisq_value = chisq_value+(table[i,j]-fe[i,j]).Power(new BigNumber("2"))/fe[i,j];
}
}
double Xsquare1;
Xsquare1= Stat.chi2Ua(0.05, (len11-1)*(len12-1));//返回卡方分布临界值
BigNumber Xsquare = new BigNumber(Xsquare1.ToString());
if (CompareNumber.Compare(chisq_value, Xsquare) == 1 )
{
return "拒绝原假设，行列变量之间不独立";
}
else
{
return "不拒绝原假设，行列变量独立";
}
}