MyMathLib系列(行列式计算)

/// <summary>     /// 行列式计算,本程序属于MyMathLib的一部分，欢迎使用，参考，提意见。     /// 有时间用函数语言改写，做自己得MathLib,里面的算法经过验证，但没经过     /// 严格测试，如需参考，请慎重.     /// </summary>     public static partial class LinearAlgebra     {         /// <summary>         /// 求逆序数         /// </summary>         /// <param name="Numbers">数字序列</param>         /// <returns></returns>         public static int CalcInverseNumber(string Numbers)         {             int theRet = 0;             if (string.IsNullOrWhiteSpace(Numbers))             {                 return theRet;             }             else             {                 string[] theNumbers = Numbers.Split(new string[] { ",", " " }, StringSplitOptions.RemoveEmptyEntries);                 return CalcInverseNumber(theNumbers);             }         }         /// <summary>         /// 求逆序数         /// </summary>         /// <param name="Numbers">数字序列</param>         /// <returns></returns>         public static int CalcInverseNumber(string[] Numbers)         {             var theRet = 0;             if (Numbers.Count() <= 0)             {                 return theRet;             }             else             {                 string[] theNumbers = Numbers.ToArray();                  int[] theNums = new int[theNumbers.Count()];                 for (int i = 0; i < theNumbers.Count(); i++)                 {                     theNums[i] = Convert.ToInt32(theNumbers[i]);                 }                 for (int theI = 0; theI < theNums.Count() - 1; theI++)                 {                     for (int theJ = theI + 1; theJ < theNums.Count(); theJ++)                     {                         if (theNums[theI] > theNums[theJ])                         {                             theRet++;                         }                     }                 }             }             return theRet;         }         private static string HandlingMultiExp(string Exp, int Sign)         {             decimal theRetNum = Sign;             var theRetLine = "";             var theDigits = Exp.Split('*');             foreach (var theD in theDigits)             {                 decimal theDec = 0;                 if (decimal.TryParse(theD, out theDec))                 {                     theRetNum *= theDec;                 }                 else                 {                     if (theRetLine == "")                     {                         theRetLine = theD;                     }                     else                     {                         theRetLine += "*" + theD;                     }                 }             }             if (theRetNum == 0)             {                 return "";             }             else             {                 if (theRetNum == 1)                 {                     return theRetLine;                 }                 if (theRetNum == -1)                 {                     return "-" + theRetLine;                 }                 return theRetNum.ToString() + theRetLine;             }         }         /// <summary>         /// 行列式表达式展开         /// </summary>         /// <param name="Determinants">N阶行列式</param>         /// <returns></returns>         public static string DeterminantToExpression(string[,] Determinants)         {             int theR = Determinants.GetLength(0);             int theC = Determinants.GetLength(1);             if (theR != theC)             {                 throw new Exception("不是N阶行列式！");             }             var theResults = new List<string>();             List<string> theNs = new List<string>();             for (int i = 1; i <= theC; i++)             {                 theNs.Add(i.ToString());             }             FullPermutation(theNs, 0, theC - 1, theResults);             var theNExp = "";             var thePExp = "";             foreach (var theAL in theResults)             {                 var theInverseNum = Convert.ToInt32(Math.Pow(-1, CalcInverseNumber(theAL)));                 var theLine = "";                 string[] theNums = theAL.Split(new string[] { "," }, StringSplitOptions.RemoveEmptyEntries);                 for (int i = 1; i <= theC; i++)                 {                     var theV = Determinants[i - 1, int.Parse(theNums[i - 1]) - 1];                     theLine += "*" + theV;                 }                 theLine = HandlingMultiExp(theLine.Substring(1), theInverseNum);                 if (!string.IsNullOrEmpty(theLine))                 {                     if (theLine[0] == '-')                     {                         theNExp += "" + theLine;                     }                     else                     {                         thePExp += "+" + theLine;                     }                 }             }             return thePExp.Substring(1) + theNExp;         }         /// <summary>         /// 对数组进行全排列         /// </summary>         /// <param name="lsArray">要进行全排列的数组</param>         /// <param name="begin">进行全排列的开始下标</param>         /// <param name="end">进行全排列的结束下标</param>         public static void FullPermutation(List<string> lsArray, int begin, int end, List<string> Result)         {             if (begin == end)             {                 string theLine = "";                 for (int i = 0; i <= end; i++)                 {                      theLine += "," + lsArray[i];                 }                 Result.Add(theLine.Substring(1));             }              for (int i = begin; i <= end; i++)             {                 Swap(lsArray, begin, i);                 FullPermutation(lsArray, begin + 1, end, Result);                 Swap(lsArray, begin, i);             }          }         /// <summary>         /// 交换数组中的下标为x,y的值         /// </summary>         /// <param name="lsArray">该数组</param>         /// <param name="x"></param>         /// <param name="y"></param>         private static void Swap(List<string> lsArray, int x, int y)         {             string t = lsArray[x];             lsArray[x] = lsArray[y];             lsArray[y] = t;         }         /// <summary>         /// 化三角法行列式计算,         /// </summary>         /// <param name="Determinants">N阶行列式</param>         /// <returns>计算结果</returns>         public static decimal CalcDeterminant(decimal[,] Determinants)         {             int theSign = 1;//正负符号，如果需要变换，将记录变换后的符号.             int theN = Determinants.GetLength(0);             //从第1列到第theN-1列             for (int i = 0; i < theN - 1; i++)             {                 //从第theN-1行到第i+1行，将D[j,i]依次变为0                 for (int j = theN - 1; j > i; j--)                 {                     //如果为当前值为0，则不处理,继续处理上一行                     if (Determinants[j, i] == 0)                     {                         continue;                     }                      //如果[j,i]的上一行[j-1, i]的值为0则交换                     if (Determinants[j - 1, i] == 0)                     {                         //每次交换，行列式的值大小不变，符号取反                         theSign = 0 - theSign;                         for (int k = 0; k < theN; k++)                         {                             decimal theTmpDec = Determinants[j, k];                             Determinants[j, k] = Determinants[j - 1, k];                             Determinants[j - 1, k] = theTmpDec;                         }                     }                     else                     {                         //将当前行减去上一行与theRate的积。                         var theRate = Determinants[j, i] / Determinants[j - 1, i];                         for (int k = 0; k < theN; k++)                         {                             Determinants[j, k] = Determinants[j, k] - Determinants[j - 1, k] * theRate;                         }                     }                 }             }             //结果为对角线上的元素的乘积，注意符号的处理。             decimal theRetDec = theSign;             for (int i = 0; i < theN; i++)             {                 theRetDec *= Determinants[i, i];             }             return theRetDec;         } }