降阶法计算行列式方法有个地方有Bug(原文也已更正,此为更正后部分)

2015-01-24 05:36:41 · 作者: · 浏览: 4
今天用此函数做方程求解时发现有误,特此更正:
/// 
        /// 降阶法计算行列式
        /// 
        /// N阶行列式
        /// 是否0优化
        /// 
  
   计算结果
  
        public static decimal CalcDeterminantAij(decimal[,] Determinants, bool ZeroOptimization = false)
        {
            var theN = Determinants.GetLength(0);
            //如果为2阶,直接计算
            if (theN == 2)
            {
                return Determinants[0, 0] * Determinants[1, 1] - Determinants[0, 1] * Determinants[1, 0];
            }
            if (theN == 1)
            {
                return Determinants[0, 0];
            }
            if (theN == 0)
            {
                throw new Exception("参数错误!");
            }
            if (ZeroOptimization)
            {
                //找0最多的行
                int theRowIndex = 0;
                int theMaxZeroCountR = -1;
                for (int i = 0; i < theN; i++)
                {
                    int theZeroNum = 0;
                    for (int j = 0; j < theN; j++)
                    {
                        if (Determinants[i, j] == 0)
                        {
                            theZeroNum++;
                        }
                    }
                    if (theZeroNum > theMaxZeroCountR)
                    {
                        theRowIndex = i;
                        theMaxZeroCountR = theZeroNum;
                    }
                }
                //找0最多的列
                int theColIndex = 0;
                int theMaxZeroCountC = -1;
                for (int i = 0; i < theN; i++)
                {
                    int theZeroNum = 0;
                    for (int j = 0; j < theN; j++)
                    {
                        if (Determinants[j, i] == 0)
                        {
                            theZeroNum++;
                        }
                    }
                    if (theZeroNum >
theMaxZeroCountC) { theColIndex = i; theMaxZeroCountC = theZeroNum; } } if (theMaxZeroCountR >= theMaxZeroCountC) { decimal theRetDec = 0; //第i=theRowIndex+1行展开 int i = theRowIndex + 1; for (int j = 1; j <= theN; j++) { var theSign = CalcDeterMijSign(i, j); var theNewMij = GetDeterminantMij(Determinants, i, j); theRetDec += theSign * Determinants[i - 1, j - 1] * CalcDeterminantAij(theNewMij, ZeroOptimization); } return theRetDec; } else { decimal theRetDec = 0; //第j=theColIndex+1列展开 int j = theColIndex + 1; for (int i = 1; i <= theN; i++) { var theSign = CalcDeterMijSign(i, j); var theNewMij = GetDeterminantMij(Determinants, i, j); theRetDec += theSign * Determinants[i, j] * CalcDeterminantAij(theNewMij, ZeroOptimization); } return theRetDec; } } else { //采用随机法展开一行 var i = new Random().Next(1, theN); decimal theRetDec = 0; for (int j = 1; j <= theN; j++) { var theSign = CalcDeterMijSign(i, j); var theNewMij = GetDeterminantMij(Determinants, i, j); //此处修改theRetDec += theSign * Determinants[i, j] * CalcDeterminantAij(theNewMij, ZeroOptimization); theRetDec += theSign * Determinants[i-1, j-1] * CalcDeterminantAij(theNewMij, ZeroOptimization); } return theRetDec; } }