MyMathLib系列(行列式计算2)_计算行列式1201 1329 -1156 2312-优快云博客

本文链接：https://blog.youkuaiyun.com/hawksoft/article/details/42049609

这个博客介绍了如何使用C#编程实现矩阵行列式的计算，包括获取余子式、计算余子式符号、降阶法计算行列式以及拉普拉斯定理计算行列式的方法。程序中的算法已经过验证，但未进行严格测试，适用于矩阵运算和数学库的开发。

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/// <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>
        /// 获取指定i,j的余子式
        /// </summary>
        /// <param name="Determinants">N阶行列式</param>
        /// <param name="i">第i行</param>
        /// <param name="j">第j列</param>
        /// <returns>计算结果</returns>
        public static T[,] GetDeterminantMij<T>(T[,] Determinants, int i, int j)
        {
            var theN = Determinants.GetLength(0);
            var theNewDeter = new T[theN - 1, theN - 1];
            int theI = -1;

            for (int k = 0; k < theN; k++)
            {
                if (k == i - 1)
                {
                    continue;
                }
                theI++;
                int theJ = -1;
                for (int l = 0; l < theN; l++)
                {
                    if (l == j - 1)
                    {
                        continue;
                    }
                    theJ++;
                    theNewDeter[theI, theJ] = Determinants[k, l];
                }
            }
            return theNewDeter;
        }
        /// <summary>
        /// 获取指定i,j的余子式
        /// </summary>
        /// <param name="Determinants">N阶行列式</param>
        /// <param name="Rows">要取得行</param>
        /// <param name="Cols">要取得列</param>
        /// <returns>计算结果</returns>
        public static T[,] GetDeterminantMij<T>(T[,] Determinants, int[] Rows, int[] Cols)
        {
            if (Rows.Length != Cols.Length)
            {
                throw new Exception("所取行数和列数必须相等!");
            }
            var theN = Determinants.GetLength(0);
            var theNewN = theN - Rows.Length;
            var theNewDeter = new T[theNewN, theNewN];
            int theI = -1;

            for (int k = 0; k < theN; k++)
            {
                if (Rows.Contains(k + 1))
                {
                    continue;
                }
                theI++;
                int theJ = -1;
                for (int l = 0; l < theN; l++)
                {
                    if (Cols.Contains(l + 1))
                    {
                        continue;
                    }
                    theJ++;
                    theNewDeter[theI, theJ] = Determinants[k, l];
                }
            }
            return theNewDeter;
        }
        /// <summary>
        /// 获取指定k阶子式N
        /// </summary>
        /// <para