线性代数之行列式的C#研究实现

行列式的C#研究实现"/>

线性代数之行列式的C#研究实现

最近学习机器学习 才发现以前数学没有学好 开始从线性代数开始学起 读完行列式一章写了些C#的代码学习一下。

直接上C#代码：

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Runtime.InteropServices;
using System.IO;namespace LYF.Math
{/// <summary>/// 行列式 Determinant/// </summary>[SerializableAttribute][ComVisibleAttribute(true)]public class Determinant<T> where T : IComparable, IFormattable, IConvertible, IComparable<T>, IEquatable<T>{T[,] tarr = null;public Determinant(int n){tarr = new T[n, n];}public Determinant(T[,] arrT){if (arrT == null || arrT.GetLength(0) != arrT.GetLength(1) || arrT.GetLength(0) < 1){throw new MathException("不正确的数组（数组必须行列数相同且大于1）");}else{tarr=new T[arrT.GetLength(0),arrT.GetLength(0)];SetItem(arrT);}}/// <summary>/// 获取元素值/// </summary>/// <param name="i"></param>/// <param name="j"></param>/// <returns></returns>public T this[int i, int j]{//实现索引器的get方法get{return GetItem(i, j);}//实现索引器的set方法set{SetItem(i, j, value);}}/// <summary>/// 获取元素的余子式/// </summary>/// <param name="i"></param>/// <param name="j"></param>/// <returns></returns>public Determinant<T> A(int i, int j){if (N == 1){return null;}else if (i>N||j>N){return null;}else{Determinant<T> a = new Determinant<T>(N - 1);for (int m = 1; m <= N - 1; m++){for (int n = 1; n <= N - 1; n++){int p = m, q = n;if (p >= i){p = m + 1;}if (q >= j){q = n + 1;}a[m, n] = this[p,q];}}return a;}}/// <summary>/// 设置行列式的值/// </summary>/// <param name="i">行数（从1开始）</param>/// <param name="j">列数（从1开始）</param>/// <param name="value">值</param>public void SetItem(int i, int j, T value){if (tarr == null){throw new MathException("行列式未正确初始化");}else if (i > N || j > N){throw new MathException("超出行列式索引范围");}else{tarr[i - 1, j - 1] = value;}}public void SetItem(T[,] arrT){if (arrT == null || tarr == null){throw new MathException("不能为空");}else if (arrT.GetLength(0) != N || arrT.GetLength(1) != N){throw new MathException("传入阶数不同");}else{for (int m = 0; m <=N-1; m++){for (int n = 0; n <= N- 1; n++){this[m + 1, n + 1] = arrT[m, n];}}}}/// <summary>/// 设置行列式的值/// </summary>/// <param name="i">行数（从1开始）</param>/// <param name="j">列数（从1开始）</param>/// <param name="value">值</param>public T GetItem(int i, int j){if (tarr == null){throw new MathException("行列式未正确初始化");}else if (i > N || j > N){throw new MathException("超出行列式索引范围");}else{return tarr[i-1, j-1];}}/// <summary>/// 输出行列式信息/// </summary>/// <returns></returns>public override string ToString(){StringBuilder sbRs = new StringBuilder();if(tarr!=null){for (int m = 0; m <= N - 1; m++){for (int n = 0; n <= N - 1; n++){sbRs.Append(string.Format("{0}\t", tarr[m, n]));}sbRs.Append("\n");}}return sbRs.ToString();}/// <summary>/// 获取行列式的阶数/// </summary>public int N{get{if (tarr != null){return tarr.GetLength(0);}else{return 0;}}}private string typeName = string.Empty;private string GetType(){if (string.IsNullOrEmpty(typeName)){typeName=typeof(T).Name;File.AppendAllText("E:\\op.txt", typeName);}return typeName;}/// <summary>/// 获取行列式的值/// </summary>public T Value{get{if (N == 1){return tarr[0, 0];}else if (N == 2){return Minus(MUL(tarr[0, 0], tarr[1, 1]), MUL(tarr[0, 1], tarr[1, 0]));}else{T sum = default(T);for (int i = 1; i <= N; i++){if ((1+i) % 2 == 0){//余子式正值sum = Add(sum, MUL(this[1, i], this.A(1, i).Value));}else{//余子式负值sum = Minus(sum, MUL(this[1, i], this.A(1, i).Value));}}return sum;}}}/// <summary>/// 加法/// </summary>/// <param name="left"></param>/// <param name="right"></param>/// <returns></returns>private T Add(T left, T right){switch (GetType()){case "Int16":return ((T)(object)((short)(object)left + (short)(object)right));case "Int32":return ((T)(object)((int)(object)left + (int)(object)right));case "Int64":return ((T)(object)((long)(object)left + (long)(object)right));case "Single":return ((T)(object)((float)(object)left + (float)(object)right));case "Double":return ((T)(object)((double)(object)left + (double)(object)right));case "Decimal":return ((T)(object)((decimal)(object)left + (decimal)(object)right));}throw new MathException("不支持的操作类型");}/// <summary>/// 减法/// </summary>/// <param name="left"></param>/// <param name="right"></param>/// <returns></returns>private T Minus(T left, T right){switch (GetType()){case "Int16":return ((T)(object)((short)(object)left - (short)(object)right));case "Int32":return ((T)(object)((int)(object)left - (int)(object)right));case "Int64":return ((T)(object)((long)(object)left - (long)(object)right));case "Single":return ((T)(object)((float)(object)left - (float)(object)right));case "Double":return ((T)(object)((double)(object)left - (double)(object)right));case "Decimal":return ((T)(object)((decimal)(object)left - (decimal)(object)right));}throw new MathException("不支持的操作类型");}/// <summary>/// 乘法/// </summary>/// <param name="left"></param>/// <param name="right"></param>/// <returns></returns>private T MUL(T left, T right){switch (GetType()){case "Int16":return ((T)(object)((short)(object)left * (short)(object)right));case "Int32":return ((T)(object)((int)(object)left * (int)(object)right));case "Int64":return ((T)(object)((long)(object)left * (long)(object)right));case "Single":return ((T)(object)((float)(object)left * (float)(object)right));case "Double":return ((T)(object)((double)(object)left * (double)(object)right));case "Decimal":return ((T)(object)((decimal)(object)left * (decimal)(object)right));}throw new MathException("不支持的操作类型");}}
}

　　以上代码就是对行列式的封装 可以求值获得余子式 很基本的东西 求值的话主要用了递归的方式 因为泛型的原因导致计算过程重复拆箱装箱 不过目前好像也没有什么太好的方法了。反正就是学习 所以性能无所谓了。

然后就是调用了直接上调用代码：

            int[,] aaa = new int[4, 4]{{1,2,3,6},{4,5,7,8},{7,8,9,10},{3,8,4,3}};//LYF.Math.Determinant<int> d = new Determinant<int>(4);LYF.Math.Determinant<int> d = new Determinant<int>(aaa);d.SetItem(aaa);Console.WriteLine("当前行列式：");Console.WriteLine(d.ToString());Console.WriteLine("余子式M11：");Console.WriteLine(d.A(1, 1).ToString());Console.WriteLine("余子式M12：");Console.WriteLine(d.A(1, 2).ToString());Console.WriteLine("余子式M22：");Console.WriteLine(d.A(2, 2).ToString());Console.WriteLine("N="+d.N);Console.WriteLine("行列式的值为:"+d.Value.ToString());Console.Read();

　　执行结果如下：

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