線性代數之行列式的C#研究實現

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最近學習機器學習 才發現以前數學沒有學好 開始從線性代數開始學起 讀完行列式一章寫了些C#的代碼學習一下。

直接上C#代碼：

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("不正確的數組（數組必須行列數相同且大於1）");            }            else            {                tarr=new T[arrT.GetLength(0),arrT.GetLength(0)];                SetItem(arrT);            }        }        /// <summary>        /// 擷取元素值        /// </summary>        /// <param name="i"></param>        /// <param name="j"></param>        /// <returns></returns>        public T this[int i, int j]        {            //實現索引器的get方法            get            {                return GetItem(i, j);            }            //實現索引器的set方法            set            {                SetItem(i, j, value);            }        }        /// <summary>        /// 擷取元素的餘子式        /// </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>        /// 設定行列式的值        /// </summary>        /// <param name="i">行數（從1開始）</param>        /// <param name="j">列數（從1開始）</param>        /// <param name="value">值</param>        public void SetItem(int i, int j, T value)        {            if (tarr == null)            {                throw new MathException("行列式未正確初始化");            }            else if (i > N || j > N)            {                throw new MathException("超出行列式索引範圍");            }            else            {                tarr[i - 1, j - 1] = value;            }        }        public void SetItem(T[,] arrT)        {            if (arrT == null || tarr == null)            {                throw new MathException("不可為空");            }            else if (arrT.GetLength(0) != N || arrT.GetLength(1) != N)            {                throw new MathException("傳入階數不同");            }            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>        /// 設定行列式的值        /// </summary>        /// <param name="i">行數（從1開始）</param>        /// <param name="j">列數（從1開始）</param>        /// <param name="value">值</param>        public T GetItem(int i, int j)        {            if (tarr == null)            {                throw new MathException("行列式未正確初始化");            }            else if (i > N || j > N)            {                throw new MathException("超出行列式索引範圍");            }            else            {                return tarr[i-1, j-1];            }        }        /// <summary>        /// 輸出行列式資訊        /// </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>        /// 擷取行列式的階數        /// </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>        /// 擷取行列式的值        /// </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)                        {                            //餘子式正值                            sum = Add(sum, MUL(this[1, i], this.A(1, i).Value));                        }                        else                        {                            //餘子式負值                            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("不支援的操作類型");        }        /// <summary>        /// 減法        /// </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("不支援的操作類型");        }        /// <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("不支援的操作類型");        }    }}

　　以上代碼就是對行列式的封裝 可以求值獲得餘子式 很基本的東西 求值的話主要用了遞迴的方式 因為泛型的原因導致計算過程重複拆箱裝箱 不過目前好像也沒有什麼太好的方法了。反正就是學習 所以效能無所謂了。

然後就是調用了直接上調用代碼：

            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("當前行列式：");            Console.WriteLine(d.ToString());            Console.WriteLine("餘子式M11：");            Console.WriteLine(d.A(1, 1).ToString());            Console.WriteLine("餘子式M12：");            Console.WriteLine(d.A(1, 2).ToString());            Console.WriteLine("餘子式M22：");            Console.WriteLine(d.A(2, 2).ToString());            Console.WriteLine("N="+d.N);            Console.WriteLine("行列式的值為:"+d.Value.ToString());            Console.Read();　　

　　執行結果如下：

 

線性代數之行列式的C#研究實現