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：