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到今天，行列式和线性方程组部分就完成了。
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
namespace MyMathLib
{
/// <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
{#region 线性方程组
/// <summary>
/// 根据拉普拉斯定理计算行列式值。
/// </summary>
/// <param name="Determinants">N阶行列式</param>
/// <returns>计算结果</returns>
public static decimal CalcDeterByLaplaceLaw(decimal[,] Determinants)
{
var n = Determinants.GetLength(0);
//如果阶数小于3，则没必要采用拉普拉斯展开
if (n <= 3)
{
return CalcDeterminantAij(Determinants, false);
}
var theRows = GetLaplaceRowsOdd(n);
return CalcDeterByLaplaceLaw(Determinants, theRows);
}
/// <summary>
/// 求解线性方程组,这里要求N
/// </summary>
/// <param name="CoefficientDeterminant">线性方程组系数行列式</param>
/// <param name="ConstantTerms">常数项</param>
/// <returns></returns>
public static decimal[] LinearEquations(int UnknownElements,decimal[,] CoefficientDeterminant, decimal[] ConstantTerms)
{
var theRowCount = CoefficientDeterminant.GetLength(0);
var theColCount = CoefficientDeterminant.GetLength(1);
if (UnknownElements == theRowCount && theColCount == UnknownElements)
{
var theD = CalcDeterByLaplaceLaw(CoefficientDeterminant);
if(theD==0)
{
return null;
}
decimal[] theResults = new decimal[UnknownElements];
for (int i = 1; i <= UnknownElements; i++)
{
//置换第i列，注意保存原来的值，下次计算时恢复
var theTemp = new decimal[UnknownElements];
for (int j = 1; j <= UnknownElements; j++)
{
theTemp[j-1] = CoefficientDeterminant[j-1, i-1];
CoefficientDeterminant[j - 1, i - 1] = ConstantTerms[j - 1];
}
var theDi = CalcDeterByLaplaceLaw(CoefficientDeterminant) / theD;
theResults[i-1] = theDi;
//复原系数行列式.
for (int j = 1; j <= UnknownElements; j++)
{
CoefficientDeterminant[j - 1, i - 1] = theTemp[j - 1];
}
}
return theResults;
}
else
{
throw new Exception("参数格式不正确!");
}
}
/// <summary>
/// 求解线性方程组(消元法),这里与化三角求行列式的方法类似，这里要求方程个数和元个数相同。
/// 如果方程个数小于元的个数，消元没问题，但涉及到一般解，会牵扯到符号运算，这里暂不考虑.
/// </summary>
/// <param name="CoefficientDeterminant">线性方程组系数行列式,最右边N+1列是常数项</param>
/// <returns></returns>
public static decimal[] LinearEquationsEM(int UnknownElements,decimal[,] CoefficientDeterminant)
{
var theRowCount = CoefficientDeterminant.GetLength(0);
var theColCount = CoefficientDeterminant.GetLength(1);
if (UnknownElements == theRowCount && theColCount == UnknownElements + 1)
{
decimal[] theResults = new decimal[UnknownElements];
int theN = UnknownElements;
//从第1列到第theN-1列
for (int i = 0; i < theN - 1; i++)
{
//从第theN-1行到第i+1行，将D[j,i]依次变为0
for (int j = theN - 1; j > i; j--)
{
//如果为当前值为0，则不处理,继续处理上一行
if (CoefficientDeterminant[j, i] == 0)
{
continue;
}
//如果[j,i]的上一行[j-1, i]的值为0则交换
if (CoefficientDeterminant[j - 1, i] == 0)
{
for (int k = 0; k <= theN; k++)//这里要交换常数项，所以是k <= theN
{
decimal theTmpDec = CoefficientDeterminant[j, k];
CoefficientDeterminant[j, k] = CoefficientDeterminant[j - 1, k];
CoefficientDeterminant[j - 1, k] = theTmpDec;
}
}
else
{
//将当前行减去上一行与theRate的积。
var theRate = CoefficientDeterminant[j, i] / CoefficientDeterminant[j - 1, i];
for (int k = 0; k <= theN; k++)//这里要计算常数项，所以是k <= theN
{
CoefficientDeterminant[j, k] = CoefficientDeterminant[j, k] - CoefficientDeterminant[j - 1, k] * theRate;
}
}
}
}
//处理结果
if (CoefficientDeterminant[UnknownElements - 1, UnknownElements - 1] == 0)
{
if (CoefficientDeterminant[UnknownElements - 1, UnknownElements] == 0)
{
throw new Exception("无效方程,有无穷个解！");
}
else
{
throw new Exception("方程无解！");
}
}
//结果处理，回代
for (int i = UnknownElements - 1; i >= 0; i--)
{
//计算已求项
decimal theTempDec = 0;
for (int j = i + 1; j < theN; j++)
{
theTempDec += CoefficientDeterminant[i, j] * theResults[j];
}
//计算结果,如果系数为0，则为无效方程
if (CoefficientDeterminant[i, i] == 0)
{
throw new Exception("无效方程");
}
theResults[i] = (CoefficientDeterminant[i, UnknownElements] - theTempDec) / CoefficientDeterminant[i, i];
}
return theResults;
}
else
{
throw new Exception("参数格式不正确!");
}
}
#endregion
}
}标签：
原文地址：http://blog.csdn.net/hawksoft/article/details/42065783
