using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
namespace 高斯完全主元消元法
{
class Program
{
//输入参数
static void InPut(ref int n, ref double[,] a,ref int []lz)
{
Console.Write("请输入方程的阶数：");
//Parese函数：将数字型的string字符转化为int型（类型转化）
n = int.Parse(Console.ReadLine());
lz = new int[n];
for(int k = 0; k < n; k++)
{
lz[k] = k + 1;
}
//开辟内存，指定下标
a = new double[n, n + 1];
Console.WriteLine("请输入方程的系数：");
for (int i = 0; i < n; i++)
{
string r = Console.ReadLine();
//Split函数：将字符串r拆分
string[] rs = r.Split(' ');
for (int j = 0; j < n + 1; j++)
{
a[i, j] = double.Parse(rs[j]);
}
}
}
//查找最大值所在的行列
static void FindMax(int k, int n, double[,] a, ref int[] IJ)
{
double Max = a[k, k];
int x = k;
int y = k;
for(int i = k; i <= n - 1; i++)
{
for(int j = k; j <= n - 1; j++)
{
if (a[i, j] > Max)
{
x = i;
y = j;
Max = a[i, j];
}
}
}
IJ[0] = x;
IJ[1] = y;
}
//行列交换
static void Exchange(int n, int k, ref double[,] a, int[] IJ,ref int[] lz)
{
double teap;
if (IJ[0] != k)
{
for (int j = k; j <= n; j++)
{
//交换行
teap = a[k, j];
a[k, j] = a[IJ[0], j];
a[IJ[0], j] = teap;
}
}
if (IJ[1] != k)
{
for (int i = k; i <= n - 1; i++)
{
//交换列
teap = a[i, k];
a[i, k] = a[i, IJ[1]];
a[i, IJ[1]] = teap;
}
//更改数组 lz
int col = lz[k];
lz[k] = lz[IJ[1]];
lz[IJ[1]] = col;
}
}
//消元
static void Elimination(int n, ref double[,] a,ref int[] IJ,int[] lz)
{
//注：i和j的初值不可以为2，因为，他们是随着k而变化的
for (int k = 0; k <= n - 2; k++)
{
FindMax(k, n, a,ref IJ);
Exchange(n, k, ref a, IJ, ref lz);
for (int i = k + 1; i <= n - 1; i++)
{
double lik = a[i, k] / a[k, k];
for (int j = k + 1; j <= n; j++)
{
a[i, j] = a[i, j] - lik * a[k, j];
}
a[i, k] = 0;
}
Console.WriteLine($"\n——————————第{k+1}次消元结果——————————\n");
OutPut(n, a);
}
}
//回代
static void BackSubstitution(int n, double[,] a, ref double[] x)
{
x = new double[n];
for (int i = n - 1; i >= 0; i--)
{
double sum = 0;
for (int j = i + 1; j <= n - 1; j++)
{
sum = sum + a[i, j] * x[j];
}
x[i] = (a[i, n] - sum) / a[i, i];
}
}
//方程系数输出
static void OutPut(int n, double[,] a)
{
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n + 1; j++)
{
Console.Write("{0,8:F2}", a[i, j]);
}
//控制换行
Console.WriteLine();
}
}
//结果输出
static void OutPut(double[] x,int[] lz)
{
for (int i = 1; i <= x.Length; i++)
{
int k = Array.IndexOf(lz, i);//直接进行搜索
//BinarySearch(lz ,i)——效率更高，但是因为它所采取的索引方法为二分法，所以需要事先排序
//int k=Array.BinarySearch(lz ,i);
//Console.WriteLine($"K[{i}]={k}");——调试用
Console.WriteLine("X[{0}]={1,8:F2}", i, x[k]);
}
}
//输出数组 lz 的值（测试用）
static void OutPut(int [] x)
{
for (int i = 0; i < x.Length; i++)
Console.Write("{0} ", x[i]);
}
static void Main(string[] args)
{
int n = 0;
double[,] a = null;
int[] lz = null;//记录下标
int[] IJ = new int[2];//记录最大值的行列值
double[] x = null;
//输入数据
InPut(ref n, ref a, ref lz);
OutPut(lz);
Console.WriteLine("\n——————————方程系数如下——————————\n");
OutPut(n, a);
//消元
Elimination(n, ref a, ref IJ, lz);
Console.WriteLine("\n————————方程最终消元结果如下————————\n");
OutPut(n, a);
BackSubstitution(n, a, ref x);
Console.WriteLine("\n——————————方程的解如下——————————\n");
OutPut(x, lz);
//OutPut(lz);
Console.Read();
}
}
}
Processed:
0.014, SQL:
9
