[C++知识库]全主元高斯消去法（C++）

#include<iostream>
using namespace std;

//动态分配建立m*n的二维数组
template<typename T>
T** Allocation2D(int m, int n)
{
	T** a;
	a = new T* [m];
	for (int i = 0;i < m;i++)
	{
		a[i] = new T[n];
	}
	return a;
}
//动态分配建立长为n的一维数组
template<typename T>
T* Allocation1D(int n)
{
	T* a;
	a = new T[n];
	return a;
}

int main()
{
	int i, j, k;//循环变量
	int n;//系数矩阵行数
	float** a;//增广矩阵
	cout << "输入系数矩阵的N值：" << endl;
	cin >> n;
	a = Allocation2D<float>(n, n + 1);

	cout << endl << "输入增广矩阵的各值：" << endl;
	for (i = 0;i < n;i++)
	{
		for (j = 0;j < n + 1;j++)
		{
			cin >> a[i][j];
		}
	}

	int* e;//e作为记录列交换过程的数组，用于最后理顺解向量
	e = Allocation1D<int>(n);
	for (i = 0;i < n;i++)
	{
		e[i] = i;
	}

	float temp;
	int row, col;
	for (k = 0;k < n - 1;k++)
	{
		temp = 0;
		row = 0;
		col = 0;
		//选主元
		for(i=k;i<n;i++)
		{
			for (j = k;j < n;j++)
			{
				if (fabs(a[i][j]) > temp)
				{
					temp = a[i][j];
					row = i;
					col = j;
				}
			}
		}
		if (temp == 0)
		{
			cout << "系数矩阵为奇异矩阵" << endl;
			return 0;
		}

		//行交换
		if (row != k)
		{
			for (j = k;j < n + 1;j++)
			{
				temp = a[k][j];
				a[k][j] = a[row][j];
				a[row][j] = temp;
			}
		}
		//列交换
		if (col != k)
		{
			e[k] = col;
			for (i = k;i < n;i++)
			{
				temp = a[i][k];
				a[i][k] = a[i][col];
				a[i][col] = temp;
			}
		}

		//消去
		for (i = k + 1;i < n;i++)
		{
			float L = -(a[i][k] / a[k][k]);
			a[i][k] = 0;
			for (j = k + 1;j < n;j++)
			{
				a[i][j] = L * a[k][k] + a[i][j];
			}
			a[i][n - 1] = L * a[k][n - 1] + a[i][n - 1];
		}
	}

	//回代过程
	float* x;
	x = Allocation1D<float>(n);
	x[n - 1] = a[n - 1][n] / a[n - 1][n - 1];
	for (k = n - 2;k >= 0;k--)
	{
		temp = 0;
		for (j = k + 1;j < n;j++)
		{
			temp = temp + a[k][j] * a[j][n];
		}
		x[k] = (a[k][n] - temp) / a[k][k];
	}

	//理顺解向量
	for (k = n - 2;k >= 0;k--)
	{
		if (e[k] != k)
		{
			temp = x[e[k]];
			x[e[k]] = x[k];
			x[k] = temp;
		}
	}
	//输出结果
	cout << "解向量为：" << endl;
	for (i = 0;i < n;i++)
	{
		cout << "x" << i + 1 << ":" << x[i] << endl;
	}
	return 0;
}