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;
}

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版权声明：本文为CSDN博主「Ethereal丶9」的原创文章，遵循CC 4.0 BY-SA版权协议，转载请附上原文出处链接及本声明。
原文链接：https://blog.csdn.net/m0_47471269/article/details/119152411