全主元高斯消元法c++

全主元高斯消元法是一种解线性方程组的方法，它可以通过消元和回代的方式求解方程组的解。以下是一个C++实现的例子：

#include <iostream>
#include <cmath>
using namespace std;

const int MAXN = 100;
const double eps = 1e-10;

class GAUS {
private:
    int n;
    double a[MAXN][MAXN], b[MAXN];
    int p[MAXN], q[MAXN];
public:
    GAUS(int n) : n(n) {}
    void input() {
        cout << "请输入系数矩阵A和常数向量B：" << endl;
        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= n; j++) {
                cin >> a[i][j];
            }
            cin >> b[i];
        }
    }
    void gauss() {
        for (int i = 1; i <= n; i++) {
            p[i] = q[i] = i;
        }
        for (int k = 1; k <= n; k++) {
            double maxa = 0;
            int maxp = 0, maxq = 0;
            for (int i = k; i <= n; i++) {
                for (int j = k; j <= n; j++) {
                    if (fabs(a[p[i]][q[j]]) > maxa) {
                        maxa = fabs(a[p[i]][q[j]]);
                        maxp = i;
                        maxq = j;
                    }
                }
            }
            if (maxa < eps) {
                cout << "矩阵奇异，无法求解！" << endl;
                return;
            }
            if (maxp != k) {
                swap(p[k], p[maxp]);
            }
            if (maxq != k) {
                swap(q[k], q[maxq]);
            }
            for (int i = k + 1; i <= n; i++) {
                double f = a[p[i]][q[k]] / a[p[k]][q[k]];
                b[p[i]] -= f * b[p[k]];
                for (int j = k + 1; j <= n; j++) {
                    a[p[i]][q[j]] -= f * a[p[k]][q[j]];
                }
            }
        }
    }
    void output() {
        cout << "方程组的解为：" << endl;
        for (int i = n; i >= 1; i--) {
            double sum = 0;
            for (int j = i + 1; j <= n; j++) {
                sum += a[p[i]][q[j]] * b[p[j]];
            }
            b[p[i]] = (b[p[i]] - sum) / a[p[i]][q[i]];
        }
        for (int i = 1; i <= n; i++) {
            cout << "x" << i << " = " << b[p[i]] << endl;
        }
    }
};

int main() {
    GAUS c(4);
    c.input();
    c.gauss();
    c.output();
    return 0;
}