doolittle直接分解法求线性方程组Ax=b c++

Doolittle分解是一种LU分解的方法，用于求解线性方程组Ax=b。下面是使用C++实现Doolittle分解的代码：

#include <iostream>
using namespace std;

const int N = 100;

double A[N][N], L[N][N], U[N][N];
double b[N], x[N], y[N];

void doolittle(int n)
{
    // Doolittle分解
    for (int k = 0; k < n; k++) {
        U[k][k] = A[k][k];
        for (int i = k; i < n; i++) {
            L[i][k] = A[i][k] / U[k][k];
            U[k][i] = A[k][i];
        }
        for (int i = k + 1; i < n; i++) {
            for (int j = k + 1; j < n; j++) {
                A[i][j] -= L[i][k] * U[k][j];
            }
        }
    }
}

void solve(int n)
{
    // 前代
    y[0] = b[0] / L[0][0];
    for (int i = 1; i < n; i++) {
        double sum = 0;
        for (int j = 0; j < i; j++) {
            sum += L[i][j] * y[j];
        }
        y[i] = (b[i] - sum) / L[i][i];
    }

    // 后代
    x[n - 1] = y[n - 1] / U[n - 1][n - 1];
    for (int i = n - 2; i >= 0; i--) {
        double sum = 0;
        for (int j = i + 1; j < n; j++) {
            sum += U[i][j] * x[j];
        }
        x[i] = (y[i] - sum) / U[i][i];
    }
}

int main()
{
    int n;
    cout << "请输入线性方程组的阶数：";
    cin >> n;
    cout << "请输入系数矩阵A：" << endl;
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            cin >> A[i][j];
        }
    }
    cout << "请输入常数向量b：" << endl;
    for (int i = 0; i < n; i++) {
        cin >> b[i];
    }

    doolittle(n); // Doolittle分解
    solve(n); // 求解方程组

    cout << "方程组的解为：" << endl;
    for (int i = 0; i < n; i++) {
        cout << "x" << i + 1 << " = " << x[i] << endl;
    }

    return 0;
}

注意：该算法中的矩阵下标从0开始。