输入向量x和dim。查找并在屏幕上显示v=x-y,||v||₂。检查不等式:||x||₂-||y||₂≤||v||₂。用c++语言
时间: 2023-11-23 14:57:39 浏览: 42
以下是C++代码实现:
```c++
#include <iostream>
#include <cmath>
using namespace std;
double f(double a, double b) {
// 定义函数f(x, y, z)
double x = a * b;
double y = a + b;
double z = a - b;
return x * y * z;
}
double dfda(double a, double b) {
// 对a求偏导数
double x = b;
double y = 1;
double z = 1;
return x * y * z;
}
double dfdb(double a, double b) {
// 对b求偏导数
double x = a;
double y = 1;
double z = -1;
return x * y * z;
}
int main() {
double a, b;
cout << "请输入a和b的值:" << endl;
cin >> a >> b;
// 计算链式法则
double u = f(a, b);
double v = sqrt(pow(dfda(a, b), 2) + pow(dfdb(a, b), 2));
// 计算不等式
double x_norm = sqrt(pow(a, 2) + pow(b, 2));
double y_norm = sqrt(pow(a - 1, 2) + pow(b - 1, 2));
double v_norm = sqrt(pow(a * b, 2) + pow(a + b, 2) + pow(a - b, 2));
double inequality = x_norm - y_norm - v_norm;
// 输出结果
cout << "v = " << dfda(a, b) << "i + " << dfdb(a, b) << "j" << endl;
cout << "||v||₂ = " << v << endl;
cout << "||x||₂ - ||y||₂ - ||v||₂ = " << inequality << endl;
return 0;
}
```