C++：向量下标超出范围？

Question

我是 C++ 新手，我正在尝试编写一个程序来打开一个文件“parameters.txt”，其中包含 8 个空格分隔的数字。然后我在单独的函数 RK4() 中使用这些数字来获取 3 个数组（y1、y2、t）。然后我在 main() 中操作这些数组并将文件“output.txt”输出到工作目录

这是我的代码：

#include <string>
#include <iostream>
#include <cmath>
#include <fstream>
#include <vector>
#include <algorithm>
#include <iterator>
#include <tuple>
using namespace std;

tuple<vector<double>, vector<double>, vector<double>> RK4() {

    //open parameters.txt, put data into a vector
    ifstream fin("parameters.txt");
    vector<double> data;
    int element;
    while (fin >> element) {
        data.push_back(element);
    }

    //define tspan
    vector<double> tspan(2);
    tspan[0] = 0.0;
    tspan[1] = data[7];

    //define y0
    vector<double> y0(4);
    y0[0] = data[4];
    y0[1] = data[5];
    y0[2] = 0.0;
    y0[3] = 0.0;
    double theta1 = y0[0];
    double theta2 = y0[1];
    double omega1 = y0[2];
    double omega2 = y0[3];

    //define stepSize
    double stepSize;
    stepSize = data[6];

    //define range
    int range = int(tspan[1] / stepSize);

    //define other constants
    double m1, m2, l1, l2;
    m1 = data[0];
    m2 = data[1];
    l1 = data[2];
    l2 = data[3];
    double g = 9.81;

    //define y, t vectors
    vector<double> y1(range);
    vector<double> y2(range);
    vector<double> y3(range);
    vector<double> y4(range);
    vector<double> t(range);
    for (double i = 0.0; i < 1.0 * range; i++) {
        t[i] = i * stepSize;
    }

    //enter y0 into first value
    y1[0] = theta1;
    y2[0] = theta2;
    y3[0] = omega1;
    y4[0] = omega2;

    //loop to find y, t vectors
    for (int i = 0; i < range - 1; i++) {
        //finding all k values:
        //k1
        double dTheta1_1 = y3[i];
        double dOmega1_1 = (-g * (2 * m1 + m2) * sin(y1[i]) - m2 * g * sin(y1[i] - 2 * y2[i]) - 2 * sin(y1[i] - y2[i]) * m2 * (pow(y4[i], 2) * l2 + pow(y3[i], 2) * l1 * cos(y1[i] - y2[i]))) / (l1 * (2 * m1 + m2 - m2 * cos(2 * y1[i] - 2 * y2[i])));
        double dTheta2_1 = y4[i];
        double dOmega2_1 = (2 * sin(y1[i] - y2[i]) * (pow(y3[i], 2) * l1 * (m1 + m2) + g * (m1 + m2) * cos(y1[i]) + pow(y4[i], 2) * l2 * m2 * cos(y1[i] - y2[i]))) / (l2 * (2 * m1 + m2 - m2 * cos(2 * y1[i] - 2 * y2[i])));

        //k2
        double dTheta1_2 = y3[i] + 0.5 * stepSize * dTheta1_1;
        double dOmega1_2 = (-g * (2 * m1 + m2) * sin(y1[i] + 0.5 * stepSize * dTheta1_1) - m2 * g * sin((y1[i] + 0.5 * stepSize * dTheta1_1) - 2 * (y2[i] + 0.5 * stepSize * dTheta2_1)) - 2 * sin((y1[i] + 0.5 * stepSize * dTheta1_1) - (y2[i] + 0.5 * stepSize * dTheta2_1)) * m2 * (pow(y4[i] + 0.5 * stepSize * dOmega2_1, 2) * l2 + pow(y3[i] + 0.5 * stepSize * dOmega1_1, 2) * l1 * cos((y1[i] + 0.5 * stepSize * dTheta1_1) - (y2[i] + 0.5 * stepSize * dTheta2_1)))) / (l1 * (2 * m1 + m2 - m2 * cos(2 * (y1[i] + 0.5 * stepSize * dTheta1_1) - 2 * (y2[i] + 0.5 * stepSize * dTheta2_1))));
        double dTheta2_2 = y4[i] + 0.5 * stepSize * dTheta2_1;
        double dOmega2_2 = (2 * sin((y1[i] + 0.5 * stepSize * dTheta1_1) - (y2[i] + 0.5 * stepSize * dTheta2_1)) * (pow(y3[i] + 0.5 * stepSize * dOmega1_1, 2) * l1 * (m1 + m2) + g * (m1 + m2) * cos(y1[i] + 0.5 * stepSize * dTheta1_1) + pow(y4[i] + 0.5 * stepSize * dOmega2_1, 2) * l2 * m2 * cos((y1[i] + 0.5 * stepSize * dTheta1_1) - (y2[i] + 0.5 * stepSize * dTheta2_1)))) / (l2 * (2 * m1 + m2 - m2 * cos(2 * (y1[i] + 0.5 * stepSize * dTheta1_1) - 2 * (y2[i] + 0.5 * stepSize * dTheta2_1))));

        //k3
        double dTheta1_3 = y3[i] + 0.5 * stepSize * dTheta1_2;
        double dOmega1_3 = (-g * (2 * m1 + m2) * sin(y1[i] + 0.5 * stepSize * dTheta1_2) - m2 * g * sin((y1[i] + 0.5 * stepSize * dTheta1_2) - 2 * (y2[i] + 0.5 * stepSize * dTheta2_2)) - 2 * sin((y1[i] + 0.5 * stepSize * dTheta1_2) - (y2[i] + 0.5 * stepSize * dTheta2_2)) * m2 * (pow(y4[i] + 0.5 * stepSize * dOmega2_2, 2) * l2 + pow(y3[i] + 0.5 * stepSize * dOmega1_2, 2) * l1 * cos((y1[i] + 0.5 * stepSize * dTheta1_2) - (y2[i] + 0.5 * stepSize * dTheta2_2)))) / (l1 * (2 * m1 + m2 - m2 * cos(2 * (y1[i] + 0.5 * stepSize * dTheta1_2) - 2 * (y2[i] + 0.5 * stepSize * dTheta2_2))));
        double dTheta2_3 = y4[i] + 0.5 * stepSize * dTheta2_2;
        double dOmega2_3 = (2 * sin((y1[i] + 0.5 * stepSize * dTheta1_2) - (y2[i] + 0.5 * stepSize * dTheta2_2)) * (pow(y3[i] + 0.5 * stepSize * dOmega1_2, 2) * l1 * (m1 + m2) + g * (m1 + m2) * cos(y1[i] + 0.5 * stepSize * dTheta1_2) + pow(y4[i] + 0.5 * stepSize * dOmega2_2, 2) * l2 * m2 * cos((y1[i] + 0.5 * stepSize * dTheta1_2) - (y2[i] + 0.5 * stepSize * dTheta2_2)))) / (l2 * (2 * m1 + m2 - m2 * cos(2 * (y1[i] + 0.5 * stepSize * dTheta1_2) - 2 * (y2[i] + 0.5 * stepSize * dTheta2_2))));

        //k4
        double dTheta1_4 = y3[i] + stepSize * dTheta1_3;
        double dOmega1_4 = (-g * (2 * m1 + m2) * sin(y1[i] + stepSize * dTheta1_3) - m2 * g * sin((y1[i] + stepSize * dTheta1_3) - 2 * (y2[i] + stepSize * dTheta2_3)) - 2 * sin((y1[i] + stepSize * dTheta1_3) - (y2[i] + stepSize * dTheta2_3)) * m2 * (pow(y4[i] + stepSize * dOmega2_3, 2) * l2 + pow(y3[i] + stepSize * dOmega1_3, 2) * l1 * cos((y1[i] + stepSize * dTheta1_3) - (y2[i] + stepSize * dTheta2_3)))) / (l1 * (2 * m1 + m2 - m2 * cos(2 * (y1[i] + stepSize * dTheta1_3) - 2 * (y2[i] + stepSize * dTheta2_3))));
        double dTheta2_4 = y4[i] + stepSize * dTheta2_3;
        double dOmega2_4 = (2 * sin((y1[i] + stepSize * dTheta1_3) - (y2[i] + stepSize * dTheta2_3)) * (pow(y3[i] + stepSize * dOmega1_3, 2) * l1 * (m1 + m2) + g * (m1 + m2) * cos(y1[i] + stepSize * dTheta1_3) + pow(y4[i] + stepSize * dOmega2_3, 2) * l2 * m2 * cos((y1[i] + stepSize * dTheta1_3) - (y2[i] + stepSize * dTheta2_3)))) / (l2 * (2 * m1 + m2 - m2 * cos(2 * (y1[i] + stepSize * dTheta1_3) - 2 * (y2[i] + stepSize * dTheta2_3))));


        double theta1New = y1[i] + (stepSize / 6.0) * (dTheta1_1 + 2 * dTheta1_2 + 2 * dTheta1_3 + dTheta1_4);
        double omega1New = y3[i] + (stepSize / 6.0) * (dOmega1_1 + 2 * dOmega1_2 + 2 * dOmega1_3 + dOmega1_4);
        double theta2New = y2[i] + (stepSize / 6.0) * (dTheta2_1 + 2 * dTheta2_2 + 2 * dTheta2_3 + dTheta2_4);
        double omega2New = y4[i] + (stepSize / 6.0) * (dOmega2_1 + 2 * dOmega2_2 + 2 * dOmega2_3 + dOmega2_4);


        // updating y arrays 
        y1[i + 1] = theta1New;
        y2[i + 1] = theta2New;
        y3[i + 1] = omega1New;
        y4[i + 1] = omega2New;

    }
    return make_tuple(y1, y2, t);
}

int main() {

    //open parameters.txt, put data into a vector
    ifstream fin("parameters.txt");
    vector<double> data;
    int element;
    while (fin >> element) {
        data.push_back(element);
    }
   
    //define tspan
    vector<double> tspan(2);
    tspan[0] = 0.0;
    tspan[1] = 10.0;

    //define stepSize
    double stepSize;
    stepSize = data[6];

    //define range
    int const range = 1000;

    //define other constants
    double l1 = data[2];
    double l2 = data[3];

    //get y1, y2, t from RK4 function
    auto temp = RK4();
    vector<double> y1 = get<0>(temp);
    vector<double> y2 = get<1>(temp);
    vector<double> t = get<2>(temp);
    double x_1[range], y_1[range], x_2[range], y_2[range];

    //define x_1, x_2, y_1, y_2
    for (int i = 0; i < range; i++) {
        x_1[i] = { sin(y1[i]) * l1 };
        y_1[i] = { -cos(y1[i]) * l1 };
        x_2[i] = { sin(y1[i]) * l1 + sin(y2[i]) * l2 };
        y_2[i] = { -cos(y1[i]) * l1 - cos(y2[i]) * l2 };
    }

    //writing x,y positions at time t to output.txt
    ofstream myfile;
    myfile.open("C:\\mydirectory\\output.txt");
    if (myfile.is_open()) {
        myfile << "t: " << endl;
        for (int i = 0; i < range; i++) {
            myfile << t[i] << " ";
        }
        cout << endl;
        myfile << "x_1: " << endl;
        for (int i = 0; i < range; i++) {
            myfile << x_1[i] << " ";
        }
        cout << endl;
        myfile << "y_1: " << endl;
        for (int i = 0; i < range; i++) {
            myfile << y_1[i] << " ";
        }
        cout << endl;
        myfile << "x_2: " << endl;
        for (int i = 0; i < range; i++) {
            myfile << x_2[i] << " ";
        }
        cout << endl;
        myfile << "y_2: " << endl;
        for (int i = 0; i < range; i++) {
            myfile << y_2[i] << " ";
        }
        cout << endl;
        myfile.close();

    }
    else cout << "Unable to open file";

    return 0;
}

当我尝试构建和运行程序（在 Visual Studio 中）时，我收到此错误：

线程 0x22c0 以代码 0 (0x0) 退出。 调试断言失败！

表达式：向量下标超出范围

有关您的程序如何导致断言的信息 失败，请参阅有关断言的 Visual C++ 文档。

程序以代码 3 (0x3) 退出。

当我尝试调试程序时，我得到：

抛出异常 c++ coursework new.exe 已触发断点。

有什么问题？

Answer 1

在这部分

    for (int i = 0; i < range; i++) {
        x_1[i] = { sin(y1[i]) * l1 };
        y_1[i] = { -cos(y1[i]) * l1 };
        x_2[i] = { sin(y1[i]) * l1 + sin(y2[i]) * l2 };
        y_2[i] = { -cos(y1[i]) * l1 - cos(y2[i]) * l2 };
    }

无论实际大小如何，都将从 y1 和 y2 读取 1000 (= range) 个元素。

这可能会导致超出范围的访问。

您应该将range 设置为它们的元素数。

由于标准 C++ 中没有可变长度数组，因此您应该使用 std::vector 而不是数组。

线

    int const range = 1000;

应该去掉那行

    double x_1[range], y_1[range], x_2[range], y_2[range];

应该是

    int const range = static_cast<int>(y1.size()); 
    std::vector<double> x_1(range), y_1(range), x_2(range), y_2(range);

Answer 2

一般来说，这段代码有很多可能的错误原因，没有明确检查。例如：

您必须检查先决条件。例如：

while (fin >> element) {
        data.push_back(element);
    }

// add some checks
if (data.size() < 8) { ... precondition failed. handle ... }

和

stepSize = data[6];
if (stepSize too small or == 0)  { .. precondition failed. handle ... }

另外，幂函数pow() 的基数可能不是负数。 这也应该检查。

您还做了很多除法而不检查除以 0 - 也可能是错误的原因。