Question

One of the example problems i am basing a program off of for secant root finding uses x, but doesn’t declare it, but runs successfully. Meanwhile when i use the nearly the same setup i get an error saying x is undeclared. Why does it work in the example program and not mine?

using namespace std;
#include<iostream>
#include<cmath>
#include<iomanip>
// Declaration of functions used
void secant(double, double, double, double,
               double, double, double&, int& );
double fx(double, double, double, double, double);
const double tol=0.0001;    // Tolerance for convergence
const int max_iter=50;      // Maximum iterations allowed
// main program
int main()
{
    int iteration;          // Number of iterations
    double a, b, c, d;      // Constants in f(x)
    double x0, x1;          // Starting values for x
    double root;           // Root found by secant method
    cout<<"Enter a, b, c, and d"<<endl<<"separated by a space ";
    cin>>a>>b>>c>>d;
    cout<<"\nEnter two initial values for x,\nseparated by a space: ";
    cin>>x0>>x1;
    secant(a, b, c, d, x0, x1, root, iteration);// Call "secant"
// Output
    cout<<"\nThe root is = "<<root<<endl;
    cout<<"The number of iterations was = "<<iteration<<endl;
    cout<<"The value of f(x) at the root = "<<fx(a,b,c,d,root)<<endl<<endl;
 system("pause");
 return 0;
}
// Definition of function "secant"
// Receives a, b, c, d and x0 values from main program
// Returns root and the iterations required
void secant(double a,double b, double c, double d, 
        double x0, double x1, double& root, int& iteration)
{
    double xnminus1, xnplus1, xn; // Local variables
    iteration=0;                  // Initialize iterations
    xnminus1=x0;
    xn=x1;
    do
    {
       ++iteration;
       xnplus1 = xn - fx(a,b,c,d,xn)*(xn-xnminus1)/
                                  (fx(a,b,c,d,xn)-fx(a,b,c,d,xnminus1));
       cout<<"x"<<iteration+1<<" = "<<xnplus1<<endl;
       xnminus1 = xn;
       xn=xnplus1;
    }  
    while ((fabs(fx(a,b,c,d,xnplus1)) >= tol )&& (iteration < max_iter));
    root=xnplus1;  
}
// Defines "fx" -- calculates f(x) = ax^3+bx^2+cx+d
double fx(double a, double b, double c, double d, double x)
{
    return a*pow(x,3)+b*pow(x,2)+c*x+d;
}

here is my program which i used the same structure but it is saying x is undeclared?

 using namespace std;
    #include<iostream>
    #include<cmath>
    #include<iomanip>
    #include<fstream>
    // Declaration of functions used
    void secant(double, double, double, double,
                   double, double, double, double, double&, int& );
    double fx( double, double, double, double, double, double, double);
    const double tol=0.0001;    // Tolerance for convergence
    const int max_iter=50;      // Maximum iterations allowed
    // main program
    int main()
    {
        int iteration;          // Number of iterations

        double kr, uc, q, b, radians;

        double x0, x1;          // Starting values for x
        double root;           // Root found by secant method
    const double PI = 4.0*atan(1.0);
    ifstream datain ("shuttle.txt");
    ofstream dataout ("results.txt");
    datain >> kr >> uc >> q >> b;
    int velocity = 16000;
    double angle =10;
    x0= 1000;
    x1 = 200;
    for (int velocity = 16000; velocity <= 17500; velocity += 500) {
        for (int angle = 10; angle <= 70; angle += 15) {
    radians= angle * PI/180  ;
                  cout << velocity << endl;
                  cout << radians << endl;
                  cout << angle << endl;
                  secant (radians, velocity, kr, uc, q, b, x0, x1, root, iteration);

    // Output
        cout<<"\nThe root is = "<<root<<endl;
        cout<<"The number of iterations was = "<<iteration<<endl;
        cout<<"The value of f(x) at the root = "<<fx(radians, velocity, kr, uc, q, b, root)<<endl<<endl;
     system("pause");
     return 0;
    }
    // Definition of function "secant"
    // Receives a, b, c, d and x0 values from main program
    // Returns root and the iterations required
    void secant(double radians,double velocity, double kr, double uc, double q, double b, double x0, double x1, double& root, int& iteration);
    {
        double xnminus1, xnplus1, xn; // Local variables
        iteration=0;                  // Initialize iterations
        xnminus1=x0;
        xn=x1;
        do
        {
           ++iteration;
           xnplus1 = xn - fx(radians, velocity, kr, uc, q, b, xn)*(xn-xnminus1)/
                                      (fx(radians, velocity, kr, uc, q, b, xn)-fx(radians, velocity, kr, uc, q, b, xnminus1));
           cout<<"x"<<iteration+1<<" = "<<xnplus1<<endl;
           xnminus1 = xn;
           xn=xnplus1;
        }  
        while ((fabs(fx(radians, velocity, kr, uc, q, b, xnplus1)) >= tol )&& (iteration < max_iter));
        root=xnplus1;  
    }
    // Defines "fx" -- calculates f(x) = ax^3+bx^2+cx+d
    double fx(double radians,double velocity, double kr, double uc, double q, double b, double x);
    {
         return kr * pow(x,4.0) + uc * x - q - pow(velocity/b, 2.0) * sin(radians);

    }}
    }

Answer 1

double fx(double radians,double velocity, double kr, double uc, double q, double b, double x);

you have an extra semicolon “;” at the end of the line. 🙂

Should be

double fx(double radians,double velocity, double kr, double uc, double q, double b, double x)

You also have the same error when defining the secant function. When you define a function you don’t put a semicolon at the end.

Final code should look something like this

#include<iostream>
#include<cmath>
#include<iomanip>
#include<fstream>
// Declaration of functions used
void secant(double, double, double, double, double, double, double, double, double&, int& );
double fx( double, double, double, double, double, double, double);
const double tol=0.0001;    // Tolerance for convergence
const int max_iter=50;      // Maximum iterations allowed

using namespace std; // <- Goes after including the headers

// main program
int main()
{
        int iteration;          // Number of iterations

        double kr, uc, q, b, radians;

        double x0, x1;          // Starting values for x
        double root;           // Root found by secant method
        const double PI = 4.0*atan(1.0);
        ifstream datain ("shuttle.txt");
        ofstream dataout ("results.txt");
        datain >> kr >> uc >> q >> b;
        int velocity = 16000;
        double angle =10;
        x0= 1000;
        x1 = 200;
        for (int velocity = 16000; velocity <= 17500; velocity += 500)
        {
            for (int angle = 10; angle <= 70; angle += 15)
        {
            radians= angle * PI/180  ;
                    cout << velocity << endl;
                    cout << radians << endl;
                    cout << angle << endl;
                    secant (radians, velocity, kr, uc, q, b, x0, x1, root, iteration);
        }
    }

    // Output
        cout<<"\nThe root is = "<<root<<endl;
        cout<<"The number of iterations was = "<<iteration<<endl;
        cout<<"The value of f(x) at the root = "<<fx(radians, velocity, kr, uc, q, b, root)<<endl<<endl;
        system("pause");
     return 0;
}


// Definition of function "secant"
// Receives a, b, c, d and x0 values from main program
// Returns root and the iterations required
void secant(double radians,double velocity, double kr, double uc, double q, double b, double x0, double x1, double& root, int& iteration)
{
        double xnminus1, xnplus1, xn; // Local variables
        iteration=0;                  // Initialize iterations
        xnminus1=x0;
        xn=x1;
        do
        {
           ++iteration;
           xnplus1 = xn - fx(radians, velocity, kr, uc, q, b, xn)*(xn-xnminus1)/
                                      (fx(radians, velocity, kr, uc, q, b, xn)-fx(radians, velocity, kr, uc, q, b, xnminus1));
           cout<<"x"<<iteration+1<<" = "<<xnplus1<<endl;
           xnminus1 = xn;
           xn=xnplus1;
        }  
        while ((fabs(fx(radians, velocity, kr, uc, q, b, xnplus1)) >= tol )&& (iteration < max_iter));
        root=xnplus1;  
}


// Defines "fx" -- calculates f(x) = ax^3+bx^2+cx+d
double fx(double radians,double velocity, double kr, double uc, double q, double b, double x)
{
        return kr * pow(x,4.0) + uc * x - q - pow(velocity/b, 2.0) * sin(radians);

}