Vcoderz Community - Secant Method using C++

Code:
/* This program uses the secant method to compute a root of the

/* provided function.  The majority of this program deals with parsing

/* input and formatting output -- after all, someone has to look at

/* the output, so it may as well be formatted nicely. */



// Secant Method Program

// Homework Assignment #1

// Author: Prof. Gray

// Language: C++

// Usage: secant < x0> < x1>



#include < iostream.h>

#include < iomanip.h>

#include < math.h>



// --- PROTOTYPES ---

double f(double);

void output_header();

void output_status(int, double, double, double);

void close_table(double, double);

// ------------------



main (int argc, char *argv[]) {

  double xn,xnp1,tempx;

  double fxn,fxnp1,df;

  double xtol = 1.0e-8;

  double ftol = 1.0e-10;

  double error;



  int iteration;

  

  if (argc != 3) // arguments were not given on the command line:

    cout << "Usage: secant <x0> <x1>" << endl;

  else {

    xn = atof(argv[1]);

    xnp1 = atof(argv[2]);

 

    cout << "Using " << xn << " and " 

     << xnp1  <<" as initial values." << endl << endl;

    cout << "Using x difference stopping criterion: " << xtol << endl

     << endl ;

  }



  fxn   = f(xn);

  fxnp1 = f(xnp1); 



  // at this point, everything is initialized.

  // output header.

  output_header();

  iteration = 0;





  /* The remaining portion of the program computes the actual

  /* secant iterations.  Note that computation terminates when

  /* |x_n-x_(n-1)| < xtol. */



  while ((error = fabs(xn - xnp1)) > xtol ) {



    tempx = xnp1;

    df = fxn-fxnp1;



    // there is danger of division by zero.  Try to head this

    // possibitity off by checking prior to division.

    if (fabs(df) < ftol) {

      cout << "Error -- division by zero possible. " << endl

       << "Terminating program.";

      return -1;

    }





    xnp1 = xn - fxn*(xn-xnp1)/df;

    xn = tempx;

    fxn = fxnp1;

    fxnp1 = f(xnp1);

    output_status(++iteration,xn,fxn,error);

     

  }

  close_table(xnp1,fxnp1); // END OF COMPUTATIONS

}





/* Definition of the function whose roots are sought is provided

/* within the function f */



double f(double val) {

  return pow(val,6) - val - 1;

}





/* output_header prints the header line for the results */

void output_header() {

  cout << "iter    x_n           f(x_n)     " 

       <<   "   abs(x_n-x_(n-1))" << endl;

  cout << "---------------------------"

       << "---------------------------" << endl;

}



/* output_status is responsible for displaying the current state of

/* the secant method in a user-readable format.  Providing a

/* formated display of the current state allows for easier visual

/* analysis of the convergence of the method. */



void output_status(int iteration, 

           double xn,

           double fxn,

           double error) {



    cout.setf(ios::fixed,ios::floatfield);

    cout << setw(3) << iteration ;



    cout.unsetf(ios::fixed); cout.unsetf(ios::floatfield);

    cout.setf(ios::fixed,ios::floatfield);

    cout << "  " << setprecision(8) << xn;



    cout.unsetf(ios::fixed); cout.unsetf(ios::floatfield);

    cout.setf(ios::scientific);

    cout << "  " << setprecision(8) << fxn;

    cout << "    " << setprecision(10) << error << endl;



}



/* close_table closes the table form */



void close_table(double c, double fc) {

  cout.unsetf(ios::fixed); cout.unsetf(ios::floatfield);

  cout.setf(ios::scientific);

  cout << "---------------------------"

       << "---------------------------" << endl << endl;



  cout << "Secant method: " << endl << '\t'

       <<"Root: " << setprecision(10) << c << endl << '\t'

       <<"Function value: "  << setprecision(12) << fc << endl<< endl;

}