Bisection.h File Reference

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Detailed Description

This file contains the bisection algorithm and the bisection_secant algorithm.

Definition in file Bisection.h.

#include <iostream>
#include <vector>
#include <stdexcept>
#include "Secant.h"

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Classes
class	Bisection< functor, real >
	: This is an encapsulation of the Bisection algorithm. More...
class	Bisection_Secant< functor, real >
	this class is a child class of Bisection. The algorithm converges faster because it changes from the bisection to the secant algorithm /// on every other iteration. More...
Functions
template<class functor, class real>
void	stradle_value (real &X0, real &X1, real &FX0, real &FX1, real Fsolve, functor &obj, real(functor::*f)(real), bool initialize_fx0=true, bool initialize_fx1=true, int direction=0, real MinX=0, real MaxX=0)
	This function solves to find a pair of X values, such that.

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Function Documentation

template<class functor, class real>

void stradle_value	(	real &	X0,
		real &	X1,
		real &	FX0,
		real &	FX1,
		real	Fsolve,
		functor &	obj,
		real(functor::*)(real)	f,
		bool	initialize_fx0 = true,
		bool	initialize_fx1 = true,
		int	direction = 0,
		real	MinX = 0,
		real	MaxX = 0
	)

This function solves to find a pair of X values, such that.

1. _F(X_a)<0 for some X_a in the interval [X0 , X1]
2. _F(X_b)>0 for some X_b in the interval [X0 , X1]

Assumes:

1. _f is assumed to be monotonic. _f can be either monotonically increasing, or decreasing.
2. _f is defined on the range 0 - infinity.

Changes: X0, X1, FX0, FX1
Throws: domain error if X0==X1 or range error if _f violates the monotonic condition
Description: This template function solves for X0 and X1 so that f(X0) < Fsolve < f(X1)

Definition at line 28 of file Bisection.h.

Referenced by option_pair::call_implied_sigma(), binomial_option::call_implied_sigma(), main(), option_pair::put_implied_sigma(), and binomial_option::put_implied_sigma().

{
  bool is_increasing, check_bounds;

  if (initialize_fx0) FX0 =(obj.*f)( X0);
  if (initialize_fx1) FX1 =(obj.*f)( X1);

  check_bounds = MinX!=0 || MaxX!=0;

  if (X0==X1) throw domain_error( "X0==X1 in stradle function");

  if (X0 > X1) {
    real tmp;
    tmp = X0;    X0 = X1;  X1 = tmp;
    tmp = FX0; FX0 = FX1; FX1 = tmp;
  }

  if (FX0 < Fsolve && Fsolve < FX1) return;

  if (direction == 0) {
    is_increasing = FX1 > FX0;
  } else {
    is_increasing = direction > 0;
  }

  if (check_bounds && (X1 > MaxX || X0 < MinX)) {
    throw domain_error( "X1 > MaxX || X0 < MinX in stradle_value");
  }

  if (is_increasing) {    // solve fx0 < fsolve < fx1
    while (FX0 > Fsolve) {
      if (FX1 < FX0) throw range_error( "FX1 < FX0 for monotonic increasing function  at label A in stradle_value");
      FX1 = FX0;
      X0 *= .5;
      if (check_bounds && X0 < MinX) {
        throw domain_error( "X0 < MinX in stradle_value");
      }
      FX0 = (obj.*f)( X0);
    }
    while (Fsolve > FX1) {
      if (FX1 < FX0) throw range_error( "FX1 < FX0 for monotonic increasing function  at label B in stradle_value");
      FX0 = FX1;
      X1 *= 2;
      if (check_bounds && X1 > MaxX) {
        throw domain_error( "X1 > MaxX in stradle_value");
      }
      FX1 = (obj.*f)( X1);
    }
  } else {  // solve fx0 > fsolve > fx1
    while (FX0 < Fsolve) {
      if (FX1 > FX0) throw range_error( "FX1 > FX0 for monotonic decreasing function at label C in stradle_value");
      FX1 = FX0;
      X0 *= .5;
      if (check_bounds && X0 < MinX) {
        throw domain_error( "X0 < MinX in stradle_value");
      }
      FX0 = (obj.*f)( X0);
    }
    while (Fsolve < FX1) {
      if (FX1 > FX0) throw range_error( "FX1 > FX0 for monotonic decreasing function at label D in stradle_value");
      FX0 = FX1;
      X1 *= 2;
      if (check_bounds && X1 > MaxX) {
        throw domain_error( "X1 > MaxX in stradle_value");
      }
      FX1 = (obj.*f)( X1);
    }
  }
}

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