#include <NewtonRaphson.h>
Collaboration diagram for NewtonRaphsonSolve0< functor, real >:
An object of class NewtonRaphsonSolve0 is created with a call to the constructor, NewtonRaphsonSolve0::NewtonRaphsonSolve0, which takes arguments for the starting point, X0, the convergance stopping point, Epsilon, and a functor f, and a functor df, which is the derivative of f.
The function do_iteration, attempts to find the value of x, _x_converge, which solves the equation, (_F.*_f(_x_converge) - _f_solve) < _epsilon.
The second derivative d2f can optionally be supplied. If check_boundary is set to true, then boundary solutions can be solved also. The member function do_iteration, starts the iterative process.
The file NewtonRaphson.cpp contains 3 examples of how this template class can be used. The source code for NewtonRaphson.cpp can be downloaded here.
Definition at line 41 of file NewtonRaphson.h.
Public Member Functions | |
| bool | get_boundary_solution () const |
| returns _boundary_solution | |
| void | set_d2f (real(functor::*d2f)(real)) |
| used to set the second order differential | |
| void | set_check_boundary (bool check_boundary) |
| used to turn boundary checking on or off | |
| void | set_min_x (real min_x) |
| used to set the minimum of the solution set | |
| void | set_max_x (real max_x) |
| used to set the maximum of the solution set | |
| real | get_x_converge () const |
| used to retrieve the convergance value | |
| real | get_f_converge () const |
| used to retrieve the final value of f | |
| functor & | get_functor () |
| this returns a reference to the parent object with the hidden variables | |
| NewtonRaphsonSolve0 (real X0, real Epsilon, bool Twice_df, unsigned int max_iter, functor &F, real(functor::*f)(real), real(functor::*df)(real), real(functor::*d2f)(real)=NULL, real fsolve=0, bool check_boundary=false, real min_x=0, real max_x=0) | |
| void | do_iteration (ostream *output) |
| This function does the calculations. | |
Protected Member Functions | |
| int | check_boundary (real &x, real df_dx) |
| this returns the number of times the bounaries have been hit. If boundaries are hit more than twice, then the loop is stoped. | |
Protected Attributes | |
| int | _max_iter |
| The maximum number of iterations of the routine. See the documentation for do_iteration, to see how this value affects the algorithm. | |
| real | _x0 |
| This is the starting point of the iteration. If _check_boundary is true, then _x0 must be between _min_x and _max_x. | |
| real | _epsilon |
| the convergence parameter. The calculations stop when F(x) < epsilon. | |
| real | _fsolve |
| the value of f to be solved. This is usually 0 in the academic literature. | |
| bool | _twice_df |
| if true then the value of the derivative is calculated twice, to calculate the average value of df, over the interval dx. This is useful, if df is easier to calculate than f. For example dprice/dsigam, can be aproximated ver | |
| real(functor::* | _f )(real) |
| this is the function whose 0 is being solved | |
| real(functor::* | _df )(real) |
| this is the derivative | |
| real(functor::* | _d2f )(real) |
| this is the second derivative. If set to null, then it isn't used | |
| functor & | _F |
| this is the object used to calculate the functions | |
| bool | _check_boundary |
| if true, then the search for the zero, has boundaries | |
| real | _min_x |
| this is the minimum value of the acceptible range | |
| real | _max_x |
| this is the maximum value of the acceptible range | |
| real | _x_converge |
| the value of x such that f(x) = 0 +/- epsilon | |
| real | _f_converge |
| the last value of f | |
| vector< real > | _x |
| the sequence of x's | |
| vector< real > | _F_x |
| the sequence of f_x's | |
| vector< real > | _abs_F_x |
| the sequence of abs(f_x)'s | |
| vector< real > | _dF_x |
| the sequence of df_x's | |
| bool | _converged |
| a boolean which is true, if convergance occurs | |
| bool | _diverged |
| a boolean which is true if the sequence diverged | |
| bool | _boundary_solution |
| true if the final x is on the bounday | |
| int | _number_boundary_hits |
| the number of times a boundary has been hit | |
| bool | _lower_boundary_hit |
| the number of times the lower boundary has been hit | |
| bool | _upper_boundary_hit |
| the number of times the uper boundary has been hit | |
| bool | _boundary_hit |
| true if the last iteration hit the boundary | |
| NewtonRaphsonSolve0< functor, real >::NewtonRaphsonSolve0 | ( | real | X0, | |
| real | Epsilon, | |||
| bool | Twice_df, | |||
| unsigned int | max_iter, | |||
| functor & | F, | |||
| real(functor::*)(real) | f, | |||
| real(functor::*)(real) | df, | |||
| real(functor::*)(real) | d2f = NULL, |
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| real | fsolve = 0, |
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| bool | check_boundary = false, |
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| real | min_x = 0, |
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| real | max_x = 0 | |||
| ) | [inline] |
This constructor sets everything needed by the algorithm.
| [in] | X0 | This is the starting point of the search. It is stored as the data member, _x0. |
| [in] | Epsilon | The is used to define the end point of the iterative procedure, do_iteration. The loop will terminate when the abs(F(xi) - fsolve)) is less than Epsilon. It is stored as the data member, _epsilon. |
| [in] | Twice_df | If Twice_df then the derivative of F, at point i, is approximated as (F(x[i])+f(x[i-1])*.5 which approximates the derivative of F over the interval x[i] to x[i-1]. It is stored as the data member, _F. |
| [in] | max_iter | The maximum number of iterations before do_iteration, will terminate. It is stored as the data member _max_iter. |
| [in] | F | This reference to a functor object serves as the object for calling the member function pointers f, df and d2f. It is stored as the data member _F. |
| [in] | f | This pointer to a member function is used to calculate the function to solved. It is stored as the data member _f. |
| [in] | df | This pointer to a member function is used to calculate the derivative of the function to solved. It is stored as the data member _df. |
| [in] | d2f | This pointer to a member function is used to calculate the second derivative of the function to solved. It is stored as the data member _d2f. |
| [in] | fsolve | This is the value of f to be solved. It's default value is 0. It is stored as the data member _fsolve. |
| [in] | check_boundary | If true then the algorithm will check constrain the search so that it only stays within min_x and max_x. If the search goes outside of the range then the solution is set to the boundary value. It is stored as the data member _check_boundary. |
Definition at line 185 of file NewtonRaphson.h.
00198 : _x0( X0), _epsilon( Epsilon), _twice_df( Twice_df), _max_iter(max_iter), _F(F), _f(f), _df(df), _d2f(d2f), _fsolve(fsolve), _check_boundary(check_boundary), _min_x(min_x), _max_x(max_x), 00199 _x_converge(0), _f_converge(0), 00200 _x(max_iter), _F_x(max_iter), _abs_F_x(max_iter), _dF_x(max_iter), _converged(false), _diverged(false), 00201 _lower_boundary_hit(false), _upper_boundary_hit(false), _boundary_hit(false) 00202 { 00203 00204 }
1.5.1