Solvers.h File Reference

#include <vector>
#include <string>
#include "CPExceptions.h"

Go to the source code of this file.

Classes
class	FuncWrapper1D
class	FuncWrapperND

Functions
double	Brent (FuncWrapper1D *f, double a, double b, double macheps, double t, int maxiter, std::string *errstr)
double	Secant (FuncWrapper1D *f, double x0, double dx, double ftol, int maxiter, std::string *errstring)
double	BoundedSecant (FuncWrapper1D *f, double x0, double xmin, double xmax, double dx, double ftol, int maxiter, std::string *errstring)
double	Newton (FuncWrapper1D *f, double x0, double ftol, int maxiter, std::string *errstring)
std::vector< double >	NDNewtonRaphson_Jacobian (FuncWrapperND *f, std::vector< double > x0, double tol, int maxiter, std::string *errstring)

Function Documentation

double BoundedSecant	(	FuncWrapper1D *	f,
		double	x0,
		double	xmin,
		double	xmax,
		double	dx,
		double	tol,
		int	maxiter,
		std::string *	errstring
	)

In the secant function, a 1-D Newton-Raphson solver is implemented. An initial guess for the solution is provided.

Parameters

f	A pointer to an instance of the FuncWrapper1D class that implements the call() function
x0	The inital guess for the solution
xmax	The upper bound for the solution
xmin	The lower bound for the solution
dx	The initial amount that is added to x in order to build the numerical derivative
tol	The absolute value of the tolerance accepted for the objective function
maxiter	Maximum number of iterations
errstring	A pointer to the std::string that returns the error from Secant. Length is zero if no errors are found

Returns

If no errors are found, the solution, otherwise the value _HUGE, the value for infinity

Definition at line 179 of file Solvers.cpp.

double Brent	(	FuncWrapper1D *	f,
		double	a,
		double	b,
		double	macheps,
		double	t,
		int	maxiter,
		std::string *	errstr
	)

This function implements a 1-D bounded solver using the algorithm from Brent, R. P., Algorithms for Minimization Without Derivatives. Englewood Cliffs, NJ: Prentice-Hall, 1973. Ch. 3-4.

a and b must bound the solution of interest and f(a) and f(b) must have opposite signs. If the function is continuous, there must be at least one solution in the interval [a,b].

Parameters

f	A pointer to an instance of the FuncWrapper1D class that must implement the class() function
a	The minimum bound for the solution of f=0
b	The maximum bound for the solution of f=0
macheps	The machine precision
t	Tolerance (absolute)
maxiter	Maximum numer of steps allowed. Will throw a SolutionError if the solution cannot be found
errstr	A pointer to the error string returned. If length is zero, no errors found.

Definition at line 235 of file Solvers.cpp.

std::vector<double> NDNewtonRaphson_Jacobian	(	FuncWrapperND *	f,
		std::vector< double >	x0,
		double	tol,
		int	maxiter,
		std::string *	errstring
	)

In this formulation of the Multi-Dimensional Newton-Raphson solver the Jacobian matrix is known. Therefore, the dx vector can be obtained from

J(x)dx=-f(x)

for a given value of x. The pointer to the class FuncWrapperND that is passed in must implement the call() and Jacobian() functions, each of which take the vector x. The data is managed using std::vector<double> vectors

Parameters

f	A pointer to an subclass of the FuncWrapperND class that implements the call() and Jacobian() functions
x0	The initial guess value for the solution
tol	The root-sum-square of the errors from each of the components
maxiter	The maximum number of iterations
errstring	A string with the returned error. If the length of errstring is zero, no errors were found

Returns

If no errors are found, the solution. Otherwise, _HUGE, the value for infinity

Definition at line 47 of file Solvers.cpp.

double Newton	(	FuncWrapper1D *	f,
		double	x0,
		double	ftol,
		int	maxiter,
		std::string *	errstring
	)

In the newton function, a 1-D Newton-Raphson solver is implemented using exact solutions. An initial guess for the solution is provided.

Parameters

f	A pointer to an instance of the FuncWrapper1D class that implements the call() function
x0	The inital guess for the solution
ftol	The absolute value of the tolerance accepted for the objective function
maxiter	Maximum number of iterations
errstring	A pointer to the std::string that returns the error from Secant. Length is zero if no errors are found

Returns

If no errors are found, the solution, otherwise the value _HUGE, the value for infinity

Definition at line 85 of file Solvers.cpp.

double Secant	(	FuncWrapper1D *	f,
		double	x0,
		double	dx,
		double	tol,
		int	maxiter,
		std::string *	errstring
	)

In the secant function, a 1-D Newton-Raphson solver is implemented. An initial guess for the solution is provided.

Parameters

f	A pointer to an instance of the FuncWrapper1D class that implements the call() function
x0	The inital guess for the solutionh
dx	The initial amount that is added to x in order to build the numerical derivative
tol	The absolute value of the tolerance accepted for the objective function
maxiter	Maximum number of iterations
errstring	A pointer to the std::string that returns the error from Secant. Length is zero if no errors are found

Returns

If no errors are found, the solution, otherwise the value _HUGE, the value for infinity

Definition at line 123 of file Solvers.cpp.