Root finders

Detailed Description

Generic root finder methods for finding the roots of a scalar function \(f(x)\).

Functions
std::pair< double, double >	triqs::bisection (std::function< double(double)> f, double x_low, double x_high, double y_target, double precision, long max_loops, std::string x_name, std::string y_name, bool verbosity)
	bisection algorithm
std::pair< double, double >	triqs::dichotomy (std::function< double(double)> f, double x_low, double x_high, double y_target, double precision, long max_loops, std::string x_name, std::string y_name, bool verbosity)
	dichotomy algorithm
std::pair< double, double >	triqs::find_bounds (std::function< double(double)> f, double x_init, double y_value, double delta_x, double precision, long max_loops=1000, bool verbosity=false)
	find upper and lower bounds of f(x)

Function Documentation

bisection()

std::pair< double, double > triqs::bisection ( std::function< double(double)>  f, double  x_low, double  x_high, double  y_target, double  precision, long  max_loops, std::string  x_name, std::string  y_name, bool  verbosity  )

inline

#include <triqs_modest/root_finder.hpp>

bisection algorithm

Parameters

f	function f(x)
x_low	lower bound on f(x)
x_high	upper bound on f(x)
y_target	target value for f(x) = y_target
precision	f(x) - y_target < precision
max_loops	maximum number of attempts
x_name	Name of x variable
y_name	Name of y variable
verbosity	Print progress

Returns

x, f(x) where f(x) = y_target

Definition at line 127 of file root_finder.hpp.

dichotomy()

std::pair< double, double > triqs::dichotomy ( std::function< double(double)>  f, double  x_low, double  x_high, double  y_target, double  precision, long  max_loops, std::string  x_name, std::string  y_name, bool  verbosity  )

inline

#include <triqs_modest/root_finder.hpp>

dichotomy algorithm

Parameters

f	function f(x)
x_low	lower bound on x
x_high	upper bound on x
y_target	target value for f(x)
precision	f(x) - y_target < precision
max_loops	maxmimum number of iterations
x_name	Name of x variable
y_name	Name of y variable
verbosity	Print progress

Returns

x, f(x) where f(x) = y_target

Definition at line 70 of file root_finder.hpp.

find_bounds()

std::pair< double, double > triqs::find_bounds ( std::function< double(double)>  f, double  x_init, double  y_value, double  delta_x, double  precision, long  max_loops = 1000, bool  verbosity = false  )

inline

#include <triqs_modest/root_finder.hpp>

find upper and lower bounds of f(x)

Parameters

f	function of f(x)
x_init	initial guess x
y_value	target value y = f(x)
delta_x	x increment
precision	f(x) - y_value < precision
max_loops	maximum number of loops
verbosity	verbosity of the algorithm

Returns

x1, x2 where f(x1) and f(x2) bound y_value

Definition at line 26 of file root_finder.hpp.