The ever-popular Powell minimizer. More...

#include <vnl_powell.h>

Inheritance diagram for vnl_powell:

Public Types
enum	ReturnCodes { ERROR_FAILURE = -1, ERROR_DODGY_INPUT = 0, CONVERGED_FTOL = 1, CONVERGED_XTOL = 2, CONVERGED_XFTOL = 3, CONVERGED_GTOL = 4, FAILED_TOO_MANY_ITERATIONS = 5, TOO_MANY_ITERATIONS = FAILED_TOO_MANY_ITERATIONS, FAILED_FTOL_TOO_SMALL = 6, FAILED_XTOL_TOO_SMALL = 7, FAILED_GTOL_TOO_SMALL = 8, FAILED_USER_REQUEST = 9 }
	Some generic return codes that apply to all minimizers. More...
Public Member Functions
	vnl_powell (vnl_cost_function *functor)
	Initialize a powell with the given cost function.
ReturnCodes	minimize (vnl_vector< double > &x)
	Run minimization, place result in x.
void	set_linmin_xtol (double tol)
	Set tolerance on line search parameter step.
void	set_initial_step (double step)
	Set initial step when bracketing minima along a line.
void	set_f_tolerance (double v)
	Set the convergence tolerance on F (sum of squared residuals).
double	get_f_tolerance () const
void	set_x_tolerance (double v)
	Set the convergence tolerance on X.
double	get_x_tolerance () const
void	set_g_tolerance (double v)
	Set the convergence tolerance on Grad(F)' * F.
double	get_g_tolerance () const
void	set_max_function_evals (int v)
	Set the termination maximum number of iterations.
int	get_max_function_evals () const
void	set_epsilon_function (double v)
	Set the step length for FD Jacobian.
double	get_epsilon_function () const
void	set_trace (bool on)
	Turn on per-iteration printouts.
bool	get_trace () const
void	set_verbose (bool verb)
	Set verbose flag.
bool	get_verbose () const
void	set_check_derivatives (int cd)
	Set check_derivatives flag. Negative values may mean fewer checks.
int	get_check_derivatives () const
double	get_start_error () const
	Return the error of the function when it was evaluated at the start point of the last minimization.
double	get_end_error () const
	Return the best error that was achieved by the last minimization, corresponding to the returned x.
int	get_num_evaluations () const
	Return the total number of times the function was evaluated by the last minimization.
int	get_num_iterations () const
	Return the number of {iterations} in the last minimization.
bool	obj_value_reduced ()
	Whether the error reduced in the last minimization.
virtual vnl_matrix< double > const &	get_covariance ()
	Return the covariance of the estimate at the end.
virtual vcl_string	is_a () const
	Return the name of the class.
virtual bool	is_class (vcl_string const &s) const
	Return true if the name of the class matches the argument.
ReturnCodes	get_failure_code () const
	Return the failure code of the last minimization.
Protected Member Functions
void	pub_report_eval (double e)
void	reset ()
void	report_eval (double f)
	Called by derived classes after each function evaluation.
virtual bool	report_iter ()
	Called by derived classes after each iteration.
Protected Attributes
vnl_cost_function *	functor_
double	linmin_xtol_
	Tolerance on line search parameter step.
double	initial_step_
	Initial step when bracketing minima along a line.
double	xtol
	Termination tolerance on X (solution vector)
long	maxfev
	Termination maximum number of iterations.
double	ftol
	Termination tolerance on F (sum of squared residuals)
double	gtol
	Termination tolerance on Grad(F)' * F = 0.
double	epsfcn
	Step length for FD Jacobian.
unsigned	num_iterations_
long	num_evaluations_
double	start_error_
double	end_error_
bool	trace
bool	verbose_
int	check_derivatives_
ReturnCodes	failure_code_
Friends
class	vnl_powell_1dfun

Detailed Description

The ever-popular Powell minimizer.

Derivative-free method which may be faster if your function is expensive to compute and many-dimensional. Implemented from scratch from NR.

Definition at line 26 of file vnl_powell.h.

Member Enumeration Documentation

enum vnl_nonlinear_minimizer::ReturnCodes [inherited]

Some generic return codes that apply to all minimizers.

Enumerator:

ERROR_FAILURE
ERROR_DODGY_INPUT
CONVERGED_FTOL
CONVERGED_XTOL
CONVERGED_XFTOL
CONVERGED_GTOL
FAILED_TOO_MANY_ITERATIONS
TOO_MANY_ITERATIONS
FAILED_FTOL_TOO_SMALL
FAILED_XTOL_TOO_SMALL
FAILED_GTOL_TOO_SMALL
FAILED_USER_REQUEST

Definition at line 102 of file vnl_nonlinear_minimizer.h.

Constructor & Destructor Documentation

vnl_powell::vnl_powell ( vnl_cost_function * functor ) [inline]

Initialize a powell with the given cost function.

Definition at line 31 of file vnl_powell.h.

Member Function Documentation

int vnl_nonlinear_minimizer::get_check_derivatives ( ) const [inline, inherited]

Definition at line 82 of file vnl_nonlinear_minimizer.h.

vnl_matrix< double > const & vnl_nonlinear_minimizer::get_covariance ( ) [virtual, inherited]

Return the covariance of the estimate at the end.

Definition at line 35 of file vnl_nonlinear_minimizer.cxx.

double vnl_nonlinear_minimizer::get_end_error ( ) const [inline, inherited]

Return the best error that was achieved by the last minimization, corresponding to the returned x.

Definition at line 92 of file vnl_nonlinear_minimizer.h.

double vnl_nonlinear_minimizer::get_epsilon_function ( ) const [inline, inherited]

Definition at line 70 of file vnl_nonlinear_minimizer.h.

double vnl_nonlinear_minimizer::get_f_tolerance ( ) const [inline, inherited]

Definition at line 46 of file vnl_nonlinear_minimizer.h.

ReturnCodes vnl_nonlinear_minimizer::get_failure_code ( ) const [inline, inherited]

Return the failure code of the last minimization.

Definition at line 132 of file vnl_nonlinear_minimizer.h.

double vnl_nonlinear_minimizer::get_g_tolerance ( ) const [inline, inherited]

Definition at line 60 of file vnl_nonlinear_minimizer.h.

int vnl_nonlinear_minimizer::get_max_function_evals ( ) const [inline, inherited]

Definition at line 64 of file vnl_nonlinear_minimizer.h.

int vnl_nonlinear_minimizer::get_num_evaluations ( ) const [inline, inherited]

Return the total number of times the function was evaluated by the last minimization.

Definition at line 95 of file vnl_nonlinear_minimizer.h.

int vnl_nonlinear_minimizer::get_num_iterations ( ) const [inline, inherited]

Return the number of {iterations} in the last minimization.

Each iteration may have comprised several function evaluations.

Definition at line 99 of file vnl_nonlinear_minimizer.h.

double vnl_nonlinear_minimizer::get_start_error ( ) const [inline, inherited]

Return the error of the function when it was evaluated at the start point of the last minimization.

For minimizers driven by a vnl_least_squares_function (Levenberg-Marquardt) this is usually the RMS error. For those driven by a vnl_cost_function (CG, LBFGS, Amoeba) it is simply the value of the vnl_cost_function at the start (usually the sum of squared residuals).

Definition at line 89 of file vnl_nonlinear_minimizer.h.

bool vnl_nonlinear_minimizer::get_trace ( ) const [inline, inherited]

Definition at line 74 of file vnl_nonlinear_minimizer.h.

bool vnl_nonlinear_minimizer::get_verbose ( ) const [inline, inherited]

Definition at line 78 of file vnl_nonlinear_minimizer.h.

double vnl_nonlinear_minimizer::get_x_tolerance ( ) const [inline, inherited]

Definition at line 56 of file vnl_nonlinear_minimizer.h.

vcl_string vnl_nonlinear_minimizer::is_a ( ) const [virtual, inherited]

Return the name of the class.

Used by polymorphic IO

Definition at line 75 of file vnl_nonlinear_minimizer.cxx.

bool vnl_nonlinear_minimizer::is_class ( vcl_string const & s ) const [virtual, inherited]

Return true if the name of the class matches the argument.

Used by polymorphic IO

Definition at line 83 of file vnl_nonlinear_minimizer.cxx.

vnl_nonlinear_minimizer::ReturnCodes vnl_powell::minimize ( vnl_vector< double > & x )

Run minimization, place result in x.

Definition at line 60 of file vnl_powell.cxx.

bool vnl_nonlinear_minimizer::obj_value_reduced ( ) [inline, inherited]

Whether the error reduced in the last minimization.

Definition at line 118 of file vnl_nonlinear_minimizer.h.

void vnl_powell::pub_report_eval ( double e ) [inline, protected]

Definition at line 49 of file vnl_powell.h.

void vnl_nonlinear_minimizer::report_eval ( double f ) [protected, inherited]

Called by derived classes after each function evaluation.

Definition at line 50 of file vnl_nonlinear_minimizer.cxx.

bool vnl_nonlinear_minimizer::report_iter ( ) [protected, virtual, inherited]

Called by derived classes after each iteration.

When true is returned, minimizer should stop with code FAILED_USER_REQUEST. Derived classes can redefine this function to make the optimizer stop when a condition is satisfied.

Definition at line 63 of file vnl_nonlinear_minimizer.cxx.

void vnl_nonlinear_minimizer::reset ( ) [protected, inherited]

Definition at line 41 of file vnl_nonlinear_minimizer.cxx.

void vnl_nonlinear_minimizer::set_check_derivatives ( int cd ) [inline, inherited]

Set check_derivatives flag. Negative values may mean fewer checks.

Definition at line 81 of file vnl_nonlinear_minimizer.h.

void vnl_nonlinear_minimizer::set_epsilon_function ( double v ) [inline, inherited]

Set the step length for FD Jacobian.

Be aware that set_x_tolerance will reset this to xtol * 0.001. The default is 1e-11.

Definition at line 69 of file vnl_nonlinear_minimizer.h.

void vnl_nonlinear_minimizer::set_f_tolerance ( double v ) [inline, inherited]

Set the convergence tolerance on F (sum of squared residuals).

When the differences in successive RMS errors is less than this, the routine terminates. So this is effectively the desired precision of your minimization. Setting it too low wastes time, too high might cause early convergence. The default of 1e-9 is on the safe side, but if speed is an issue, you can try raising it.

Definition at line 45 of file vnl_nonlinear_minimizer.h.

void vnl_nonlinear_minimizer::set_g_tolerance ( double v ) [inline, inherited]

Set the convergence tolerance on Grad(F)' * F.

Definition at line 59 of file vnl_nonlinear_minimizer.h.

void vnl_powell::set_initial_step ( double step ) [inline]

Set initial step when bracketing minima along a line.

Default value is 1.0

Definition at line 43 of file vnl_powell.h.

void vnl_powell::set_linmin_xtol ( double tol ) [inline]

Set tolerance on line search parameter step.

Default value is 0.0001

Definition at line 39 of file vnl_powell.h.

void vnl_nonlinear_minimizer::set_max_function_evals ( int v ) [inline, inherited]

Set the termination maximum number of iterations.

Definition at line 63 of file vnl_nonlinear_minimizer.h.

void vnl_nonlinear_minimizer::set_trace ( bool on ) [inline, inherited]

Turn on per-iteration printouts.

Definition at line 73 of file vnl_nonlinear_minimizer.h.

void vnl_nonlinear_minimizer::set_verbose ( bool verb ) [inline, inherited]

Set verbose flag.

Definition at line 77 of file vnl_nonlinear_minimizer.h.

void vnl_nonlinear_minimizer::set_x_tolerance ( double v ) [inline, inherited]

Set the convergence tolerance on X.

When the length of the steps taken in X are about this long, the routine terminates. The default is 1e-8, which should work for many problems, but if you can get away with 1e-4, say, minimizations will be much quicker.

Definition at line 52 of file vnl_nonlinear_minimizer.h.