Limited memory Broyden Fletcher Goldfarb Shannon minimization with constraints. More...

#include <vnl_lbfgsb.h>

Inheritance diagram for vnl_lbfgsb:

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_lbfgsb ()
	vnl_lbfgsb (vnl_cost_function &f)
bool	minimize (vnl_vector< double > &x)
	Find a minimum in the feasible region given an initial guess.
void	set_bound_selection (vnl_vector< long > const &nbd)
	Set the bounds to be enforced on each variable.
void	get_bound_selection (vnl_vector< long > &nbd) const
	Get the bounds currently enforced on each variable.
void	set_lower_bound (vnl_vector< double > const &l)
	Set the lower bounds for all variables.
void	get_lower_bound (vnl_vector< double > &l) const
	Get the lower bounds for all variables.
void	set_upper_bound (vnl_vector< double > const &u)
	Set the upper bounds for all variables.
void	get_upper_bound (vnl_vector< double > &u) const
	Get the upper bounds for all variables.
void	set_max_variable_metric_corrections (long m)
	Set the maximum number of variable metric corrections.
long	get_max_variable_metric_corrections () const
	Get the maximum number of variable metric corrections.
void	set_cost_function_convergence_factor (double factor)
	Set the cost function convergence factor.
double	get_cost_function_convergence_factor () const
	Get the cost function convergence factor.
void	set_projected_gradient_tolerance (double tol)
	Set the projected gradient tolerance.
double	get_projected_gradient_tolerance () const
	Get the projected gradient tolerance.
double	get_inf_norm_projected_gradient () const
	Get the current infinity norm of the projected gradient.
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	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_vector< double >	lower_bound_
vnl_vector< double >	upper_bound_
vnl_vector< long >	bound_selection_
long	max_corrections_
double	convergence_factor_
double	projected_gradient_tolerance_
double	inf_norm_projected_gradient_
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_
Private Member Functions
void	init_parameters ()
Private Attributes
vnl_cost_function *	f_

Detailed Description

Limited memory Broyden Fletcher Goldfarb Shannon minimization with constraints.

Lower and upper bounds may be specified for the variables to be optimized. The algorithm minimizes a nonlinear function f(x) of n variables subject to simple bound constraints of l <= x <= u.

Definition at line 28 of file vnl_lbfgsb.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_lbfgsb::vnl_lbfgsb ( )

Definition at line 19 of file vnl_lbfgsb.cxx.

vnl_lbfgsb::vnl_lbfgsb ( vnl_cost_function & f )

Definition at line 25 of file vnl_lbfgsb.cxx.

Member Function Documentation

void vnl_lbfgsb::get_bound_selection ( vnl_vector< long > & nbd ) const [inline]

Get the bounds currently enforced on each variable.

Definition at line 49 of file vnl_lbfgsb.h.

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

Definition at line 82 of file vnl_nonlinear_minimizer.h.

double vnl_lbfgsb::get_cost_function_convergence_factor ( ) const [inline]

Get the cost function convergence factor.

Definition at line 92 of file vnl_lbfgsb.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.

double vnl_lbfgsb::get_inf_norm_projected_gradient ( ) const [inline]

Get the current infinity norm of the projected gradient.

Definition at line 107 of file vnl_lbfgsb.h.

void vnl_lbfgsb::get_lower_bound ( vnl_vector< double > & l ) const [inline]

Get the lower bounds for all variables.

Definition at line 60 of file vnl_lbfgsb.h.

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

Definition at line 64 of file vnl_nonlinear_minimizer.h.

long vnl_lbfgsb::get_max_variable_metric_corrections ( ) const [inline]

Get the maximum number of variable metric corrections.

Definition at line 81 of file vnl_lbfgsb.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_lbfgsb::get_projected_gradient_tolerance ( ) const [inline]

Get the projected gradient tolerance.

Definition at line 103 of file vnl_lbfgsb.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.

void vnl_lbfgsb::get_upper_bound ( vnl_vector< double > & u ) const [inline]

Get the upper bounds for all variables.

Definition at line 71 of file vnl_lbfgsb.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.

void vnl_lbfgsb::init_parameters ( ) [private]

Definition at line 31 of file vnl_lbfgsb.cxx.

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.

bool vnl_lbfgsb::minimize ( vnl_vector< double > & x )

Find a minimum in the feasible region given an initial guess.

Returns true if a minimum is found and false for failure.

Definition at line 42 of file vnl_lbfgsb.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_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_lbfgsb::set_bound_selection ( vnl_vector< long > const & nbd ) [inline]

Set the bounds to be enforced on each variable.

The argument should have one entry per unknown. Each entry may have one of these values: 0 - variable is not constrained 1 - variable has only a lower bound 2 - variable has both lower and upper bounds 3 - variable has only an upper bound

Definition at line 45 of file vnl_lbfgsb.h.

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_lbfgsb::set_cost_function_convergence_factor ( double factor ) [inline]

Set the cost function convergence factor.

When an iteration changes the function value by an amount smaller than this factor times the machine epsilon (scaled by function magnitude) convergence is assumed. The default value is 1e+7.

Definition at line 88 of file vnl_lbfgsb.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_lbfgsb::set_lower_bound ( vnl_vector< double > const & l ) [inline]

Set the lower bounds for all variables.

The argument should have one entry per unknown. The lower bound is used only if the corresponding entry in the bound selection vector is set to 1 or 2.

Definition at line 56 of file vnl_lbfgsb.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_lbfgsb::set_max_variable_metric_corrections ( long m ) [inline]

Set the maximum number of variable metric corrections.

This is used to determine the size of the limited-memory matrix. The default value is 5.

Definition at line 77 of file vnl_lbfgsb.h.

void vnl_lbfgsb::set_projected_gradient_tolerance ( double tol ) [inline]

Set the projected gradient tolerance.

When the projected gradient vector has no component larger than the given value convergence is assumed. The default value is 1e-5.

Definition at line 99 of file vnl_lbfgsb.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_lbfgsb::set_upper_bound ( vnl_vector< double > const & u ) [inline]

Set the upper bounds for all variables.

The argument should have one entry per unknown. The upper bound is used only if the corresponding entry in the bound selection vector is set to 2 or 3.

Definition at line 67 of file vnl_lbfgsb.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.