Sparse Levenberg Marquardt nonlinear least squares. More...

#include <vnl_sparse_lm.h>

Inheritance diagram for vnl_sparse_lm:

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_sparse_lm (vnl_sparse_lst_sqr_function &f)
	Initialize with the function object that is to be minimized.
	~vnl_sparse_lm ()
	Destructor.
bool	minimize (vnl_vector< double > &a, vnl_vector< double > &b, vnl_vector< double > &c, bool use_gradient=true, bool use_weights=true)
	Minimize the function supplied in the constructor until convergence or failure.
void	diagnose_outcome () const
	Provide an ASCII diagnosis of the last minimization on vcl_ostream.
void	diagnose_outcome (vcl_ostream &) const
vnl_matrix< double > const &	get_JtJ ()
	Return J'*J computed at last minimum.
const vnl_vector< double > &	get_weights () const
	Access the final weights after optimization.
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	init (vnl_sparse_lst_sqr_function *f)
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
double	tau_
	used to compute the initial damping.
vnl_sparse_lst_sqr_function *	f_
	the function to minimize.
vnl_matrix< double >	inv_covar_
bool	set_covariance_
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	allocate_matrices ()
	allocate matrix memory by setting all the matrix sizes.
bool	check_vector_sizes (vnl_vector< double > const &a, vnl_vector< double > const &b, vnl_vector< double > const &c)
	check vector sizes and verify that they match the problem size.
void	compute_normal_equations ()
	compute the blocks making up the the normal equations: Jt J d = Jt e.
vnl_vector< double >	extract_diagonal () const
	extract the vector on the diagonal of Jt J.
void	set_diagonal (const vnl_vector< double > &diag)
	set the vector on the diagonal of Jt J.
void	compute_invV_Y ()
	compute all inv(Vi) and Yij.
void	compute_Z_Sa (vnl_matrix< double > &Sa)
	compute Z and Sa.
void	compute_Ma (const vnl_matrix< double > &H)
	compute Ma.
void	compute_Mb ()
	compute Mb.
void	solve_dc (vnl_vector< double > &dc)
	solve for dc.
void	compute_sea (vnl_vector< double > const &dc, vnl_vector< double > &sea)
	compute sea using ea, Z, dc, Y, and eb.
void	compute_Sa_sea (vnl_matrix< double > &Sa, vnl_vector< double > &sea)
	compute Sa and sea.
void	backsolve_db (vnl_vector< double > const &da, vnl_vector< double > const &dc, vnl_vector< double > &db)
	back solve to find db using da and dc.
Private Attributes
const int	num_a_
const int	num_b_
const int	num_e_
const int	num_nz_
const int	size_a_
const int	size_b_
const int	size_c_
const int	size_e_
vcl_vector< vnl_matrix< double > >	A_
	Storage for each of the Jacobians A_ij, B_ij, and C_ij.
vcl_vector< vnl_matrix< double > >	B_
vcl_vector< vnl_matrix< double > >	C_
vcl_vector< vnl_matrix< double > >	U_
	Storage for normal equation blocks.
vcl_vector< vnl_matrix< double > >	V_
vnl_matrix< double >	T_
vcl_vector< vnl_matrix< double > >	W_
vcl_vector< vnl_matrix< double > >	R_
vcl_vector< vnl_matrix< double > >	Q_
vnl_vector< double >	ea_
vnl_vector< double >	eb_
vnl_vector< double >	ec_
vnl_vector< double >	e_
vnl_vector< double >	weights_
vcl_vector< vnl_matrix< double > >	inv_V_
vcl_vector< vnl_matrix< double > >	Y_
vcl_vector< vnl_matrix< double > >	Z_
vcl_vector< vnl_matrix< double > >	Ma_
vcl_vector< vnl_matrix< double > >	Mb_

Detailed Description

Sparse Levenberg Marquardt nonlinear least squares.

Unlike vnl_levenberg_marquardt this does not use the MINPACK routines. This class implements sparse Levenberg Marquardt as described in the Hartley and Zisserman "Multiple View Geometry" book and further described in a technical report on sparse bundle adjustment available at http://www.ics.forth.gr/~lourakis/sba

Definition at line 33 of file vnl_sparse_lm.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_sparse_lm::vnl_sparse_lm ( vnl_sparse_lst_sqr_function & f )

Initialize with the function object that is to be minimized.

Definition at line 29 of file vnl_sparse_lm.cxx.

vnl_sparse_lm::~vnl_sparse_lm ( )

Destructor.

Definition at line 80 of file vnl_sparse_lm.cxx.

Member Function Documentation

void vnl_sparse_lm::allocate_matrices ( ) [private]

allocate matrix memory by setting all the matrix sizes.

Definition at line 364 of file vnl_sparse_lm.cxx.

void vnl_sparse_lm::backsolve_db	(	vnl_vector< double > const &	da,
		vnl_vector< double > const &	dc,
		vnl_vector< double > &	db
	)		`[private]`

back solve to find db using da and dc.

Definition at line 777 of file vnl_sparse_lm.cxx.

bool vnl_sparse_lm::check_vector_sizes	(	vnl_vector< double > const &	a,
		vnl_vector< double > const &	b,
		vnl_vector< double > const &	c
	)		`[private]`

check vector sizes and verify that they match the problem size.

Definition at line 327 of file vnl_sparse_lm.cxx.

void vnl_sparse_lm::compute_invV_Y ( ) [private]

compute all inv(Vi) and Yij.

Definition at line 508 of file vnl_sparse_lm.cxx.

void vnl_sparse_lm::compute_Ma ( const vnl_matrix< double > & H ) [private]

compute Ma.

Definition at line 598 of file vnl_sparse_lm.cxx.

void vnl_sparse_lm::compute_Mb ( ) [private]

compute Mb.

Definition at line 618 of file vnl_sparse_lm.cxx.

void vnl_sparse_lm::compute_normal_equations ( ) [private]

compute the blocks making up the the normal equations: Jt J d = Jt e.

Definition at line 406 of file vnl_sparse_lm.cxx.

void vnl_sparse_lm::compute_Sa_sea	(	vnl_matrix< double > &	Sa,
		vnl_vector< double > &	sea
	)		`[private]`

compute Sa and sea.

only used when size_c_ == 0

Definition at line 719 of file vnl_sparse_lm.cxx.

void vnl_sparse_lm::compute_sea	(	vnl_vector< double > const &	dc,
		vnl_vector< double > &	sea
	)		`[private]`

compute sea using ea, Z, dc, Y, and eb.

Definition at line 690 of file vnl_sparse_lm.cxx.

void vnl_sparse_lm::compute_Z_Sa ( vnl_matrix< double > & Sa ) [private]

compute Z and Sa.

Definition at line 538 of file vnl_sparse_lm.cxx.

void vnl_sparse_lm::diagnose_outcome ( ) const

Provide an ASCII diagnosis of the last minimization on vcl_ostream.

Definition at line 809 of file vnl_sparse_lm.cxx.

void vnl_sparse_lm::diagnose_outcome ( vcl_ostream & s ) const

Definition at line 816 of file vnl_sparse_lm.cxx.

vnl_vector< double > vnl_sparse_lm::extract_diagonal ( ) const [private]

extract the vector on the diagonal of Jt J.

Definition at line 466 of file vnl_sparse_lm.cxx.

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.

vnl_matrix< double > const & vnl_sparse_lm::get_JtJ ( )

Return J'*J computed at last minimum.

it is an approximation of inverse of covariance

Definition at line 864 of file vnl_sparse_lm.cxx.

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.

const vnl_vector<double>& vnl_sparse_lm::get_weights ( ) const [inline]

Access the final weights after optimization.

Definition at line 67 of file vnl_sparse_lm.h.

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

Definition at line 56 of file vnl_nonlinear_minimizer.h.

void vnl_sparse_lm::init ( vnl_sparse_lst_sqr_function * f ) [protected]

Definition at line 63 of file vnl_sparse_lm.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_sparse_lm::minimize	(	vnl_vector< double > &	a,
		vnl_vector< double > &	b,
		vnl_vector< double > &	c,
		bool	use_gradient = `true`,
		bool	use_weights = `true`
	)

Minimize the function supplied in the constructor until convergence or failure.

On return, a, b, and c are such that f(a,b,c) is the lowest value achieved. Returns true for convergence, false for failure. If use_gradient is set to false, a finite difference approximation will be used, even if the Jacobian functions have been provided. If use_weights is set to false, weights will not be computed even if a weighting function has been provided.

Systems to solve will be Sc*dc=sec and Sa*da=sea.

Definition at line 92 of file vnl_sparse_lm.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_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_sparse_lm::set_diagonal ( const vnl_vector< double > & diag ) [private]

set the vector on the diagonal of Jt J.

Definition at line 489 of file vnl_sparse_lm.cxx.

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_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.

void vnl_sparse_lm::solve_dc ( vnl_vector< double > & dc ) [private]

solve for dc.

Definition at line 646 of file vnl_sparse_lm.cxx.