lsst::meas::modelfit::Optimizer Class Reference

A numerical optimizer customized for least-squares problems with Bayesian priors. More...

#include <optimizer.h>

Public Types
enum	StateFlags {   CONVERGED_GRADZERO = 0x0001 , CONVERGED_TR_SMALL = 0x0002 , CONVERGED = CONVERGED_GRADZERO | CONVERGED_TR_SMALL , FAILED_MAX_INNER_ITERATIONS = 0x0010 ,   FAILED_MAX_OUTER_ITERATIONS = 0x0020 , FAILED_MAX_ITERATIONS = 0x0030 , FAILED_EXCEPTION = 0x0040 , FAILED_NAN = 0x0080 ,   FAILED = FAILED_MAX_INNER_ITERATIONS | FAILED_MAX_OUTER_ITERATIONS | FAILED_EXCEPTION | FAILED_NAN , STATUS_STEP_REJECTED = 0x0100 , STATUS_STEP_ACCEPTED = 0x0200 , STATUS_STEP = STATUS_STEP_REJECTED | STATUS_STEP_ACCEPTED ,   STATUS_TR_UNCHANGED = 0x1000 , STATUS_TR_DECREASED = 0x2000 , STATUS_TR_INCREASED = 0x4000 , STATUS_TR = STATUS_TR_UNCHANGED | STATUS_TR_DECREASED | STATUS_TR_INCREASED ,   STATUS = STATUS_STEP | STATUS_TR }
typedef OptimizerObjective	Objective
typedef OptimizerControl	Control
typedef OptimizerHistoryRecorder	HistoryRecorder

Public Member Functions
	Optimizer (std::shared_ptr< Objective const > objective, ndarray::Array< Scalar const, 1, 1 > const &parameters, Control const &ctrl)
std::shared_ptr< Objective const >	getObjective () const
Control const &	getControl () const
bool	step ()
bool	step (HistoryRecorder const &recorder, afw::table::BaseCatalog &history)
int	run ()
int	run (HistoryRecorder const &recorder, afw::table::BaseCatalog &history)
int	getState () const
Scalar	getObjectiveValue () const
ndarray::Array< Scalar const, 1, 1 >	getParameters () const
ndarray::Array< Scalar const, 1, 1 >	getResiduals () const
ndarray::Array< Scalar const, 1, 1 >	getGradient () const
ndarray::Array< Scalar const, 2, 2 >	getHessian () const
void	removeSR1Term ()
	Remove the symmetric-rank-1 secant term from the Hessian, making it just (J^T J)

Friends
class	OptimizerHistoryRecorder

Detailed Description

A numerical optimizer customized for least-squares problems with Bayesian priors.

The algorithm used by Optimizer combines the Gauss-Newton approach of approximating the second-derivative (Hessian) matrix as the inner product of the Jacobian of the residuals, while maintaining a matrix of corrections to this to account for large residuals, which is updated using a symmetric rank-1 (SR1) secant formula. We assume the prior has analytic first and second derivatives, but use numerical derivatives to compute the Jacobian of the residuals at every step. A trust region approach is used to ensure global convergence.

We consider the function \(f(x)\) we wish to optimize to have two terms, which correspond to negative log likelihood ( \(\chi^2/2=\|r(x)|^2\), where \(r(x)\) is the vector of residuals at \(x\)) and negative log prior \(q(x)=-\ln P(x)\):

\[ f(x) = \frac{1}{2}\|r(x)\|^2 + q(x) \]

At each iteration \(k\), we expand \(f(x)\) in a Taylor series in \(s=x_{k+1}-x_{k}\):

\[ f(x) \approx m(s) = f(x_k) + g_k^T s + \frac{1}{2}s^T H_k s \]

where

\[ g_k \equiv \left.\frac{\partial f}{\partial x}\right|_{x_k} = J_k^T r_k + \nabla q_k;\quad\quad J_k \equiv \left.\frac{\partial r}{\partial x}\right|_{x_k} \]

\[ H_k = J_k^T J_k + \nabla^2 q_k + B_k \]

Here, \(B_k\) is the SR1 approximation term to the second derivative term:

\[ B_k \approx \sum_i \frac{\partial^2 r^{(i)}_k}{\partial x^2}r^{(i)}_k \]

which we initialize to zero and then update with the following formula:

\[ B_{k+1} = B_{k} + \frac{v v^T}{v^T s};\quad\quad v\equiv J^T_{k+1} r_{k+1} - J^T_k r_k \]

Unlike the more common rank-2 BFGS update formula, SR1 updates are not guaranteed to produce a positive definite Hessian. This can result in more accurate approximations of the Hessian (and hence more accurate covariance matrices), but it rules out line-search methods and the simple dog-leg approach to the trust region problem. As a result, we should require fewer steps to converge, but spend more time computing each step; this is ideal when we expect the time spent in function evaluation to dominate the time per step anyway.

Definition at line 399 of file optimizer.h.

Member Typedef Documentation

Control

typedef OptimizerControl lsst::meas::modelfit::Optimizer::Control

Definition at line 403 of file optimizer.h.

HistoryRecorder

typedef OptimizerHistoryRecorder lsst::meas::modelfit::Optimizer::HistoryRecorder

Definition at line 404 of file optimizer.h.

Objective

typedef OptimizerObjective lsst::meas::modelfit::Optimizer::Objective

Definition at line 402 of file optimizer.h.

Member Enumeration Documentation

StateFlags

enum lsst::meas::modelfit::Optimizer::StateFlags

Enumerator
CONVERGED_GRADZERO
CONVERGED_TR_SMALL
CONVERGED
FAILED_MAX_INNER_ITERATIONS
FAILED_MAX_OUTER_ITERATIONS
FAILED_MAX_ITERATIONS
FAILED_EXCEPTION
FAILED_NAN
FAILED
STATUS_STEP_REJECTED
STATUS_STEP_ACCEPTED
STATUS_STEP
STATUS_TR_UNCHANGED
STATUS_TR_DECREASED
STATUS_TR_INCREASED
STATUS_TR
STATUS

Definition at line 406 of file optimizer.h.

                    {
        CONVERGED_GRADZERO = 0x0001,
        CONVERGED_TR_SMALL = 0x0002,
        CONVERGED = CONVERGED_GRADZERO | CONVERGED_TR_SMALL,
        FAILED_MAX_INNER_ITERATIONS = 0x0010,
        FAILED_MAX_OUTER_ITERATIONS = 0x0020,
        FAILED_MAX_ITERATIONS = 0x0030,
        FAILED_EXCEPTION = 0x0040,
        FAILED_NAN = 0x0080,
        FAILED = FAILED_MAX_INNER_ITERATIONS | FAILED_MAX_OUTER_ITERATIONS | FAILED_EXCEPTION | FAILED_NAN,
        STATUS_STEP_REJECTED = 0x0100,
        STATUS_STEP_ACCEPTED = 0x0200,
        STATUS_STEP = STATUS_STEP_REJECTED | STATUS_STEP_ACCEPTED,
        STATUS_TR_UNCHANGED = 0x1000,
        STATUS_TR_DECREASED = 0x2000,
        STATUS_TR_INCREASED = 0x4000,
        STATUS_TR = STATUS_TR_UNCHANGED | STATUS_TR_DECREASED | STATUS_TR_INCREASED,
        STATUS = STATUS_STEP | STATUS_TR,
    };

Constructor & Destructor Documentation

Optimizer()

lsst::meas::modelfit::Optimizer::Optimizer	(	std::shared_ptr< Objective const >	objective,
		ndarray::Array< Scalar const, 1, 1 > const &	parameters,
		Control const &	ctrl )

Member Function Documentation

getControl()

Control const & lsst::meas::modelfit::Optimizer::getControl ( ) const

inline

Definition at line 434 of file optimizer.h.

{ return _ctrl; }

getGradient()

ndarray::Array< Scalar const, 1, 1 > lsst::meas::modelfit::Optimizer::getGradient ( ) const

inline

Definition at line 456 of file optimizer.h.

{ return _gradient; }

getHessian()

ndarray::Array< Scalar const, 2, 2 > lsst::meas::modelfit::Optimizer::getHessian ( ) const

inline

Definition at line 458 of file optimizer.h.

{ return _hessian; }

getObjective()

std::shared_ptr< Objective const > lsst::meas::modelfit::Optimizer::getObjective ( ) const

inline

Definition at line 432 of file optimizer.h.

{ return _objective; }

getObjectiveValue()

Scalar lsst::meas::modelfit::Optimizer::getObjectiveValue ( ) const

inline

Definition at line 450 of file optimizer.h.

{ return _current.objectiveValue; }

getParameters()

ndarray::Array< Scalar const, 1, 1 > lsst::meas::modelfit::Optimizer::getParameters ( ) const

inline

Definition at line 452 of file optimizer.h.

{ return _current.parameters; }

getResiduals()

ndarray::Array< Scalar const, 1, 1 > lsst::meas::modelfit::Optimizer::getResiduals ( ) const

inline

Definition at line 454 of file optimizer.h.

{ return _current.residuals; }

getState()

int lsst::meas::modelfit::Optimizer::getState ( ) const

inline

Definition at line 448 of file optimizer.h.

{ return _state; }

removeSR1Term()

void lsst::meas::modelfit::Optimizer::removeSR1Term

(

)

Remove the symmetric-rank-1 secant term from the Hessian, making it just (J^T J)

run() [1/2]

int lsst::meas::modelfit::Optimizer::run ( )

inline

Definition at line 442 of file optimizer.h.

{ return _runImpl(); }

run() [2/2]

int lsst::meas::modelfit::Optimizer::run ( HistoryRecorder const & recorder, afw::table::BaseCatalog & history )

inline

Definition at line 444 of file optimizer.h.

                                                                             {
        return _runImpl(&recorder, &history);
    }

step() [1/2]

bool lsst::meas::modelfit::Optimizer::step ( )

inline

Definition at line 436 of file optimizer.h.

{ return _stepImpl(0); }

step() [2/2]

bool lsst::meas::modelfit::Optimizer::step ( HistoryRecorder const & recorder, afw::table::BaseCatalog & history )

inline

Definition at line 438 of file optimizer.h.

                                                                               {
        return _stepImpl(0, &recorder, &history);
    }

Friends And Related Symbol Documentation

OptimizerHistoryRecorder

friend class OptimizerHistoryRecorder

friend

Definition at line 476 of file optimizer.h.

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The documentation for this class was generated from the following file:

• /j/snowflake/release/lsstsw/stack/lsst-scipipe-9.0.0/Linux64/meas_modelfit/ga5288a1d22+2903d499ea/include/lsst/meas/modelfit/optimizer.h