lsst::meas::modelfit::Likelihood Class Reference

Base class for optimizer/sampler likelihood functions that compute likelihood at a point. More...

#include <Likelihood.h>

Inheritance diagram for lsst::meas::modelfit::Likelihood:

Public Member Functions
int	getDataDim () const
	Return the number of data points.
int	getAmplitudeDim () const
	Return the number of linear parameters (columns of the model matrix)
int	getNonlinearDim () const
	Return the number of nonlinear parameters (which parameterize the model matrix)
int	getFixedDim () const
	Return the number of fixed nonlinear parameters (set on Likelihood construction)
ndarray::Array< Scalar const, 1, 1 >	getFixed () const
	Return the vector of fixed nonlinear parameters.
ndarray::Array< Pixel const, 1, 1 >	getData () const
	Return the vector of weighted, scaled data points \(z\).
ndarray::Array< Pixel const, 1, 1 >	getUnweightedData () const
	Return the vector of unweighted data points \(y\).
ndarray::Array< Pixel const, 1, 1 >	getWeights () const
	Return the vector of weights \(w\) applied to data points and model matrix rows.
ndarray::Array< Pixel const, 1, 1 >	getVariance () const
	Return the vector of per-data-point variances.
std::shared_ptr< Model >	getModel () const
	Return an object that defines the model and its parameters.
virtual void	computeModelMatrix (ndarray::Array< Pixel, 2,-1 > const &modelMatrix, ndarray::Array< Scalar const, 1, 1 > const &nonlinear, bool doApplyWeights=true) const =0
	Evaluate the model for the given vector of nonlinear parameters.
virtual	~Likelihood ()
	Likelihood (const Likelihood &)=delete
Likelihood &	operator= (const Likelihood &)=delete
	Likelihood (Likelihood &&)=delete
Likelihood &	operator= (Likelihood &&)=delete

Protected Member Functions
	Likelihood (std::shared_ptr< Model > model, ndarray::Array< Scalar const, 1, 1 > const &fixed)

Protected Attributes
std::shared_ptr< Model >	_model
ndarray::Array< Scalar const, 1, 1 >	_fixed
ndarray::Array< Pixel, 1, 1 >	_data
ndarray::Array< Pixel, 1, 1 >	_unweightedData
ndarray::Array< Pixel, 1, 1 >	_variance
ndarray::Array< Pixel, 1, 1 >	_weights

Detailed Description

Base class for optimizer/sampler likelihood functions that compute likelihood at a point.

Likelihood abstracts the problem of computing the likelihood over different kinds of data. It is responsible for creating a "model matrix" that maps amplitudes to data values, and maintaining a vector of scaled, weighted data values that corresponds to it. Its components can be represented best in the mathematical formula for a -log likelihood assuming Gaussian data and a model with both nonlinear parameters \(\theta\) and linear ("amplitude") parameters \(\alpha\):

\[ L(\alpha,\theta) = \frac{1}{2}\left(y - A(\theta)\alpha\right)^T\, \Sigma^{-1}\,\left(y - A(\theta)\alpha\right) \]

where \(y\) is the data vector, \(\Sigma\) is the data covariance matrix (assumed to be diagonal), and \(A(\theta)\) is the "true" model matrix (parametrized on the nonlinear parameters).

When fitting or sampling from the likelihood, however, we don't want to use these quantities directly, and they aren't what the Likelihood class provides. Instead, we reparametrize with:

\[ w_i \equiv \Sigma_{i,i}^{-1/2} \]

\[ z_i = w_i y_i \]

\[ B_{i,j} = w_i A_{i,j} \]

resulting in the equivalent formula:

\[ L(\alpha,\theta) = \frac{1}{2}\left(z-B(\theta)\alpha\right)^T\,\left(z-B(\theta)\alpha\right) \]

The \(w_i\) are the weights, which are applied to both the data vector and the model matrix to account for the noise in the data. In some cases, we may choose to use a constant weight rather than per-pixel weights, but will will still use a vector to represent it.

Definition at line 69 of file Likelihood.h.

Constructor & Destructor Documentation

~Likelihood()

virtual lsst::meas::modelfit::Likelihood::~Likelihood ( )

inlinevirtual

Definition at line 126 of file Likelihood.h.

{}

Likelihood() [1/3]

lsst::meas::modelfit::Likelihood::Likelihood ( const Likelihood & )

delete

Likelihood() [2/3]

lsst::meas::modelfit::Likelihood::Likelihood ( Likelihood && )

delete

Likelihood() [3/3]

lsst::meas::modelfit::Likelihood::Likelihood ( std::shared_ptr< Model > model, ndarray::Array< Scalar const, 1, 1 > const & fixed )

inlineprotected

Definition at line 138 of file Likelihood.h.

                                                                                         :
        _model(model), _fixed(fixed) {
        LSST_THROW_IF_NE(
            fixed.getSize<0>(), static_cast<std::size_t>(model->getFixedDim()),
            pex::exceptions::LengthError,
            "Fixed parameter vector size (%d) does not match Model fixed parameter dimensionality (%d)"
        );
    }

Member Function Documentation

computeModelMatrix()

virtual void lsst::meas::modelfit::Likelihood::computeModelMatrix ( ndarray::Array< Pixel, 2,-1 > const & modelMatrix, ndarray::Array< Scalar const, 1, 1 > const & nonlinear, bool doApplyWeights = true ) const

pure virtual

Evaluate the model for the given vector of nonlinear parameters.

Parameters

[out]	modelMatrix	The dataDim x amplitudeDim matrix \(B\) that expresses the model projected in such a way that it can be compared to the data when multiplied by an amplitude vector \(\alpha\). It should be weighted if the data vector is. The caller is responsible for guaranteeing that the shape of the matrix correct, but implementations should not assume anything about the initial values of the matrix elements.
[in]	nonlinear	Vector of nonlinear parameters at which to evaluate the model.
[in]	doApplyWeights	If False, do not apply the weights to the modelMatrix.

Implemented in lsst::meas::modelfit::MultiShapeletPsfLikelihood, and lsst::meas::modelfit::UnitTransformedLikelihood.

getAmplitudeDim()

int lsst::meas::modelfit::Likelihood::getAmplitudeDim ( ) const

inline

Return the number of linear parameters (columns of the model matrix)

Definition at line 77 of file Likelihood.h.

{ return _model->getAmplitudeDim(); }

getData()

ndarray::Array< Pixel const, 1, 1 > lsst::meas::modelfit::Likelihood::getData ( ) const

inline

Return the vector of weighted, scaled data points \(z\).

Definition at line 89 of file Likelihood.h.

{ return _data; }

getDataDim()

int lsst::meas::modelfit::Likelihood::getDataDim ( ) const

inline

Return the number of data points.

Definition at line 74 of file Likelihood.h.

{ return _data.getSize<0>(); }

getFixed()

ndarray::Array< Scalar const, 1, 1 > lsst::meas::modelfit::Likelihood::getFixed ( ) const

inline

Return the vector of fixed nonlinear parameters.

Definition at line 86 of file Likelihood.h.

{ return _fixed; }

getFixedDim()

int lsst::meas::modelfit::Likelihood::getFixedDim ( ) const

inline

Return the number of fixed nonlinear parameters (set on Likelihood construction)

Definition at line 83 of file Likelihood.h.

{ return _model->getFixedDim(); }

getModel()

std::shared_ptr< Model > lsst::meas::modelfit::Likelihood::getModel ( ) const

inline

Return an object that defines the model and its parameters.

Definition at line 105 of file Likelihood.h.

{ return _model; }

getNonlinearDim()

int lsst::meas::modelfit::Likelihood::getNonlinearDim ( ) const

inline

Return the number of nonlinear parameters (which parameterize the model matrix)

Definition at line 80 of file Likelihood.h.

{ return _model->getNonlinearDim(); }

getUnweightedData()

ndarray::Array< Pixel const, 1, 1 > lsst::meas::modelfit::Likelihood::getUnweightedData ( ) const

inline

Return the vector of unweighted data points \(y\).

Definition at line 92 of file Likelihood.h.

{ return _unweightedData; }

getVariance()

ndarray::Array< Pixel const, 1, 1 > lsst::meas::modelfit::Likelihood::getVariance ( ) const

inline

Return the vector of per-data-point variances.

Definition at line 102 of file Likelihood.h.

{ return _variance; }

getWeights()

ndarray::Array< Pixel const, 1, 1 > lsst::meas::modelfit::Likelihood::getWeights ( ) const

inline

Return the vector of weights \(w\) applied to data points and model matrix rows.

Will be an empty array if no weights are applied.

Definition at line 99 of file Likelihood.h.

{ return _weights; }

operator=() [1/2]

Likelihood & lsst::meas::modelfit::Likelihood::operator= ( const Likelihood & )

delete

operator=() [2/2]

Likelihood & lsst::meas::modelfit::Likelihood::operator= ( Likelihood && )

delete

Member Data Documentation

_data

ndarray::Array<Pixel,1,1> lsst::meas::modelfit::Likelihood::_data

protected

Definition at line 149 of file Likelihood.h.

_fixed

ndarray::Array<Scalar const,1,1> lsst::meas::modelfit::Likelihood::_fixed

protected

Definition at line 148 of file Likelihood.h.

_model

std::shared_ptr<Model> lsst::meas::modelfit::Likelihood::_model

protected

Definition at line 147 of file Likelihood.h.

_unweightedData

ndarray::Array<Pixel,1,1> lsst::meas::modelfit::Likelihood::_unweightedData

protected

Definition at line 150 of file Likelihood.h.

_variance

ndarray::Array<Pixel,1,1> lsst::meas::modelfit::Likelihood::_variance

protected

Definition at line 151 of file Likelihood.h.

_weights

ndarray::Array<Pixel,1,1> lsst::meas::modelfit::Likelihood::_weights

protected

Definition at line 152 of file Likelihood.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+2a84bb7594/include/lsst/meas/modelfit/Likelihood.h