lsst::meas::modelfit::Likelihood Class Referenceabstract

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

Return the number of data points. More...

int getAmplitudeDim () const
Return the number of linear parameters (columns of the model matrix) More...

int getNonlinearDim () const
Return the number of nonlinear parameters (which parameterize the model matrix) More...

int getFixedDim () const
Return the number of fixed nonlinear parameters (set on Likelihood construction) More...

ndarray::Array< Scalar const, 1, 1 > getFixed () const
Return the vector of fixed nonlinear parameters. More...

ndarray::Array< Pixel const, 1, 1 > getData () const
Return the vector of weighted, scaled data points $$z$$. More...

ndarray::Array< Pixel const, 1, 1 > getUnweightedData () const
Return the vector of unweighted data points $$y$$. More...

ndarray::Array< Pixel const, 1, 1 > getWeights () const
Return the vector of weights $$w$$ applied to data points and model matrix rows. More...

ndarray::Array< Pixel const, 1, 1 > getVariance () const
Return the vector of per-data-point variances. More...

std::shared_ptr< ModelgetModel () const
Return an object that defines the model and its parameters. More...

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. More...

virtual ~Likelihood ()

Likelihood (const Likelihood &)=delete

Likelihoodoperator= (const Likelihood &)=delete

Likelihood (Likelihood &&)=delete

Likelihoodoperator= (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.

## ◆ ~Likelihood()

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

Definition at line 126 of file Likelihood.h.

126 {}

## ◆ 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.

138  :
139  _model(model), _fixed(fixed) {
141  fixed.getSize<0>(), static_cast<std::size_t>(model->getFixedDim()),
142  pex::exceptions::LengthError,
143  "Fixed parameter vector size (%d) does not match Model fixed parameter dimensionality (%d)"
144  );
145  }
#define LSST_THROW_IF_NE(N1, N2, EXC_CLASS, MSG)
Check whether the given values are equal, and throw an LSST Exception if they are not.
Definition: asserts.h:38
std::shared_ptr< Model > _model
Definition: Likelihood.h:147
ndarray::Array< Scalar const, 1, 1 > _fixed
Definition: Likelihood.h:148
T fixed(T... args)

## ◆ 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.

## ◆ 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.

77 { return _model->getAmplitudeDim(); }

## ◆ getData()

 ndarray::Array lsst::meas::modelfit::Likelihood::getData ( ) const
inline

Return the vector of weighted, scaled data points $$z$$.

Definition at line 89 of file Likelihood.h.

89 { return _data; }
ndarray::Array< Pixel, 1, 1 > _data
Definition: Likelihood.h:149

inline

Return the number of data points.

Definition at line 74 of file Likelihood.h.

74 { return _data.getSize<0>(); }

## ◆ getFixed()

 ndarray::Array lsst::meas::modelfit::Likelihood::getFixed ( ) const
inline

Return the vector of fixed nonlinear parameters.

Definition at line 86 of file Likelihood.h.

86 { 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.

83 { return _model->getFixedDim(); }

## ◆ getModel()

 std::shared_ptr 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.

105 { 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.

80 { return _model->getNonlinearDim(); }

## ◆ getUnweightedData()

 ndarray::Array lsst::meas::modelfit::Likelihood::getUnweightedData ( ) const
inline

Return the vector of unweighted data points $$y$$.

Definition at line 92 of file Likelihood.h.

92 { return _unweightedData; }
ndarray::Array< Pixel, 1, 1 > _unweightedData
Definition: Likelihood.h:150

## ◆ getVariance()

 ndarray::Array lsst::meas::modelfit::Likelihood::getVariance ( ) const
inline

Return the vector of per-data-point variances.

Definition at line 102 of file Likelihood.h.

102 { return _variance; }
ndarray::Array< Pixel, 1, 1 > _variance
Definition: Likelihood.h:151

## ◆ getWeights()

 ndarray::Array 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.

99 { return _weights; }
ndarray::Array< Pixel, 1, 1 > _weights
Definition: Likelihood.h:152

## ◆ operator=() [1/2]

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

## ◆ operator=() [2/2]

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

## ◆ _data

 ndarray::Array lsst::meas::modelfit::Likelihood::_data
protected

Definition at line 149 of file Likelihood.h.

## ◆ _fixed

 ndarray::Array lsst::meas::modelfit::Likelihood::_fixed
protected

Definition at line 148 of file Likelihood.h.

## ◆ _model

 std::shared_ptr lsst::meas::modelfit::Likelihood::_model
protected

Definition at line 147 of file Likelihood.h.

## ◆ _unweightedData

 ndarray::Array lsst::meas::modelfit::Likelihood::_unweightedData
protected

Definition at line 150 of file Likelihood.h.

## ◆ _variance

 ndarray::Array lsst::meas::modelfit::Likelihood::_variance
protected

Definition at line 151 of file Likelihood.h.

## ◆ _weights

 ndarray::Array lsst::meas::modelfit::Likelihood::_weights
protected

Definition at line 152 of file Likelihood.h.

The documentation for this class was generated from the following file:
• /j/snowflake/release/lsstsw/stack/lsst-scipipe-0.7.0/Linux64/meas_modelfit/22.0.1-4-g44f2e3d+9e4ab0f4fa/include/lsst/meas/modelfit/Likelihood.h