A class representing a Gaussian likelihood with block-diagonal covariance matrix. More...

#include <GaussianLikelihoodBlockDiagonalCovarianceRandomCoefficients.h>

Inheritance diagram for QUESO::GaussianLikelihoodBlockDiagonalCovarianceRandomCoefficients< V, M >:

Collaboration diagram for QUESO::GaussianLikelihoodBlockDiagonalCovarianceRandomCoefficients< V, M >:

Public Member Functions
virtual double	lnValue (const V &domainVector) const
	Logarithm of the value of the scalar function. More...

Constructor/Destructor methods.
	GaussianLikelihoodBlockDiagonalCovarianceRandomCoefficients (const char *prefix, const VectorSet< V, M > &domainSet, const V &observations, const GslBlockMatrix &covariance)
	Default constructor. More...

virtual	~GaussianLikelihoodBlockDiagonalCovarianceRandomCoefficients ()
	Destructor. More...

Public Member Functions inherited from QUESO::LikelihoodBase< V, M >
virtual void	evaluateModel (const V &domainVector, const V domainDirection, V &modelOutput, V gradVector, M hessianMatrix, V hessianEffect) const
	Deprecated. Evaluates the user's model at the point `domainVector`. More...

virtual void	evaluateModel (const V &domainVector, V &modelOutput) const
	Evaluates the user's model at the point `domainVector`. More...

virtual double	actualValue (const V &domainVector, const V , V , M , V ) const
	Actual value of the scalar function. More...

	LikelihoodBase (const char *prefix, const VectorSet< V, M > &domainSet, const V &observations)
	Default constructor. More...

virtual	~LikelihoodBase ()=0
	Destructor, pure to make this class abstract. More...

Public Member Functions inherited from QUESO::BaseScalarFunction< V, M >
void	setFiniteDifferenceStepSize (double fdStepSize)
	Sets the step size for finite differencing gradients. More...

void	setFiniteDifferenceStepSize (unsigned int i, double fdStepSize)

	BaseScalarFunction (const char *prefix, const VectorSet< V, M > &domainSet)
	Default constructor. More...

virtual	~BaseScalarFunction ()
	Destructor. More...

const VectorSet< V, M > &	domainSet () const
	Access to the protected attribute `m_domainSet:` domain set of the scalar function. More...

virtual double	lnValue (const V &domainVector, const V domainDirection, V gradVector, M hessianMatrix, V hessianEffect) const
	Logarithm of the value of the scalar function. Deprecated. More...

virtual double	lnValue (const V &domainVector, V &gradVector) const
	Returns the logarithm of the function and its gradient at `domainVector`. More...

virtual double	lnValue (const V &domainVector, V &gradVector, const V &domainDirection, V &hessianEffect) const

Private Attributes
const GslBlockMatrix &	m_covariance

Additional Inherited Members
Protected Attributes inherited from QUESO::LikelihoodBase< V, M >
const V &	m_observations

Protected Attributes inherited from QUESO::BaseScalarFunction< V, M >
const BaseEnvironment &	m_env

std::string	m_prefix

const VectorSet< V, M > &	m_domainSet
	Domain set of the scalar function. More...

Detailed Description

template<class V = GslVector, class M = GslMatrix>
class QUESO::GaussianLikelihoodBlockDiagonalCovarianceRandomCoefficients< V, M >

A class representing a Gaussian likelihood with block-diagonal covariance matrix.

Each block diagonal matrix has a multiplicative coefficient that is treated as a hyperparameter to be inferred during the sampling procedure.

Definition at line 47 of file GaussianLikelihoodBlockDiagonalCovarianceRandomCoefficients.h.

Constructor & Destructor Documentation

template<class V , class M >

QUESO::GaussianLikelihoodBlockDiagonalCovarianceRandomCoefficients< V, M >::GaussianLikelihoodBlockDiagonalCovarianceRandomCoefficients	(	const char *	prefix,
		const VectorSet< V, M > &	domainSet,
		const V &	observations,
		const GslBlockMatrix &	covariance
	)

Default constructor.

Instantiates a Gaussian likelihood function, given a prefix, its domain, a vector of observations and a block diagonal covariance matrix. The diagonal covariance matrix is of type GslBlockMatrix. Each block in the block diagonal matrix is an object of type GslMatrix.

Each block diagonal matrix has a multiplicative coefficient that is treated as a hyperparameter to be inferred during the sampling procedure.

Definition at line 33 of file GaussianLikelihoodBlockDiagonalCovarianceRandomCoefficients.C.

References QUESO::GslBlockMatrix::getBlock(), QUESO::GaussianLikelihoodBlockDiagonalCovarianceRandomCoefficients< V, M >::m_covariance, QUESO::GslBlockMatrix::numBlocks(), and QUESO::GslMatrix::numRowsLocal().

   : LikelihoodBase<V, M>(prefix, domainSet, observations),
     m_covariance(covariance)
 {
   unsigned int totalDim = 0;
 
   for (unsigned int i = 0; i < this->m_covariance.numBlocks(); i++) {
     totalDim += this->m_covariance.getBlock(i).numRowsLocal();
   }
 
   if (totalDim != observations.sizeLocal()) {
     queso_error_msg("Covariance matrix not same dimension as observation vector");
   }
 }

template<class V , class M >

QUESO::GaussianLikelihoodBlockDiagonalCovarianceRandomCoefficients< V, M >::~GaussianLikelihoodBlockDiagonalCovarianceRandomCoefficients ( )

virtual

Destructor.

Definition at line 51 of file GaussianLikelihoodBlockDiagonalCovarianceRandomCoefficients.C.

52 {

53 }

Member Function Documentation

template<class V , class M >

double QUESO::GaussianLikelihoodBlockDiagonalCovarianceRandomCoefficients< V, M >::lnValue ( const V & domainVector ) const

virtual

Logarithm of the value of the scalar function.

The last n elements of domainVector, where n is the number of blocks in the block diagonal covariance matrix, are treated as hyperparameters and will be sample in a statistical inversion.

The user need not concern themselves with handling these in the model evaluation routine, since they are handled by the likelihood evaluation routine.

Reimplemented from QUESO::BaseScalarFunction< V, M >.

Definition at line 57 of file GaussianLikelihoodBlockDiagonalCovarianceRandomCoefficients.C.

 {
   V modelOutput(this->m_observations, 0, 0);  // At least it's not a copy
   V weightedMisfit(this->m_observations, 0, 0);  // At least it's not a copy
 
   this->evaluateModel(domainVector, modelOutput);
 
   // Compute misfit G(x) - y
   modelOutput -= this->m_observations;
 
   // Solve \Sigma u = G(x) - y for u
   this->m_covariance.invertMultiply(modelOutput, weightedMisfit);
 
   // Deal with the multiplicative coefficients for each of the blocks
   unsigned int numBlocks = this->m_covariance.numBlocks();
   unsigned int offset = 0;
 
   // For each block...
   double cov_norm_factor = 0.0;
   for (unsigned int i = 0; i < this->m_covariance.numBlocks(); i++) {
 
     // ...find the right hyperparameter
     unsigned int index = domainVector.sizeLocal() + (i - numBlocks);
     double coefficient = domainVector[index];
 
     // ...divide the appropriate parts of the solution by the coefficient
     unsigned int blockDim = this->m_covariance.getBlock(i).numRowsLocal();
     for (unsigned int j = 0; j < blockDim; j++) {
       // 'coefficient' is a variance, so we divide by it
       modelOutput[offset+j] /= coefficient;
     }
 
     // Keep track of the part of the covariance matrix that appears in the
     // normalising constant because of the hyperparameter
     double cov_determinant = this->m_covariance.getBlock(i).determinant();
     cov_determinant = std::sqrt(cov_determinant);
 
     coefficient = std::sqrt(coefficient);
     cov_norm_factor += std::log(std::pow(coefficient, blockDim) * cov_determinant);
 
     offset += blockDim;
   }
 
   // Compute (G(x) - y)^T \Sigma^{-1} (G(x) - y)
   modelOutput *= weightedMisfit;
 
   double norm2_squared = modelOutput.sumOfComponents();  // This is square of 2-norm
 
   return -0.5 * norm2_squared - cov_norm_factor;
 }

Member Data Documentation

template<class V = GslVector, class M = GslMatrix>

const GslBlockMatrix& QUESO::GaussianLikelihoodBlockDiagonalCovarianceRandomCoefficients< V, M >::m_covariance

private

Definition at line 82 of file GaussianLikelihoodBlockDiagonalCovarianceRandomCoefficients.h.

Referenced by QUESO::GaussianLikelihoodBlockDiagonalCovarianceRandomCoefficients< V, M >::GaussianLikelihoodBlockDiagonalCovarianceRandomCoefficients().

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

src/stats/inc/GaussianLikelihoodBlockDiagonalCovarianceRandomCoefficients.h
src/stats/src/GaussianLikelihoodBlockDiagonalCovarianceRandomCoefficients.C

Public Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<class V = GslVector, class M = GslMatrix> class QUESO::GaussianLikelihoodBlockDiagonalCovarianceRandomCoefficients< V, M >

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<class V = GslVector, class M = GslMatrix>
class QUESO::GaussianLikelihoodBlockDiagonalCovarianceRandomCoefficients< V, M >