Tomographer::DenseDM::TSpace::LLHMHWalker< DenseLLHType_, RngType_, LoggerType_ > Class Template Reference

A random walk in the density matrix space of a Hilbert state space of a quantum system (uniform random unitary jumps; slower) More...

#include <tomographer/densedm/tspacellhwalker.h>

Inheritance diagram for Tomographer::DenseDM::TSpace::LLHMHWalker< DenseLLHType_, RngType_, LoggerType_ >:

Collaboration diagram for Tomographer::DenseDM::TSpace::LLHMHWalker< DenseLLHType_, RngType_, LoggerType_ >:

Public Types
enum
	see MHWalker Interface More...
typedef DenseLLHType_	DenseLLHType
	The DenseLLH interface object type.
typedef RngType_	RngType
	The random number generator type.
typedef LoggerType_	LoggerType
	The logger type.
typedef DenseLLHType::DMTypes	DMTypes
	The data types of our problem.
typedef DenseLLHType::LLHValueType	LLHValueType
	The loglikelihood function value type (see DenseLLH Interface e.g. IndepMeasLLH)
typedef DMTypes::MatrixType	MatrixType
	The matrix type for a density operator on our quantum system.
typedef DMTypes::VectorParamType	VectorParamType
	Type of an X-parameterization of a density operator (see X Parameterization)
typedef DMTypes::RealScalar	RealScalar
	The real scalar corresponding to our data types. Usually a double.
typedef DMTypes::ComplexScalar	ComplexScalar
	The complex real scalar corresponding to our data types. Usually a std::complex<double>.
typedef MHWalkerParamsStepSize< RealScalar >	WalkerParams
	The real scalar type for the step size — this scalar type is the only parameter we need (see MHWalker Interface)
typedef MatrixType	PointType
	Provided for MHRandomWalk. A point in our random walk = a density matrix.
typedef LLHValueType	FnValueType
	Provided for MHRandomWalk. The function value type is the loglikelihood value type.

Public Member Functions
	LLHMHWalker (const MatrixType &startpt, const DenseLLHType &llh, RngType &rng, LoggerType &log_)
	Constructor which just initializes the given fields. More...
void	init ()
	Provided for MHRandomWalk. Initializes some fields and prepares for a random walk. More...
const MatrixType &	startPoint ()
	Return the starting point given in the constructor, or a random start point.
void	thermalizingDone ()
	Callback for after thermalizing is done. No-op.
void	done ()
	Callback for after random walk is finished. No-op.
LLHValueType	fnLogVal (const MatrixType &T) const
	Calculate the logarithm of the Metropolis-Hastings function value. More...
MatrixType	jumpFn (const MatrixType &cur_T, WalkerParams params)
	Decides of a new point to jump to for the random walk.

Detailed Description

template<typename DenseLLHType_, typename RngType_, typename LoggerType_>
class Tomographer::DenseDM::TSpace::LLHMHWalker< DenseLLHType_, RngType_, LoggerType_ >

A random walk in the density matrix space of a Hilbert state space of a quantum system (uniform random unitary jumps; slower)

The random walk explores the density operators on a Hilbert space of a given dimension, according to the distribution given by the likelihood function on the Hilbert-schmidt uniform prior.

Template Parameters

DenseLLHType	A type satisfying the DenseLLH Interface
RngType	A std::random random number generator (such as std::mt19937)
LoggerType	A logger type (see Logging and Loggers)

Definition at line 120 of file tspacellhwalker.h.

Member Enumeration Documentation

anonymous enum

template<typename DenseLLHType_ , typename RngType_ , typename LoggerType_ >

anonymous enum

see MHWalker Interface

Enumerator
UseFnSyntaxType	We will calculate the log-likelihood function, which is the logarithm of the Metropolis-Hastings function we should be calculating.

Definition at line 154 of file tspacellhwalker.h.

Constructor & Destructor Documentation

LLHMHWalker()

template<typename DenseLLHType_ , typename RngType_ , typename LoggerType_ >

Tomographer::DenseDM::TSpace::LLHMHWalker< DenseLLHType_, RngType_, LoggerType_ >::LLHMHWalker ( const MatrixType &  startpt, const DenseLLHType &  llh, RngType &  rng, LoggerType &  log_  )

inline

Constructor which just initializes the given fields.

The llh object is responsible for calculating the log-likelihood function of the tomography experiment (see class documentation).

The startpt argument specifies the starting point for the random walk (matrix in T Parameterization). If you provide a zero startpt here, then a random starting point will be chosen using the rng random number generator to generate a random point on the sphere.

Definition at line 184 of file tspacellhwalker.h.

Member Function Documentation

fnLogVal()

template<typename DenseLLHType_ , typename RngType_ , typename LoggerType_ >

LLHValueType Tomographer::DenseDM::TSpace::LLHMHWalker< DenseLLHType_, RngType_, LoggerType_ >::fnLogVal ( const MatrixType &  T ) const

inline

Calculate the logarithm of the Metropolis-Hastings function value.

Returns

the log-likelihood, which is computed via the DenseLLH object.

Definition at line 248 of file tspacellhwalker.h.

init()

template<typename DenseLLHType_ , typename RngType_ , typename LoggerType_ >

void Tomographer::DenseDM::TSpace::LLHMHWalker< DenseLLHType_, RngType_, LoggerType_ >::init ( )

inline

Provided for MHRandomWalk. Initializes some fields and prepares for a random walk.

Note

If the startpt given to the constructor is zero (or has very small norm), then a uniformly random starting point is chosen. The starting point is chosen randomly according to the Haar-invariant measure on the state space. This corresponds to choosing a uniform point on the sphere corresponding to the T-parameterization of the density matrices.

Definition at line 204 of file tspacellhwalker.h.

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

• tomographer/densedm/tspacellhwalker.h (v5.2)