Tomographer::DMStateSpaceLLHMHWalker< TomoProblem, Rng, Log > Class Template Reference

A random walk in the density matrix space of a Hilbert state space of a quantum system. More...

#include <tomographer/dmmhrw.h>

Public Types
enum
typedef TomoProblem::MatrQ	MatrQ
	The data types of our problem.
typedef TomoProblem::LLHValueType	LLHValueType
	The loglikelihood function value type (see IndepMeasTomoProblem)
typedef MatrQ::MatrixType	MatrixType
	The matrix type for a density operator on our quantum system.
typedef MatrQ::VectorParamType	VectorParamType
	Type of an X-parameterization of a density operator (see param_x_to_herm())
typedef MatrQ::RealScalar	RealScalar
	The real scalar corresponding to our data types. Usually a double.
typedef MatrQ::ComplexScalar	ComplexScalar
	The complex real scalar corresponding to our data types. Usually a std::complex<double>.
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
	DMStateSpaceLLHMHWalker (const MatrixType &startpt, const TomoProblem &tomo, Rng &rng, Log &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	thermalizing_done ()
	Callback for after thermalizing is done. No-op.
void	done ()
	Callback for after random walk is finished. No-op.
LLHValueType	fnlogval (const MatrixType &T)
	Calculate the logarithm of the Metropolis-Hastings function value. More...
MatrixType	jump_fn (const MatrixType &cur_T, RealScalar step_size)
	Decides of a new point to jump to for the random walk.

Detailed Description

template<typename TomoProblem, typename Rng, typename Log>
class Tomographer::DMStateSpaceLLHMHWalker< TomoProblem, Rng, Log >

A random walk in the density matrix space of a Hilbert state space of a quantum system.

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

TomoProblem	the tomography data, expected to be a priori a IndepMeasTomoProblem
Rng	a std::random random number generator (such as std::mt19937)
MHRWStatsCollector	a type implementing a StatsCollector interface (MHRWStatsCollector Interface)

Definition at line 70 of file dmmhrw.h.

Member Enumeration Documentation

template<typename TomoProblem , typename Rng , typename Log >

anonymous enum

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 90 of file dmmhrw.h.

Constructor & Destructor Documentation

template<typename TomoProblem , typename Rng , typename Log >

Tomographer::DMStateSpaceLLHMHWalker< TomoProblem, Rng, Log >::DMStateSpaceLLHMHWalker ( const MatrixType &  startpt, const TomoProblem &  tomo, Rng &  rng, Log &  log_  )

inline

Constructor which just initializes the given fields.

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 114 of file dmmhrw.h.

Member Function Documentation

template<typename TomoProblem , typename Rng , typename Log >

LLHValueType Tomographer::DMStateSpaceLLHMHWalker< TomoProblem, Rng, Log >::fnlogval ( const MatrixType &  T )

inline

Calculate the logarithm of the Metropolis-Hastings function value.

Returns

-0.5 * (-2-log-likelihood), where the -2-log-likelihood is computed using IndepMeasTomoProblem::calc_llh()

Definition at line 177 of file dmmhrw.h.

template<typename TomoProblem , typename Rng , typename Log >

void Tomographer::DMStateSpaceLLHMHWalker< TomoProblem, Rng, Log >::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 133 of file dmmhrw.h.

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

• tomographer/dmmhrw.h (v1.0a)