A random walk in the density matrix space of a Hilbert state space of a quantum system. More...
#include <tomographer/densedm/tspacellhwalker.h>
Inheritance diagram for Tomographer::DenseDM::TSpace::LLHMHWalker< DenseLLH_, Rng, LoggerType >: Collaboration diagram for Tomographer::DenseDM::TSpace::LLHMHWalker< DenseLLH_, Rng, LoggerType >:Public Types | |
| enum | |
| see MHWalker Interface More... | |
| typedef DenseLLH_ | DenseLLH |
| The DenseLLH interface object type. | |
| typedef DenseLLH::DMTypes | DMTypes |
| The data types of our problem. | |
| typedef DenseLLH::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 RealScalar | StepRealType |
| The real scalar type for the step size — this is our scalar type (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 DenseLLH &llh, Rng &rng, LoggerType &log_) | |
| Constructor which just initializes the given fields. More... | |
| LLHMHWalker (LLHMHWalker &&moveother) | |
| A MHWalker Interface needs to have a move constructor. 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. | |
| template<ENABLED_IF( DenseLLH::LLHCalcType==LLHCalcTypeX) > | |
| LLHValueType | fnLogVal (const MatrixType &T) const |
| Calculate the logarithm of the Metropolis-Hastings function value. More... | |
| template<ENABLED_IF( DenseLLH::LLHCalcType==LLHCalcTypeRho) > | |
| LLHValueType | fnLogVal (const MatrixType &T) const |
| Calculate the logarithm of the Metropolis-Hastings function value. More... | |
| MatrixType | jumpFn (const MatrixType &cur_T, RealScalar step_size) |
| Decides of a new point to jump to for the random walk. | |
Detailed Description
template<typename DenseLLH_, typename Rng, typename LoggerType>
class Tomographer::DenseDM::TSpace::LLHMHWalker< DenseLLH_, Rng, LoggerType >
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
-
DenseLLH a type satisfying the DenseLLH type interface (DenseLLH Interface) Rng a std::randomrandom number generator (such as std::mt19937)LoggerType a logger type (see Logging and Loggers)
Definition at line 72 of file tspacellhwalker.h.
Member Enumeration Documentation
§ anonymous enum
| 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 101 of file tspacellhwalker.h.
Constructor & Destructor Documentation
§ LLHMHWalker() [1/2]
|
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 131 of file tspacellhwalker.h.
§ LLHMHWalker() [2/2]
|
inline |
A MHWalker Interface needs to have a move constructor.
[This explicit definition seems to be needed for g++ 4.6.]
Definition at line 146 of file tspacellhwalker.h.
Member Function Documentation
§ fnLogVal() [1/2]
|
inline |
Calculate the logarithm of the Metropolis-Hastings function value.
- Returns
- the log-likelihood, which is computed via the DenseLLH object.
This implementation deals for DenseLLH objects which expose a logLikelihoodX() function (see DenseLLH Interface)
Definition at line 213 of file tspacellhwalker.h.
§ fnLogVal() [2/2]
|
inline |
Calculate the logarithm of the Metropolis-Hastings function value.
- Returns
- the log-likelihood, which is computed via the DenseLLH object.
This implementation deals for DenseLLH objects which expose a logLikelihoodRho() function (see DenseLLH Interface)
Definition at line 230 of file tspacellhwalker.h.
§ 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 166 of file tspacellhwalker.h.
The documentation for this class was generated from the following file:
- tomographer/densedm/tspacellhwalker.h (v4.0)