#include <dynamMetric.h>

Inheritance diagram for dynamMetric:

Public Member Functions
	dynamMetric (int dim)
virtual double	tau ()=0
	Return the quadratic form of the kinetic energy.
double	phi ()
	Return the pseudo-potential.
void	setMaxNumFixedPoint (int n)
	Set the maximum number of fixed-point iterations for implicit updates.
void	setFixedPointThreshold (double t)
	Set the difference threshold for terminating fixed-point iterations.
void	evolveQ (const double epsilon)
	Evolve the position through some time epsilon.
void	beginEvolveP (const double epsilon)
	Evolve the momenta through an initial half step of time epsilon.
void	finishEvolveP (const double epsilon)
	Evolve the momenta through a final half step of time epsilon.
virtual void	prepareEvolution ()
Protected Member Functions
virtual void	fComputeMetric ()=0
	Compute the metric at the current position.
virtual void	fUpdateP ()
	Update any momenta-dependent auxiliary terms.
virtual void	fPrepareSpatialGradients ()
virtual void	fHatT (const double epsilon)
	Evolve $\hat{T} = p_{i} \Lambda^{ij} \frac{ \partial }{ \partial q_{j} }$ .
virtual void	fHatTau (const double epsilon, const int numFixedPoint)
void	fHatPhi (const double epsilon)
virtual VectorXd &	dTaudp ()=0
	Gradient of the quadrtic form with respect to the momenta.
virtual VectorXd &	dTaudq ()=0
	Gradient of the quadratic form with respect to the position.
virtual VectorXd &	dPhidq ()=0
	Gradient of the psuedo-potential with respect to the momenta.
Protected Attributes
int	mMaxNumFixedPoint
	Maximum number of fixed-point iterations for implicit updates.
double	mFixedPointThreshold
	Difference threshold for terminating fixed-point iterations.
VectorXd	mAuxVector
	Auxiliary vector for storing various gradients.
VectorXd	mInit
	Auxiliary vector for fixed-point iterations.
VectorXd	mDelta
	Auxiliary vector for fixed-point iteration termination criteria.
double	mLogDetMetric
	Log determinant of the metric.

Detailed Description

Author:: Michael Betancourt

Abstract base class defining the interface for a Hamiltonian defined on a Riemannian manifold, $H = \tau + \phi$ , where

$\tau = \frac{1}{2} p_{i} p_{j} \Lambda^{ij} \! \left( \mathbf{q} \right)$

and

$\frac{1}{2} \log \! \left| \mathbf{\Sigma} \! \left( \mathbf{q} \right) \right| + V ! \left( \mathbf{q} \right).$

The Poisson operators are defined as

$\hat{H} = \frac{1}{2} \hat{\phi} + \frac{1}{2} \hat{\tau} + \hat{T} + \frac{1}{2} \hat{\tau} + \frac{1}{2} \hat{\phi},$

where

$\hat{\phi} = \frac{\partial}{\partial q_{i}} \left( \frac{1}{2} \log \! \left| \mathbf{\Sigma} \right| + V \right) \frac{ \partial }{ \partial p_{i} },$

$\hat{\tau} = - \frac{\partial}{\partial q_{k}} \left( \frac{1}{2} p_{i} p_{j} \Lambda^{ij} \right) \frac{ \partial }{ \partial p_{k} },$

and

$\hat{T} = p_{i} \left(\Lambda \right)^{ij} \frac{ \partial }{ \partial q_{j} }.$

Constructor & Destructor Documentation

dynamMetric::dynamMetric ( int dim ) [explicit]

Constructor

Parameters:

dim	Dimension of the target space

Member Function Documentation

void dynamMetric::fHatPhi ( const double epsilon ) [protected]

Evolve

$\hat{\phi} = \frac{\partial}{\partial q_{i}} \left( \frac{1}{2} \log \! \left| \mathbf{\Sigma} \right| + V \right) \frac{ \partial }{ \partial p_{i} }$

void dynamMetric::fHatTau	(	const double	epsilon,
		const int	numFixedPoint
	)		`[protected, virtual]`

Evolve

$\hat{\tau} = - \frac{\partial}{\partial q_{k}} \left( \frac{1}{2} p_{i} p_{j} \Lambda^{ij} \right) \frac{ \partial }{ \partial p_{k} }.$

virtual void dynamMetric::fPrepareSpatialGradients ( ) [inline, protected, virtual]

Update any position-dependent auxiliary terms in preparation for spatial gradients

Reimplemented in diagOuterSoftAbsMetric, diagSoftAbsMetric, outerSoftAbsMetric, and softAbsMetric.

virtual void dynamMetric::prepareEvolution ( ) [inline, virtual]

Perform any necessary calculations before simulation Hamiltonian dynamics

Reimplemented from baseHamiltonian.

Reimplemented in denseFisherMetric, and outerSoftAbsMetric.

Examples:: examples/main.cpp.

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

base/dynamMetric.h
base/dynamMetric.cpp

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation