This is an Integrator that can be used to implemented arbitrary, user defined integration algorithms. More...

#include <CustomIntegrator.h>

Inheritance diagram for CustomIntegrator:

Public Types
enum	ComputationType { ComputeGlobal = 0, ComputePerDof = 1, ComputeSum = 2, ConstrainPositions = 3, ConstrainVelocities = 4, UpdateContextState = 5 }
	This is an enumeration of the different types of computations that may appear in an integration algorithm. More...

Public Member Functions
	CustomIntegrator (double stepSize)
	Create a CustomIntegrator.

int	getNumGlobalVariables () const
	Get the number of global variables that have been defined.

int	getNumPerDofVariables () const
	Get the number of per-DOF variables that have been defined.

int	getNumComputations () const
	Get the number of computation steps that have been added.

int	addGlobalVariable (const std::string &name, double initialValue)
	Define a new global variable.

const std::string &	getGlobalVariableName (int index) const
	Get the name of a global variable.

int	addPerDofVariable (const std::string &name, double initialValue)
	Define a new per-DOF variable.

const std::string &	getPerDofVariableName (int index) const
	Get the name of a per-DOF variable.

double	getGlobalVariable (int index) const
	Get the current value of a global variable.

void	setGlobalVariable (int index, double value)
	Set the value of a global variable.

void	setGlobalVariableByName (const std::string &name, double value)
	Set the value of a global variable, specified by name.

void	getPerDofVariable (int index, std::vector< Vec3 > &values) const
	Get the value of a per-DOF variable.

void	setPerDofVariable (int index, const std::vector< Vec3 > &values)
	Set the value of a per-DOF variable.

void	setPerDofVariableByName (const std::string &name, const std::vector< Vec3 > &values)
	Set the value of a per-DOF variable, specified by name.

int	addComputeGlobal (const std::string &variable, const std::string &expression)
	Add a step to the integration algorithm that computes a global value.

int	addComputePerDof (const std::string &variable, const std::string &expression)
	Add a step to the integration algorithm that computes a per-DOF value.

int	addComputeSum (const std::string &variable, const std::string &expression)
	Add a step to the integration algorithm that computes a sum over degrees of freedom.

int	addConstrainPositions ()
	Add a step to the integration algorithm that updates particle positions so all constraints are satisfied.

int	addConstrainVelocities ()
	Add a step to the integration algorithm that updates particle velocities so the net velocity along all constraints is 0.

int	addUpdateContextState ()
	Add a step to the integration algorithm that allows Forces to update the context state.

void	getComputationStep (int index, ComputationType &type, std::string &variable, std::string &expression) const
	Get the details of a computation step that has been added to the integration algorithm.

const std::string &	getKineticEnergyExpression () const
	Get the expression to use for computing the kinetic energy.

void	setKineticEnergyExpression (const std::string &expression)
	Set the expression to use for computing the kinetic energy.

int	getRandomNumberSeed () const
	Get the random number seed.

void	setRandomNumberSeed (int seed)
	Set the random number seed.

void	step (int steps)
	Advance a simulation through time by taking a series of time steps.

Public Member Functions inherited from Integrator
	Integrator ()

virtual	~Integrator ()

double	getStepSize () const
	Get the size of each time step, in picoseconds.

void	setStepSize (double size)
	Set the size of each time step, in picoseconds.

double	getConstraintTolerance () const
	Get the distance tolerance within which constraints are maintained, as a fraction of the constrained distance.

void	setConstraintTolerance (double tol)
	Set the distance tolerance within which constraints are maintained, as a fraction of the constrained distance.

Protected Member Functions
void	initialize (ContextImpl &context)
	This will be called by the Context when it is created.

void	cleanup ()
	This will be called by the Context when it is destroyed to let the Integrator do any necessary cleanup.

void	stateChanged (State::DataType changed)
	When the user modifies the state, we need to mark that the forces need to be recalculated.

std::vector< std::string >	getKernelNames ()
	Get the names of all Kernels used by this Integrator.

double	computeKineticEnergy ()
	Compute the kinetic energy of the system at the current time.

Additional Inherited Members
Protected Attributes inherited from Integrator
ContextImpl *	context

Context *	owner

Detailed Description

This is an Integrator that can be used to implemented arbitrary, user defined integration algorithms.

It is flexible enough to support a wide range of methods including both deterministic and stochastic integrators, Metropolized integrators, and integrators that must integrate additional quantities along with the particle positions and momenta.

To create an integration algorithm, you first define a set of variables the integrator will compute. Variables come in two types: global variables have a single value, while per-DOF variables have a value for every degree of freedom (x, y, or z coordinate of a particle). You can define as many variables as you want of each type. The value of any variable can be computed by the integration algorithm, or set directly by calling a method on the CustomIntegrator. All variables are persistent between integration steps; once a value is set, it keeps that value until it is changed by the user or recomputed in a later integration step.

Next, you define the algorithm as a series of computations. To execute a time step, the integrator performs the list of computations in order. Each computation updates the value of one global or per-DOF value. There are several types of computations that can be done:

Global: You provide a mathematical expression involving only global variables. It is evaluated and stored into a global variable.
Per-DOF: You provide a mathematical expression involving both global and per-DOF variables. It is evaluated once for every degree of freedom, and the values are stored into a per-DOF variable.
Sum: You provide a mathematical expression involving both global and per-DOF variables. It is evaluated once for every degree of freedom. All of those values are then added together, and the sum is stored into a global variable.
Constrain Positions: The particle positions are updated so that all distance constraints are satisfied.
Constrain Velocities: The particle velocities are updated so the net velocity along any constrained distance is 0.

Like all integrators, CustomIntegrator ignores any particle whose mass is 0. It is skipped when doing per-DOF computations, and is not included when computing sums over degrees of freedom.

In addition to the variables you define by calling addGlobalVariable() and addPerDofVariable(), the integrator provides the following pre-defined variables:

dt: (global) This is the step size being used by the integrator.
energy: (global, read-only) This is the current potential energy of the system.
energy0, energy1, energy2, ...: (global, read-only) This is similar to energy, but includes only the contribution from forces in one force group. A single computation step may only depend on a single energy variable (energy, energy0, energy1, etc.).
x: (per-DOF) This is the current value of the degree of freedom (the x, y, or z coordinate of a particle).
v: (per-DOF) This is the current velocity associated with the degree of freedom (the x, y, or z component of a particle's velocity).
f: (per-DOF, read-only) This is the current force acting on the degree of freedom (the x, y, or z component of the force on a particle).
f0, f1, f2, ...: (per-DOF, read-only) This is similar to f, but includes only the contribution from forces in one force group. A single computation step may only depend on a single force variable (f, f0, f1, etc.).
m: (per-DOF, read-only) This is the mass of the particle the degree of freedom is associated with.
uniform: (either global or per-DOF, read-only) This is a uniformly distributed random number between 0 and 1. Every time an expression is evaluated, a different value will be used. When used in a per-DOF expression, a different value will be used for every degree of freedom. Note, however, that if this variable appears multiple times in a single expression, the same value is used everywhere it appears in that expression.
gaussian: (either global or per-DOF, read-only) This is a Gaussian distributed random number with mean 0 and variance 1. Every time an expression is evaluated, a different value will be used. When used in a per-DOF expression, a different value will be used for every degree of freedom. Note, however, that if this variable appears multiple times in a single expression, the same value is used everywhere it appears in that expression.
A global variable is created for every adjustable parameter defined in the integrator's Context.

The following example uses a CustomIntegrator to implement a velocity Verlet integrator:


CustomIntegrator integrator(0.001);
integrator.addComputePerDof("v", "v+0.5*dt*f/m");
integrator.addComputePerDof("x", "x+dt*v");
integrator.addComputePerDof("v", "v+0.5*dt*f/m");

The first step updates the velocities based on the current forces. The second step updates the positions based on the new velocities, and the third step updates the velocities again. Although the first and third steps look identical, the forces used in them are different. You do not need to tell the integrator that; it will recognize that the positions have changed and know to recompute the forces automatically.

The above example has two problems. First, it does not respect distance constraints. To make the integrator work with constraints, you need to add extra steps to tell it when and how to apply them. Second, it never gives Forces an opportunity to update the context state. This should be done every time step so that, for example, an AndersenThermostat can randomize velocities or a MonteCarloBarostat can scale particle positions. You need to add a step to tell the integrator when to do this. The following example corrects both these problems, using the RATTLE algorithm to apply constraints:


CustomIntegrator integrator(0.001);
integrator.addPerDofVariable("x1", 0);
integrator.addUpdateContextState();
integrator.addComputePerDof("v", "v+0.5*dt*f/m");
integrator.addComputePerDof("x", "x+dt*v");
integrator.addComputePerDof("x1", "x");
integrator.addConstrainPositions();
integrator.addComputePerDof("v", "v+0.5*dt*f/m+(x-x1)/dt");
integrator.addConstrainVelocities();

CustomIntegrator can be used to implement multiple time step integrators. The following example shows an r-RESPA integrator. It assumes the quickly changing forces are in force group 0 and the slowly changing ones are in force group 1. It evaluates the "fast" forces four times as often as the "slow" forces.


CustomIntegrator integrator(0.004);
integrator.addComputePerDof("v", "v+0.5*dt*f1/m");
for (int i = 0; i < 4; i++) {
    integrator.addComputePerDof("v", "v+0.5*(dt/4)*f0/m");
    integrator.addComputePerDof("x", "x+(dt/4)*v");
    integrator.addComputePerDof("v", "v+0.5*(dt/4)*f0/m");
}
integrator.addComputePerDof("v", "v+0.5*dt*f1/m");

An Integrator has one other job in addition to evolving the equations of motion: it defines how to compute the kinetic energy of the system. Depending on the integration method used, simply summing mv²/2 over all degrees of freedom may not give the correct answer. For example, in a leapfrog integrator the velocities are "delayed" by half a time step, so the above formula would give the kinetic energy half a time step ago, not at the current time.

Call setKineticEnergyExpression() to set an expression for the kinetic energy. It is computed for every degree of freedom (excluding ones whose mass is 0) and the result is summed. The default expression is "m*v*v/2", which is correct for many integrators.

As example, the following line defines the correct way to compute kinetic energy when using a leapfrog algorithm:


integrator.setKineticEnergyExpression("m*v1*v1/2; v1=v+0.5*dt*f/m");

The kinetic energy expression may depend on the following pre-defined variables: x, v, f, m, dt. It also may depend on user-defined global and per-DOF variables, and on the values of adjustable parameters defined in the integrator's Context. It may not depend on any other variable, such as the potential energy, the force from a single force group, or a random number.

Expressions may involve the operators + (add), - (subtract), * (multiply), / (divide), and ^ (power), and the following functions: sqrt, exp, log, sin, cos, sec, csc, tan, cot, asin, acos, atan, sinh, cosh, tanh, erf, erfc, min, max, abs, step, delta. All trigonometric functions are defined in radians, and log is the natural logarithm. step(x) = 0 if x is less than 0, 1 otherwise. delta(x) = 1 if x is 0, 0 otherwise. An expression may also involve intermediate quantities that are defined following the main expression, using ";" as a separator.

Member Enumeration Documentation

enum ComputationType

This is an enumeration of the different types of computations that may appear in an integration algorithm.

Enumerator:

ComputeGlobal	Compute an expression and store it in a global variable.
ComputePerDof	Compute an expression for every degree of freedom and store it in a per-DOF variable.
ComputeSum	Compute an expression for every degree of freedom, sum the values, and store the result in a global variable.
ConstrainPositions	Update particle positions so all constraints are satisfied.
ConstrainVelocities	Update particle velocities so the net velocity along all constraints is 0.
UpdateContextState	Allow Forces to update the context state.

Constructor & Destructor Documentation

CustomIntegrator ( double stepSize )

Create a CustomIntegrator.

Parameters

stepSize the step size with which to integrate the system (in picoseconds)

Member Function Documentation

int addComputeGlobal	(	const std::string &	variable,
		const std::string &	expression
	)

Add a step to the integration algorithm that computes a global value.

Parameters

variable	the global variable to store the computed value into
expression	a mathematical expression involving only global variables. In each integration step, its value is computed and stored into the specified variable.

Returns: the index of the step that was added

int addComputePerDof	(	const std::string &	variable,
		const std::string &	expression
	)

Add a step to the integration algorithm that computes a per-DOF value.

Parameters

variable	the per-DOF variable to store the computed value into
expression	a mathematical expression involving both global and per-DOF variables. In each integration step, its value is computed for every degree of freedom and stored into the specified variable.

Returns: the index of the step that was added

int addComputeSum	(	const std::string &	variable,
		const std::string &	expression
	)

Add a step to the integration algorithm that computes a sum over degrees of freedom.

Parameters

variable	the global variable to store the computed value into
expression	a mathematical expression involving both global and per-DOF variables. In each integration step, its value is computed for every degree of freedom. Those values are then added together, and the sum is stored in the specified variable.

Returns: the index of the step that was added

int addConstrainPositions ( )

Add a step to the integration algorithm that updates particle positions so all constraints are satisfied.

Returns: the index of the step that was added

int addConstrainVelocities ( )

Add a step to the integration algorithm that updates particle velocities so the net velocity along all constraints is 0.

Returns: the index of the step that was added

int addGlobalVariable	(	const std::string &	name,
		double	initialValue
	)

Define a new global variable.

Parameters

name	the name of the variable
initialValue	the variable will initially be set to this value

Returns: the index of the variable that was added

int addPerDofVariable	(	const std::string &	name,
		double	initialValue
	)

Define a new per-DOF variable.

Parameters

name	the name of the variable
initialValue	the variable will initially be set to this value for all degrees of freedom

Returns: the index of the variable that was added

int addUpdateContextState ( )

Add a step to the integration algorithm that allows Forces to update the context state.

Returns: the index of the step that was added

void cleanup ( )

protectedvirtual

This will be called by the Context when it is destroyed to let the Integrator do any necessary cleanup.

It will also get called again if the application calls reinitialize() on the Context.

Reimplemented from Integrator.

double computeKineticEnergy ( )

protectedvirtual

Compute the kinetic energy of the system at the current time.

Implements Integrator.

void getComputationStep	(	int	index,
		ComputationType &	type,
		std::string &	variable,
		std::string &	expression
	)		const

Get the details of a computation step that has been added to the integration algorithm.

Parameters

index	the index of the computation step to get
type	on exit, the type of computation this step performs
variable	on exit, the variable into which this step stores its result. If this step does not store a result in a variable, this will be an empty string.
expression	on exit, the expression this step evaluates. If this step does not evaluate an expression, this will be an empty string.

double getGlobalVariable ( int index ) const

Get the current value of a global variable.

Parameters

index the index of the variable to get

Returns: the current value of the variable

const std::string& getGlobalVariableName ( int index ) const

Get the name of a global variable.

Parameters

index the index of the variable to get

Returns: the name of the variable

std::vector<std::string> getKernelNames ( )

protectedvirtual

Get the names of all Kernels used by this Integrator.

Implements Integrator.

const std::string& getKineticEnergyExpression ( ) const

Get the expression to use for computing the kinetic energy.

The expression is evaluated for every degree of freedom. Those values are then added together, and the sum is reported as the current kinetic energy.

int getNumComputations ( ) const

inline

Get the number of computation steps that have been added.

int getNumGlobalVariables ( ) const

inline

Get the number of global variables that have been defined.

int getNumPerDofVariables ( ) const

inline

Get the number of per-DOF variables that have been defined.

void getPerDofVariable	(	int	index,
		std::vector< Vec3 > &	values
	)		const

Get the value of a per-DOF variable.

Parameters

index	the index of the variable to get
values	the values of the variable for all degrees of freedom are stored into this

const std::string& getPerDofVariableName ( int index ) const

Get the name of a per-DOF variable.

Parameters

index the index of the variable to get

Returns: the name of the variable

int getRandomNumberSeed ( ) const

inline

Get the random number seed.

See setRandomNumberSeed() for details.

void initialize ( ContextImpl & context )

protectedvirtual

This will be called by the Context when it is created.

It informs the Integrator of what context it will be integrating, and gives it a chance to do any necessary initialization. It will also get called again if the application calls reinitialize() on the Context.

Implements Integrator.

void setGlobalVariable	(	int	index,
		double	value
	)

Set the value of a global variable.

Parameters

index	the index of the variable to set
value	the new value of the variable

void setGlobalVariableByName	(	const std::string &	name,
		double	value
	)

Set the value of a global variable, specified by name.

Parameters

name	the name of the variable to set
value	the new value of the variable

void setKineticEnergyExpression ( const std::string & expression )

Set the expression to use for computing the kinetic energy.

The expression is evaluated for every degree of freedom. Those values are then added together, and the sum is reported as the current kinetic energy.

void setPerDofVariable	(	int	index,
		const std::vector< Vec3 > &	values
	)

Set the value of a per-DOF variable.

Parameters

index	the index of the variable to set
values	the new values of the variable for all degrees of freedom

void setPerDofVariableByName	(	const std::string &	name,
		const std::vector< Vec3 > &	values
	)

Set the value of a per-DOF variable, specified by name.

Parameters

name	the name of the variable to set
values	the new values of the variable for all degrees of freedom

void setRandomNumberSeed ( int seed )

inline

Set the random number seed.

The precise meaning of this parameter is undefined, and is left up to each Platform to interpret in an appropriate way. It is guaranteed that if two simulations are run with different random number seeds, the sequence of random numbers will be different. On the other hand, no guarantees are made about the behavior of simulations that use the same seed. In particular, Platforms are permitted to use non-deterministic algorithms which produce different results on successive runs, even if those runs were initialized identically.

void stateChanged ( State::DataType changed )

protectedvirtual

When the user modifies the state, we need to mark that the forces need to be recalculated.

Reimplemented from Integrator.

void step ( int steps )

virtual

Advance a simulation through time by taking a series of time steps.

Parameters

steps the number of time steps to take

Implements Integrator.

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

CustomIntegrator.h

Public Types

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation