Stand-Alone Integration Library
Contents
- Introduction
- class Integrator
- typedef derivsFunc
- class FirstOrderODEIntegrator
- class FirstOrderODEVariableStepIntegrator
- class EulerIntegrator
- class HeunsMethod
- class RK2Integrator
- class RK4Integrator
- class RK3_8Integrator
- class EulerCromerIntegrator
- class ABM2Integrator
- class ABM4Integrator
Introduction
The Stand-Alone Integration Library can be used within a Trick simulation, or independent of it.
Some examples of using these integrators can be found in the examples/ directory.
- CannonBall uses the RK2Integrator.
- MassSpringDamper uses the EulerCromerIntegrator.
- Orbit uses the EulerCromerIntegrator.
- DoubleIntegral shows an example of a double integral.
class Integrator
Description
This class represents an integrator.
Constructor
Integrator(double h, void* user_data);
| Parameter | Type | Description |
|---|---|---|
| h | double |
Default step-size |
| user_data | void* |
A pointer to user defined data that will be passed to a derivsFunc when called by the Integrator. |
Member Functions
virtual void step();
Increment the independent variable by the default step-size.
virtual void load() = 0;
Load the input state.
virtual void unload() = 0;
Load the output state.
double getIndyVar();
Return the value of the independent variable (i.e, the variable you are integrating over.) If you are integrating over time, this value will be the accumulated time.
double setIndyVar( double t);
Set the value of the independent variable. (i.e, the variable you are integrating over.) If you are integrating over time, this value will be the accumulated time.
typedef derivsFunc
typedef void (*derivsFunc)( double x, double state[], double derivs[], void* user_data);
where:
| Parameter | Type | Description |
|---|---|---|
| x | double |
independent variable |
| state | double* |
(input) an array of state variable values |
| derivs | double* |
(output) an array into which derivatives are to be returned |
| user_data | void* |
a pointer to user_data |
Example
void my_derivs( double t, double state[], double deriv[], void* udata) { ... }
class FirstOrderODEIntegrator
Derived from Integrator.
Description
This class represents an integrator for a first order Ordinary Differential Equation (ODE).
Constructor
FirstOrderODEIntegrator( double h,
int N,
double* in_vars[],
double* out_vars[],
derivsFunc func,
void* user_data);
where:
| Parameter | Type | Description |
|---|---|---|
| h | double |
Default integration step-size. |
| N | int |
Number of state variables to be integrated |
| in_vars | double* |
Array of pointers to the state variables from which we load() the integrator state (in_vars and out_vars will generally point to the same array of pointers.) |
| out_vars | double* |
Array of pointers to the state variables to which we unload() the integrator state (in_vars and out_vars will generally point to the same array of pointers.) |
| derivs_func | derivsFunc | A function that returns |
| user_data | void* |
A pointer to user defined data that will be passed to a derivsFunc when called by the Integrator. |
Member Functions
void step( double h )
Integrate over step-size specified by h.
| Parameter | Type | Description |
|---|---|---|
| h | double | The integration step-size |
virtual void undo_step()
If the integrator has not already been reset then :
- Subtract the last step-size from the independent variable.
- Copy the input state back to the origin variables.
- Set the integrator's 'reset' mode to true.
Calling load() sets the 'reset' mode to false.
void step()
Integrate over the default step-size.
void load()
Load the integrator's initial state from the variables specified by in_vars.
void unload();
Unload the integrator's result state to the variables specified by out_vars.
class FirstOrderODEVariableStepIntegrator
Description
This class represents an integrator for a first order ODE, that be
Constructor
Member Functions
virtual void step( double h );
class EulerIntegrator
Derived from FirstOrderODEIntegrator.
Description
The Euler method is a first order numerical integration method. It is the simplest, explicit Runge–Kutta method.
Constructor
EulerIntegrator(double h, int N, double* in_vars[], double* out_vars[], derivsFunc func, void* user_data)
Constructor Parameters are those FirstOrderODEIntegrator.
class HeunsMethod
Derived from FirstOrderODEIntegrator.
Description
This integrator implements Heun's Method.
Constructor
HeunsMethod( double h, int N, double* in_vars[], double* out_vars[], derivsFunc func, void* user_data)
Constructor Parameters are those FirstOrderODEIntegrator.
class RK2Integrator
Derived from FirstOrderODEIntegrator.
Description
The Runga-Kutta-2 method is a second order, explicit, numerical integration method.
Constructor
RK2Integrator( double h, int N, double* in_vars[], double* out_vars[], derivsFunc func, void* user_data)
Constructor Parameters are those FirstOrderODEIntegrator.
class RK4Integrator
Derived from FirstOrderODEIntegrator.
Description
The Runga-Kutta-4 method is a fourth order, explicit, numerical integration method.
Constructor
RK4Integrator( double h, int N, double* in_vars[], double* out_vars[], derivsFunc func, void* user_data)
Constructor Parameters are those FirstOrderODEIntegrator.
class RK3_8Integrator
Derived from FirstOrderODEIntegrator.
Description
The Runga-Kutta-3/8 method is a fourth order, explicit, numerical integration method.
Constructor
RK3_8Integrator( double h, int N, double* in_vars[], double* out_vars[], derivsFunc func, void* user_data)
Constructor Parameters are those FirstOrderODEIntegrator.
class ABM2Integrator
Derived from FirstOrderODEIntegrator.
Description
The ABM2Integrator implements the second-order Adams-Bashforth-Moulton predictor/corrector method. Adams methods maintain a history of derivatives rather than calculating intermediate values like Runga-Kutta methods.
Constructor
ABM2Integrator ( double h, int N, double* in_vars[], double* out_vars[], derivsFunc func, void* user_data)
Constructor Parameters are those FirstOrderODEIntegrator.
class ABM4Integrator
Derived from FirstOrderODEIntegrator.
Description
The ABM2Integrator implements the second-order Adams-Bashforth-Moulton predictor/corrector method. Adams methods maintain a history of derivatives rather than calculating intermediate values like Runga-Kutta methods.
Constructor
ABM4Integrator ( double h, int N, double* in_vars[], double* out_vars[], derivsFunc func, void* user_data)
Constructor Parameters are those FirstOrderODEIntegrator.
EulerCromerIntegrator
Derived from class-Integrator.
Description
EulerCromer is integration method that conserves energy in oscillatory systems better than Runge-Kutta. So, it's good for mass-spring-damper systems, and orbital systems.
Constructor
SemiImplicitEuler(double dt, int N, double* xp[], double* vp[], derivsFunc gfunc, derivsFunc ffunc, void* user_data)
| Parameter | Type | Description |
|---|---|---|
| dt | double |
Default time step value |
| N | int |
Number of state variables to be integrated |
| xp | double* |
Array of pointers to the variables from which we load() and to which we unload() the integrator's position values . |
| vp | double* |
Array of pointers to the variables from which we load() and to which we unload() the integrator's velocity values . |
| gfunc | derivsFunc | A function that returns acceleration |
| ffunc | derivsFunc | A function that returns velocity |
| user_data | void* |
A pointer to user defined data that will be passed to a derivsFunc when called by the Integrator. |