# Interface FieldSecondaryODE<T extends CalculusFieldElement<T>>

Type Parameters:
T - the type of the field elements

public interface FieldSecondaryODE<T extends CalculusFieldElement<T>>
This interface allows users to add secondary differential equations to a primary set of differential equations.

In some cases users may need to integrate some problem-specific equations along with a primary set of differential equations. One example is optimal control where adjoined parameters linked to the minimized Hamiltonian must be integrated.

This interface allows users to add such equations to a primary set of first order differential equations thanks to the FieldExpandableODE.addSecondaryEquations(FieldSecondaryODE) method.

• ## Method Summary

Modifier and Type
Method
Description
T[]
computeDerivatives(T t, T[] primary, T[] primaryDot, T[] secondary)
Compute the derivatives related to the secondary state parameters.
int
getDimension()
Get the dimension of the secondary state parameters.
default void
init(T t0, T[] primary0, T[] secondary0, T finalTime)
Initialize equations at the start of an ODE integration.
• ## Method Details

• ### getDimension

int getDimension()
Get the dimension of the secondary state parameters.
Returns:
dimension of the secondary state parameters
• ### init

default void init(T t0, T[] primary0, T[] secondary0, T finalTime)
Initialize equations at the start of an ODE integration.

This method is called once at the start of the integration. It may be used by the equations to initialize some internal data if needed.

The default implementation does nothing.

Parameters:
t0 - value of the independent time variable at integration start
primary0 - array containing the value of the primary state vector at integration start
secondary0 - array containing the value of the secondary state vector at integration start
finalTime - target time for the integration
• ### computeDerivatives

T[] computeDerivatives(T t, T[] primary, T[] primaryDot, T[] secondary) throws
Compute the derivatives related to the secondary state parameters.

In some cases, additional equations can require to change the derivatives of the primary state (i.e. the content of the primaryDot array). One use case is optimal control, when the secondary equations handle co-state, which changes control, and the control changes the primary state. In this case, the primary and secondary equations are not really independent from each other, so if possible it would be better to put state and co-state and their equations all in the primary equations. As this is not always possible, this method explicitly allows to modify the content of the primaryDot array. This array will be used to evolve the primary state only after all secondary equations have computed their derivatives, hence allowing this side effect.

Parameters:
t - current value of the independent time variable
primary - array containing the current value of the primary state vector
primaryDot - array containing the derivative of the primary state vector (the method is allowed to change the derivatives here, when the additional equations do have an effect on the primary equations)
secondary - array containing the current value of the secondary state vector
Returns:
derivative of the secondary state vector
Throws:
MathIllegalStateException - if the number of functions evaluations is exceeded
MathIllegalArgumentException - if arrays dimensions do not match equations settings