# Class FirstOrderR¶

class FirstOrderR : public Relation

FirstOrder Relation.

This is an abstract class for all relation operating on first order systems. It should not be used. Rather, the following classes should be used:

• FirstOrderNonlinearR: for fully nonlinear relations: $$y = h(t, X, \lambda, Z)$$, $$R = g(t, X, \lambda, Z)$$.

• FirstOrderType2R: specialization with $$y = h(t, X, \lambda, Z)$$, $$R = g(t, \lambda, Z)$$.

• FirstOrderType1R: further specialization with $$y = h(t, X, Z)$$, $$R = g(t, \lambda, Z)$$.

• FirstOrderLinearR: linear case: $$y = C(t)x + D(t)\lambda + F(t) z + e$$, $$R = B(t)\lambda$$.

• FirstOrderLinearR: time-invariant linear case: $$y = Cx + D\lambda + F z + e$$, $$R = B\lambda$$.

If the relation involves only one DynamicalSystem, then $$R = r$$, $$X = x$$, and $$Z = z$$. With two, then $$R = [r_1, r_2]$$, $$X = [x_1 x_2]$$, and $$Z = [z_1 z_2]$$.

Remember that $y$ and  are relation from the Interaction, and have the same size.

Public Functions

virtual ~FirstOrderR()

destructor

SP::SimpleMatrix B() const

get B

Return

B matrix

SP::SimpleMatrix C() const

get C

Return

C matrix

virtual void checkSize(Interaction &inter) = 0

check sizes of the relation specific operators.

Parameters
• inter: an Interaction using this relation

SP::SimpleMatrix D() const

get D

Return

D matrix

SP::SimpleMatrix F() const

get F

Return

F matrix

virtual void initialize(Interaction &inter)

initialize the relation (check sizes, memory allocation …)

Parameters
• inter: the interaction using this relation

SP::SimpleMatrix K() const

get K

Return

K matrix

void setBPtr(SP::SimpleMatrix newB)

set B to pointer newB

Parameters
• newB: the B matrix

void setCPtr(SP::SimpleMatrix newC)

set C to pointer newC

Parameters
• newC: the C matrix

void setDPtr(SP::SimpleMatrix newD)

set D to pointer newPtr

Parameters
• newD: the D matrix

void setFPtr(SP::SimpleMatrix newF)

set F to pointer newPtr

Parameters
• newF: the F matrix