# Class FirstOrderLinearDS#

class FirstOrderLinearDS : public FirstOrderNonLinearDS#

First Order Linear Systems - $$M(t) \dot x = A(t)x(t)+ b(t) + r, \quad x(t_0)=x_0$$.

This class represents first order linear systems of the form:

$M(t) \dot x = A(t)x(t)+ b(t) + r, x(t_0)=x_0$
where

• $$x \in R^{n}$$ is the state,

• $$r \in R^{n}$$ the input due to the Non Smooth Interaction.

• $$M \in R^{n\times n}$$ is an invertible matrix

• $$A \in R^{n\times n}$$

• $$b \in R^{n}$$

The following operators can be plugged, in the usual way (see User Guide)

• $$A(t)$$

• $$b(t)$$

• $$M(t)$$

Subclassed by FirstOrderLinearTIDS

Public Types

typedef void (*LDSPtrFunction)(double, unsigned int, double*, unsigned int, double*)#

plugin signature

Public Functions

FirstOrderLinearDS(SP::SiconosVector newX0, const std::string &APlugin, const std::string &bPlugin)#

constructor from initial state and plugins

Parameters:
• newX0 – the initial state of this DynamicalSystem

• APlugin – plugin for A

• bPlugin – plugin for b

FirstOrderLinearDS(SP::SiconosVector newX0, SP::SiconosMatrix newA)#

constructor from initial state and plugin for A

Parameters:
FirstOrderLinearDS(SP::SiconosVector newX0)#

constructor from initial state

Parameters:

newX0 – the initial state of this DynamicalSystem

FirstOrderLinearDS(SP::SiconosVector newX0, SP::SiconosMatrix newA, SP::SiconosVector newB)#

constructor from a initial state and constant matrices

Parameters:
• newX0 – the initial state of this DynamicalSystem

• newA – matrix A

• newB – b

FirstOrderLinearDS(const FirstOrderLinearDS &FOLDS)#

Copy constructor.

Parameters:

FOLDS – the original FirstOrderLinearDS we want to copy

inline virtual ~FirstOrderLinearDS()#

destructor

virtual void initRhs(double time) override#

Initialization function for the rhs and its jacobian.

Parameters:

time – time of initialization.

virtual void computeRhs(double time) override#

update right-hand side for the current state

Parameters:

time – of interest

virtual void computeJacobianRhsx(double time) override#

update $$\nabla_x rhs$$ for the current state

Parameters:

time – of interest

inline SP::SiconosMatrix A() const#

get the matrix $$A$$

Returns:

pointer (SP) on a matrix

inline virtual SP::SiconosMatrix jacobianfx() const override#

get jacobian of f(x,t,z) with respect to x (pointer link)

Returns:

SP::SiconosMatrix

inline void setAPtr(SP::SiconosMatrix newA)#

set A to pointer newPtr

Parameters:

newA – the new A matrix

void setA(const SiconosMatrix &newA)#

set A to a new matrix

Parameters:

newA – the new A matrix

inline SP::SiconosVector b() const#

Returns:

a SP::SiconosVector

inline void setbPtr(SP::SiconosVector b)#

Parameters:

b – a SiconosVector

void setb(const SiconosVector &b)#

set b vector (copy)

Parameters:

b – a SiconosVector

virtual void updatePlugins(double time) override#

Call all plugged-function to initialize plugged-object values.

Parameters:

time – value

void setComputeAFunction(const std::string &pluginPath, const std::string &functionName)#

set a specified function to compute the matrix A => same action as setComputeJacobianfxFunction

Parameters:
• pluginPath – the complete path to the plugin

• functionName – the function name to use in this plugin

void setComputeAFunction(LDSPtrFunction fct)#

set a specified function to compute the matrix A

Parameters:

fct – a pointer on a function

void setComputebFunction(const std::string &pluginPath, const std::string &functionName)#

set a specified function to compute the vector b

Parameters:
• pluginPath – the complete path to the plugin file

• functionName – the function name to use in this plugin

void setComputebFunction(LDSPtrFunction fct)#

set a specified function to compute the vector b

Parameters:

fct – a pointer on a function

virtual void computeA(double time)#

default function to compute matrix A => same action as computeJacobianfx

Parameters:

time – time instant used to compute A

virtual void computeb(double time)#

default function to compute vector b

Parameters:

time – time instant used to compute b

inline SP::PluggedObject getPluginA() const#

Get _pluginA.

Returns:

the plugin for A

inline SP::PluggedObject getPluginB() const#

Get _pluginb.

Returns:

the plugin for b

inline void setPluginA(SP::PluggedObject newPluginA)#

Set _pluginA.

Parameters:

newPluginA – the new plugin

inline void setPluginB(SP::PluggedObject newPluginB)#

Set _pluginb.

Parameters:

newPluginB – the new plugin

virtual void display(bool brief = true) const override#

data display on screen

inline virtual bool isLinear() override#

True if the system is linear.

Returns:

a boolean