Expression Class Reference

Base class for all variables within the symbolic expressions family. More...

#include <expression.hpp>

Inheritance diagram for Expression:

Public Member Functions
Expression	ADbackward (const Expression &arg) const
Expression	ADbackward (const Expression &arg, const Expression &seed) const
Expression	ADforward (const Expression &arg) const
Expression	ADforward (const VariableType &varType_, const int *arg, int nV) const
Expression	ADforward (const Expression &arg, const Expression &seed) const
Expression	ADforward (const VariableType &varType_, const int *arg, const Expression &seed) const
Expression	ADforward (const VariableType *varType_, const int *arg, const Expression &seed) const
Expression	ADsymmetric (const Expression &arg, const Expression &S, const Expression &l, Expression *dfS=0, Expression *ldf=0) const
Expression	ADsymmetric (const Expression &arg, const Expression &l, Expression *dfS=0, Expression *ldf=0) const
Expression &	appendCols (const Expression &arg)
Expression &	appendRows (const Expression &arg)
virtual Expression *	clone () const
	Expression ()
	Expression (const Operator &tree_)
	Expression (const std::string &name_)
	Expression (const std::string &name_, uint nRows_, uint nCols_, VariableType variableType_=VT_UNKNOWN, uint globalTypeID=0)
	Expression (int nRows_, int nCols_=1, VariableType variableType_=VT_UNKNOWN, int globalTypeID=0)
	Expression (uint nRows_, uint nCols_=1, VariableType variableType_=VT_UNKNOWN, uint globalTypeID=0)
	Expression (const double &rhs)
	Expression (const DVector &rhs)
	Expression (const DMatrix &rhs)
	Expression (const Expression &rhs)
Expression	getAcos () const
Expression	getAsin () const
Expression	getAtan () const
Expression	getCol (const uint &colIdx) const
Expression	getCols (const uint &colIdx1, const uint &colIdx2) const
uint	getComponent (const unsigned int idx) const
Expression	getCos () const
DMatrix	getDependencyPattern (const Expression &arg) const
uint	getDim () const
Expression	getDot () const
Expression	getEntropy () const
Expression	getEuclideanNorm () const
Expression	getExp () const
Expression	getInverse () const
Expression	getLn () const
Expression	getLogSumExp () const
Expression	getNext () const
uint	getNumCols () const
uint	getNumRows () const
Expression	getODEexpansion (const int &order, const int *arg) const
Operator *	getOperatorClone (uint idx) const
Expression	getPow (const Expression &arg) const
Expression	getPowInt (const int &arg) const
Expression	getRow (const uint &rowIdx) const
Expression	getRows (const uint &rowIdx1, const uint &rowIdx2) const
Expression	getSin () const
DMatrix	getSparsityPattern () const
Expression	getSqrt () const
Expression	getSubMatrix (const uint &rowIdx1, const uint &rowIdx2, const uint &colIdx1, const uint &colIdx2) const
Expression	getSumSquare () const
Expression	getTan () const
VariableType	getVariableType () const
BooleanType	isDependingOn (VariableType type) const
BooleanType	isDependingOn (const Expression &e) const
BooleanType	isVariable () const
Expression	operator() (uint idx) const
Expression	operator() (uint rowIdx, uint colIdx) const
Operator &	operator() (uint idx)
Operator &	operator() (uint rowIdx, uint colIdx)
Expression &	operator*= (const Expression &arg)
Expression &	operator+= (const Expression &arg)
Expression	operator- () const
Expression &	operator-= (const Expression &arg)
Expression &	operator/= (const Expression &arg)
Expression &	operator<< (const Expression &arg)
Expression &	operator= (const Expression &arg)
std::ostream &	print (std::ostream &stream) const
returnValue	substitute (int idx, const Expression &arg) const
Expression	transpose () const
virtual	~Expression ()

Protected Member Functions
Expression	add (const Expression &arg) const
Expression &	assignmentSetup (const Expression &arg)
void	construct (VariableType variableType_, uint globalTypeID_, uint nRows_, uint nCols_, const std::string &name_)
void	copy (const Expression &rhs)
void	deleteAll ()
Expression	div (const Expression &arg) const
Expression	mul (const Expression &arg) const
Operator *	product (const Operator *a, const Operator *b) const
Expression	sub (const Expression &arg) const

Protected Attributes
uint	component
uint	dim
Operator **	element
std::string	name
uint	nCols
uint	nRows
VariableType	variableType

Friends
class	CFunction
class	COperator
class	FunctionEvaluationTree
Expression	operator* (const Expression &arg1, const Expression &arg2)
Expression	operator+ (const Expression &arg1, const Expression &arg2)
Expression	operator- (const Expression &arg1, const Expression &arg2)
Expression	operator/ (const Expression &arg1, const Expression &arg2)
std::ostream &	operator<< (std::ostream &stream, const Expression &arg)

Detailed Description

Base class for all variables within the symbolic expressions family.

The class Expression serves as a base class for all symbolic variables within the symbolic expressions family. Moreover, the Expression class defines all kind of matrix and vector operations on a symbolic level.

Author

Boris Houska, Hans Joachim Ferreau, Milan Vukov

Definition at line 56 of file expression.hpp.

Constructor & Destructor Documentation

BEGIN_NAMESPACE_ACADO Expression::Expression

(

)

Default constructor.

Definition at line 47 of file expression.cpp.

Expression::Expression

(

const Operator &

tree_

)

Casting constructor.

Definition at line 72 of file expression.cpp.

Expression::Expression ( const std::string &  name_ )

explicit

Casting constructor.

Definition at line 57 of file expression.cpp.

Expression::Expression ( const std::string &  name_, uint  nRows_, uint  nCols_, VariableType  variableType_ = VT_UNKNOWN, uint  globalTypeID = 0  )

explicit

Constructor which takes the arguments.

Parameters

name_	the name
nRows_	number of rows
nCols_	number of columns
variableType_	the variable type
globalTypeID	the global type ID

Definition at line 52 of file expression.cpp.

Expression::Expression ( int  nRows_, int  nCols_ = 1, VariableType  variableType_ = VT_UNKNOWN, int  globalTypeID = 0  )

explicit

Constructor which takes the arguments.

Parameters

nRows_	number of rows
nCols_	number of columns
variableType_	the variable type
globalTypeID	the global type ID

Definition at line 67 of file expression.cpp.

Expression::Expression ( uint  nRows_, uint  nCols_ = 1, VariableType  variableType_ = VT_UNKNOWN, uint  globalTypeID = 0  )

explicit

Constructor which takes the arguments.

Parameters

nRows_	number of rows
nCols_	number of columns
variableType_	the variable type
globalTypeID	the global type ID

Definition at line 62 of file expression.cpp.

Expression::Expression

(

const double &

rhs

)

Copy constructor (deep copy).

Definition at line 90 of file expression.cpp.

Expression::Expression

(

const DVector &

rhs

)

Definition at line 97 of file expression.cpp.

Expression::Expression

(

const DMatrix &

rhs

)

Definition at line 107 of file expression.cpp.

Expression::Expression

(

const Expression &

rhs

)

Definition at line 121 of file expression.cpp.

Expression::~Expression ( )

virtual

Destructor.

Definition at line 126 of file expression.cpp.

Member Function Documentation

Expression Expression::ADbackward

(

const Expression &

arg

)

const

Definition at line 1032 of file expression.cpp.

Expression Expression::ADbackward	(	const Expression &	arg,
		const Expression &	seed
	)		const

Definition at line 1206 of file expression.cpp.

Expression Expression::add ( const Expression &  arg ) const

protected

Definition at line 319 of file expression.cpp.

Expression Expression::ADforward

(

const Expression &

arg

)

const

Definition at line 971 of file expression.cpp.

Expression Expression::ADforward	(	const VariableType &	varType_,
		const int *	arg,
		int	nV
	)		const

Definition at line 1002 of file expression.cpp.

Expression Expression::ADforward	(	const Expression &	arg,
		const Expression &	seed
	)		const

Definition at line 1063 of file expression.cpp.

Expression Expression::ADforward	(	const VariableType &	varType_,
		const int *	arg,
		const Expression &	seed
	)		const

Definition at line 1086 of file expression.cpp.

Expression Expression::ADforward	(	const VariableType *	varType_,
		const int *	arg,
		const Expression &	seed
	)		const

Definition at line 1098 of file expression.cpp.

Expression Expression::ADsymmetric	(	const Expression &	arg,
		const Expression &	S,
		const Expression &	l,
		Expression *	dfS = 0,
		Expression *	ldf = 0
	)		const

Second order symmetric AD routine returning
S^T*(l^T*f'')*S with f'' being the second
order derivative of the current expression.
The matrix S and the vector l can be
interpreted as forward/backward seeds,
respectively. Optionally, this routine also
returns expressions for the first order
order terms f'*S and l^T*f' computed by
first order forward and first order backward
automatic differentiation, respectively.
Caution: this routine is tailored for
full Hessian computation exploiting symmetry.
If only single elements of the Hessian are
needed, forward-over-adjoint or ajoint-over-
forward differentiation may be more
efficient.

Parameters

S	argument
l	forward seed
dfS	backward seed
ldf	first order forward result first order backward result

Definition at line 1260 of file expression.cpp.

Expression Expression::ADsymmetric	(	const Expression &	arg,
		const Expression &	l,
		Expression *	dfS = 0,
		Expression *	ldf = 0
	)		const

Second order symmetric AD routine returning
l^T*f'' with f'' being the second
order derivative of the current expression.
The he vector l can be
interpreted as backward seed,
respectively. Optionally, this routine also
returns expressions for the first order
order terms f'*S and l^T*f' computed by
first order forward and first order backward
automatic differentiation, respectively.
Caution: this routine is tailored for
full Hessian computation exploiting symmetry.
If only single elements of the Hessian are
needed, forward-over-adjoint or ajoint-over-
forward differentiation may be more
efficient.

Parameters

l	argument
dfS	backward seed
ldf	first order forward result first order backward result

Definition at line 1303 of file expression.cpp.

Expression & Expression::appendCols

(

const Expression &

arg

)

Appends an Expression matrix (n x m) with an argument matrix (n x s) in the column direction, such that the result is ( n x (m + s) ).

As a special case, when applied on an empty Expression, the Expression will be assigned the argument.

Definition at line 162 of file expression.cpp.

Expression & Expression::appendRows

(

const Expression &

arg

)

Appends an Expression matrix (n x m) with an argument matrix (s x m) in the row direction, such that the result is ( (n + s) x m).

As a special case, when applied on an empty Expression, the Expression will be assigned the argument.

Definition at line 141 of file expression.cpp.

Expression & Expression::assignmentSetup ( const Expression &  arg )

protected

Generic copy routine (protected, only for internal use).

Definition at line 1518 of file expression.cpp.

virtual Expression* Expression::clone ( ) const

inlinevirtual

Function for cloning.

Reimplemented in ExpressionType< Derived, Type, AllowCounter >, ExpressionType< Output, VT_OUTPUT >, ExpressionType< IntermediateState, VT_INTERMEDIATE_STATE >, ExpressionType< IntegerParameter, VT_INTEGER_PARAMETER >, ExpressionType< Parameter, VT_PARAMETER >, ExpressionType< DifferentialStateDerivative, VT_DDIFFERENTIAL_STATE >, ExpressionType< AlgebraicState, VT_ALGEBRAIC_STATE >, ExpressionType< OnlineData, VT_ONLINE_DATA >, ExpressionType< DifferentialState, VT_DIFFERENTIAL_STATE >, ExpressionType< TIME, VT_TIME, false >, ExpressionType< Control, VT_CONTROL >, ExpressionType< Disturbance, VT_DISTURBANCE >, and ExpressionType< IntegerControl, VT_INTEGER_CONTROL >.

Definition at line 105 of file expression.hpp.

void Expression::construct ( VariableType  variableType_, uint  globalTypeID_, uint  nRows_, uint  nCols_, const std::string &  name_  )

protected

Generic constructor (protected, only for internal use).

Parameters

variableType_	The variable type.
globalTypeID_	the global type ID
nRows_	The number of rows.
nCols_	The number of columns.
name_	The name

Definition at line 1471 of file expression.cpp.

void Expression::copy ( const Expression &  rhs )

protected

Generic copy routine (protected, only for internal use).

Definition at line 1496 of file expression.cpp.

void Expression::deleteAll ( )

protected

Generic destructor (protected, only for internal use).

Definition at line 1555 of file expression.cpp.

Expression Expression::div ( const Expression &  arg ) const

protected

Definition at line 474 of file expression.cpp.

Expression Expression::getAcos

(

)

const

Definition at line 721 of file expression.cpp.

Expression Expression::getAsin

(

)

const

Definition at line 709 of file expression.cpp.

Expression Expression::getAtan

(

)

const

Definition at line 733 of file expression.cpp.

Expression Expression::getCol

(

const uint &

colIdx

)

const

Definition at line 567 of file expression.cpp.

Expression Expression::getCols	(	const uint &	colIdx1,
		const uint &	colIdx2
	)		const

Definition at line 582 of file expression.cpp.

uint Expression::getComponent ( const unsigned int  idx ) const

inline

Returns the global type idea of the idx-component.

Returns

The global type ID.

Expression Expression::getCos

(

)

const

Definition at line 685 of file expression.cpp.

DMatrix Expression::getDependencyPattern

(

const Expression &

arg

)

const

When operated on an n x 1 Expression, returns an m x n DMatrix. The element (i,j) of this matrix is zero when this(i) does not depend on arg(j)

Parameters

arg	m x 1 Expression

Definition at line 623 of file expression.cpp.

uint Expression::getDim ( ) const

inline

Returns dimension of vector space.

Returns

Dimension of vector space.

Expression Expression::getDot

(

)

const

Definition at line 952 of file expression.cpp.

Expression Expression::getEntropy

(

)

const

Definition at line 945 of file expression.cpp.

Expression Expression::getEuclideanNorm

(

)

const

Definition at line 912 of file expression.cpp.

Expression Expression::getExp

(

)

const

Definition at line 745 of file expression.cpp.

Expression Expression::getInverse

(

)

const

Returns the symbolic inverse of a matrix (only for square matrices)

Definition at line 490 of file expression.cpp.

Expression Expression::getLn

(

)

const

Definition at line 769 of file expression.cpp.

Expression Expression::getLogSumExp

(

)

const

Definition at line 860 of file expression.cpp.

Expression Expression::getNext

(

)

const

Definition at line 965 of file expression.cpp.

uint Expression::getNumCols ( ) const

inline

Returns the number of columns.

Returns

The number of columns.

uint Expression::getNumRows ( ) const

inline

Returns the number of rows.

Returns

The number of rows.

Expression Expression::getODEexpansion	(	const int &	order,
		const int *	arg
	)		const

Definition at line 1149 of file expression.cpp.

Operator * Expression::getOperatorClone

(

uint

idx

)

const

Returns a clone of the operator with index idx.

Returns

A clone of the requested operator.

Definition at line 1590 of file expression.cpp.

Expression Expression::getPow

(

const Expression &

arg

)

const

Definition at line 782 of file expression.cpp.

Expression Expression::getPowInt

(

const int &

arg

)

const

Definition at line 797 of file expression.cpp.

Expression Expression::getRow

(

const uint &

rowIdx

)

const

Definition at line 533 of file expression.cpp.

Expression Expression::getRows	(	const uint &	rowIdx1,
		const uint &	rowIdx2
	)		const

Definition at line 548 of file expression.cpp.

Expression Expression::getSin

(

)

const

Definition at line 673 of file expression.cpp.

DMatrix Expression::getSparsityPattern

(

)

const

Definition at line 656 of file expression.cpp.

Expression Expression::getSqrt

(

)

const

Definition at line 757 of file expression.cpp.

Expression Expression::getSubMatrix	(	const uint &	rowIdx1,
		const uint &	rowIdx2,
		const uint &	colIdx1,
		const uint &	colIdx2
	)		const

Definition at line 601 of file expression.cpp.

Expression Expression::getSumSquare

(

)

const

Definition at line 828 of file expression.cpp.

Expression Expression::getTan

(

)

const

Definition at line 697 of file expression.cpp.

VariableType Expression::getVariableType ( ) const

inline

Returns the variable type

Returns

The the variable type.

BooleanType Expression::isDependingOn

(

VariableType

type

)

const

Definition at line 1569 of file expression.cpp.

BooleanType Expression::isDependingOn

(

const Expression &

e

)

const

Definition at line 1582 of file expression.cpp.

BooleanType Expression::isVariable ( ) const

inline

Returns the number of columns.

Returns

The number of columns.

Expression Expression::mul ( const Expression &  arg ) const

protected

Definition at line 412 of file expression.cpp.

Expression Expression::operator()

(

uint

idx

)

const

Definition at line 218 of file expression.cpp.

Expression Expression::operator()	(	uint	rowIdx,
		uint	colIdx
	)		const

Definition at line 233 of file expression.cpp.

Operator & Expression::operator()

(

uint

idx

)

Definition at line 250 of file expression.cpp.

Operator & Expression::operator()	(	uint	rowIdx,
		uint	colIdx
	)

Definition at line 273 of file expression.cpp.

Expression & Expression::operator*=

(

const Expression &

arg

)

Definition at line 313 of file expression.cpp.

Expression & Expression::operator+=

(

const Expression &

arg

)

Definition at line 307 of file expression.cpp.

Expression Expression::operator-

(

)

const

Definition at line 1448 of file expression.cpp.

Expression & Expression::operator-=

(

const Expression &

arg

)

Definition at line 310 of file expression.cpp.

Expression & Expression::operator/=

(

const Expression &

arg

)

Definition at line 316 of file expression.cpp.

Expression & Expression::operator<<

(

const Expression &

arg

)

An operator for adding elements.

Definition at line 175 of file expression.cpp.

Expression & Expression::operator=

(

const Expression &

arg

)

Assignment Operator.

Definition at line 131 of file expression.cpp.

std::ostream & Expression::print

(

std::ostream &

stream

)

const

Definition at line 198 of file expression.cpp.

Operator * Expression::product ( const Operator *  a, const Operator *  b  ) const

protected

Internal product routine (protected, only for internal use).

Definition at line 382 of file expression.cpp.

Expression Expression::sub ( const Expression &  arg ) const

protected

Definition at line 350 of file expression.cpp.

returnValue Expression::substitute	(	int	idx,
		const Expression &	arg
	)		const

Substitutes a given variable with an expression.

Definition at line 1436 of file expression.cpp.

Expression Expression::transpose

(

)

const

Returns the transpose of this expression.

Returns

The transposed expression.

Definition at line 811 of file expression.cpp.

Friends And Related Function Documentation

friend class CFunction

friend

Definition at line 59 of file expression.hpp.

friend class COperator

friend

Definition at line 58 of file expression.hpp.

friend class FunctionEvaluationTree

friend

Definition at line 60 of file expression.hpp.

Expression operator* ( const Expression &  arg1, const Expression &  arg2  )

friend

Definition at line 302 of file expression.cpp.

Expression operator+ ( const Expression &  arg1, const Expression &  arg2  )

friend

Definition at line 298 of file expression.cpp.

Expression operator- ( const Expression &  arg1, const Expression &  arg2  )

friend

Definition at line 300 of file expression.cpp.

Expression operator/ ( const Expression &  arg1, const Expression &  arg2  )

friend

Definition at line 304 of file expression.cpp.

std::ostream& operator<< ( std::ostream &  stream, const Expression &  arg  )

friend

Definition at line 213 of file expression.cpp.

Member Data Documentation

uint Expression::component

protected

The expression component

Definition at line 315 of file expression.hpp.

uint Expression::dim

protected

DVector space dimension.

Definition at line 312 of file expression.hpp.

Operator** Expression::element

protected

Element of vector space.

Definition at line 311 of file expression.hpp.

std::string Expression::name

protected

The name of the expression

Definition at line 316 of file expression.hpp.

uint Expression::nCols

protected

DMatrix dimension.

Definition at line 313 of file expression.hpp.

uint Expression::nRows

protected

Definition at line 313 of file expression.hpp.

VariableType Expression::variableType

protected

Variable type.

Definition at line 314 of file expression.hpp.

---

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

• expression.hpp
• expression.cpp