Expression base class. More...

#include <CouenneExpression.hpp>

Inheritance diagram for Couenne::expression:

Public Types
enum	auxSign { AUX_UNDEF =-2, AUX_LEQ =-1, AUX_EQ, AUX_GEQ }
	"sign" of the constraint defining an auxiliary. More...

Public Member Functions
	expression ()
	Constructor. More...

	expression (const expression &e, Domain *d=NULL)
	Copy constructor. More...

virtual	~expression ()
	Destructor. More...

virtual expression *	clone (Domain *d=NULL) const
	Cloning method. More...

virtual int	Index () const
	Return index of variable (only valid for exprVar and exprAux) More...

virtual int	nArgs () const
	return number of arguments (when applicable, that is, with N-ary functions) More...

virtual expression **	ArgList () const
	return arglist (when applicable, that is, with N-ary functions) More...

virtual void	ArgList (expression **al)
	set arglist (used in deleting nodes without deleting children) More...

virtual expression *	Argument () const
	return argument (when applicable, i.e., with univariate functions) More...

virtual expression **	ArgPtr ()
	return pointer to argument (when applicable, i.e., with univariate functions) More...

virtual enum nodeType	Type () const
	node type More...

virtual expression *	Image () const
	return pointer to corresponding expression (for auxiliary variables only) More...

virtual void	Image (expression *image)
	set expression associated with this auxiliary variable (for compatibility with exprAux) More...

virtual CouNumber	Value () const
	value (empty) More...

virtual const expression *	Original () const
	If this is an exprClone of a exprClone of an expr???, point to the original expr??? instead of an exprClone – improve computing efficiency. More...

virtual void	print (std::ostream &s=std::cout, bool=false) const
	print expression to iostream More...

virtual CouNumber	operator() ()=0
	null function for evaluating the expression More...

virtual CouNumber	gradientNorm (const double *x)
	return l-2 norm of gradient at given point More...

virtual expression *	differentiate (int)
	differentiation More...

virtual int	dependsOn (int *ind, int n, enum dig_type type=STOP_AT_AUX)
	dependence on variable set: return cardinality of subset of the set of indices in first argument which occur in expression. More...

int	dependsOn (int singleton, enum dig_type type=STOP_AT_AUX)
	version with one index only More...

virtual int	DepList (std::set< int > &deplist, enum dig_type type=ORIG_ONLY)
	fill std::set with indices of variables on which this expression depends. More...

virtual expression *	simplify ()
	simplify expression (useful for derivatives) More...

virtual int	Linearity ()
	get a measure of "how linear" the expression is (see CouenneTypes.h) More...

virtual bool	isDefinedInteger ()
	is this expression defined as an integer? More...

virtual bool	isInteger ()
	is this expression integer? More...

virtual void	getBounds (expression &, expression &)
	Get lower and upper bound of an expression (if any) More...

virtual void	getBounds (CouNumber &, CouNumber &)
	Get lower and upper bound of an expression (if any) – real values. More...

virtual exprAux *	standardize (CouenneProblem *p, bool addAux=true)
	Create standard form of this expression, by: More...

virtual void	generateCuts (expression w, OsiCuts &cs, const CouenneCutGenerator cg, t_chg_bounds *chg=NULL, int wind=-1, CouNumber lb=-COUENNE_INFINITY, CouNumber ub=COUENNE_INFINITY)
	generate convexification cut for constraint w = this More...

virtual enum expr_type	code ()
	return integer for comparing expressions (used to recognize common expression) More...

virtual enum convexity	convexity () const
	either CONVEX, CONCAVE, AFFINE, or NONCONVEX More...

virtual int	compare (expression &)
	compare expressions More...

virtual int	compare (exprCopy &)
	compare copies of expressions More...

virtual int	rank ()
	used in rank-based branching variable choice: original variables have rank 1; auxiliary w=f(x) has rank r(w) = r(x)+1; finally, auxiliary w=f(x1,x2...,xk) has rank r(w) = 1+max{r(xi):i=1..k}. More...

virtual bool	impliedBound (int, CouNumber , CouNumber , t_chg_bounds *, enum auxSign=expression::AUX_EQ)
	does a backward implied bound processing on every expression, including exprSums although already done by Clp (useful when repeated within Couenne). More...

virtual int	Multiplicity ()
	multiplicity of a variable More...

virtual CouNumber	selectBranch (const CouenneObject obj, const OsiBranchingInformation info, expression &var, double &brpts, double *&brDist, int &way)
	set up branching object by evaluating many branching points for each expression's arguments. More...

virtual void	replace (exprVar , exprVar )
	replace expression with another More...

virtual void	fillDepSet (std::set< DepNode , compNode > , DepGraph *)
	update dependence set with index of variables on which this expression depends More...

virtual void	linkDomain (Domain *d)
	empty function to update domain pointer More...

virtual void	realign (const CouenneProblem *p)
	empty function to redirect variables to proper variable vector More...

virtual bool	isBijective () const
	indicating if function is monotonically increasing More...

virtual CouNumber	inverse (expression *vardep) const
	compute the inverse function More...

virtual void	closestFeasible (expression varind, expression vardep, CouNumber &left, CouNumber &right) const
	closest feasible points in function in both directions More...

virtual bool	isCuttable (CouenneProblem *problem, int index) const
	can this expression be further linearized or are we on its concave ("bad") side More...

virtual bool	isaCopy () const
	return true if this is a copy of something (i.e. an exprCopy) More...

virtual expression *	Copy () const
	return copy of this expression (only makes sense in exprCopy) More...

Detailed Description

Expression base class.

An empty expression class with no type or operator() from which all other expression classes (for constants, variables, and operators) are derived.

Definition at line 48 of file CouenneExpression.hpp.

Member Enumeration Documentation

enum Couenne::expression::auxSign

"sign" of the constraint defining an auxiliary.

If the auxiliary is defined as $w \le f(x)$ , then it is LEQ. It is EQ and GEQ, respectively, if it is defined with $=$ and $\ge$ .

Enumerator
AUX_UNDEF
AUX_LEQ
AUX_EQ
AUX_GEQ

Definition at line 55 of file CouenneExpression.hpp.

Constructor & Destructor Documentation

Couenne::expression::expression ( )

inline

Constructor.

Definition at line 58 of file CouenneExpression.hpp.

Couenne::expression::expression	(	const expression &	e,
		Domain *	d = `NULL`
	)

inline

Copy constructor.

Pass pointer to variable vector when generating new problem, whose set of variables is equivalent but may be changed or whose value is independent.

Definition at line 63 of file CouenneExpression.hpp.

virtual Couenne::expression::~expression ( )

inlinevirtual

Destructor.

Definition at line 66 of file CouenneExpression.hpp.

Member Function Documentation

virtual expression* Couenne::expression::clone ( Domain * d = NULL ) const

inlinevirtual

Cloning method.

Reimplemented in Couenne::exprUpperBound, Couenne::exprUBMul, Couenne::exprQuad, Couenne::exprUBDiv, Couenne::exprUBCos, Couenne::exprUBSin, Couenne::exprAux, Couenne::exprUBQuad, Couenne::exprVar, Couenne::exprCopy, Couenne::exprGroup, Couenne::exprSin, Couenne::exprLowerBound, Couenne::exprStore, Couenne::exprConst, Couenne::exprLBMul, Couenne::exprPow, Couenne::exprLBDiv, Couenne::exprMin, Couenne::exprInv, Couenne::exprLBQuad, Couenne::exprLBCos, Couenne::exprLBSin, Couenne::exprEvenPow, Couenne::exprClone, Couenne::exprIVar, Couenne::exprMax, Couenne::exprDiv, Couenne::exprOpp, Couenne::exprSum, Couenne::exprAbs, Couenne::exprMul, Couenne::exprOddPow, Couenne::exprSub, Couenne::exprTrilinear, Couenne::exprExp, Couenne::exprLog, Couenne::exprCeil, Couenne::exprCos, and Couenne::exprFloor.

Definition at line 69 of file CouenneExpression.hpp.

Referenced by Couenne::exprOp::clonearglist().

virtual int Couenne::expression::Index ( ) const

inlinevirtual

Return index of variable (only valid for exprVar and exprAux)

Reimplemented in Couenne::exprCopy, and Couenne::exprVar.

Definition at line 73 of file CouenneExpression.hpp.

Referenced by Couenne::exprCeil::gradientNorm(), Couenne::exprCos::gradientNorm(), Couenne::exprFloor::gradientNorm(), Couenne::exprExp::gradientNorm(), Couenne::exprAbs::gradientNorm(), Couenne::exprOpp::gradientNorm(), Couenne::exprSin::gradientNorm(), Couenne::exprCos::impliedBound(), Couenne::exprSin::impliedBound(), and Couenne::exprQuad::operator()().

virtual int Couenne::expression::nArgs ( ) const

inlinevirtual

return number of arguments (when applicable, that is, with N-ary functions)

Reimplemented in Couenne::exprCopy, Couenne::exprOp, and Couenne::exprUnary.

Definition at line 77 of file CouenneExpression.hpp.

virtual expression** Couenne::expression::ArgList ( ) const

inlinevirtual

return arglist (when applicable, that is, with N-ary functions)

Reimplemented in Couenne::exprCopy, and Couenne::exprOp.

Definition at line 81 of file CouenneExpression.hpp.

virtual void Couenne::expression::ArgList ( expression ** al )

inlinevirtual

set arglist (used in deleting nodes without deleting children)

Reimplemented in Couenne::exprCopy, and Couenne::exprOp.

Definition at line 85 of file CouenneExpression.hpp.

virtual expression* Couenne::expression::Argument ( ) const

inlinevirtual

return argument (when applicable, i.e., with univariate functions)

Reimplemented in Couenne::exprCopy, and Couenne::exprUnary.

Definition at line 88 of file CouenneExpression.hpp.

virtual expression** Couenne::expression::ArgPtr ( )

inlinevirtual

return pointer to argument (when applicable, i.e., with univariate functions)

Reimplemented in Couenne::exprCopy, and Couenne::exprUnary.

Definition at line 92 of file CouenneExpression.hpp.

virtual enum nodeType Couenne::expression::Type ( ) const

inlinevirtual

node type

Reimplemented in Couenne::exprLowerBound, Couenne::exprUpperBound, Couenne::exprAux, Couenne::exprVar, Couenne::exprUnary, Couenne::exprOp, Couenne::exprCopy, and Couenne::exprConst.

Definition at line 96 of file CouenneExpression.hpp.

References Couenne::EMPTY.

virtual expression* Couenne::expression::Image ( ) const

inlinevirtual

return pointer to corresponding expression (for auxiliary variables only)

Reimplemented in Couenne::exprAux, and Couenne::exprCopy.

Definition at line 100 of file CouenneExpression.hpp.

virtual void Couenne::expression::Image ( expression * image )

inlinevirtual

set expression associated with this auxiliary variable (for compatibility with exprAux)

Reimplemented in Couenne::exprAux.

Definition at line 105 of file CouenneExpression.hpp.

virtual CouNumber Couenne::expression::Value ( ) const

inlinevirtual

value (empty)

Reimplemented in Couenne::exprCopy, Couenne::exprClone, and Couenne::exprConst.

Definition at line 108 of file CouenneExpression.hpp.

virtual const expression* Couenne::expression::Original ( ) const

inlinevirtual

If this is an exprClone of a exprClone of an expr???, point to the original expr??? instead of an exprClone – improve computing efficiency.

Only overloaded for exprClones/exprCopy, of course.

Reimplemented in Couenne::exprCopy.

Definition at line 114 of file CouenneExpression.hpp.

virtual void Couenne::expression::print	(	std::ostream &	s = `std::cout`,
		bool	= `false`
	)		const

inlinevirtual

print expression to iostream

descend into auxiliaries' image?

Reimplemented in Couenne::exprUpperBound, Couenne::exprCopy, Couenne::exprQuad, Couenne::exprAux, Couenne::exprVar, Couenne::exprUBQuad, Couenne::exprOp, Couenne::exprUnary, Couenne::exprGroup, Couenne::exprLowerBound, Couenne::exprClone, Couenne::exprConst, Couenne::exprInv, Couenne::exprLBQuad, Couenne::exprStore, Couenne::exprOpp, and Couenne::exprIVar.

Definition at line 118 of file CouenneExpression.hpp.

virtual CouNumber Couenne::expression::operator() ( )

pure virtual

virtual CouNumber Couenne::expression::gradientNorm ( const double * x )

inlinevirtual

return l-2 norm of gradient at given point

Reimplemented in Couenne::exprCopy, Couenne::exprQuad, Couenne::exprVar, Couenne::exprGroup, Couenne::exprSin, Couenne::exprPow, Couenne::exprInv, Couenne::exprDiv, Couenne::exprOpp, Couenne::exprMul, Couenne::exprAbs, Couenne::exprExp, Couenne::exprCeil, Couenne::exprCos, Couenne::exprFloor, Couenne::exprLog, Couenne::exprTrilinear, Couenne::exprBinProd, and Couenne::exprMultiLin.

Definition at line 126 of file CouenneExpression.hpp.

virtual expression* Couenne::expression::differentiate ( int )

virtual

virtual int Couenne::expression::dependsOn	(	int *	ind,
		int	n,
		enum dig_type	type = `STOP_AT_AUX`
	)

virtual

dependence on variable set: return cardinality of subset of the set of indices in first argument which occur in expression.

Reimplemented in Couenne::exprUpperBound, Couenne::exprLowerBound, and Couenne::exprConst.

Referenced by dependsOn().

int Couenne::expression::dependsOn	(	int	singleton,
		enum dig_type	type = `STOP_AT_AUX`
	)

inline

version with one index only

Definition at line 137 of file CouenneExpression.hpp.

References dependsOn().

virtual int Couenne::expression::DepList	(	std::set< int > &	deplist,
		enum dig_type	type = `ORIG_ONLY`
	)

inlinevirtual

fill std::set with indices of variables on which this expression depends.

Also deal with expressions that have no variable pointers (exprGroup, exprQuad)

Reimplemented in Couenne::exprQuad, Couenne::exprCopy, Couenne::exprAux, Couenne::exprVar, Couenne::exprOp, Couenne::exprUnary, and Couenne::exprGroup.

Definition at line 143 of file CouenneExpression.hpp.

virtual expression* Couenne::expression::simplify ( )

inlinevirtual

simplify expression (useful for derivatives)

Reimplemented in Couenne::exprCopy, Couenne::exprVar, Couenne::exprAux, Couenne::exprQuad, Couenne::exprOp, Couenne::exprUnary, Couenne::exprGroup, Couenne::exprPow, Couenne::exprMin, Couenne::exprMax, Couenne::exprOpp, Couenne::exprDiv, Couenne::exprMul, Couenne::exprSum, Couenne::exprSub, Couenne::exprBinProd, and Couenne::exprMultiLin.

Definition at line 148 of file CouenneExpression.hpp.

virtual int Couenne::expression::Linearity ( )

inlinevirtual

get a measure of "how linear" the expression is (see CouenneTypes.h)

Reimplemented in Couenne::exprCopy, Couenne::exprUpperBound, Couenne::exprVar, Couenne::exprAux, Couenne::exprQuad, Couenne::exprOp, Couenne::exprUnary, Couenne::exprGroup, Couenne::exprLowerBound, Couenne::exprPow, Couenne::exprConst, Couenne::exprInv, Couenne::exprOpp, Couenne::exprDiv, Couenne::exprMul, Couenne::exprSum, Couenne::exprSub, Couenne::exprBinProd, and Couenne::exprMultiLin.

Definition at line 152 of file CouenneExpression.hpp.

References Couenne::NONLINEAR.

virtual bool Couenne::expression::isDefinedInteger ( )

inlinevirtual

is this expression defined as an integer?

Reimplemented in Couenne::exprCopy, Couenne::exprAux, Couenne::exprVar, and Couenne::exprIVar.

Definition at line 156 of file CouenneExpression.hpp.

References isInteger().

virtual bool Couenne::expression::isInteger ( )

inlinevirtual

is this expression integer?

Reimplemented in Couenne::exprQuad, Couenne::exprAux, Couenne::exprCopy, Couenne::exprVar, Couenne::exprOp, Couenne::exprGroup, Couenne::exprUnary, Couenne::exprConst, Couenne::exprDiv, Couenne::exprOpp, Couenne::exprPow, Couenne::exprAbs, and Couenne::exprIVar.

Definition at line 160 of file CouenneExpression.hpp.

Referenced by isDefinedInteger().

virtual void Couenne::expression::getBounds	(	expression *&	,
		expression *&
	)

virtual

Get lower and upper bound of an expression (if any)

Reimplemented in Couenne::exprCopy, Couenne::exprVar, Couenne::exprQuad, Couenne::exprGroup, Couenne::exprPow, Couenne::exprSin, Couenne::exprConst, Couenne::exprMin, Couenne::exprInv, Couenne::exprDiv, Couenne::exprMax, Couenne::exprOpp, Couenne::exprSub, Couenne::exprMul, Couenne::exprSum, Couenne::exprAbs, Couenne::exprCeil, Couenne::exprCos, Couenne::exprFloor, Couenne::exprExp, Couenne::exprLog, Couenne::exprEvenPow, Couenne::exprOddPow, Couenne::exprBinProd, Couenne::exprMultiLin, and Couenne::exprTrilinear.

virtual void Couenne::expression::getBounds	(	CouNumber &	,
		CouNumber &
	)

virtual

Get lower and upper bound of an expression (if any) – real values.

Reimplemented in Couenne::exprCopy, Couenne::exprVar, Couenne::exprQuad, Couenne::exprGroup, Couenne::exprPow, Couenne::exprConst, Couenne::exprSin, Couenne::exprInv, Couenne::exprDiv, Couenne::exprOpp, Couenne::exprSub, Couenne::exprMul, Couenne::exprSum, Couenne::exprAbs, Couenne::exprCeil, Couenne::exprCos, Couenne::exprFloor, Couenne::exprExp, Couenne::exprLog, Couenne::exprEvenPow, Couenne::exprOddPow, Couenne::exprBinProd, Couenne::exprMultiLin, and Couenne::exprTrilinear.

virtual exprAux* Couenne::expression::standardize	(	CouenneProblem *	p,
		bool	addAux = `true`
	)

inlinevirtual

Create standard form of this expression, by:

creating auxiliary w variables and corresponding expressions
returning linear counterpart as new constraint (to replace current one)

For the base exprOp class we only do the first part (for argument list components only), and the calling class (Sum, Sub, Mul, Pow, and the like) will do the part for its own object

addAux is true if a new auxiliary variable should be added associated with the standardized expression

Reimplemented in Couenne::exprCopy, Couenne::exprOp, Couenne::exprUnary, Couenne::exprOpp, Couenne::exprPow, Couenne::exprDiv, Couenne::exprSub, Couenne::exprMul, Couenne::exprSum, Couenne::exprEvenPow, Couenne::exprOddPow, Couenne::exprBinProd, and Couenne::exprMultiLin.

Definition at line 181 of file CouenneExpression.hpp.

virtual void Couenne::expression::generateCuts	(	expression *	w,
		OsiCuts &	cs,
		const CouenneCutGenerator *	cg,
		t_chg_bounds *	chg = `NULL`,
		int	wind = `-1`,
		CouNumber	lb = `-COUENNE_INFINITY`,
		CouNumber	ub = `COUENNE_INFINITY`
	)

inlinevirtual

generate convexification cut for constraint w = this

Reimplemented in Couenne::exprCopy, Couenne::exprVar, Couenne::exprQuad, Couenne::exprGroup, Couenne::exprPow, Couenne::exprConst, Couenne::exprSin, Couenne::exprDiv, Couenne::exprInv, Couenne::exprSub, Couenne::exprMul, Couenne::exprOpp, Couenne::exprSum, Couenne::exprAbs, Couenne::exprCeil, Couenne::exprCos, Couenne::exprEvenPow, Couenne::exprFloor, Couenne::exprOddPow, Couenne::exprExp, Couenne::exprBinProd, Couenne::exprMultiLin, Couenne::exprLog, and Couenne::exprTrilinear.

Definition at line 185 of file CouenneExpression.hpp.

virtual enum expr_type Couenne::expression::code ( )

inlinevirtual

return integer for comparing expressions (used to recognize common expression)

Reimplemented in Couenne::exprQuad, Couenne::exprCopy, Couenne::exprVar, Couenne::exprUpperBound, Couenne::exprOp, Couenne::exprGroup, Couenne::exprUnary, Couenne::exprPow, Couenne::exprMin, Couenne::exprConst, Couenne::exprSin, Couenne::exprMax, Couenne::exprLowerBound, Couenne::exprDiv, Couenne::exprInv, Couenne::exprSub, Couenne::exprMul, Couenne::exprOpp, Couenne::exprSum, Couenne::exprEvenPow, Couenne::exprOddPow, Couenne::exprAbs, Couenne::exprCeil, Couenne::exprCos, Couenne::exprFloor, Couenne::exprExp, Couenne::exprBinProd, Couenne::exprMultiLin, Couenne::exprLog, and Couenne::exprTrilinear.

Definition at line 193 of file CouenneExpression.hpp.

References Couenne::COU_EXPRESSION.

virtual enum convexity Couenne::expression::convexity ( ) const

inlinevirtual

either CONVEX, CONCAVE, AFFINE, or NONCONVEX

Reimplemented in Couenne::exprVar, and Couenne::exprCopy.

Definition at line 197 of file CouenneExpression.hpp.

References Couenne::NONCONVEX.

virtual int Couenne::expression::compare ( expression & )

virtual

compare expressions

Reimplemented in Couenne::exprCopy.

virtual int Couenne::expression::compare ( exprCopy & )

virtual

compare copies of expressions

virtual int Couenne::expression::rank ( )

inlinevirtual

used in rank-based branching variable choice: original variables have rank 1; auxiliary w=f(x) has rank r(w) = r(x)+1; finally, auxiliary w=f(x1,x2...,xk) has rank r(w) = 1+max{r(xi):i=1..k}.

Reimplemented in Couenne::exprQuad, Couenne::exprCopy, Couenne::exprVar, Couenne::exprAux, Couenne::exprOp, Couenne::exprUnary, Couenne::exprGroup, and Couenne::exprConst.

Definition at line 209 of file CouenneExpression.hpp.

virtual bool Couenne::expression::impliedBound	(	int	,
		CouNumber *	,
		CouNumber *	,
		t_chg_bounds *	,
		enum	auxSign = `expression::AUX_EQ`
	)

inlinevirtual

does a backward implied bound processing on every expression, including exprSums although already done by Clp (useful when repeated within Couenne).

Parameters are the index of the (auxiliary) variable in question and the current lower/upper bound. The method returns true if there has been a change on any bound on the variables on which the expression depends.

Reimplemented in Couenne::exprQuad, Couenne::exprVar, Couenne::exprPow, Couenne::exprSum, Couenne::exprSin, Couenne::exprDiv, Couenne::exprOpp, Couenne::exprInv, Couenne::exprSub, Couenne::exprEvenPow, Couenne::exprOddPow, Couenne::exprAbs, Couenne::exprCeil, Couenne::exprCos, Couenne::exprFloor, Couenne::exprExp, and Couenne::exprLog.

Definition at line 218 of file CouenneExpression.hpp.

virtual int Couenne::expression::Multiplicity ( )

inlinevirtual

multiplicity of a variable

Reimplemented in Couenne::exprCopy, and Couenne::exprAux.

Definition at line 222 of file CouenneExpression.hpp.

virtual CouNumber Couenne::expression::selectBranch	(	const CouenneObject *	obj,
		const OsiBranchingInformation *	info,
		expression *&	var,
		double *&	brpts,
		double *&	brDist,
		int &	way
	)