monomial.h File Reference

Definition of the Tmonomial type and the associated functions. More...

#include "boolean.h"
#include "interval.h"
#include "variables.h"
#include "variable_set.h"
#include <stdlib.h>

Go to the source code of this file.

Data Structures
struct	Tmonomial
	A scaled product of powers of variables. More...
Functions
void	InitMonomial (Tmonomial *f)
	Constructor.
void	ResetMonomial (Tmonomial *f)
	Reset the monomial information.
void	FixVariableInMonomial (unsigned int nv, double v, Tmonomial *f)
	Replaces a variable by a constant.
void	ReplaceVariableInMonomial (unsigned int nv, double ct, unsigned int nvNew, Tmonomial *f)
	Replaces a variable.
boolean	EmptyMonomial (Tmonomial *f)
	Checks if a monomial is empty.
boolean	CtMonomial (Tmonomial *f)
	Checks if a monomial is constant.
boolean	QuadraticMonomial (Tmonomial *f)
	Checks if a monomial is quadratic: Kx^2*, with K a constant.
boolean	BilinearMonomial (Tmonomial *f)
	Checks if a monomial is bilienal: Kxy, with K a constant.
boolean	LinearMonomial (Tmonomial *f)
	Checks if a monomial is lienal: Kx*, with K a constant.
unsigned int	MonomialOrder (Tmonomial *f)
	Gets the order of a monomial.
void	CopyMonomial (Tmonomial f_dst, Tmonomial f_orig)
	Copy constructor.
unsigned int	CmpMonomial (Tmonomial f1, Tmonomial f2)
	Monomial comparison.
void	SetMonomialCt (double k, Tmonomial *f)
	Changes the scale factor of a monomial.
double	GetMonomialCt (Tmonomial *f)
	Gets the scale factor of a monomial.
Tvariable_set *	GetMonomialVariables (Tmonomial *f)
	Gets the variables of a monomial.
void	AddCt2Monomial (double k, Tmonomial *f)
	Scales a monomial.
void	AddVariable2Monomial (unsigned int varid, unsigned int p, Tmonomial *f)
	Adds a power variable to the monomial.
double	EvaluateMonomial (double varValues, Tmonomial f)
	Evaluates a monomial for a given set of value for the variables.
void	EvaluateMonomialInt (Tinterval varValues, Tinterval i_out, Tmonomial *f)
	Evaluates a monomial for a given set of ranges for the variables.
void	DeriveMonomial (unsigned int nv, Tmonomial df, Tmonomial f)
	Derives an monomial.
void	PrintMonomial (FILE file, boolean first, char varNames, Tmonomial f)
	Prints a monomial.
void	DeleteMonomial (Tmonomial *f)
	Destructor.

Detailed Description

Definition of the Tmonomial type and the associated functions.

See also:: Tmonomial, monomial.c.

Definition in file monomial.h.

Function Documentation

void InitMonomial ( Tmonomial * f )

Defines an empty monomial.

Parameters:

f

The monomial to be initialized.

Definition at line 17 of file monomial.c.

References Tmonomial::ct, Tmonomial::empty, InitVarSet(), TRUE, and Tmonomial::vars.

Referenced by AddTerm2SearchCriterion(), ApplyLinkRot(), DeriveMonomial(), DummifyAndAddEquation(), EquationFromLinearConstraint(), EquationFromLinearConstraintProduct(), GenerateCrossProductEquations(), GenerateDotProductEquation(), GenerateEquationsFromBranch(), GenerateGeneralNormEquation(), GenerateJointEquations(), GenerateJointEquationsInBranch(), GenerateJointRangeEquations(), GenerateScaledParabolaEquation(), GenerateScaledSaddleEquation(), and VarScaleEquation().

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void ResetMonomial ( Tmonomial * f )

Removes the information stored in the monomial, but does not frees the memory. It is more efficient to use ResetMonomial instead of DeleteMonomial plus InitMonomial again.

Parameters:

f

The monomial to be initialized.

Definition at line 24 of file monomial.c.

References Tmonomial::ct, Tmonomial::empty, ResetVarSet(), TRUE, and Tmonomial::vars.

Referenced by AddTerm2SearchCriterion(), ApplyLinkRot(), FixVariableInMonomial(), GenerateCrossProductEquations(), GenerateDotProductEquation(), GenerateEquationsFromBranch(), GenerateGeneralNormEquation(), GenerateJointEquations(), GenerateJointEquationsInBranch(), GenerateJointRangeEquations(), GenerateScaledParabolaEquation(), GenerateScaledSaddleEquation(), ReplaceVariableInMonomial(), and SetMonomialCt().

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void FixVariableInMonomial	(	unsigned int	nv,
		double	v,
		Tmonomial *	f
	)

Removes a variable from a monomial converting it into a constant. Note, that variables are indexed and that removing a variable shifts down the index of variables with index above the removed variable.

Parameters:

	nv	Numerical identifier of the variable to remove.
	v	Value for the variable to remove.
	f	The monomial to be updated.

Definition at line 31 of file monomial.c.

References Tmonomial::ct, GetPlaceinSet(), GetVariablePowerN(), NO_UINT, RemoveVariableFromSet(), ResetMonomial(), ShiftVarIndexes(), Tmonomial::vars, and ZERO.

Referenced by ReplaceVariableInEquation().

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void ReplaceVariableInMonomial	(	unsigned int	nv,
		double	ct,
		unsigned int	nvNew,
		Tmonomial *	f
	)

Replaces a variable from a monomial converting it into a another variable via a linear relation

VarToBeReplaced = a * NewVar + b

Note, that variables are indexed and that removing a variable shifts down the index of variables with index above the removed variable.

Parameters:

	nv	Numerical identifier of the variable to remove.
	ct	Scale factor for the new variable.
	nvNew	Numerical identifier of the new variable.
	f	The monomial to be updated.

Definition at line 50 of file monomial.c.

References AddVariable2Set(), Tmonomial::ct, GetPlaceinSet(), GetVariablePowerN(), NO_UINT, RemoveVariableFromSet(), ResetMonomial(), ShiftVarIndexes(), Tmonomial::vars, and ZERO.

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boolean EmptyMonomial ( Tmonomial * f )

Checks if a monomial is empty.

Parameters:

f

The monomial to be checked.

Returns:: TRUE if the input monomia is empty.

Definition at line 71 of file monomial.c.

References Tmonomial::empty.

Referenced by AddMonomial().

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boolean CtMonomial ( Tmonomial * f )

Checks if a monomial is constant.

Parameters:

f

The monomial to be checked.

Returns:: TRUE if the input monomial is constant.

Definition at line 76 of file monomial.c.

References Tmonomial::empty, VariableSetSize(), and Tmonomial::vars.

Referenced by AddMonomial(), BilinearEquation(), and LinearEquation().

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boolean QuadraticMonomial ( Tmonomial * f )

Checks if a monomial is quadratic: K*x^2, with K a constant.

Parameters:

f

The monomial to be checked.

Returns:: TRUE if the input monomial is quadratic.

Definition at line 82 of file monomial.c.

References GetVariablePowerN(), VariableSetSize(), and Tmonomial::vars.

Referenced by BilinearEquation(), CircleEquation(), ParabolaEquation(), and SphereEquation().

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boolean BilinearMonomial ( Tmonomial * f )

Checks if a monomial is bilineal: K*x*y, with K a constant.

Parameters:

f

The monomial to be checked.

Returns:: TRUE if the input monomial is bilienal.

Definition at line 88 of file monomial.c.

References GetVariablePowerN(), VariableSetSize(), and Tmonomial::vars.

Referenced by BilinearEquation(), and SaddleEquation().

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boolean LinearMonomial ( Tmonomial * f )

Checks if a monomial is bilineal: K*y, with K a constant.

Parameters:

f

The monomial to be checked.

Returns:: TRUE if the input monomial is lineal.

Definition at line 95 of file monomial.c.

References GetVariablePowerN(), VariableSetSize(), and Tmonomial::vars.

Referenced by BilinearEquation(), LinearEquation(), ParabolaEquation(), and SaddleEquation().

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unsigned int MonomialOrder ( Tmonomial * f )

Gets the order of a monomial. Here the order is the sum of the powers of the variables in the monomial (0 for constant, 1 for lineal, 2 for quadratic and bilineal).

Parameters:

f

The monomial to be checked.

Returns:: The monomial order as defined above.

Definition at line 101 of file monomial.c.

References Tmonomial::vars, and VarSetOrder().

Referenced by AddMonomial(), and RewriteEquation().

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void CopyMonomial	(	Tmonomial *	f_dst,
		Tmonomial *	f_orig
	)

Copies a constructor copying the data from another monomial.

Parameters:

	f_dst	The monomial to be created.
	f_orig	The monomial from where to copy.

Definition at line 106 of file monomial.c.

References CopyVarSet(), Tmonomial::ct, Tmonomial::empty, and Tmonomial::vars.

Referenced by AccumulateEquations(), AddMonomial(), and ReplaceVariableInEquation().

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unsigned int CmpMonomial	(	Tmonomial *	f1,
		Tmonomial *	f2
	)

Compare two given monomials. Monomials are compared first taking into account the variables and then their scale factor.

Parameters:

	f1	The first monomial to compare.
	f2	The second monomial to compare.

Returns:: 1 if f1 is larger than f2, 0 if they are equal and 2 if f2 is larger than f1.

See also:: CmpVarSet

Definition at line 113 of file monomial.c.

References CmpVarSet(), Tmonomial::ct, Tmonomial::empty, and Tmonomial::vars.

Referenced by AddMonomial(), and CmpEquations().

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void SetMonomialCt	(	double	k,
		Tmonomial *	f
	)

Changes the scale factor of a monomial.

Parameters:

	k	the new monomial scale factor.
	f	The monomial to update.

Definition at line 154 of file monomial.c.

References Tmonomial::ct, Tmonomial::empty, FALSE, ResetMonomial(), and ZERO.

Referenced by AddMonomial(), and NormalizeEquation().

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double GetMonomialCt ( Tmonomial * f )

Gets the scale factor of a monomial.

Parameters:

f

The monomial to update.

Returns:: The scale factor of the monomial.

Definition at line 146 of file monomial.c.

References Tmonomial::ct, and Tmonomial::empty.

Referenced by AddMonomial(), CircleEquation(), CropEquation(), DummifyAndAddEquation(), GaussianElimination(), IsSimplificable(), LinearEquation2LinearConstraint(), NormalizeEquation(), ParabolaEquation(), PurgeEquation(), RewriteEquation(), SaddleEquation(), SetEquationInfo(), and SphereEquation().

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Tvariable_set* GetMonomialVariables ( Tmonomial * f )

Gets the variables of a monomial.

Parameters:

f

The monomial to update.

Returns:: A pointer to the set of variables in the monomial.

Definition at line 163 of file monomial.c.

References Tmonomial::vars.

Referenced by AddMonomial(), CropEquation(), DummifyAndAddEquation(), FindMonomial(), IsSimplificable(), LinearEquation2LinearConstraint(), LinearizeParabolaEquation(), LinearizeSaddleEquation(), ReplaceVariableInEquation(), RewriteEquation(), SetEquationInfo(), and VarScaleEquation().

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void AddCt2Monomial	(	double	k,
		Tmonomial *	f
	)

Scales a monomial.

Parameters:

	k	The scale factor to apply to the monomial.
	f	The monomial to update.

Definition at line 168 of file monomial.c.

References Tmonomial::ct, Tmonomial::empty, FALSE, and ZERO.

Referenced by AccumulateEquations(), AddTerm2SearchCriterion(), ApplyLinkRot(), CtScaleEquation(), DummifyAndAddEquation(), EquationFromLinearConstraint(), EquationFromLinearConstraintProduct(), GenerateCrossProductEquations(), GenerateDotProductEquation(), GenerateEquationsFromBranch(), GenerateJointEquations(), GenerateJointEquationsInBranch(), GenerateJointRangeEquations(), GenerateScaledParabolaEquation(), GenerateScaledSaddleEquation(), NormalizeEquation(), ReplaceVariableInEquation(), and VarScaleEquation().

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void AddVariable2Monomial	(	unsigned int	varid,
		unsigned int	p,
		Tmonomial *	f
	)

Adds a power variable to the monomial.

Parameters:

	varid	The identifier of the variable to be added to the monomial.
	p	The power for the variable.
	f	The monomial to update.

Definition at line 181 of file monomial.c.

References AddVariable2Set(), Tmonomial::ct, Tmonomial::empty, FALSE, and Tmonomial::vars.

Referenced by AddTerm2SearchCriterion(), ApplyLinkRot(), DummifyAndAddEquation(), EquationFromLinearConstraint(), EquationFromLinearConstraintProduct(), GenerateCrossProductEquations(), GenerateDotProductEquation(), GenerateEquationsFromBranch(), GenerateGeneralNormEquation(), GenerateJointEquations(), GenerateJointEquationsInBranch(), GenerateJointRangeEquations(), GenerateScaledParabolaEquation(), GenerateScaledSaddleEquation(), ReplaceVariableInEquation(), and VarScaleEquation().

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double EvaluateMonomial	(	double *	varValues,
		Tmonomial *	f
	)

Evaluates a monomial for a given set of value for the variables.

Parameters:

	varValues	An array of doubles with the values for the variables in the problem.
	f	The monomial to evaluate.

Returns:: The value of the monomial.

Definition at line 193 of file monomial.c.

References Tmonomial::ct, Tmonomial::empty, EvaluateVarSet(), VariableSetSize(), and Tmonomial::vars.

Referenced by EvaluateEquation().

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void EvaluateMonomialInt	(	Tinterval *	varValues,
		Tinterval *	i_out,
		Tmonomial *	f
	)

Evaluates a monomial for a given set of ranges for the variables using interval arithmetics.

Parameters:

	varValues	An array with the ranges for the variables in the problem.
	i_out	The output interval.
	f	The monomial to evaluate.

Definition at line 206 of file monomial.c.

References Tmonomial::ct, Tmonomial::empty, EvaluateVarSetInt(), IntervalProduct(), NewInterval(), VariableSetSize(), Tmonomial::vars, and ZERO.

Referenced by EvaluateEquationInt().

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void DeriveMonomial	(	unsigned int	nv,
		Tmonomial *	df,
		Tmonomial *	f
	)

Derives a monomial with respect to a given variable.

Parameters:

	nv	Identifier of the variable with respect to the one we have to derive.
	df	Output monomial with the derived monomial.
	f	The monomial to derive.

Definition at line 234 of file monomial.c.

References Tmonomial::ct, DeriveVarSet(), Tmonomial::empty, FALSE, InitMonomial(), VarIncluded(), and Tmonomial::vars.

Referenced by DeriveEquation().

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void PrintMonomial	(	FILE *	file,
		boolean	first,
		char **	varNames,
		Tmonomial *	f
	)

Writes a monomial to a given stream.

Parameters:

	file	The stream where to print the monomial.
	first	TRUE if the monomial is the first one in an equation. This is used to avoid a '+' sign at the beginning of the equation.
	varNames	The name of the variables. If this parameter is NULL the printed names for the variables are v_X with X the index of the variable.
	f	The monomial to print.