Detailed Description

Implementation of the functions operating on sets of Tequations.

See Also: Tequations, TequationInfo, equations.h.

Definition in file equations.c.

Functions
void	CacheScalarEQUInfo (Tequations *eqs)
	Collects information about scalar equality equations. More...

void	SetEquationInfo (Tequation e, TequationInfo ei)
	TequationInfo constructor. More...

Tequation *	GetOriginalEquation (TequationInfo *ei)
	Returns the equation stored in a TequationInfo. More...

void	CopyEquationInfo (TequationInfo ei_dst, TequationInfo ei_src)
	TequationInfo copy constructor. More...

void	GetFirstOrderApproximationToEquation (Tbox b, double c, TLinearConstraint lc, TequationInfo ei)
	Gets a first order approximation to a given equation. More...

void	ErrorDueToVariable (unsigned int m, double c, Tinterval is, double ev, TequationInfo ei)
	Computes the linealization error for a given equation for each variable involved in the equation. More...

boolean	LinearizeSaddleEquation (double epsilon, unsigned int safeSimplex, Tbox b, TSimplex lp, TequationInfo *ei)
	Produces a linear relaxation for a saddle equation. More...

boolean	LinearizeBilinealMonomialEquation (double epsilon, double lr2tm, unsigned int safeSimplex, Tbox b, TSimplex lp, TequationInfo *ei)
	Produces a linear relaxation for a bilienal monomial equation. More...

boolean	LinearizeParabolaEquation (double epsilon, unsigned int safeSimplex, Tbox b, TSimplex lp, TequationInfo *ei)
	Produces a linear relaxation for a parabola equation. More...

boolean	LinearizeCircleEquation (double epsilon, unsigned int safeSimplex, Tbox b, TSimplex lp, TequationInfo *ei)
	Produces a linear relaxation for a circle equation. More...

boolean	LinearizeSphereEquation (double epsilon, unsigned int safeSimplex, Tbox b, TSimplex lp, TequationInfo *ei)
	Produces a linear relaxation for a sphere equation. More...

boolean	LinearizeGeneralEquationInt (unsigned int cmp, double epsilon, unsigned int safeSimplex, Tbox b, double c, TSimplex lp, TequationInfo ei)
	Produces a linear relaxation for a general equation at a given point. More...

boolean	LinearizeGeneralEquation (double epsilon, unsigned int safeSimplex, Tbox b, TSimplex lp, TequationInfo *ei)
	Produces a linear relaxation for a general equation at the central point of the sub-box defined by the variables involved in the equation. More...

void	DeleteEquationInfo (TequationInfo *ei)
	Destructor. More...

void	AddEquationInt (Tequation equation, Tequations eqs)
	Adds an equation to a set. More...

void	InitEquations (Tequations *eqs)
	Constructor. More...

void	CopyEquations (Tequations eqs_dst, Tequations eqs_src)
	Copy constructor. More...

void	MergeEquations (Tequations eqs1, Tequations eqs)
	Copy constructor. More...

boolean	UsedVarInNonDummyEquations (unsigned int nv, Tequations *eqs)
	Checks if a variable is used in the set of equations. More...

boolean	UsedVarInEquations (unsigned int nv, Tequations *eqs)
	Checks if a variable is used in the set of equations. More...

void	RemoveEquationsWithVar (double epsilon, unsigned int nv, Tequations *eqs)
	Removes all equations that include a given variable. More...

boolean	ReplaceVariableInEquations (double epsilon, unsigned int nv, TLinearConstraint lc, Tequations eqs)
	Replaces a variable with a linear expression. More...

boolean	GaussianElimination (Tequations *eqs)
	Perform Gaussian elimination on the set of equations. More...

unsigned int	NEquations (Tequations *eqs)
	Number of equations in the set. More...

unsigned int	NSystemEquations (Tequations *eqs)
	Number of system equations in the set. More...

unsigned int	NCoordEquations (Tequations *eqs)
	Number of coordenalization equations in the set. More...

unsigned int	NDummyEquations (Tequations *eqs)
	Number of dummy equations in the set. More...

unsigned int	NEqualityEquations (Tequations *eqs)
	Number of equalities in the set. More...

unsigned int	NInequalityEquations (Tequations *eqs)
	Number of inequalities in the set. More...

boolean	PolynomialEquations (Tequations *eqs)
	Identify polynomial system of equations. More...

boolean	ScalarEquations (Tequations *eqs)
	Identifies scalar systems. More...

boolean	IsSystemEquation (unsigned int i, Tequations *eqs)
	Identify system equations. More...

boolean	IsCoordEquation (unsigned int i, Tequations *eqs)
	Identify coordenalization equations. More...

boolean	IsDummyEquation (unsigned int i, Tequations *eqs)
	Identify dummy equations. More...

unsigned int	GetEquationTypeN (unsigned int i, Tequations *eqs)
	Gets the type of a particular equation. More...

boolean	HasEquation (Tequation equation, Tequations eqs)
	Checks if a given equation is already in the set. More...

unsigned int	CropEquation (unsigned int ne, unsigned int varType, double epsilon, double rho, Tbox b, Tvariables vs, Tequations *eqs)
	Equation-wise crop. More...

void	AddEquation (Tequation equation, Tequations eqs)
	Adds an equation to the set. More...

void	AddEquationNoSimp (Tequation equation, Tequations eqs)
	Adds an equation to the set. More...

void	AddMatrixEquation (TMequation equation, Tequations eqs)
	Adds a matrix equation to the set. More...

Tequation *	GetEquation (unsigned int n, Tequations *eqs)
	Gets an equation from the set. More...

boolean	AddEquation2Simplex (unsigned int ne, double lr2tm_q, double lr2tm_s, double epsilon, unsigned int safeSimplex, double rho, Tbox b, Tvariables vs, TSimplex lp, Tequations eqs)
	Adds an equation to the simplex. More...

void	UpdateSplitWeight (unsigned int ne, double splitDim, Tbox b, Tequations *eqs)
	Computes the linearization error induced by the variables of a given equation. More...

void	EvaluateEqualityEquations (boolean systemOnly, double v, double r, Tequations *eqs)
	Evaluates all equality equations in the set. More...

void	EvaluateSubSetEqualityEquations (double v, boolean se, double r, Tequations eqs)
	Evaluates a subset of the equality equations in the set. More...

void	EvaluateEqualitySparseEquations (double v, double r, Tequations *eqs)
	Evaluates the set of equality equations for sparse systems. More...

void	EvaluateSubSetEqualitySparseEquations (double v, boolean se, double r, Tequations eqs)
	Evaluates a subset of the set of equality equations for sparse systems. More...

void	EvaluateEquationsXVectors (double v, unsigned int ng, unsigned int g, double p, double r, Tequations *eqs)
	Evaluates the matrix equations multiplied by some given vectors. More...

void	EvaluateInequalityEquations (double v, double r, Tequations *eqs)
	Error in inequalities. More...

void	DeriveEqualityEquations (unsigned int v, Tequations deqs, Tequations eqs)
	Derives an equation set. More...

void	PrintEquations (FILE f, char varNames, Tequations eqs)
	Prints a set of equations. More...

void	DeleteEquations (Tequations *eqs)
	Destructor. More...

Function Documentation

void CacheScalarEQUInfo ( Tequations * eqs )

Collects information about scalar equality equations to accelerate the evaluatoin when the equation set is sparse. This happens quite often in the equation systems of the Jacobian. We collect the information with the aim of accelerating the evaluation of these equation systems, which is fundamental in atlas-based tools.

Parameters

eqs	The equation system to analyse.

Definition at line 2541 of file equations.c.

References EmptyEquation(), Tequations::eqEQU, EQU, Tequations::equation, GetEquationCmp(), GetOriginalEquation(), Tequations::n, NEW, and Tequations::nsEQU.

Referenced by EvaluateEqualitySparseEquations(), and EvaluateSubSetEqualitySparseEquations().

void SetEquationInfo	(	Tequation *	e,
		TequationInfo *	ei
	)

Defines all the information associated with an equation.

Parameters

e	The equation.
ei	The equation information to create..

See Also: TequationInfo

Definition at line 297 of file equations.c.

References AddTerm2LinearConstraint(), BILINEAL_MONOMIAL_EQUATION, BilinealMonomialEquation(), CIRCLE_EQUATION, CircleEquation(), CopyEquation(), DeriveEquation(), EMPTY_EQUATION, TequationInfo::EqType, TequationInfo::equation, Error(), GENERAL_EQUATION, GetEquationCmp(), GetEquationValue(), GetEquationVariables(), GetMonomial(), GetMonomialCt(), GetMonomialVariables(), GetNumMonomials(), GetVariableN(), TequationInfo::Hessian, InitLinearConstraint(), TequationInfo::Jacobian, TequationInfo::lc, LINEAR_EQUATION, LinearEquation(), TequationInfo::n, NEW, NewInterval(), PARABOLA_EQUATION, ParabolaEquation(), SADDLE_EQUATION, SaddleEquation(), SetLinearConstraintError(), SimplexExpandBounds(), SPHERE_EQUATION, SphereEquation(), and VariableSetSize().

Referenced by AddEquation2Simplex(), and AddEquationInt().

Tequation * GetOriginalEquation ( TequationInfo * ei )

inline

Returns the equation stored in a TequationInfo.

Parameters

ei	The equation information.

Returns: A pointer to the equation from which the equation information was created.

Definition at line 407 of file equations.c.

References TequationInfo::equation.

Referenced by AddEquation(), AddEquation2Simplex(), CacheScalarEQUInfo(), CropEquation(), DeriveEqualityEquations(), EvaluateEqualityEquations(), EvaluateInequalityEquations(), EvaluateSubSetEqualityEquations(), GaussianElimination(), GetEquation(), GetEquationTypeN(), HasEquation(), IsCoordEquation(), IsDummyEquation(), IsSystemEquation(), LinearizeBilinealMonomialEquation(), LinearizeCircleEquation(), LinearizeGeneralEquation(), LinearizeGeneralEquationInt(), LinearizeParabolaEquation(), LinearizeSaddleEquation(), LinearizeSphereEquation(), MergeEquations(), PrintEquations(), RemoveEquationsWithVar(), ReplaceVariableInEquations(), UsedVarInEquations(), and UsedVarInNonDummyEquations().

void CopyEquationInfo	(	TequationInfo *	ei_dst,
		TequationInfo *	ei_src
	)

Creates a TequationInfo copying data from another TequationInfo.

Parameters

ei_dst	The equation information to create.
ei_src	The equation information from where to copy the data.

Definition at line 412 of file equations.c.

References CopyEquation(), CopyLinearConstraint(), EMPTY_EQUATION, TequationInfo::EqType, TequationInfo::equation, TequationInfo::Hessian, TequationInfo::Jacobian, TequationInfo::lc, LINEAR_EQUATION, TequationInfo::n, and NEW.

Referenced by CopyEquations().

void GetFirstOrderApproximationToEquation	(	Tbox *	b,
		double *	c,
		TLinearConstraint *	lc,
		TequationInfo *	ei
	)

Defines a first order approximation to a given equation from the information we have of this equation.

Parameters

b	The box with the ranges for the variables.
c	The linearization point.
lc	The linear constraint to be created.
ei	The equation information from which to create the linear approximation.

See Also: TlinearConstraint

Definition at line 471 of file equations.c.

References AddTerm2LinearConstraint(), TequationInfo::equation, Error(), EvaluateEquationInt(), GetBoxIntervals(), GetBoxMaxSizeVarSet(), GetBoxNIntervals(), GetEquationValue(), GetEquationVariables(), GetVariableN(), TequationInfo::Hessian, INF, InitLinearConstraint(), IntervalAdd(), IntervalInvert(), IntervalOffset(), IntervalPow(), IntervalProduct(), IntervalScale(), TequationInfo::Jacobian, LowerLimit(), TequationInfo::n, NEW, NewInterval(), SetLinearConstraintError(), and ZERO.

Referenced by CropEquation(), and LinearizeGeneralEquationInt().

void ErrorDueToVariable	(	unsigned int	m,
		double *	c,
		Tinterval *	is,
		double *	ev,
		TequationInfo *	ei
	)

Computes the linealization error for a given equation for each variable involved in the equation.

Parameters

m	Number of variables in the system of equations.
c	The linealization point.
is	Ranges for the variables in the system.
ev	Array of double where to add the linealization error induced by each variable for the equation.
ei	The equation information.

Definition at line 629 of file equations.c.

References EMPTY_EQUATION, TequationInfo::EqType, TequationInfo::equation, Error(), EvaluateEquationInt(), GetEquationValue(), GetEquationVariables(), GetVariableN(), TequationInfo::Hessian, IntervalAdd(), IntervalOffset(), IntervalPow(), IntervalProduct(), IntervalScale(), IntervalSize(), LINEAR_EQUATION, TequationInfo::n, NEW, and NewInterval().

Referenced by UpdateSplitWeight().

boolean LinearizeSaddleEquation	(	double	epsilon,
		unsigned int	safeSimplex,
		Tbox *	b,
		TSimplex *	lp,
		TequationInfo *	ei
	)

Produces a linear relaxation for a saddle equations of the form $x y + \alpha z =\beta$ . It consists of four planes each derived from a linealization of the saddle funcion at the corners of the x-y box.

The same routine is used to linearize single monomial bilineal equations of the form $x y =\beta$ .

Parameters

epsilon	Threshold to remove tiny terms in the generated linear constraints.
safeSimplex	Degree of numerical stability in the simplex as specified by the user in the SAFE SIMPLEX parameter.
b	The box with the ranges for the varibles.
lp	The simplex where to add the linear constraints.
ei	The equation information to use.

Returns: TRUE if the simplex is still feasible after adding the constraints.

Definition at line 1708 of file equations.c.

References GEQ, GetBoxIntervals(), GetBoxNIntervals(), GetMonomial(), GetMonomialVariables(), GetOriginalEquation(), GetVariableN(), LEQ, LinearizeGeneralEquation(), LinearizeGeneralEquationInt(), LowerLimit(), NEW, TRUE, and UpperLimit().

Referenced by AddEquation2Simplex().

boolean LinearizeBilinealMonomialEquation	(	double	epsilon,
		double	lr2tm,
		unsigned int	safeSimplex,
		Tbox *	b,
		TSimplex *	lp,
		TequationInfo *	ei
	)

Produces a linear relaxation for a bilineal monomial equations of the form $x y =\beta$ (an equation formed by a single bilineal monomial). This equation can be seen as a degenerate saddle but a particular treatment results beneficial.

Parameters

epsilon	Threshold to remove tiny terms in the generated linear constraints.
lr2tm	Maximum size to switch from linear relaxations to taylor models.
safeSimplex	Degree of numerical stability in the simplex as specified by the user in the SAFE SIMPLEX parameter.
b	The box with the ranges for the varibles.
lp	The simplex where to add the linear constraints.
ei	The equation information to use.

Returns: TRUE if the simplex is still feasible after adding the constraints.

Definition at line 1766 of file equations.c.

References GEQ, GetBoxIntervals(), GetBoxNIntervals(), GetEquationValue(), GetMonomial(), GetMonomialVariables(), GetOriginalEquation(), GetVariableN(), LEQ, LinearizeGeneralEquation(), LinearizeGeneralEquationInt(), LowerLimit(), NEW, TRUE, and UpperLimit().

Referenced by AddEquation2Simplex().

boolean LinearizeParabolaEquation	(	double	epsilon,
		unsigned int	safeSimplex,
		Tbox *	b,
		TSimplex *	lp,
		TequationInfo *	ei
	)

Produces a linear relaxation for a parabola equation $x^2 + \alpha z =\beta$ . It consists of two lines derived from a linear approximation of the parabola at the center of the x interval. Additionaly, we define linear constraints on the extremes of the range of x.

Parameters

epsilon	Threshold to remove tiny terms in the generated linear constraints.
safeSimplex	Degree of numerical stability in the simplex as specified by the user in the SAFE SIMPLEX parameter.
b	The box with the ranges for the varibles.
lp	The simplex where to add the linear constraints.
ei	The equation information to use.

Returns: TRUE if the simplex is still feasible after adding the constraints.

Definition at line 1871 of file equations.c.

References EQU, GetBoxIntervals(), GetBoxNIntervals(), GetMonomial(), GetMonomialVariables(), GetOriginalEquation(), GetVariableN(), IntervalCenter(), LEQ, LinearizeGeneralEquationInt(), LowerLimit(), NEW, TRUE, and UpperLimit().

Referenced by AddEquation2Simplex().

boolean LinearizeCircleEquation	(	double	epsilon,
		unsigned int	safeSimplex,
		Tbox *	b,
		TSimplex *	lp,
		TequationInfo *	ei
	)

Produces a linear relaxation for a circle equation $x^2 + y^2 =r^2$ . It consists of two lines derived from a linear approximation of the circle at the center of the x-y box. Additionaly, we define linear constraints for the corners of the x-y box that are out of the circle.

Parameters

epsilon	Threshold to remove tiny terms in the generated linear constraints.
safeSimplex	Degree of numerical stability in the simplex as specified by the user in the SAFE SIMPLEX parameter.
b	The box with the ranges for the varibles.
lp	The simplex where to add the linear constraints.
ei	The equation information to use.

Returns: TRUE if the simplex is still feasible after adding the constraints.

Definition at line 1917 of file equations.c.

References GEQ, GetBoxIntervals(), GetBoxNIntervals(), GetEquationCmp(), GetEquationValue(), GetEquationVariables(), GetOriginalEquation(), GetVariableN(), IntervalCenter(), LEQ, LinearizeGeneralEquationInt(), LowerLimit(), NEW, ROUNDDOWN, ROUNDNEAR, TRUE, and UpperLimit().

Referenced by AddEquation2Simplex().

boolean LinearizeSphereEquation	(	double	epsilon,
		unsigned int	safeSimplex,
		Tbox *	b,
		TSimplex *	lp,
		TequationInfo *	ei
	)

Produces a linear relaxation for a sphere equation $x^2 + y^2 + z^2=r^2$ . It consists of two lines derived from a linear approximation of the sphere at the center of the x-y-z box. Additionaly, we define linear constraints for the corners of the x-y-z box that are out of the sphere.

Parameters

epsilon	Threshold to remove tiny terms in the generated linear constraints.
safeSimplex	Degree of numerical stability in the simplex as specified by the user in the SAFE SIMPLEX parameter.
b	The box with the ranges for the varibles.
lp	The simplex where to add the linear constraints.
ei	The equation information to use.

Returns: TRUE if the simplex is still feasible after adding the constraints.

Definition at line 2017 of file equations.c.

References GEQ, GetBoxIntervals(), GetBoxNIntervals(), GetEquationCmp(), GetEquationValue(), GetEquationVariables(), GetOriginalEquation(), GetVariableN(), IntervalCenter(), LEQ, LinearizeGeneralEquationInt(), LowerLimit(), NEW, ROUNDDOWN, ROUNDNEAR, TRUE, and UpperLimit().

Referenced by AddEquation2Simplex().

boolean LinearizeGeneralEquationInt	(	unsigned int	cmp,
		double	epsilon,
		unsigned int	safeSimplex,
		Tbox *	b,
		double *	c,
		TSimplex *	lp,
		TequationInfo *	ei
	)

Produces a linear relaxation for a general equation. It consists of two lines derived from a linear approximation of the equation at the given point.

Parameters

cmp	LEQ, GEQ, EQU Used to select which one of the two linear constraints are to be added to the simplex.
epsilon	Threshold to remove tiny terms in the generated linear constraints.
safeSimplex	Degree of numerical stability in the simplex as specified by the user in the SAFE SIMPLEX parameter.
b	The box with the ranges for the varibles.
c	The linearization point.
lp	The simplex where to add the linear constraints.
ei	The equation information to use.

Returns: TRUE if the simplex is still feasible after adding the constraints.

Definition at line 2127 of file equations.c.

References DeleteLinearConstraint(), GetBoxIntervals(), GetBoxMaxSizeVarSet(), GetEquationVariables(), GetFirstOrderApproximationToEquation(), GetOriginalEquation(), INF, SimplexAddNewConstraint(), and TRUE.

Referenced by LinearizeBilinealMonomialEquation(), LinearizeCircleEquation(), LinearizeGeneralEquation(), LinearizeParabolaEquation(), LinearizeSaddleEquation(), and LinearizeSphereEquation().

boolean LinearizeGeneralEquation	(	double	epsilon,
		unsigned int	safeSimplex,
		Tbox *	b,
		TSimplex *	lp,
		TequationInfo *	ei
	)

Produces a linear relaxation for a general equation at the central point of the sub-box defined by the variables involved in the equation using LinearizeGeneralEquationInt.

Parameters

epsilon	Threshold to remove tiny terms in the generated linear constraints.
safeSimplex	Degree of numerical stability in the simplex as specified by the user in the SAFE SIMPLEX parameter.
b	The box with the ranges for the varibles.
lp	The simplex where to add the linear constraints.
ei	The equation information to use.

Returns: TRUE if the simplex is still feasible after adding the constraints.

Definition at line 2151 of file equations.c.

References GetBoxIntervals(), GetBoxNIntervals(), GetEquationCmp(), GetEquationVariables(), GetOriginalEquation(), GetVariableN(), IntervalCenter(), LinearizeGeneralEquationInt(), TequationInfo::n, and NEW.

Referenced by AddEquation2Simplex(), LinearizeBilinealMonomialEquation(), and LinearizeSaddleEquation().

void DeleteEquationInfo ( TequationInfo * ei )

Deletes the equation information stored in the and frees the allocated memory space.

Parameters

ei	The equation information to delete.

Definition at line 693 of file equations.c.

References DeleteEquation(), DeleteLinearConstraint(), EMPTY_EQUATION, TequationInfo::EqType, TequationInfo::equation, TequationInfo::Hessian, TequationInfo::Jacobian, TequationInfo::lc, LINEAR_EQUATION, and TequationInfo::n.

Referenced by AddEquation2Simplex(), and DeleteEquations().

void AddEquationInt	(	Tequation *	equation,
		Tequations *	eqs
	)

This is the same as AddEquation but it does not take into accoun whether the added equation is empty or whether it is repeated. Moreover, it does not re-order equations in the set.

This is used as a sub-function of AddEquation and also when deriving equation sets. In this case it is relevant to obtain an ordered set of equations with the correct size (the same as the input set of equations) even if they are repeated or empty.

Parameters

equation	The equation to add.
eqs	The equation set.

Definition at line 1596 of file equations.c.

References Tequations::c, COORD_EQ, Tequations::d, DUMMY_EQ, Tequations::e, Tequations::eqEQU, EQU, Tequations::equation, GetEquationCmp(), GetEquationType(), Tequations::m, MEM_DUP, Tequations::n, Tequations::neq, NEW, Tequations::nsEQU, Tequations::polynomial, PolynomialEquation(), Tequations::s, SetEquationInfo(), and SYSTEM_EQ.

Referenced by AddEquation(), AddEquationNoSimp(), and DeriveEqualityEquations().

void InitEquations ( Tequations * eqs )

Initializes a set of equations.

Parameters

eqs	The equation set to be initialized.

Definition at line 733 of file equations.c.

References Tequations::c, Tequations::d, Tequations::e, Tequations::eqEQU, Tequations::equation, INIT_NUM_EQUATIONS, Tequations::m, Tequations::mequation, Tequations::mm, Tequations::n, Tequations::neq, NEW, Tequations::nm, Tequations::nsEQU, Tequations::polynomial, Tequations::s, Tequations::scalar, and TRUE.

Referenced by DeriveEqualityEquations(), DummifyCuikSystem(), GaussianElimination(), GenerateWorldEquations(), InitCuikSystem(), RemoveEquationsWithVar(), and ReplaceVariableInEquations().

void CopyEquations	(	Tequations *	eqs_dst,
		Tequations *	eqs_src
	)

Initializes a set of equations from another set.

Parameters

eqs_dst	The equation set to be initialized.
eqs_src	The equation set from where to get the information.

Definition at line 768 of file equations.c.

References Tequations::c, CopyEquationInfo(), CopyMEquation(), Tequations::d, Tequations::e, Tequations::eqEQU, Tequations::equation, Tequations::m, Tequations::mequation, Tequations::mm, Tequations::n, Tequations::neq, NEW, Tequations::nm, Tequations::nsEQU, Tequations::polynomial, Tequations::s, and Tequations::scalar.

Referenced by CopyCuikSystem(), CopyJacobian(), CuikSystemMerge(), DummifyCuikSystem(), GaussianElimination(), GetCSEquations(), RemoveEquationsWithVar(), ReplaceVariableInEquations(), and SimplifyCuikSystem().

void MergeEquations	(	Tequations *	eqs1,
		Tequations *	eqs
	)

Adds a set of equations to another.

Parameters

eqs1	The equation set to add.
eqs	The set where to add the equations.

Definition at line 815 of file equations.c.

References AddEquation(), AddMatrixEquation(), Tequations::eqEQU, Tequations::equation, GetOriginalEquation(), Tequations::m, Tequations::mequation, Tequations::mm, and Tequations::nsEQU.

Referenced by CuikSystemMerge().

boolean UsedVarInNonDummyEquations	(	unsigned int	nv,
		Tequations *	eqs
	)

Checks if a variable is used in non-dummy equations of the set of equations.

Parameters

nv	The identifier of the variable to look for.
eqs	The equation set from where to get the information.

Returns: TRUE if the variable nv appears in any of the non-dummy equations of the set eqs.

Definition at line 835 of file equations.c.

References DUMMY_EQ, Tequations::equation, FALSE, GetEquationType(), GetEquationVariables(), GetOriginalEquation(), Tequations::mequation, VarIncluded(), and VarIncludedinMEquation().

Referenced by CSRemoveUnusedVars().

boolean UsedVarInEquations	(	unsigned int	nv,
		Tequations *	eqs
	)

Checks if a variable is used in the set of equations.

Parameters

nv	The identifier of the variable to look for.
eqs	The equation set from where to get the information.

Returns: TRUE if the variable nv appears in the set eqs.

Definition at line 860 of file equations.c.

References Tequations::equation, FALSE, GetEquationVariables(), GetOriginalEquation(), Tequations::mequation, VarIncluded(), and VarIncludedinMEquation().

Referenced by CSRemoveUnusedVars(), and SampleCuikSystemInBox().

void RemoveEquationsWithVar	(	double	epsilon,
		unsigned int	nv,
		Tequations *	eqs
	)

Removes all equations that include a given variable. This is one of the steps to remove a variable from a problem. Therefore, equations that do not include the given variable are also affected by this function: we have to shift all the variable indexes higher than the given one.

The use of this function without using function RemoveVariable right immediately after it leaves the cuiksystem in a incoherent state.

Parameters

epsilon	Monomials with a constant below epsilon are eliminated.
nv	The identifier of the variable to remove.
eqs	The set of equations to update.

Definition at line 882 of file equations.c.

References AddEquation(), CopyEquations(), DeleteEquations(), Tequations::equation, Error(), FALSE, FixVariableInEquation(), GetEquationVariables(), GetOriginalEquation(), InitEquations(), Tequations::mequation, Tequations::n, Tequations::nm, ShiftVariablesInMEquation(), VarIncluded(), and VarIncludedinMEquation().

Referenced by CSRemoveUnusedVars().

boolean ReplaceVariableInEquations	(	double	epsilon,
		unsigned int	nv,
		TLinearConstraint *	lc,
		Tequations *	eqs
	)

Replaces a variable by linear combination of variables (including an offset).

The use of this function without using function RemoveVariable right immediately after it leaves the cuiksystem in a incoherent state.

Parameters

epsilon	Monomials with a constant below epsilon are eliminated.
nv	The variable to replace.
lc	The linear constraint to use in the replacement.
eqs	The equation set from where to get the information.

Returns: TRUE the equation set still holds after replacing the equation.

See Also: SimplifyCuikSystem

Definition at line 925 of file equations.c.

References AddEquation(), CopyEquations(), DeleteEquations(), Tequations::equation, Error(), FALSE, GetOriginalEquation(), InitEquations(), ReplaceVariableInEquation(), Tequations::scalar, and TRUE.

Referenced by CSRemoveLCVars(), and CSRemoveVarsWithCtRange().

boolean GaussianElimination ( Tequations * eqs )

Operates linearly pairs of equations (scale one of the and then sum them) with the objective of getting a simpler equation (i.e., one with less monomials). The rationale is that equations with less monomials produce simpler problems and, in some cases, they can trigger simplifications that are not evident at first sight.

The use of this function without using function RemoveVariable right immediately after it leaves the cuiksystem in a incoherent state.

Parameters

eqs	The equation set to be simplified.

Returns: TRUE the equation set still holds after replacing the equation.

See Also: AccumulateEquations, SimplifyCuikSystem

Definition at line 963 of file equations.c.

References AccumulateEquations(), AddEquation(), CopyEquation(), CopyEquations(), DeleteEquation(), DeleteEquations(), DUMMY_EQ, EQU, Tequations::equation, Error(), FALSE, FindMonomial(), GetEquationCmp(), GetEquationNumVariables(), GetEquationType(), GetMonomial(), GetMonomialCt(), GetNumMonomials(), GetOriginalEquation(), InitEquations(), NEquations(), NO_UINT, PrintEquation(), Tequations::scalar, and TRUE.

Referenced by SimplifyCuikSystem().

unsigned int NEquations ( Tequations * eqs )

Number of equations in the set.

Parameters

eqs	The equation set.

Returns: The number of equations in the set.

Definition at line 1075 of file equations.c.

References Tequations::neq.

Referenced by CSRemoveLCVars(), DummifyCuikSystem(), GaussianElimination(), GetCSNumEquations(), and UpdateCuikSystem().

unsigned int NSystemEquations ( Tequations * eqs )

Number of system equations in the set.

Parameters

eqs	The equation set.

Returns: The number of system equations in the set.

Definition at line 1080 of file equations.c.

References Tequations::s.

unsigned int NCoordEquations ( Tequations * eqs )

Number of coordenalization equations in the set.

Parameters

eqs	The equation set.

Returns: The number of coordenalization equations in the set.

Definition at line 1085 of file equations.c.

References Tequations::c.

unsigned int NDummyEquations ( Tequations * eqs )

Number of dummy equations in the set.

Parameters

eqs	The equation set.

Returns: The number of dummy equations in the set.

Definition at line 1090 of file equations.c.

References Tequations::d.

unsigned int NEqualityEquations ( Tequations * eqs )

Number of equality equations in the set.

Parameters

eqs	The equation set.

Returns: The number of equality equations in the set.

Definition at line 1095 of file equations.c.

References Tequations::e.

Referenced by ErrorInCSEquations(), ErrorInSimpCSEquations(), ErrorInSolution(), InitJacobian(), and UpdateCuikSystem().

unsigned int NInequalityEquations ( Tequations * eqs )

Number of inequality equations in the set.

Parameters

eqs	The equation set.

Returns: The number of inequality equations in the set.

Definition at line 1100 of file equations.c.

References Tequations::e, and Tequations::neq.

Referenced by ErrorInInequalities(), ErrorInSimpInequalitiesOnPoint(), InequalitiesHoldOnPoint(), and SimpInequalitiesHoldOnPoint().

boolean PolynomialEquations ( Tequations * eqs )

Identify polynomial system of equations.

Parameters

eqs	The equation set to query.

Returns: TRUE if the set is composed only by polynomial equations.

Definition at line 1105 of file equations.c.

References Tequations::polynomial.

Referenced by IsCSPolynomial(), and SimplifyCuikSystem().

boolean ScalarEquations ( Tequations * eqs )

Identifies scalar systems (systems with no matrix equations).

Parameters

eqs	The equation to check.

Definition at line 1110 of file equations.c.

References Tequations::scalar.

Referenced by CuikSystemMerge().

boolean IsSystemEquation	(	unsigned int	i,
		Tequations *	eqs
	)

Identify system equations.

Parameters

i	The identifier of the equation to check.
eqs	The equation set.

Returns: TRUE if the selecte equation is a system equation.

Definition at line 1115 of file equations.c.

References Tequations::equation, Error(), GetEquationType(), GetOriginalEquation(), Tequations::neq, SYSTEM_EQ, and TRUE.

Referenced by PrintEquations().

boolean IsCoordEquation	(	unsigned int	i,
		Tequations *	eqs
	)

Identify coordenalization equations.

Parameters

i	The identifier of the equation to check.
eqs	The equation set.

Returns: TRUE if the selected equation is a coordenalization equation.

Definition at line 1126 of file equations.c.

References COORD_EQ, Tequations::equation, Error(), GetEquationType(), GetOriginalEquation(), and Tequations::neq.

Referenced by PrintEquations(), and RegenerateSolution().

boolean IsDummyEquation	(	unsigned int	i,
		Tequations *	eqs
	)

Identify dummy equations.

Parameters

i	The identifier of the equation to check.
eqs	The equation set.

Returns: TRUE if the selected equation is a dummy equation.

Definition at line 1135 of file equations.c.

References DUMMY_EQ, Tequations::equation, Error(), GetEquationType(), GetOriginalEquation(), and Tequations::neq.

Referenced by PrintEquations(), and RegenerateSolution().

unsigned int GetEquationTypeN	(	unsigned int	i,
		Tequations *	eqs
	)

Gets the type of a particular equation.

Parameters

i	The identifier of the equation to check.
eqs	The equation set.

Returns: The type of the selected eqution of NOTYPE_EQ if there is no equation with the given identifier in the set.

Definition at line 1144 of file equations.c.

References Tequations::equation, Error(), GetEquationType(), GetOriginalEquation(), Tequations::neq, NOTYPE_EQ, and SYSTEM_EQ.

boolean HasEquation	(	Tequation *	equation,
		Tequations *	eqs
	)

Checks if a given equation is already in the set.

Parameters

equation	The equation.
eqs	The equation set.

Returns: TRUE if the given equation is already in the set.

Definition at line 1160 of file equations.c.

References CmpEquations(), Tequations::equation, FALSE, and GetOriginalEquation().

Referenced by AddEquation().

unsigned int CropEquation	(	unsigned int	ne,
		unsigned int	varType,
		double	epsilon,
		double	rho,
		Tbox *	b,
		Tvariables *	vs,
		Tequations *	eqs
	)

Gets a box (as an array of parameters is of size m) and uses the equation number ne to reduce the ranges of the variables involved in the equation as much as possible.
Only equalities are used for crop (LEQ and GEQ equations are not taken into account).
We use different crop procedures according to the type of equation: LINEAR_EQ, PARABOLA_EQ, SADDLE_EQ, CIRCLE_EQ, SPHERE_EQ or GENERAL_EQ. In the GENERAL_EQ case, equations a the linear approximation is used for the crop. This does not produce the stronger possible crop. For this reason, we implemented non-linear crop for the non-linear equations that appear often in the systems of equations (due to dummification, for instance).

Parameters

ne	The equation to use in the crop.
varType	The type of variables to which apply the crop. Use ANY_TYPE_VAR for the crop to affect all types of variables.
epsilon	Only ranges with a size larger than epsilon are reduced.
rho	The crop is repeated as far as the ranges for the variables in the equation reduce a ratio larger than rho.
b	The box with the ranges to crop.
vs	The variable set on which the equations are defined. Used to get the type of variables.
eqs	The equation set.

Returns: NOT_REDUCED_BOX, EMPTY_BOX, REDUCED_BOX

See Also: ReduceBoxEquationWise

Definition at line 1175 of file equations.c.

References BILINEAL_MONOMIAL_EQUATION, BoxSaddleClipping(), BoxSphereClipping(), CIRCLE_EQUATION, CopyBox(), CopyInterval(), CropLinearConstraint(), DeleteBox(), DeleteLinearConstraint(), EMPTY_BOX, TequationInfo::EqType, EQU, Tequations::equation, Error(), EvaluateEquationInt(), FALSE, GENERAL_EQUATION, GetBoxIntervals(), GetBoxNIntervals(), GetEquationBounds(), GetEquationCmp(), GetEquationValue(), GetEquationVariables(), GetFirstOrderApproximationToEquation(), GetLinearConstraintError(), GetMonomial(), GetMonomialCt(), GetMonomialVariables(), GetNumMonomials(), GetOriginalEquation(), GetVariableN(), GetVariableTypeN(), INF, Intersect(), IntervalCenter(), IntervalSize(), TequationInfo::lc, LINEAR_EQUATION, LowerLimit(), TequationInfo::n, Tequations::n, Tequations::neq, NEW, NewInterval(), NOT_REDUCED_BOX, PARABOLA_EQUATION, PolynomialEquation(), PrintEquation(), PrintInterval(), RectangleCircleClipping(), RectangleParabolaClipping(), REDUCED_BOX, SADDLE_EQUATION, SetLinearConstraintError(), SimplexExpandBounds(), SPHERE_EQUATION, TRUE, UpperLimit(), VariableSetSize(), and ZERO.

Referenced by AddEquation2Simplex(), ReduceBoxEquationWise(), and RegenerateSolution().

void AddEquation	(	Tequation *	equation,
		Tequations *	eqs
	)

Adds an equation to the set and computes its associated information. Empty equations (equations with no monomials) or repeated equations are not added to the set. Moreover, equations are sorted from simplest to more complex.

Parameters

equation	The equation to be added.
eqs	The equation set.

See Also: TequationInfo.

Definition at line 1629 of file equations.c.

References AddEquationInt(), CmpEquations(), Tequations::equation, Error(), GetEquationCmp(), GetEquationType(), GetNumMonomials(), GetOriginalEquation(), HasEquation(), Tequations::n, NOCMP, NormalizeEquation(), and NOTYPE_EQ.

Referenced by AddEquation2CS(), DummifyAndAddEquation(), GaussianElimination(), MergeEquations(), RemoveEquationsWithVar(), and ReplaceVariableInEquations().

void AddEquationNoSimp	(	Tequation *	equation,
		Tequations *	eqs
	)

Adds an equation to the set and computes its associated information. This is like AddEquation but all equations are considered (even the empty or repeated ones) and equations are not sorted. This must be used in equation sets where the order of the equations must be preserved. This happens for some equations sets defined in the Tworld.

Parameters

equation	The equation to be added.
eqs	The equation set.

See Also: TequationInfo.

Definition at line 1656 of file equations.c.

References AddEquationInt(), Error(), GetEquationCmp(), GetEquationType(), NOCMP, and NOTYPE_EQ.

Referenced by GenerateWorldEquations().

void AddMatrixEquation	(	TMequation *	equation,
		Tequations *	eqs
	)

Adds a matrix equation to the set and computes its associated information.

Parameters

equation	The equation to be added.
eqs	The equation set.

Definition at line 1665 of file equations.c.

References CopyMEquation(), Tequations::e, Tequations::eqEQU, FALSE, HasRotations(), MEM_DUP, Tequations::mequation, Tequations::mm, Tequations::neq, NEW, Tequations::nm, Tequations::nsEQU, NumberScalarEquations(), Tequations::polynomial, Tequations::s, and Tequations::scalar.

Referenced by AddMatrixEquation2CS(), DeriveEqualityEquations(), GenerateWorldEquations(), and MergeEquations().

Tequation* GetEquation	(	unsigned int	n,
		Tequations *	eqs
	)

Returns a pointer to the n-th equation stored in the set.

Parameters

n	The number of equation to get.
eqs	The equation set.

Definition at line 1697 of file equations.c.

References Tequations::equation, Error(), GetOriginalEquation(), and Tequations::scalar.

Referenced by CSRemoveLCVars(), DummifyCuikSystem(), GenerateWorldSingularityEquations(), GetCSEquation(), and GetJacobianEquation().

boolean AddEquation2Simplex	(	unsigned int	ne,
		double	lr2tm_q,
		double	lr2tm_s,
		double	epsilon,
		unsigned int	safeSimplex,
		double	rho,
		Tbox *	b,
		Tvariables *	vs,
		TSimplex *	lp,
		Tequations *	eqs
	)

Adds linear constraints representing the selected equation (i.e., a linear relaxation of the equation) to a simplex tableau. Linear constraints are directly added to the simplex using the information cached in the TequationInfo structure. Non linear equations are linearized using the information stored in the Jacobian and Hessian fields in the corresponding TequationInfo too. Different equations are linearized in a different way

For Parabola equations y=x^2: Two planes defined at the center of the x range and, if the variables in the equation are larger than lr2tm_q, we add one plane at each one of the extremes of the x range.
For Circle equations x^2+y^2=r^2: Two planes defined at the center of the x-y range and, if the variables in the equation are larger than lr2tm_q, we add one plane tangent to the circle for the corners of the x-y box that are out of the circle.
- For Sphere equations x^2+y^2+z^2=r^2: Two planes defined at the center of the x-y-z range and, if the variables in the equation are larger than lr2tm_q, we add one plane tangent to the sphere for the corners of the x-y-z box that are out of the sphere.
For Saddle equations z=x*y: if the variables in the equation are larger than lr2tm_s, we add one plane for each corner of the x-y square. Otherwise we linearize the equation as a general equation (two planes defined at the center of the x,y,z box).
For the rest of equations, a couple of planes defined from the linearization of the equation at the center of the sub-box defined by the variables involved in the equation plus-less an error defined from the remainder of the linearization. For equalities we add the two planes defined in such a way but for inequalities only one plane is necessary.

By using small lr2tm_q and lr2tm_s we generate linear relaxations that tightly bound the functions and this reduces the number of iterations to found the solution. The drawnback is that we we add more constraints to the simplex and this slows downs each iteration.

Equations that define particular variables (cartesian or dummy ones) are only added to the simplex if the variable is used in any of the other constraints already in the simplex. Otherwise we will add useless constraints. This filter is implemented with the array of booleans usedVar. This array is updated as we add equations to the simplex and is checked to see if defined variables are used before adding the corresponding equation to the simplex. For this to be operative, equations are ordered so that system equations are added first to the simplex, then cartesian equations and, finally, dummyfications equations.

There is no need to equations that involves almost constant variables to the simplex. Thus, before adding an EQU equation to the simplex, we evaluate the equations using interval arithmetics and if the result is almost constant(this occurs if the variables involved in the equation are have tiny ranges) we just check if the equation holds or not. If not, the system has no solution.

The same applies to inequalities that already hold. An inequality (LEQ, GEQ equations) that trivially holds do not add any constrain to the simplex and, consequently we do not add it to the Tableau.

Parameters

ne	The number of the equation to add.
lr2tm_q	Size of the variables in the equation to switch between a specific linearization and a general one for spheres, circles, and parabolas.
lr2tm_s	Size of the variables in the equation to switch between a specific linearization and a general one for saddle equations.
epsilon	When generating a linear constraints, coefficients below epsilon are discarted, since the simplex process has troubles with too small values.
safeSimplex	Degree of numerical stability in the simplex as specified by the user in the SAFE SIMPLEX parameter.
rho	Before adding the equation to the simplex it is croped and the crop process is repeated as far as the variables reduce more than rho. Ranges smaller than epsilon are not reduced any further.
b	The box with the variable ranges. It defines the area where to linearize the equations and where to compute the linearization error, if necessary.
vs	The set of variables. Used to get the type of variables in GetDefinedVar
lp	The simplex structure where to add the constraints.
eqs	The equation set.

See Also: CropEquation, GetDefinedVar

Returns: TRUE if the simplex is still feasible after adding the linear constraints.

Definition at line 2185 of file equations.c.

References ANY_TYPE_VAR, BILINEAL_MONOMIAL_EQUATION, CIRCLE_EQUATION, CleanInfEquation(), CropEquation(), DeleteEquation(), DeleteEquationInfo(), EMPTY_BOX, TequationInfo::EqType, EQU, Tequations::equation, Error(), EvaluateEquationInt(), FALSE, GENERAL_EQUATION, GEQ, GetBoxIntervals(), GetBoxMinSizeVarSet(), GetEquationCmp(), GetEquationValue(), GetEquationVariables(), GetOriginalEquation(), INF, IntervalOffset(), IntervalSize(), IsInside(), TequationInfo::lc, LEQ, LINEAR_EQUATION, LinearizeBilinealMonomialEquation(), LinearizeCircleEquation(), LinearizeGeneralEquation(), LinearizeParabolaEquation(), LinearizeSaddleEquation(), LinearizeSphereEquation(), LowerLimit(), NEW, PARABOLA_EQUATION, PrintEquation(), PrintInterval(), SADDLE_EQUATION, Tequations::scalar, SetEquationInfo(), SimplexAddNewConstraint(), SPHERE_EQUATION, TRUE, and UpperLimit().

Referenced by ReduceBox().

void UpdateSplitWeight	(	unsigned int	ne,
		double *	splitDim,
		Tbox *	b,
		Tequations *	eqs
	)

When the SPLIT_ERROR parameter is set to TRUE, we select the split variable for a box from the linearization error induced by the variables. This function updates the error induced by the variables in a given equation.

Parameters

ne	The equation to use in the update.
splitDim	The array with the linearization errors induced by the variables to be updated.
b	The box with the ranges for the variables.
eqs	The equation set.

Definition at line 2430 of file equations.c.

References TequationInfo::EqType, TequationInfo::equation, Tequations::equation, Error(), ErrorDueToVariable(), GetBoxIntervals(), GetBoxNIntervals(), GetEquationVariables(), GetVariableN(), IntervalCenter(), LINEAR_EQUATION, TequationInfo::n, NEW, and Tequations::scalar.

Referenced by ComputeSplitDimInt().

void EvaluateEqualityEquations	(	boolean	systemOnly,
		double *	v,
		double *	r,
		Tequations *	eqs
	)

Evaluates all equality equations in the set. This includes the equality scalar equations and all matrix equations.

Parameters

systemOnly	TRUE to evaluate only the system equalities. The rest are evalated to 0 (as if they hold).
v	The value for the variables.
r	the array where to store the result.
eqs	The equations to evaluate.

Definition at line 2477 of file equations.c.

References EQU, Tequations::equation, EvaluateMEquation(), EvaluateWholeEquation(), GetEquationCmp(), GetEquationType(), GetOriginalEquation(), Tequations::mequation, Tequations::n, Tequations::nm, and SYSTEM_EQ.

Referenced by CuikNewtonInBox(), CuikNewtonSimp(), ErrorInCSEquations(), ErrorInSimpCSEquations(), ErrorInSolution(), EvaluateCSEquations(), EvaluateHessian(), EvaluateJacobian(), EvaluateSimpCSEquations(), GetLinkTransformsFromSolution(), and PrintWorldAxes().

void EvaluateSubSetEqualityEquations	(	double *	v,
		boolean *	se,
		double *	r,
		Tequations *	eqs
	)

Evaluates a subset of the equality equations in the set. This includes the equality scalar equations and some of the matrix equations.

Parameters

v	The value for the variables.
se	The selected equations. This is a subset of the equality equations, not of all equations. Thus the size of this boolean array must the one returned by NEqualityEquations.
r	the array where to store the result. The size of this array is the same as the number of TRUE entries in array 'se'. The space must be allocated externally.
eqs	The equations to evaluate.

Definition at line 2505 of file equations.c.

References EQU, Tequations::equation, EvaluateMEquation(), EvaluateWholeEquation(), GetEquationCmp(), GetOriginalEquation(), MAX_EQ_MATRIX, Tequations::mequation, Tequations::n, and Tequations::nm.

Referenced by EvaluateSubSetSimpCSEquations().

void EvaluateEqualitySparseEquations	(	double *	v,
		double *	r,
		Tequations *	eqs
	)

In sparse systems, many equations are empty. This function is a variant of EvaluateEqualityEquations specialy efficient for this kind of systems.

Parameters

v	The value for the variables.
r	the array where to store the result.
eqs	The equations to evaluate.

Definition at line 2563 of file equations.c.

References CacheScalarEQUInfo(), Tequations::eqEQU, EvaluateMEquation(), EvaluateWholeEquation(), Tequations::mequation, Tequations::n, Tequations::nm, and Tequations::nsEQU.

Referenced by EvaluateJacobianInVector(), and EvaluateTransposedJacobianInVector().

void EvaluateSubSetEqualitySparseEquations	(	double *	v,
		boolean *	se,
		double *	r,
		Tequations *	eqs
	)

In sparse systems, many equations are empty. This function is a variant of EvaluateSubSetEqualityEquations specialy efficient for this kind of systems.

Parameters

v	The value for the variables.
se	The selected equations. This is a subset of the equality equations, not of all equations. Thus the size of this boolean array must the one returned by NEqualityEquations.
r	the array where to store the result. The size of this array is the same as the number of TRUE entries in array 'se'. The space must be allocated externally.
eqs	The equations to evaluate.

Definition at line 2586 of file equations.c.

References CacheScalarEQUInfo(), Tequations::eqEQU, EvaluateMEquation(), EvaluateWholeEquation(), MAX_EQ_MATRIX, Tequations::mequation, Tequations::n, Tequations::nm, and Tequations::nsEQU.

Referenced by EvaluateJacobianSubSetInVector(), and EvaluateTransposedJacobianSubSetInVector().

void EvaluateEquationsXVectors	(	double *	v,
		unsigned int	ng,
		unsigned int *	g,
		double *	p,
		double *	r,
		Tequations *	eqs
	)

This is a funcition with a very particular purpose. It evaluates a matrix equation M, and it returns M*v[i] for a set of 3D vectors, v[i].

See EvaluateJacobianXVectors for more details on why this is necessary.

This function triggeres an error if the equation set includes scalar equations.

Parameters

v	The values for the variables.
ng	Number of groups of vectors. We must have one group for each matrix equation.
g	Number of vectors in each group.
p	The 3D vectors (stacked in one array).
r	The output vector.
eqs	The matrix equations to evaluate.

Definition at line 2624 of file equations.c.

References Error(), EvaluateMEquationXVectors(), Tequations::mequation, Tequations::n, and Tequations::nm.

Referenced by EvaluateJacobianXVectors().

void EvaluateInequalityEquations	(	double *	v,
		double *	r,
		Tequations *	eqs
	)

Evaluates all inequalities and returns and array with the error in each of them. The error is 0 if the inequality hold.

Parameters

v	The value for the variables.
r	the array where to store the result.
eqs	The equations to evaluate.

Definition at line 2643 of file equations.c.

References EQU, Tequations::equation, EvaluateEquation(), GEQ, GetEquationCmp(), GetEquationValue(), GetOriginalEquation(), and Tequations::n.

Referenced by ErrorInInequalities(), ErrorInSimpInequalitiesOnPoint(), InequalitiesHoldOnPoint(), and SimpInequalitiesHoldOnPoint().

void DeriveEqualityEquations	(	unsigned int	v,
		Tequations *	deqs,
		Tequations *	eqs
	)

Derives an equation set with respect to a given variable. The derivative is only computed for equality equations.

Parameters

v	The derivation variable.
deqs	The resulting derived equations.
eqs	The equations to derive.

Definition at line 2668 of file equations.c.

References AddEquationInt(), AddMatrixEquation(), DeleteEquation(), DeleteMEquation(), DeriveEquation(), DeriveMEquation(), EQU, Tequations::equation, GetEquationCmp(), GetOriginalEquation(), InitEquations(), Tequations::mequation, Tequations::n, and Tequations::nm.

Referenced by InitHessian(), and InitJacobian().

void PrintEquations	(	FILE *	f,
		char **	varNames,
		Tequations *	eqs
	)

Writes a set of equations into a stream.

Parameters

f	The stream where to write the equations.
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.
eqs	The equation set to print.

Definition at line 2694 of file equations.c.

References Tequations::c, Tequations::d, Tequations::equation, GetOriginalEquation(), IsCoordEquation(), IsDummyEquation(), IsSystemEquation(), Tequations::mequation, Tequations::n, Tequations::nm, PrintEquation(), PrintMEquation(), and Tequations::s.

Referenced by CSRemoveLCVars(), CSRemoveVarsWithCtRange(), PrintCuikSystem(), PrintCuikSystemWithSimplification(), PrintJacobian(), and SimplifyCuikSystem().

void DeleteEquations ( Tequations * eqs )

Deletes the information stored in the set of equations and frees the allocated memory space.

Parameters

eqs	The set of equations to delete.

Definition at line 2750 of file equations.c.

References DeleteEquationInfo(), DeleteMEquation(), Tequations::eqEQU, Tequations::equation, Tequations::mequation, Tequations::n, Tequations::nm, and Tequations::nsEQU.

Referenced by DeleteCuikSystem(), DeleteHessian(), DeleteJacobian(), DeleteWorldCS(), DummifyCuikSystem(), GaussianElimination(), RemoveEquationsWithVar(), ReplaceVariableInEquations(), and UnUpdateCuikSystem().

Institut de Robòtica i Informàtica Industrial

Detailed Description

Functions

Function Documentation

Institut de Robòtica
i Informàtica Industrial