Detailed Description

Implementation of the matrix equation operations.

See Also: TMequation, mequation.h.

Definition in file mequation.c.

Functions
void	RecomputeScalarEquations (TMequation *me)
	Recomputes the scalar equations derived from a metrix one. More...

void	InitMEquation (TMequation *me)
	Construtor. More...

void	CopyMEquation (TMequation me_dst, TMequation me_src)
	Copy constructor. More...

void	ResetMEquation (TMequation *me)
	Resets the information stored in the matrix equation. More...

boolean	IsEmptyMEquation (TMequation *me)
	Identify empty matrix equations. More...

unsigned int	MEquationSize (TMequation *me)
	Size of the matrix equation. More...

boolean	HasRotations (TMequation *me)
	Cheks if a matrix equation includes rotations. More...

void	SetTranslationMEquation (TMequation *me)
	Sets a matrix equation as a translation equation. More...

boolean	VarIncludedinMEquation (unsigned int v, TMequation *me)
	Checks if the matrix equation includes a given variable. More...

void	AddDispTrans2MEquation (int s, unsigned int v, double vect, TMequation me)
	Adds a displacement along a vector. More...

void	AddVarTrans2MEquation (unsigned int t, int s, unsigned int v, TMequation *me)
	Adds a variable transform to the matrix equation. More...

void	AddPatchTrans2MEquation (unsigned int t, int s, unsigned int u, unsigned int v, double *p, TMequation me)
	Adds a Parametrized-Patch transform to a matrix equation. More...

void	AddCtTrans2MEquation (THTransform t, TMequation me)
	Adds a constant transform to a matrix equation. More...

void	AddTransSeq2MEquation (int s, TTransSeq ts, TMequation me)
	Concatenates a transform sequence to the matrix equation. More...

unsigned int	NumberScalarEquations (TMequation *me)
	Number of scaler equations defined by a matrix equation. More...

void	ShiftVariablesInMEquation (unsigned int nv, TMequation *me)
	Adjust variable indices after removina a variable. More...

boolean	SimplifiedMEquation (TMequation *me)
	Identifies simplified equations. More...

void	SimplifyMEquation (TMequation *me)
	Tries to reduce the complexity of the matrix equation. More...

void	DeriveMEquation (unsigned int v, TMequation dme, TMequation me)
	Derives a matrix equation. More...

unsigned int	EvaluateMEquation (double v, double r, TMequation *me)
	Evaluates a matrix equation. More...

void	EvaluateMEquationXVectors (double v, unsigned int n, double p, double r, TMequation me)
	Equation x vector evaluation. More...

void	PrintMEquation (FILE f, char varNames, TMequation me)
	Prints a Transform sequence to a file. More...

void	DeleteMEquation (TMequation *me)
	Destructor. More...

Function Documentation

void RecomputeScalarEquations ( TMequation * me )

Recomputes the scalar equations derived from a metrix one taking into account the used dof.

Parameters

me	The matrix equation to update.

Definition at line 30 of file mequation.c.

References AXIS_H, AXIS_X, AXIS_Y, AXIS_Z, TMequation::c, HasCtRotTransSeq(), TMequation::n, TMequation::neq, TMequation::r, RX, RY, RZ, TRUE, TMequation::ts, TX, TY, TZ, and UpdateUsedDOF().

Referenced by AddCtTrans2MEquation(), AddPatchTrans2MEquation(), AddTransSeq2MEquation(), AddVarTrans2MEquation(), InitMEquation(), and SimplifyMEquation().

void InitMEquation ( TMequation * me )

Initializes a matrix equation Id=Id

Parameters

me	The matrix equation.

Definition at line 99 of file mequation.c.

References AddCtTrans2TransSeq(), FALSE, HTransformIdentity(), InitTransSeq(), TMequation::n, TMequation::neq, NEW, RecomputeScalarEquations(), TMequation::rhs, TMequation::simp, and TMequation::ts.

Referenced by GenerateMEquationFromBranch().

void CopyMEquation	(	TMequation *	me_dst,
		TMequation *	me_src
	)

Copies one matix equation into another.

Parameters

me_dst	The matrix equation to generate.
me_src	The matrix equation from which to get the data.

Definition at line 113 of file mequation.c.

References TMequation::c, CopyTransSeq(), HTransformCopy(), TMequation::n, TMequation::neq, NEW, TMequation::r, TMequation::rhs, TMequation::simp, and TMequation::ts.

Referenced by AddMatrixEquation(), and CopyEquations().

void ResetMEquation ( TMequation * me )

Resets the information stored in the matrix equation so that it can be re-used without delete/init.

Parameters

me	The matrix equation to reset.

Definition at line 134 of file mequation.c.

References Error(), FALSE, HTransformIdentity(), TMequation::n, TMequation::neq, ResetTransSeq(), TMequation::rhs, TMequation::simp, and TMequation::ts.

boolean IsEmptyMEquation ( TMequation * me )

Identifies empty matrix equations.

Parameters

me	The matrix equation to check.

Definition at line 145 of file mequation.c.

References TMequation::neq.

unsigned int MEquationSize ( TMequation * me )

Size of the matrix equation where the size is considered as the lenght of the largest tranform sequence included in the matrix equation.

Parameters

me	The matrix equation to query.

Returns: The size of the matrix equation.

Definition at line 150 of file mequation.c.

References TMequation::n, TransSeqSize(), and TMequation::ts.

boolean HasRotations ( TMequation * me )

Cheks if a matrix equation includes rotations.

Parameters

me	The matrix equation to check.

Returns: TRUE if the matrix equation includes rotations.

Definition at line 163 of file mequation.c.

References TMequation::n, RX, RY, RZ, TMequation::ts, and UpdateUsedDOF().

Referenced by AddMatrixEquation().

void SetTranslationMEquation ( TMequation * me )

Modifies a matrix equation so that only their translation part is taken into consideration when evaluating them.

Parameters

me	The matrix to modify.

Definition at line 174 of file mequation.c.

References AXIS_H, TMequation::c, Error(), TMequation::neq, TMequation::r, TMequation::simp, and TRUE.

boolean VarIncludedinMEquation	(	unsigned int	v,
		TMequation *	me
	)

Checks if the matrix equation includes a given variable.

Parameters

v	The variable identifier.
me	The matrix equation to check.

Returns: TRUE if the matrix equations includes variable 'v'.

Definition at line 191 of file mequation.c.

References FALSE, TMequation::ts, and VarIncludedinTransSeq().

Referenced by RemoveEquationsWithVar(), UsedVarInEquations(), and UsedVarInNonDummyEquations().

void AddDispTrans2MEquation	(	int	s,
		unsigned int	v,
		double *	vect,
		TMequation *	me
	)

Adds a variable transform that represents a scaled displacement along a vector.

Parameters

s	The sign for 'v'.
v	Variable involved in the transform.
vect	Vector defining the displacement.
me	The matrix equation to enlarge.

Definition at line 206 of file mequation.c.

References AddDispTrans2TransSeq(), and TMequation::ts.

void AddVarTrans2MEquation	(	unsigned int	t,
		int	s,
		unsigned int	v,
		TMequation *	me
	)

Adds a variable transform at the end of a matrix equation.

Parameters

t	Type of transform.
s	The sign for 'v'.
v	Variable involved in the transform.
me	The matrix equation to enlarge.

Definition at line 212 of file mequation.c.

References AddVarTrans2TransSeq(), Error(), TMequation::n, RecomputeScalarEquations(), TMequation::simp, and TMequation::ts.

void AddPatchTrans2MEquation	(	unsigned int	t,
		int	s,
		unsigned int	u,
		unsigned int	v,
		double **	p,
		TMequation *	me
	)

Adds a Parametrized-Patch transform to a matrix equation.

Parameters

t	Subtype of PA transform (PA,dPA_U,dPA_V,ddPA_UU,d2PA_UV,ddPA_VV).
s	The sign of the transform (-1 means to invert the transform).
u	First variable (parameter) involved in the transform.
v	Second variable (parameter) involved in the transform.
p	The four points defining the patch.
me	The matrix equation to enlarge.

Definition at line 224 of file mequation.c.

References AddPatchTrans2TransSeq(), Error(), TMequation::n, RecomputeScalarEquations(), TMequation::simp, and TMequation::ts.

void AddCtTrans2MEquation	(	THTransform *	t,
		TMequation *	me
	)

Adds a constant transform at the end of a matrix equation.

Note that identity transforms or matrices that result in identity transforms when added at the end of the sequence are skipped.

Parameters

t	The transform to add.
me	The matrix equation to enlarge..

Definition at line 238 of file mequation.c.

References AddCtTrans2TransSeq(), Error(), TMequation::n, RecomputeScalarEquations(), TMequation::simp, and TMequation::ts.

void AddTransSeq2MEquation	(	int	s,
		TTransSeq *	ts,
		TMequation *	me
	)

Concatenates a transform sequence to the matrix equation.

Parameters

s	The sign of the transform. If below 0, the tranform sequence has to be inverted before adding it.
ts	The transform to add.
me	The matrix equation to update.

Definition at line 250 of file mequation.c.

References AddTrans2TransSeq(), DeleteTrans(), Error(), GetElementFromTransSeq(), TMequation::n, RecomputeScalarEquations(), TMequation::simp, TransInvert(), TransSeqSize(), and TMequation::ts.

Referenced by GenerateMEquationFromBranch().

unsigned int NumberScalarEquations ( TMequation * me )

Number of scaler equations defined by a matrix equation.

Parameters

me	The matrix equation to check.

Returns: Number of scaler equations defined by a matrix equation.

Definition at line 281 of file mequation.c.

References TMequation::neq.

Referenced by AddMatrixEquation().

void ShiftVariablesInMEquation	(	unsigned int	nv,
		TMequation *	me
	)

After removing a variable not used in the system we have to shift down the indices of the variables with larger index than the removed one.

Parameters

nv	The removed variable.
me	The matrix equation.

Definition at line 286 of file mequation.c.

References TMequation::n, ShiftVariablesInTransSeq(), and TMequation::ts.

Referenced by RemoveEquationsWithVar().

boolean SimplifiedMEquation ( TMequation * me )

Identifies simplified equations. The simplification is the last step in the definition of a matrix equation. Only simplified equations can be added to cuiksystem.

Parameters

me	The equation to query.

Returns: TRUE if the equation is already simplified.

Definition at line 294 of file mequation.c.

References TMequation::simp.

Referenced by AddMatrixEquation2CS().

void SimplifyMEquation ( TMequation * me )

Performs operations in order to simplify the computations with the matrix equation. This should only be used when the matrix equation is fully defined. If new terms are added to the matrix equatoin after the simplification, the equation might become inconsistent.

Right now we only simplify single transforms sequence equated to the identity. Other simplifications might be possible (i,e, move to the right hand side constant terms in the sum of matrix expressions). Howerver these cases are less frequent and, thus we do not consider them.

Parameters

me	The equaton to simplify.

Definition at line 299 of file mequation.c.

References Error(), TMequation::n, TMequation::neq, RecomputeScalarEquations(), TMequation::simp, SimplifyTransSeq(), TRUE, and TMequation::ts.

Referenced by GenerateMEquationFromBranch().

void DeriveMEquation	(	unsigned int	v,
		TMequation *	dme,
		TMequation *	me
	)

Derives a matrix equation. This results in one or more matrix product sequences equated to zero.

Parameters

v	The derivation variable.
dme	The output derived matrix equation.
me	The matrix equation to derive.

Definition at line 312 of file mequation.c.

References TMequation::c, DeriveTransSeq(), Error(), HTransformZero(), MEM_EXPAND, TMequation::n, TMequation::neq, NEW, TMequation::r, TMequation::rhs, TMequation::simp, TRUE, and TMequation::ts.

Referenced by DeriveEqualityEquations().

unsigned int EvaluateMEquation	(	double *	v,
		double *	r,
		TMequation *	me
	)

Evaluates a matrix equation and stores the result on a given array. Note that the result only includes values for the scalar equations derived from the matrix equation.

Parameters

v	Value for the variables.
r	The array where to store the results.
me	The matrix equation to evaluate.

Returns: The number of output values stores in r (

See Also: NumberScalarEquations).

Definition at line 356 of file mequation.c.

References TMequation::c, EvaluateTransSeq(), HTransformDelete(), HTransformGetElement(), TMequation::n, TMequation::neq, TMequation::r, TMequation::rhs, and TMequation::ts.

Referenced by EvaluateEqualityEquations(), EvaluateEqualitySparseEquations(), EvaluateSubSetEqualityEquations(), and EvaluateSubSetEqualitySparseEquations().

void EvaluateMEquationXVectors	(	double *	v,
		unsigned int	n,
		double *	p,
		double *	r,
		TMequation *	me
	)

Evalutes a matrix equation and returns the result of muliplying the resulting matrix with a set of 3D vectors.

See EvaluateJacobianXVectors why this is useful at all.

Parameters

v	The value for the variables.
n	The number of vectors.
p	The 3D vectors (stacked in one array).
r	The output vector with the evaluation.
me	The matrix equation to use in the evaluation.