Introduction

Definition of the TJacobian type and the associated functions.

See also: TJacobian, jacobian.c.

Definition in file jacobian.h.

Data Structures
struct	TJacobian
	The Jacobian of a set of equations. More...

Functions
void	InitJacobian (Tvariables vs, Tequations eqs, TJacobian *j)
	Constructor. More...

void	InitPositionJacobian (Tvariables vs, Tequations eqs, TJacobian *j)
	Constructor. More...

void	InitScalarPositionJacobian (Tvariables vs, Tequations eqs, TJacobian *j)
	Constructor. More...

void	CopyJacobian (TJacobian j_dst, TJacobian j_src)
	Constructor. More...

void	CopyNonDynamicsJacobian (TJacobian j_dstP, TJacobian j_dstO, TJacobian *j_src)
	Copies the non-dynamics Jacobian. More...

void	CopyPositionJacobian (TJacobian j_dst, TJacobian j_src)
	Copies the position Jacobian. More...

void	GetJacobianSize (unsigned int nr, unsigned int nc, TJacobian *j)
	Returns the size of the Jacobian. More...

Tequations *	GetJacobianColumn (unsigned int nv, TJacobian *J)
	Returns one of the Jacobian element. More...

Tequation *	GetJacobianEquation (unsigned int r, unsigned int c, TJacobian *j)
	Returns one element of the Jacobian. More...

void	RewriteJacobian2Orig (Tmapping map, TJacobian j)
	Rewrites the equations in a Jacobian to the original system. More...

void	JacobianLinearCombination (boolean selectedVars, unsigned int nv, Tequations eqs, TJacobian j)
	Linear combination of the columns of the Jacobian. More...

void	AllocateJacobianEvaluation (double **m, TJacobian j)
	Allocate space for the Jacobian evaluation. More...

void	EvaluateJacobian (double v, double m, TJacobian j)
	Evaluates the Jacobian. More...

void	EvaluateJacobianInVector (double v, unsigned int nr, unsigned int nc, double m, TJacobian *j)
	Evaluates the Jacobian. More...

void	EvaluateJacobianSubSetInVector (double v, boolean sr, unsigned int nr, unsigned int nc, double m, TJacobian j)
	Evaluates some of the Jacobian equations. More...

void	EvaluateTransposedJacobianInVector (double v, unsigned int nr, unsigned int nc, double m, TJacobian *j)
	Evaluates the transposed Jacobian. More...

void	EvaluateTransposedJacobianSubSetInVector (double v, boolean sr, unsigned int nr, unsigned int nc, double m, TJacobian j)
	Evaluates a subset of the transposed Jacobian. More...

void	PrintJacobianEvaluation (FILE f, double m, TJacobian j)
	Prints the result of evaluating the Jacobian. More...

void	FreeJacobianEvaluation (double *m, TJacobian j)
	Release space for the Jacobian evaluation. More...

void	EvaluateJacobianXVectors (double p, unsigned int n, unsigned int ng, unsigned int g, double v, unsigned int nr, unsigned int nc, double *m, TJacobian j)
	Evaluates the Jacobian multiplied by some given vectors. More...

void	PrintJacobian (FILE f, char varNames, TJacobian j)
	Prints the symbolic Jacobian. More...

void	DeleteJacobian (TJacobian *j)
	Destructor. More...

Function Documentation

◆ InitJacobian()

void InitJacobian	(	Tvariables *	vs,
		Tequations *	eqs,
		TJacobian *	j
	)

Initializes the Jacobian deriving a set of equations.

Parameters

vs	The variables involved in the equations.
eqs	The equations to derive.
j	The resulting Jacobian.

Definition at line 20 of file jacobian.c.

References CacheScalarEQUInfo(), DeriveEqualityEquations(), TJacobian::eqs, Error(), TJacobian::J, TJacobian::neqs, NEqualityEquations(), NEW, NVariables(), TJacobian::nvars, and TJacobian::vars.

Referenced by AddSimplifiedJacobianEquations(), EvaluateCSJacobian(), GenerateWorldEquations(), GetCSJacobian(), GetSimpCSJacobian(), and UpdateCuikSystem().

◆ InitPositionJacobian()

void InitPositionJacobian	(	Tvariables *	vs,
		Tequations *	eqs,
		TJacobian *	j
	)

Initializes the Jacobian deriving the subset of position of equations.

Parameters

vs	The variables involved in the equations.
eqs	The equations to derive.
j	The resulting Jacobian.

Definition at line 46 of file jacobian.c.

References CacheScalarEQUInfo(), DeriveEqualityPositionEquations(), TJacobian::eqs, Error(), GetNumPositionVariables(), IsPositionVariable(), TJacobian::J, TJacobian::neqs, NEqualityPositionEquations(), NEW, NVariables(), TJacobian::nvars, and TJacobian::vars.

Referenced by AddVelocityEquations().

◆ InitScalarPositionJacobian()

void InitScalarPositionJacobian	(	Tvariables *	vs,
		Tequations *	eqs,
		TJacobian *	j
	)

Initializes the Jacobian deriving the subset of scalar position of equations.

Parameters

vs	The variables involved in the equations.
eqs	The equations to derive.
j	The resulting Jacobian.

Definition at line 82 of file jacobian.c.

References CacheScalarEQUInfo(), DeriveEqualityScalarPositionEquations(), TJacobian::eqs, Error(), GetNumPositionVariables(), IsPositionVariable(), TJacobian::J, TJacobian::neqs, NEqualityScalarPositionEquations(), NEW, NVariables(), TJacobian::nvars, and TJacobian::vars.

Referenced by InitNJacobian().

◆ CopyJacobian()

void CopyJacobian	(	TJacobian *	j_dst,
		TJacobian *	j_src
	)

Initializes a Jacobian from another Jacobian.

Parameters

j_dst	The Jacobian to initialize.
j_src	The Jacobian from where to get the data.

Definition at line 118 of file jacobian.c.

References CacheScalarEQUInfo(), CopyEquations(), TJacobian::eqs, TJacobian::J, TJacobian::neqs, NEW, TJacobian::nvars, and TJacobian::vars.

Referenced by CopyCuikSystem().

◆ CopyNonDynamicsJacobian()

void CopyNonDynamicsJacobian	(	TJacobian *	j_dstP,
		TJacobian *	j_dstO,
		TJacobian *	j_src
	)

Gets a copy of the part of the Jacobian not directly related with the dynamics: equations not related to position/velocity derived with respect to the position equations. This block is used in a chain rule to obtain the time derivative of the non-dynamics (non position/velocity) equations.

Parameters

j_dstP	The Jacobian with respect to position variables.
j_dstO	The Jacobian with respect to the nont-dynamic variables.
j_src	The Jacobian from where to get the data.

Definition at line 142 of file jacobian.c.

References CacheScalarEQUInfo(), CopyNonDynamicEquations(), TJacobian::eqs, GetNumNonDynamicVariables(), GetNumPositionVariables(), IsPositionVariable(), IsVelocityVariable(), TJacobian::J, TJacobian::neqs, NEW, NNonDynamicEquations(), TJacobian::nvars, and TJacobian::vars.

Referenced by InitDynamicSpace().

◆ CopyPositionJacobian()

void CopyPositionJacobian	(	TJacobian *	j_dst,
		TJacobian *	j_src
	)

Gets a copy of the position Jacobian (part of the Jacobian corresponding to position variables and equations).

Parameters

j_dst	The Jacobian to initialize.
j_src	The Jacobian from where to get the data.

Definition at line 192 of file jacobian.c.

References CacheScalarEQUInfo(), CopyPositionEquations(), TJacobian::eqs, GetNumPositionVariables(), IsPositionVariable(), TJacobian::J, TJacobian::neqs, NEW, NPositionEquations(), TJacobian::nvars, and TJacobian::vars.

Referenced by InitDynamicSpace().

◆ GetJacobianSize()

void GetJacobianSize	(	unsigned int *	nr,
		unsigned int *	nc,
		TJacobian *	j
	)

Gives the Jacobian size.

Parameters

nr	Number of rows of the Jacobian (output).
nc	Number of columns of the Jacobian (output).
j	The Jacobian to query.

Definition at line 221 of file jacobian.c.

References TJacobian::neqs, and TJacobian::nvars.

Referenced by AddJacobianEquationsInt(), ConnectSamplesChart(), GradientSmooth(), InitAtlas(), InitChartInt(), InitDynamicSpace(), InitHessian(), LoadAtlas(), and ManifoldDimension().

◆ GetJacobianColumn()

Tequations* GetJacobianColumn	(	unsigned int	nv,
		TJacobian *	J
	)

Returns the derivative of all equations with respect to a given variable, i.e, one of the columns of the Jacobian.

Parameters

nv	The derivation variable.
J	The Jacobian to query.

Returns: A pointer to the equations giving the column of the Jacobian.

Definition at line 227 of file jacobian.c.

References Error(), TJacobian::J, TJacobian::neqs, and TJacobian::nvars.

Referenced by InitHessian().

◆ GetJacobianEquation()

Tequation* GetJacobianEquation	(	unsigned int	r,
		unsigned int	c,
		TJacobian *	j
	)

Returns a pointer to one element of the Jacobian. This only works for scalar systems.

Parameters

r	Row of the element to retrive.
c	Column of the element to retrive.
j	The Jacobian to query.

Definition at line 238 of file jacobian.c.

References Error(), GetEquation(), TJacobian::J, TJacobian::neqs, and TJacobian::nvars.

Referenced by AddJacobianEquationsInt(), AddSimplifiedJacobianEquations(), and GetSCpSystem().

◆ RewriteJacobian2Orig()

void RewriteJacobian2Orig	(	Tmapping *	map,
		TJacobian *	j
	)

For a Jacobian of a simplified system of equations, we change the variable identifiers by those in the orignal system. Note that this is just a variable identifier replacement since all the variables in the simplified system are also in the original.

Parameters

map	The map from the simplified system to the original.
j	The Jacobian to map.

Definition at line 249 of file jacobian.c.

References TJacobian::J, TJacobian::neqs, TJacobian::nvars, and RewriteEqs2Orig().

Referenced by AddSimplifiedJacobianEquations(), and AddVelocityEquations().

◆ JacobianLinearCombination()

void JacobianLinearCombination	(	boolean *	selectedVars,
		unsigned int *	nv,
		Tequations *	eqs,
		TJacobian *	j
	)

Generate linear combinations of the columns of the Jacobian and adds them to a given equation set.

This is used when defining velocity equations.

Parameters

selectedVars	If not NULL, it allows selecting the columns of the Jacobian to be combined. Also only the selected variables are actually used.
nv	The variable identifier to use as coefficients of the linear combination to generate.
eqs	The equation set where to add the linear combination.
j	The Jacobian with the columns to combine.

Definition at line 260 of file jacobian.c.

References CopyEquations(), DeleteEquations(), Error(), FALSE, TJacobian::J, MergeEquations(), TJacobian::neqs, TJacobian::nvars, TRUE, VarAccumulateEqualityEquations(), and VarScaleEqualityEquations().

Referenced by AddVelocityEquations().

◆ AllocateJacobianEvaluation()

void AllocateJacobianEvaluation	(	double ***	m,
		TJacobian *	j
	)

Allocate space for the Jacobian evaluation.

Parameters

m	The allocated space.
j	The Jacobian to evaluate.

Definition at line 295 of file jacobian.c.

References TJacobian::neqs, NEW, and TJacobian::nvars.

Referenced by EvaluateCSJacobian().

◆ EvaluateJacobian()

void EvaluateJacobian	(	double *	v,
		double **	m,
		TJacobian *	j
	)

Evaluates the Jacobian for a given value of the variables.

Parameters

v	The value for the variables.
m	The matrix where to store the result (see AllocateJacobianEvaluation).
j	The Jacobian to evalute.

Definition at line 309 of file jacobian.c.

References EvaluateEqualityEquations(), FALSE, TJacobian::J, TJacobian::neqs, NEW, and TJacobian::nvars.

Referenced by EvaluateCSJacobian().

◆ EvaluateJacobianInVector()

void EvaluateJacobianInVector	(	double *	v,
		unsigned int	nr,
		unsigned int	nc,
		double *	m,
		TJacobian *	j
	)

Evaluates the Jacobian for a given value of the variables and stores the result in a vector instead of in a matrix.

Parameters

v	The value for the variables.
nr	Number of rows of the space to store the Jacobian.
nc	Number of columns of the space to store the Jacobian.
m	The vector where to store the result.
j	The Jacobian to evalute.

Definition at line 327 of file jacobian.c.

References EvaluateEqualitySparseEquations(), TJacobian::J, TJacobian::neqs, NEW, TJacobian::nvars, and SubMatrixFromMatrix().

Referenced by Chart2Manifold(), ComputeAcceleration(), CuikGradientInBox(), CuikNewtonInBox(), CuikNewtonSimp(), Newton2ManifoldPlane(), and RefineSingularPoint().

◆ EvaluateJacobianSubSetInVector()

void EvaluateJacobianSubSetInVector	(	double *	v,
		boolean *	sr,
		unsigned int	nr,
		unsigned int	nc,
		double *	m,
		TJacobian *	j
	)

Evaluates some of the Jacobian equations for a given value of the variables and stores the result in a vector instead of in a matrix.

Parameters

v	The value for the variables.
sr	Boolean array with the selected rows to store in the output.
nr	Number of rows. This typically is the number of equations but can be larger in cases where extra constratins are added to the system.
nc	Number of columns. This typically is the number of variables but can be larger in cases where extra variables are added to the system.
m	The vector where to store the result.
j	The Jacobian to evalute.

Definition at line 344 of file jacobian.c.

References EvaluateSubSetEqualitySparseEquations(), TJacobian::J, TJacobian::neqs, NEW, TJacobian::nvars, and SubMatrixFromMatrix().

Referenced by Chart2Manifold(), and GetChartDegree().

◆ EvaluateTransposedJacobianInVector()

void EvaluateTransposedJacobianInVector	(	double *	v,
		unsigned int	nr,
		unsigned int	nc,
		double *	m,
		TJacobian *	j
	)

Evaluates the transposed Jacobian for a given value of the variables and stores the result in a vector instead of in a matrix. The vector is organized column wise (1st column 2nr column, etc).

Parameters

v	The value for the variables.
nr	Number of rows of the space to store the transposed Jacobian
nc	Number of columns of the space to store the transposed Jacobian.
m	The vector where to store the result.
j	The Jacobian to evalute.

Definition at line 384 of file jacobian.c.

References EvaluateEqualitySparseEquations(), TJacobian::J, TJacobian::neqs, NEW, TJacobian::nvars, and SubMatrixFromMatrix().

Referenced by ComputeJacobianKernelBasis(), FindRightNullVector(), GetPositionJacobian(), ManifoldDimension(), and RefineSingularPoint().

◆ EvaluateTransposedJacobianSubSetInVector()

void EvaluateTransposedJacobianSubSetInVector	(	double *	v,
		boolean *	sr,
		unsigned int	nr,
		unsigned int	nc,
		double *	m,
		TJacobian *	j
	)

Evaluates a subset of the transposed Jacobian for a given value of the variables and stores the result in a vector instead of in a matrix. The vector is organized column wise (1st column 2nr column, etc).

Parameters

v	The value for the variables.
sr	Selection of the rows of the Jacobian to store (they becoome columns in the output array).
nr	Number of rows of the the space to store the transposed Jacobian.
nc	Number of columns of the space to store the transposed Jacobian.
m	The vector where to store the result.
j	The Jacobian to evalute.

Definition at line 401 of file jacobian.c.

References EvaluateSubSetEqualitySparseEquations(), TJacobian::J, TJacobian::neqs, NEW, TJacobian::nvars, and SubMatrixFromMatrix().

Referenced by EvaluateTransposedNJacobianSubSetInVector(), and GetPositionJacobian().

◆ PrintJacobianEvaluation()

void PrintJacobianEvaluation	(	FILE *	f,
		double **	m,
		TJacobian *	j
	)

Prints the result of evaluating the Jacobian. This is basically used for debug.

Parameters

f	The file where to store the jacobian.
m	The matrix with the Jacobian evaluation.
j	The Jacobian.

Definition at line 442 of file jacobian.c.

References TJacobian::neqs, and TJacobian::nvars.

◆ FreeJacobianEvaluation()

void FreeJacobianEvaluation	(	double **	m,
		TJacobian *	j
	)

Release space for the Jacobian evaluation typically allocated using AllocateJacobianEvaluation.

Parameters

m	The space to release.
j	The corresponding Jacobian.

Definition at line 462 of file jacobian.c.

References TJacobian::neqs.

◆ EvaluateJacobianXVectors()

void EvaluateJacobianXVectors	(	double *	p,
		unsigned int	n,
		unsigned int	ng,
		unsigned int *	g,
		double *	v,
		unsigned int *	nr,
		unsigned int *	nc,
		double ***	m,
		TJacobian *	j
	)

This is a funcition with a very particular purpose. It evaluates the matrix equations in the Jacobian on a given point and then, for each matrix equation in the Jacobian, M, it evaluates M*v[i] for a set of 3D vectors, v[i]. This is used when generating the Jacobian of a given set of atom positions with respect ot the internal coordinates. In this case the Jacobian is derived from equations giving the pose P of each link from the internal coordinates. The position of an atom is P*v[i], with v[i] the center of the atom. The derivative of P*v[i] is M*v[i] with M the derivative of P w.r.t. the internal variables.

The output of this function is a matrix with 3*n rows and m columns (n=number of atoms and m= number of internal coordinates).

This is not the default size of the Jacobian and, thus, FreeJacobianEvaluation can not be used to de-allocate the space for the evaluation.

IMPORTANT: This only operates on matrix equations.

Parameters

p	The point where to evaluate the Jacobian.
n	The number of 3D vectors in v (number of atoms).
ng	Number of rigid groups of atoms (groups of vectors in v).
g	The nubmer of atoms to apply to each matrix equation. In principle the Jacobian must include one matrix equation for each link (i.e., rigid group of atoms).
v	The vector with the atom positions.
nr	The number of rows of the output Jacobian.
nc	The number of columsn of the output Jacobian.
m	The output Jacobian.
j	The Jacobian to use in the evaluation.

Definition at line 474 of file jacobian.c.

References EvaluateEquationsXVectors(), TJacobian::J, TJacobian::neqs, NEW, and TJacobian::nvars.

Referenced by WorldAtomJacobian().

◆ PrintJacobian()

void PrintJacobian	(	FILE *	f,
		char **	varNames,
		TJacobian *	j
	)

Prints the equations in the symbolic Jacobian column-wise.

Parameters

f	The file where to store the equations.
varNames	The name for each variable. Use NULL to print generic names.
j	The Jacobian structure.

Definition at line 509 of file jacobian.c.

References TJacobian::J, TJacobian::neqs, TJacobian::nvars, and PrintEquations().

◆ DeleteJacobian()

void DeleteJacobian ( TJacobian * j )

Release a Jacobian structure.

Parameters

j	The Jacobian structure to release.

Definition at line 523 of file jacobian.c.

References DeleteEquations(), TJacobian::J, TJacobian::neqs, and TJacobian::nvars.

Referenced by AddJacobianEquations(), AddSimplifiedJacobianEquations(), AddVelocityEquations(), DeleteAtlas(), DeleteAtlasRRT(), DeleteDynamicSpace(), DeleteNJacobian(), DeleteWorldCS(), EvaluateCSJacobian(), GetSCpSystem(), GradientSmooth(), InitNJacobian(), kinobiRRT(), kinoEST(), kinoRRT(), main(), PathEffort(), RandomSmooth(), ShortcutSmooth(), and UnUpdateCuikSystem().

Institut de Robòtica i Informàtica Industrial

Introduction

Data Structures

Functions

Function Documentation

◆ InitJacobian()

◆ InitPositionJacobian()

◆ InitScalarPositionJacobian()

◆ CopyJacobian()

◆ CopyNonDynamicsJacobian()

◆ CopyPositionJacobian()

◆ GetJacobianSize()

◆ GetJacobianColumn()

◆ GetJacobianEquation()

◆ RewriteJacobian2Orig()

◆ JacobianLinearCombination()

◆ AllocateJacobianEvaluation()

◆ EvaluateJacobian()

◆ EvaluateJacobianInVector()

◆ EvaluateJacobianSubSetInVector()

◆ EvaluateTransposedJacobianInVector()

◆ EvaluateTransposedJacobianSubSetInVector()

◆ PrintJacobianEvaluation()

◆ FreeJacobianEvaluation()

◆ EvaluateJacobianXVectors()

◆ PrintJacobian()

◆ DeleteJacobian()

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i Informàtica Industrial