Detailed Description

Implementation of the TJacobian type and the associated functions.

See Also: TJacobian, jacobian.h.

Definition in file jacobian.c.

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

void	CopyJacobian (TJacobian j_dst, TJacobian j_src)
	Constructor. 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	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

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 16 of file jacobian.c.

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

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

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 34 of file jacobian.c.

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

Referenced by CopyCuikSystem().

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 evaluate.

Definition at line 49 of file jacobian.c.

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

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

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 55 of file jacobian.c.

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

Referenced by InitHessian().

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 63 of file jacobian.c.

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

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

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 71 of file jacobian.c.

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

Referenced by EvaluateCSJacobian().

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 85 of file jacobian.c.

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

Referenced by EvaluateCSJacobian().

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 103 of file jacobian.c.

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

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

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 120 of file jacobian.c.

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

Referenced by Chart2Manifold(), and GetChartDegree().

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 143 of file jacobian.c.

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

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

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 160 of file jacobian.c.

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

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 183 of file jacobian.c.

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

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 200 of file jacobian.c.

References TJacobian::neqs.

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.