Introduction

Definition of the THessian type and the associated functions.

See also: THessian, hessian.c.

Definition in file hessian.h.

Data Structures
struct	THessian
	Hessian of a set of equations. More...

Functions
void	InitHessian (TJacobian j, THessian h)
	Constructor. More...

unsigned int	GetHessianNVars (THessian *h)
	Number of variables. More...

unsigned int	GetHessianNEqs (THessian *h)
	Number of equations. More...

void	AllocateHessianEvaluation (double ***m, THessian h)
	Allocate space for the Hessian evaluation. More...

void	AllocateHessianEvaluationAsVectors (unsigned int nie, double **m, THessian h)
	Allocates space for the Hessian evaluation. More...

void	EvaluateHessian (double v, double *m, THessian h)
	Evaluates the Hessian. More...

unsigned int	EvaluateScalarHessian (double v, boolean independentEq, unsigned int neq, double *m, THessian h)
	Evaluates an scalar Hessian. More...

void	EvaluateHessianVector (double x, double v, unsigned int nie, boolean independentEq, double m, double mf, THessian *h)
	Evaluates the product of the Hessian with a vector. More...

void	EvaluateHessianVector2 (double x, double v, unsigned int nie, boolean independentEq, double m, double mf, double o, THessian h)
	Evaluates the double product of the Hessian with a vector. More...

void	FreeHessianEvaluation (double **m, THessian h)
	Release space for the Hessian evaluation. More...

void	FreeHessianEvaluationAsVectors (double *m, THessian h)
	Release space for the Hessian evaluation. More...

void	DeleteHessian (THessian *h)
	Destructor. More...

Function Documentation

◆ InitHessian()

void InitHessian	(	TJacobian *	j,
		THessian *	h
	)

Initializes the Hessian deriving the Jacobian of a set of equations.

Parameters

j	The Jacobian
h	The resulting Hessian.

Definition at line 21 of file hessian.c.

References CacheScalarEQUInfo(), DeriveEqualityEquations(), GetJacobianColumn(), GetJacobianSize(), and NEW.

Referenced by InitDynamicSpace(), InitNHessian(), and RefineSingularPoint().

◆ GetHessianNVars()

unsigned int GetHessianNVars ( THessian * h )

Number of variables in the Hessian.

Returns: Number of variables.

Definition at line 41 of file hessian.c.

◆ GetHessianNEqs()

unsigned int GetHessianNEqs ( THessian * h )

Number of equations in the Hessian.

Returns: Number of equations.

Definition at line 46 of file hessian.c.

◆ AllocateHessianEvaluation()

void AllocateHessianEvaluation	(	double ****	m,
		THessian *	h
	)

Allocate space for the Hessian evaluation.

Parameters

m	The allocated space.
h	The Hessian.

Definition at line 52 of file hessian.c.

References NEW.

Referenced by RefineSingularPoint().

◆ AllocateHessianEvaluationAsVectors()

void AllocateHessianEvaluationAsVectors	(	unsigned int	nie,
		double ***	m,
		THessian *	h
	)

This is allocates the space in sub-matrices, one for each equation where each submatrix (of size nvars x nvars) is stored as a vector. This format is specific to speed up the execution of EvaluateHessianVector

Parameters

nie	Number of independent equations. NO_UINT if all equations are independent.
m	The allocated space.
h	The Hessian.

Definition at line 65 of file hessian.c.

References Error(), NEW, and NO_UINT.

Referenced by EvaluateHessianVector(), EvaluateHessianVector2(), and InitDynamicSpace().

◆ EvaluateHessian()

void EvaluateHessian	(	double *	v,
		double ***	m,
		THessian *	h
	)

Evaluates the Hessian for a given value of the variables.

Parameters

v	The value for the variables.
m	The matrix where to store the result (see AllocateHessianEvaluation).
h	The Hessian to evalute.

Definition at line 79 of file hessian.c.

References EvaluateEqualityEquations(), FALSE, and NEW.

Referenced by RefineSingularPoint().

◆ EvaluateScalarHessian()

unsigned int EvaluateScalarHessian	(	double *	v,
		boolean *	independentEq,
		unsigned int	neq,
		double **	m,
		THessian *	h
	)

Evaluates the Hessian for a given value of the variables.

Here the Hessian is supossed to include only the scalar part of a larger system and we implicitly assume that the scalar part is always the first part of the larger system.

A Hessian with only the position scalar equations is obtained from a Jacobian including only these equations (see InitScalarPositionJacobian).

This is the similar to EvaluateHessian but the output matrix m is organized in a different way. Instead of being numEqs x numVars x numVars it is numVars x numEqs x numVars and the (numEqs x numVars) matrices are stored as vectors.

So, the matrix m IS NOT allocated with AllocateHessianEvaluationAsVectors but must be allocated by the caller

Parameters

v	The value for the variables.
independentEq	The independent equations. NULL if all equations are independent. This is a vector over all the equations in the system and we are only interested in the scalar ones (the first part).
neq	Rows of each matrix m[i]. This is the number of equations including both the scalar and the matrix ones.
m	The matrices where to store the result.
h	The Hessian to evalute.

Returns: The number of independent scalar equations. The size of the top part of each matrix m[] filled in this function.

Definition at line 97 of file hessian.c.

References EvaluateSubSetEqualitySparseEquations(), NEW, and RC2INDEX.

Referenced by EvaluateNHessianVector2().

◆ EvaluateHessianVector()

void EvaluateHessianVector	(	double *	x,
		double *	v,
		unsigned int	nie,
		boolean *	independentEq,
		double **	m,
		double *	mf,
		THessian *	h
	)

Evaluates H*v. This has to be interpreted as

[ H[1][]*v H[2][]*v ... H[n][]*v]

were H[i][j] is the derivative of the whole set of equation with respect to variables i and j. That is, H[i][j] is a vector with as many elements as equations in the system. Then, H[i][] is a matrix of neqs x nvars elements and H[i][]*v is a vector of neqs elements. Such vectors for all variables i for a matrix of neqs x nvars elements.

Parameters

x	The point where to evaluate the Hessian.
v	The vector to use in the products. The size of this vector is the number of variables in the system.
nie	Number of independent equations. NO_UINT if all equations are independent.
independentEq	The independent equations. NULL if all equations are independent.
m	The space where to evaluate the hessian. See AllocateHessianEvaluationAsVectors. If NULL the space is allocated internally.
mf	Space for the matrix resulting from the Hessian-vector product. The size of this is neqs x nvars. If NULL, the space is allocated internally
h	The Hessian to evaluate.

Definition at line 131 of file hessian.c.

References AllocateHessianEvaluationAsVectors(), EvaluateEqualitySparseEquations(), EvaluateSubSetEqualitySparseEquations(), FreeHessianEvaluationAsVectors(), MatrixVectorProduct(), NEW, NO_UINT, and SetColumn().

Referenced by EvaluateHessianVector2().

◆ EvaluateHessianVector2()

void EvaluateHessianVector2	(	double *	x,
		double *	v,
		unsigned int	nie,
		boolean *	independentEq,
		double **	m,
		double *	mf,
		double *	o,
		THessian *	h
	)

Evaluates H*v*v. This has to be interpreted as

[ H[1][]*v H[2][]*v ... H[n][]*v] *v

were H[i][j] is the derivative of the whole set of equation with respect to variables i and j. That is, H[i][j] is a vector with as many elements as equations in the system. Then, H[i][] is a matrix of neqs x nvars elements and H[i][]*v is a vector of neqs elements. Such vectors for all variables i form a matrix of neqs x nvars elements. This matrix, when multiplied by 'v' generate a vector (the output 'o') of neqs elements.

Parameters

x	The point where to evaluate the Hessian.
v	The vector to use in the products. The size of this vector is the number of variables in the system.
nie	Number of independent equations. NO_UINT if all equations are independent.
independentEq	The independent equations. NULL if all equations are independent.
m	The space where to evaluate the hessian. See AllocateHessianEvaluationAsVectors. If null the space is allocated internally.
mf	Space for the matrix resulting from the first Hessian-vector product. The size of this is neqs x nvars. If null, the space is allocated internally
o	The output vector. Must be allocated/deallocated externally. The size of this vector is number of equations in the system.
h	The Hessian to evaluate.

Definition at line 178 of file hessian.c.

References AllocateHessianEvaluationAsVectors(), EvaluateHessianVector(), FreeHessianEvaluationAsVectors(), MatrixVectorProduct(), NEW, and NO_UINT.

Referenced by ComputeAcceleration().

◆ FreeHessianEvaluation()

void FreeHessianEvaluation	(	double ***	m,
		THessian *	h
	)

Release space for the Hessian evaluation typically allocated using AllocateHessianEvaluation.

Parameters

m	The space to release.
h	The corresponding Hessian.

Definition at line 209 of file hessian.c.

Referenced by RefineSingularPoint().

◆ FreeHessianEvaluationAsVectors()

void FreeHessianEvaluationAsVectors	(	double **	m,
		THessian *	h
	)

Release space for the Hessian evaluation typically allocated using AllocateHessianEvaluationAsVectors.

Parameters

m	The space to release.
h	The corresponding Hessian.

Definition at line 222 of file hessian.c.

Referenced by DeleteDynamicSpace(), EvaluateHessianVector(), and EvaluateHessianVector2().

◆ DeleteHessian()

void DeleteHessian ( THessian * h )

Release a Hessian structure.

Parameters

h	The Hessian structure to release.

Definition at line 231 of file hessian.c.

References DeleteEquations().

Referenced by DeleteAtlas(), DeleteDynamicSpace(), and DeleteNHessian().

Institut de Robòtica i Informàtica Industrial

Introduction

Data Structures

Functions

Function Documentation

◆ InitHessian()

◆ GetHessianNVars()

◆ GetHessianNEqs()

◆ AllocateHessianEvaluation()

◆ AllocateHessianEvaluationAsVectors()

◆ EvaluateHessian()

◆ EvaluateScalarHessian()

◆ EvaluateHessianVector()

◆ EvaluateHessianVector2()

◆ FreeHessianEvaluation()

◆ FreeHessianEvaluationAsVectors()

◆ DeleteHessian()

Institut de Robòtica
i Informàtica Industrial