jive_helpers Namespace Reference

namespace for all helper functions

Typedefs
typedef Array< double, 4 >	Quadix
typedef Array< IdxVector, 2 >	IdxVectorMatrix

Functions
Vector	funcGrad (const Ref< Function > func, const Vector &args)
	gets the gradient of a multivariate function.
Vector	evalFuncs (const FuncUtils::FuncArray funcs, const Vector &args)
	evaluates an array of multivariate functions.
Matrix	funcHessian (const Ref< Function > func, const Vector &args)
	gets the Hessian of a multivariate function.
Matrix	gradFuncs (const FuncUtils::FuncArray funcs, const Vector &args)
	gets the gradients of an array of multivariate functions.
Matrix	eye (const idx_t dim=3)
	generates an identity matrix of the given dimension.
void	logMat (const Vector &rv, const Matrix &R)
	compute rotational vector from rotation matrix.
void	vec2mat (const Matrix &mat, const Vector &vec)
	rearrange a vector into a matrix.
void	mat2vec (const Vector &vec, const Matrix &mat)
	rearrange a matrix into a vector.
void	expVec (const Matrix &Exp, const Vector &v)
	compute the exponential of a axial vector.
void	expVecP (const Matrix &ExpP, const Vector &v, const Vector &vP)
	derivative of jive_helpers::expVec.
double	trace (const Matrix &mat)
	calculate the trace of a matrix.
idx_t	factorial (const idx_t n)
	calculates the factorial of an integer.
idx_t	binom (const idx_t n, const idx_t k)
	calculate the binomial coefficient.
double	matrixNorm2 (const Matrix &mat)
	calculates the 2-norm of a matrix.
Matrix	skew (const Vector &vec)
	construct a skew symetric matrix from a given vector.
Vector	unskew (const Matrix &mat)
	construct a axial vector from a given skew-symmetric matrix

Variables
const Vector	e1 = {1., 0., 0.}
const Vector	e2 = {0., 1., 0.}
const Vector	e3 = {0., 0., 1.}
const Vector	vec0 = {0., 0., 0.}
const double	TINY = __DBL_EPSILON__ * 1e6

Typedef Documentation

IdxVectorMatrix

typedef Array<IdxVector, 2> jive_helpers::IdxVectorMatrix

Quadix

typedef Array<double, 4> jive_helpers::Quadix

Function Documentation

binom()

idx_t jive_helpers::binom	(	const idx_t	n,
		const idx_t	k
	)

Parameters

n	parameter n
k	parameter k

Returns

binomial coefficient nCk

evalFuncs()

Vector jive_helpers::evalFuncs	(	const FuncUtils::FuncArray	funcs,
		const Vector &	args
	)

Parameters

funcs	array of functions to evaluate
args	point to evaluate at

Returns

results of the evaluation

expVec()

void jive_helpers::expVec	(	const Matrix &	Exp,
		const Vector &	v
	)

It computes the matrix exponential of the skew-symmetric matrix of this vector so when \(\Theta=[\theta\times]\) this function will return \(\exp(\Theta)\).

See also

Wikipedia

Parameters

[out]	Exp	resulting matrix exponential
[in]	v	axial rotation vector

expVecP()

void jive_helpers::expVecP	(	const Matrix &	ExpP,
		const Vector &	v,
		const Vector &	vP
	)

See also

jive_helpers::expVec

Differentiation rules

Parameters

[out]	ExpP	resulting matrix exponential
[in]	v	axial rotation vector
[in]	vP	derivative of the axial rotation vector

eye()

Matrix jive_helpers::eye

(

const idx_t

dim = 3

)

Parameters

dim	dimension of the identity matrix (default 3)

Returns

identity matrix

factorial()

idx_t jive_helpers::factorial

(

const idx_t

n

)

Parameters

n	integer to calculate the factorial from

Returns

the calculated factorial

funcGrad()

Vector jive_helpers::funcGrad	(	const Ref< Function >	func,
		const Vector &	args
	)

Parameters

func	function of which to evaluate the gradient
args	point to evaluate the gradient

Returns

gradient

funcHessian()

Matrix jive_helpers::funcHessian	(	const Ref< Function >	func,
		const Vector &	args
	)

Parameters

func	function of which to evaluate the Hessian
args	point to evaluate the Hessian

Returns

Hessian

gradFuncs()

Matrix jive_helpers::gradFuncs	(	const FuncUtils::FuncArray	funcs,
		const Vector &	args
	)

Parameters

funcs	array of functions of which to evaluate the gradient
args	point to evaluate the gradient

Returns

Matrix of the gradients

logMat()

void jive_helpers::logMat	(	const Vector &	rv,
		const Matrix &	R
	)

This function computes the logarithmic map of a rotation matrix as a member of the Lie group SO(3) to the Lie algebra \(\mathfrak{so}(3)\). It returns the axial vector of the rotation matrix.

See also

Wikipedia

Parameters

[out]	rv	rotational vector
[in]	R	rotational matrix

mat2vec()

void jive_helpers::mat2vec	(	const Vector &	vec,
		const Matrix &	mat
	)

Parameters

[out]	mat	matrix of given dimensions
[in]	vec	vector (needs to have fitting dimension)

matrixNorm2()

double jive_helpers::matrixNorm2

(

const Matrix &

mat

)

Parameters

mat

matrix

Returns

resulting 2-norm

skew()

Matrix jive_helpers::skew

(

const Vector &

vec

)

Parameters

vec	vector to be changed to skew symmetric matrix

Returns

skew symmetric matrix

trace()

double jive_helpers::trace

(

const Matrix &

mat

)

Parameters

mat	matrix to get the trace of

Returns

the trace of the given matrix

unskew()

Vector jive_helpers::unskew

(

const Matrix &

mat

)

Parameters

mat	skew symmetric matrix

Returns

axial vector

vec2mat()

void jive_helpers::vec2mat	(	const Matrix &	mat,
		const Vector &	vec
	)

Parameters

[out]	mat	matrix of given dimensions
[in]	vec	vector (needs to have fitting dimension)

Variable Documentation

e1

const Vector jive_helpers::e1 = {1., 0., 0.}

e2

const Vector jive_helpers::e2 = {0., 1., 0.}

e3

const Vector jive_helpers::e3 = {0., 0., 1.}

TINY

const double jive_helpers::TINY = __DBL_EPSILON__ * 1e6

vec0

const Vector jive_helpers::vec0 = {0., 0., 0.}