#include "cont_math.h"

Include dependency graph for cont_math.c:

Functions
int	cont_SU2_conjugate (matrix_double_t qin, matrix_double_t qout)
	Conjugate an element of SU(2) More...

int	cont_SU2_product (matrix_double_t q, matrix_double_t p, matrix_double_t *out)
	Product of two elements of SU(2) More...

int	cont_SU2_vee (matrix_double_t in, matrix_double_t out)
	The vee map on SU(2) More...

int	cont_SU2_hat (matrix_double_t in, matrix_double_t out)
	The hat map on SU(2) More...

int	cont_SU2_Exp (matrix_double_t in, matrix_double_t out)
	The Exp map on SU(2) More...

int	cont_SU2_triple (double a, double b, double c, matrix_double_t *out)
	Computes a triple product on SU(2) More...

double	cont_SU2_distance (matrix_double_t q1, matrix_double_t q2)
	Evaluate distance Gamma(q1, q2) in [0,2] defined on SU2. More...

int	cont_quat_2_SO3 (matrix_double_t q, matrix_double_t R)
	Embedding relating SU(2) to SO(3) More...

int	cont_SO3_hat (matrix_double_t in, matrix_double_t out)
	The hat operator on SO3. More...

int	cont_SO3_vee (matrix_double_t in, matrix_double_t out)
	The hat operator on SO3. More...

int	cont_SO3_Exp (matrix_double_t in, matrix_double_t out)
	The Exp map on SO3. More...

int	cont_SO3_Log (matrix_double_t in, matrix_double_t out)
	The Log map on SO3. More...

double	cont_SO3_distance (matrix_double_t R1, matrix_double_t R2)
	The distance Phi(R1, R2) defined on SO3. More...

double	cont_sinc (double x)
	Evaluates the sinc function as f(x) = sin(x)/x. More...

double	cont_dot_product (matrix_double_t vecA, matrix_double_t vecB)
	Evaluates the dot product of two vectors. More...

void	cont_cross_product (matrix_double_t inAm, matrix_double_t inBm, matrix_double_t *outm)
	Cross product operation, To be migrated to the cont_math stack. More...

double	cont_sign_func (double in)
	Takes the sign of the input, returning +1 if the input is zero. More...

int	cont_normalize (matrix_double_t *vec)
	Normalizes the vector. More...

Function Documentation

◆ cont_cross_product()

void cont_cross_product	(	matrix_double_t *	inAm,
		matrix_double_t *	inBm,
		matrix_double_t *	outm
	)

Cross product operation, To be migrated to the cont_math stack.

Parameters

[in]	inAm	- Input vector A in R^3
[in]	inBm	- Input vector B in R^3
[out]	outm	- Output as the cross-product of A and B, out=AxB, in R^3

Returns: void

Definition at line 359 of file cont_math.c.

◆ cont_dot_product()

double cont_dot_product	(	matrix_double_t *	vecA,
		matrix_double_t *	vecB
	)

Evaluates the dot product of two vectors.

Parameters

[in]	vecA	- Input vector
[in]	vecB	- Input vector

Returns: output - dot product

Definition at line 343 of file cont_math.c.

◆ cont_normalize()

int cont_normalize ( matrix_double_t * vec )

Normalizes the vector.

Parameters

[out] vec - Input vector with either 1 row, or 1 column

Returns: output - 1 if successful, 0 otherwise

Definition at line 378 of file cont_math.c.

◆ cont_quat_2_SO3()

int cont_quat_2_SO3	(	matrix_double_t *	q,
		matrix_double_t *	R
	)

Embedding relating SU(2) to SO(3)

Parameters

[in]	q	- Pointer to a four-dimensional input quaternion
[out]	R	- Pointer to an output 3x3 rotation matrix

Returns: status - 1 if successful, 0 otherwise

Definition at line 157 of file cont_math.c.

◆ cont_sign_func()

double cont_sign_func ( double in )

Takes the sign of the input, returning +1 if the input is zero.

Parameters

[in] in - Input argument

Returns: output - Output sign in {-1.0, 1.0}

Definition at line 370 of file cont_math.c.

◆ cont_sinc()

double cont_sinc ( double x )

Evaluates the sinc function as f(x) = sin(x)/x.

Parameters

[in] x - the value at which the function is to be evaluated

Returns: output - the output of the function f(x)

Definition at line 333 of file cont_math.c.

◆ cont_SO3_distance()

double cont_SO3_distance	(	matrix_double_t *	R1,
		matrix_double_t *	R2
	)

The distance Phi(R1, R2) defined on SO3.

This distance is defined as Phi(R1, R2) = (1/2)Tr(I - R1'*R2) in [0,2]

Parameters

[in]	R1	- Pointer to an output 3x3 rotation matrix
[in]	R2	- Pointer to an output 3x3 rotation matrix

Returns: distance - The evaluated distance on SO(3)

Definition at line 302 of file cont_math.c.

◆ cont_SO3_Exp()

int cont_SO3_Exp	(	matrix_double_t *	u,
		matrix_double_t *	R
	)

The Exp map on SO3.

Parameters

[in]	u	- Pointer to a three-dimensional vector (one parameter group)
[out]	R	- Pointer to an output 3x3 rotation matrix

Returns: status - 1 if successful, 0 otherwise

Definition at line 224 of file cont_math.c.

◆ cont_SO3_hat()

int cont_SO3_hat	(	matrix_double_t *	in,
		matrix_double_t *	out
	)

The hat operator on SO3.

Parameters

[in]	in	- Pointer to a three-dimensional vector (one parameter group)
[out]	out	- Pointer to an element of the 3x3 lie algebra of SO(3)

Returns: status - 1 if successful, 0 otherwise

Definition at line 186 of file cont_math.c.

◆ cont_SO3_Log()

int cont_SO3_Log	(	matrix_double_t *	R,
		matrix_double_t *	u
	)

The Log map on SO3.

Parameters

[in]	R	- Pointer to an output 3x3 rotation matrix
[out]	u	- Pointer to a three-dimensional vector (one parameter group)

Returns: status - 1 if successful, 0 otherwise

Definition at line 265 of file cont_math.c.

◆ cont_SO3_vee()

int cont_SO3_vee	(	matrix_double_t *	in,
		matrix_double_t *	out
	)

The hat operator on SO3.

Parameters

[in]	in	- Pointer to an element of the 3x3 lie algebra of SO(3)
[out]	out	- Pointer to a three-dimensional vector (one parameter group)

Returns: status - 1 if successful, 0 otherwise

Definition at line 207 of file cont_math.c.

◆ cont_SU2_conjugate()

int cont_SU2_conjugate	(	matrix_double_t *	qin,
		matrix_double_t *	qout
	)

Conjugate an element of SU(2)

Parameters

[in]	qin	- Pointer to a four-dimensional input quaternion
[out]	qout	- Pointer to a four-dimensional output quaternion

Returns: status - 1 if successful, 0 otherwise

Definition at line 10 of file cont_math.c.

◆ cont_SU2_distance()

double cont_SU2_distance	(	matrix_double_t *	q1,
		matrix_double_t *	q2
	)

Evaluate distance Gamma(q1, q2) in [0,2] defined on SU2.

This distance is defined as Gamma(X1, X2) = (1/2)Tr(I - X1'*X2) in [0,2]

Parameters

[in]	q1	- Pointer to a four-dimensional input quaternion
[in]	q2	- Pointer to a four-dimensional output quaternion

Returns: distance - The evaluated distance on SU2

Definition at line 138 of file cont_math.c.

◆ cont_SU2_Exp()

int cont_SU2_Exp	(	matrix_double_t *	in,
		matrix_double_t *	out
	)

The Exp map on SU(2)

Parameters

[in]	in	- Pointer to a three-dimensional vector (one parameter group)
[out]	out	- Pointer to an element of SU(2) (here a 4-dimenisonal vector)

Returns: status - 1 if successful, 0 otherwise

Definition at line 86 of file cont_math.c.

◆ cont_SU2_hat()

int cont_SU2_hat	(	matrix_double_t *	in,
		matrix_double_t *	out
	)

The hat map on SU(2)

Parameters

[in]	in	- Pointer to a three-dimensional output (one parameter group)
[out]	out	- Pointer to an input element of the lie-agbera of SU(2)

Returns: status - 1 if successful, 0 otherwise

Definition at line 69 of file cont_math.c.

◆ cont_SU2_product()

int cont_SU2_product	(	matrix_double_t *	q,
		matrix_double_t *	p,
		matrix_double_t *	out
	)

Product of two elements of SU(2)

Parameters

[in]	q	- Pointer to an input element of SU(2) (four-dimensional vector)
[in]	p	- Pointer to an input element of SU(2) (four-dimensional vector)
[out]	out	- Pointer to an output quaternion product (four-dimensional vector)

Returns: status - 1 if successful, 0 otherwise

Definition at line 28 of file cont_math.c.

◆ cont_SU2_triple()

int cont_SU2_triple	(	double	a,
		double	b,
		double	c,
		matrix_double_t *	out
	)

Computes a triple product on SU(2)

The inputs a, b, and c all represent angles in radians, and the triple product is computed by taking the exponential map with respect to these angles as

qa = Exp([a, 0, 0])
qb = Exp([0, b, 0])
qc = Exp([0, 0, c])

and then computing their consequtive product

out = qa * qb * qc

Parameters

[in]	a	- Angle in radians
[in]	b	- Angle in radians
[in]	c	- Angle in radians
[out]	out	- Pointer to an element of SU(2) (here a 4-dimenisonal vector)

Returns: status - 1 if successful, 0 otherwise

Definition at line 110 of file cont_math.c.

◆ cont_SU2_vee()

int cont_SU2_vee	(	matrix_double_t *	in,
		matrix_double_t *	out
	)

The vee map on SU(2)

Parameters

[in]	in	- Pointer to an input element of the lie-agbera of SU(2)
[out]	out	- Pointer to a three-dimensional output (one parameter group)

Returns: status - 1 if successful, 0 otherwise

Definition at line 53 of file cont_math.c.

Functions

Function Documentation

◆ cont_cross_product()

◆ cont_dot_product()

◆ cont_normalize()

◆ cont_quat_2_SO3()

◆ cont_sign_func()

◆ cont_sinc()

◆ cont_SO3_distance()

◆ cont_SO3_Exp()

◆ cont_SO3_hat()

◆ cont_SO3_Log()

◆ cont_SO3_vee()

◆ cont_SU2_conjugate()

◆ cont_SU2_distance()

◆ cont_SU2_Exp()

◆ cont_SU2_hat()

◆ cont_SU2_product()

◆ cont_SU2_triple()

◆ cont_SU2_vee()