jacobians.h File Reference

#include <mrpt/math/num_jacobian.h>
#include <mrpt/math/CQuaternion.h>
#include <mrpt/poses/CPose3D.h>
#include <mrpt/poses/CPosePDF.h>
#include <mrpt/poses/CPose3DQuatPDF.h>
#include <mrpt/poses/CPose3DPDF.h>
#include <functional>

Go to the source code of this file.

Namespaces
	mrpt
	This is the global namespace for all Mobile Robot Programming Toolkit (MRPT) libraries.

	mrpt::math
	This base provides a set of functions for maths stuff.

	mrpt::math::jacobians
	A collection of functions to compute jacobians of diverse transformations, etc (some functions are redirections to existing methods elsewhere, so this namespace is actually used with grouping purposes).

Functions
void	mrpt::math::jacobians::jacob_quat_from_yawpitchroll (mrpt::math::CMatrixFixedNumeric< double, 4, 3 > &out_dq_dr, const double yaw, const double pitch, const double roll)
	Computes the 4x3 Jacobian of the transformation from a 3D pose angles (yaw pitch roll) into a Quaternion, that is, the Jacobian of: $\mathbf{q} = \left( \begin{array}{c} \cos (\phi /2) \cos (\theta /2) \cos (\psi /2) + \sin (\phi /2) \sin (\theta /2) \sin (\psi /2) \\ \sin (\phi /2) \cos (\theta /2) \cos (\psi /2) - \cos (\phi /2) \sin (\theta /2) \sin (\psi /2) \\ \cos (\phi /2) \sin (\theta /2) \cos (\psi /2) + \sin (\phi /2) \cos (\theta /2) \sin (\psi /2) \\ \cos (\phi /2) \cos (\theta /2) \sin (\psi /2) - \sin (\phi /2) \sin (\theta /2) \cos (\psi /2) \\ \end{array}\right)$ With : $\phi = roll$ , $\theta = pitch$ and $\psi = yaw$ . More...

void	mrpt::math::jacobians::jacob_quat_from_yawpitchroll (mrpt::math::CMatrixFixedNumeric< double, 4, 3 > &out_dq_dr, const mrpt::poses::CPose3D &in_pose)
	Computes the 4x3 Jacobian of the transformation from a 3D pose angles (yaw pitch roll) into a Quaternion, that is, the Jacobian of: $\mathbf{q} = \left( \begin{array}{c} \cos (\phi /2) \cos (\theta /2) \cos (\psi /2) + \sin (\phi /2) \sin (\theta /2) \sin (\psi /2) \\ \sin (\phi /2) \cos (\theta /2) \cos (\psi /2) - \cos (\phi /2) \sin (\theta /2) \sin (\psi /2) \\ \cos (\phi /2) \sin (\theta /2) \cos (\psi /2) + \sin (\phi /2) \cos (\theta /2) \sin (\psi /2) \\ \cos (\phi /2) \cos (\theta /2) \sin (\psi /2) - \sin (\phi /2) \sin (\theta /2) \cos (\psi /2) \\ \end{array}\right)$ With : $\phi = roll$ , $\theta = pitch$ and $\psi = yaw$ . More...

void	mrpt::math::jacobians::jacob_yawpitchroll_from_quat (mrpt::math::CMatrixFixedNumeric< double, 3, 4 > &out_dr_dq)
	Computes the 3x4 Jacobian of the transformation from a quaternion (qr qx qy qz) to 3D pose angles (yaw pitch roll). More...

template<class QUATERNION , class MATRIXLIKE >
void	mrpt::math::jacobians::jacob_quat_rotation (const QUATERNION &quaternion, MATRIXLIKE &out_mat4x4)
	Compute the Jacobian of the rotation composition operation $p = f(\cdot) = q_{this} \times r$ , that is the 4x4 matrix $\frac{\partial f}{\partial q_{this} }$ . More...

void	mrpt::math::jacobians::jacobs_6D_pose_comp (const mrpt::poses::CPose3D &x, const mrpt::poses::CPose3D &u, CMatrixDouble66 &out_df_dx, CMatrixDouble66 &out_df_du)
	Given the 3D(6D) pose composition $f(x,u) = x \oplus u$ , compute the two 6x6 Jacobians $\frac{\partial f}{\partial x}$ and $\frac{\partial f}{\partial u}$ . More...

void	mrpt::math::jacobians::jacobs_6D_pose_comp (const mrpt::poses::CPose3DQuat &x, const mrpt::poses::CPose3DQuat &u, CMatrixDouble77 &out_df_dx, CMatrixDouble77 &out_df_du)
	Given the 3D(6D) pose composition $f(x,u) = x \oplus u$ , compute the two 6x6 Jacobians $\frac{\partial f}{\partial x}$ and $\frac{\partial f}{\partial u}$ . More...

void	mrpt::math::jacobians::jacobs_2D_pose_comp (const mrpt::poses::CPosePDFGaussian &x, const mrpt::poses::CPosePDFGaussian &u, CMatrixDouble33 &out_df_dx, CMatrixDouble33 &out_df_du)
	Given the 2D pose composition $f(x,u) = x \oplus u$ , compute the two 3x3 Jacobians $\frac{\partial f}{\partial x}$ and $\frac{\partial f}{\partial u}$ . More...

template<class VECTORLIKE , class VECTORLIKE2 , class VECTORLIKE3 , class MATRIXLIKE , class USERPARAM >
void	mrpt::math::jacobians::jacob_numeric_estimate (const VECTORLIKE &x, std::function< void(const VECTORLIKE &x, const USERPARAM &y, VECTORLIKE3 &out)> functor, const VECTORLIKE2 &increments, const USERPARAM &userParam, MATRIXLIKE &out_Jacobian)
	Numerical estimation of the Jacobian of a user-supplied function - this template redirects to mrpt::math::estimateJacobian, see that function for documentation. More...

Namespaces

Functions