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Functions
mrpt::math::jacobians Namespace Reference

Detailed Description

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).

Since most functions in this namespace are inline, their use implies no execution time overload and the code may be more clear to read, so it's recommended to use them where needed.

Functions

void 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 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 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 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 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 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 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 jacob_numeric_estimate (const VECTORLIKE &x, void(*functor)(const VECTORLIKE &x, const USERPARAM &y, VECTORLIKE3 &out), 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...
 

Function Documentation

template<class VECTORLIKE , class VECTORLIKE2 , class VECTORLIKE3 , class MATRIXLIKE , class USERPARAM >
void mrpt::math::jacobians::jacob_numeric_estimate ( const VECTORLIKE &  x,
void(*)(const VECTORLIKE &x, const USERPARAM &y, VECTORLIKE3 &out)  functor,
const VECTORLIKE2 &  increments,
const USERPARAM &  userParam,
MATRIXLIKE &  out_Jacobian 
)
inline
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 
)
inline

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 $.

See Also
jacob_yawpitchroll_from_quat, mrpt::poses::CPose3D::getAsQuaternion

Definition at line 34 of file jacobians.h.

References mrpt::poses::CPose3D::getAsQuaternion(), and mrpt::math::UNINITIALIZED_QUATERNION.

void mrpt::math::jacobians::jacob_quat_from_yawpitchroll ( mrpt::math::CMatrixFixedNumeric< double, 4, 3 > &  out_dq_dr,
const mrpt::poses::CPose3D in_pose 
)
inline

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 $.

See Also
jacob_yawpitchroll_from_quat, mrpt::poses::CPose3D::getAsQuaternion

Definition at line 51 of file jacobians.h.

References mrpt::poses::CPose3D::getAsQuaternion(), and mrpt::math::UNINITIALIZED_QUATERNION.

template<class QUATERNION , class MATRIXLIKE >
void mrpt::math::jacobians::jacob_quat_rotation ( const QUATERNION &  quaternion,
MATRIXLIKE &  out_mat4x4 
)
inline

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} } $.

The output matrix can be a dynamic or fixed size (4x4) matrix. The input quaternion can be mrpt::math::CQuaternionFloat or mrpt::math::CQuaternionDouble.

Definition at line 76 of file jacobians.h.

void mrpt::math::jacobians::jacob_yawpitchroll_from_quat ( mrpt::math::CMatrixFixedNumeric< double, 3, 4 > &  out_dr_dq)
inline

Computes the 3x4 Jacobian of the transformation from a quaternion (qr qx qy qz) to 3D pose angles (yaw pitch roll).

See Also
jacob_quat_from_yawpitchroll

Definition at line 64 of file jacobians.h.

References MRPT_UNUSED_PARAM, and THROW_EXCEPTION.

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 
)
inline

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} $.

For the equations, see CPosePDF::jacobiansPoseComposition

Definition at line 108 of file jacobians.h.

References mrpt::poses::CPosePDF::jacobiansPoseComposition().

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 
)
inline

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} $.

For the equations, see CPose3DPDF::jacobiansPoseComposition

Definition at line 84 of file jacobians.h.

References mrpt::poses::CPose3DPDF::jacobiansPoseComposition().

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 
)
inline

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} $.

For the equations, see CPose3DQuatPDF::jacobiansPoseComposition

Definition at line 96 of file jacobians.h.

References mrpt::poses::CPose3DQuatPDF::jacobiansPoseComposition().




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