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<div class="title">jacobians.h File Reference</div> </div>
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<div class="textblock"><code>#include <<a class="el" href="_c_quaternion_8h_source.html">mrpt/math/CQuaternion.h</a>></code><br/>
<code>#include <<a class="el" href="base_2include_2mrpt_2math_2utils_8h_source.html">mrpt/math/utils.h</a>></code><br/>
<code>#include <<a class="el" href="_c_pose3_d_8h_source.html">mrpt/poses/CPose3D.h</a>></code><br/>
<code>#include <<a class="el" href="_c_pose3_d_p_d_f_gaussian_8h_source.html">mrpt/poses/CPose3DPDFGaussian.h</a>></code><br/>
<code>#include <<a class="el" href="_c_pose_p_d_f_gaussian_8h_source.html">mrpt/poses/CPosePDFGaussian.h</a>></code><br/>
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Include dependency graph for jacobians.h:</div>
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<p><a href="jacobians_8h_source.html">Go to the source code of this file.</a></p>
<table class="memberdecls">
<tr><td colspan="2"><h2><a name="namespaces"></a>
Namespaces</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">namespace  </td><td class="memItemRight" valign="bottom"><a class="el" href="namespacemrpt.html">mrpt</a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight"><p>This is the global namespace for all Mobile Robot Programming Toolkit (MRPT) libraries. </p>
<br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">namespace  </td><td class="memItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math.html">mrpt::math</a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight"><p>This base provides a set of functions for maths stuff. </p>
<br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">namespace  </td><td class="memItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math_1_1jacobians.html">mrpt::math::jacobians</a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight"><p>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). </p>
<br/></td></tr>
<tr><td colspan="2"><h2><a name="func-members"></a>
Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math_1_1jacobians.html#a30e4241b019f9b1160df7bca4afb783d">mrpt::math::jacobians::jacob_quat_from_yawpitchroll</a> (<a class="el" href="classmrpt_1_1math_1_1_c_matrix_fixed_numeric.html">CMatrixFixedNumeric</a>< double, 4, 3 > &out_dq_dr, const double yaw, const double pitch, const double roll)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes the 4x3 Jacobian of the transformation from a 3D pose angles (yaw pitch roll) into a Quaternion, that is, the Jacobian of: </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \mathbf{q} = \left( \begin{array}{c} \cos (\phi /2) \cos (\theta /2) \cos (\psi /2) + \sin (\phi /2) \sin (\theta /2) \sin (\psi /2) \\ \sin (\phi /2) \cos (\theta /2) \cos (\psi /2) - \cos (\phi /2) \sin (\theta /2) \sin (\psi /2) \\ \cos (\phi /2) \sin (\theta /2) \cos (\psi /2) + \sin (\phi /2) \cos (\theta /2) \sin (\psi /2) \\ \cos (\phi /2) \cos (\theta /2) \sin (\psi /2) - \sin (\phi /2) \sin (\theta /2) \cos (\psi /2) \\ \end{array}\right) \]" src="form_24.png"/>
</p>
<p> With : <img class="formulaInl" alt="$ \phi = roll $" src="form_25.png"/>, <img class="formulaInl" alt="$ \theta = pitch $" src="form_26.png"/> and <img class="formulaInl" alt="$ \psi = yaw $" src="form_27.png"/>. <a href="#a30e4241b019f9b1160df7bca4afb783d"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math_1_1jacobians.html#ad8c2781c9bbd4c32743bf0be99bf8c33">mrpt::math::jacobians::jacob_quat_from_yawpitchroll</a> (<a class="el" href="classmrpt_1_1math_1_1_c_matrix_fixed_numeric.html">CMatrixFixedNumeric</a>< double, 4, 3 > &out_dq_dr, const <a class="el" href="classmrpt_1_1poses_1_1_c_pose3_d.html">CPose3D</a> &in_pose)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes the 4x3 Jacobian of the transformation from a 3D pose angles (yaw pitch roll) into a Quaternion, that is, the Jacobian of: </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \mathbf{q} = \left( \begin{array}{c} \cos (\phi /2) \cos (\theta /2) \cos (\psi /2) + \sin (\phi /2) \sin (\theta /2) \sin (\psi /2) \\ \sin (\phi /2) \cos (\theta /2) \cos (\psi /2) - \cos (\phi /2) \sin (\theta /2) \sin (\psi /2) \\ \cos (\phi /2) \sin (\theta /2) \cos (\psi /2) + \sin (\phi /2) \cos (\theta /2) \sin (\psi /2) \\ \cos (\phi /2) \cos (\theta /2) \sin (\psi /2) - \sin (\phi /2) \sin (\theta /2) \cos (\psi /2) \\ \end{array}\right) \]" src="form_24.png"/>
</p>
<p> With : <img class="formulaInl" alt="$ \phi = roll $" src="form_25.png"/>, <img class="formulaInl" alt="$ \theta = pitch $" src="form_26.png"/> and <img class="formulaInl" alt="$ \psi = yaw $" src="form_27.png"/>. <a href="#ad8c2781c9bbd4c32743bf0be99bf8c33"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math_1_1jacobians.html#ae82c0c77eb8140df495cdb9312bcf49a">mrpt::math::jacobians::jacob_yawpitchroll_from_quat</a> (<a class="el" href="classmrpt_1_1math_1_1_c_matrix_fixed_numeric.html">CMatrixFixedNumeric</a>< double, 3, 4 > &out_dr_dq)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Computes the 3x4 Jacobian of the transformation from a quaternion (qr qx qy qz) to 3D pose angles (yaw pitch roll). <a href="#ae82c0c77eb8140df495cdb9312bcf49a"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class QUATERNION , class MATRIXLIKE > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math_1_1jacobians.html#a0af89c27b4e68ac11002b015873da8c8">mrpt::math::jacobians::jacob_quat_rotation</a> (const QUATERNION &quaternion, MATRIXLIKE &out_mat4x4)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Compute the Jacobian of the rotation composition operation <img class="formulaInl" alt="$ p = f(\cdot) = q_{this} \times r $" src="form_7.png"/>, that is the 4x4 matrix <img class="formulaInl" alt="$ \frac{\partial f}{\partial q_{this} } $" src="form_8.png"/>. <a href="#a0af89c27b4e68ac11002b015873da8c8"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math_1_1jacobians.html#acb6a24540a986fe0f20d73c8c72f1b50">mrpt::math::jacobians::jacobs_6D_pose_comp</a> (const <a class="el" href="classmrpt_1_1poses_1_1_c_pose3_d.html">CPose3D</a> &x, const <a class="el" href="classmrpt_1_1poses_1_1_c_pose3_d.html">CPose3D</a> &u, <a class="el" href="namespacemrpt_1_1math.html#a69ac788617e87d06107cd7a32a1352b7">CMatrixDouble66</a> &out_df_dx, <a class="el" href="namespacemrpt_1_1math.html#a69ac788617e87d06107cd7a32a1352b7">CMatrixDouble66</a> &out_df_du)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Given the 3D(6D) pose composition <img class="formulaInl" alt="$ f(x,u) = x \oplus u $" src="form_28.png"/>, compute the two 6x6 Jacobians <img class="formulaInl" alt="$ \frac{\partial f}{\partial x} $" src="form_29.png"/> and <img class="formulaInl" alt="$ \frac{\partial f}{\partial u} $" src="form_30.png"/>. <a href="#acb6a24540a986fe0f20d73c8c72f1b50"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math_1_1jacobians.html#ab49860321328e9d934c2e9f019e1c464">mrpt::math::jacobians::jacobs_2D_pose_comp</a> (const <a class="el" href="classmrpt_1_1poses_1_1_c_pose_p_d_f_gaussian.html">CPosePDFGaussian</a> &x, const <a class="el" href="classmrpt_1_1poses_1_1_c_pose_p_d_f_gaussian.html">CPosePDFGaussian</a> &u, <a class="el" href="namespacemrpt_1_1math.html#a58d0ee60eee38e990848ccb8b83e8338">CMatrixDouble33</a> &out_df_dx, <a class="el" href="namespacemrpt_1_1math.html#a58d0ee60eee38e990848ccb8b83e8338">CMatrixDouble33</a> &out_df_du)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Given the 2D pose composition <img class="formulaInl" alt="$ f(x,u) = x \oplus u $" src="form_28.png"/>, compute the two 3x3 Jacobians <img class="formulaInl" alt="$ \frac{\partial f}{\partial x} $" src="form_29.png"/> and <img class="formulaInl" alt="$ \frac{\partial f}{\partial u} $" src="form_30.png"/>. <a href="#ab49860321328e9d934c2e9f019e1c464"></a><br/></td></tr>
<tr><td class="memTemplParams" colspan="2">template<class VECTORLIKE , class VECTORLIKE2 , class VECTORLIKE3 , class MATRIXLIKE , class USERPARAM > </td></tr>
<tr><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespacemrpt_1_1math_1_1jacobians.html#a6bfc725b0889aa6b7eee78bb91f19441">mrpt::math::jacobians::jacob_numeric_estimate</a> (const VECTORLIKE &x, void(*functor)(const VECTORLIKE &x, const USERPARAM &y, VECTORLIKE3 &out), const VECTORLIKE2 &increments, const USERPARAM &userParam, MATRIXLIKE &out_Jacobian)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Numerical estimation of the Jacobian of a user-supplied function - this template redirects to <a class="el" href="group__container__ops__grp.html#ga13e2e339d944b37f2386fc4e0bb56935" title="Estimate the Jacobian of a multi-dimensional function around a point "x", using finite differences of...">mrpt::math::estimateJacobian</a>, see that function for documentation. <a href="#a6bfc725b0889aa6b7eee78bb91f19441"></a><br/></td></tr>
</table>
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<br><hr><br> <table border="0" width="100%"> <tr> <td> Page generated by <a href="http://www.doxygen.org" target="_blank">Doxygen 1.7.5</a> for MRPT 0.9.5 SVN: at Sun Sep 25 17:20:18 UTC 2011</td><td></td> <td width="100"> </td> <td width="150"> </td></tr> </table> </body></html>
