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https://github.com/ceres-solver/ceres-solver.git
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Sergiu Deitsch
84 lines
3.6 KiB
ReStructuredText
84 lines
3.6 KiB
ReStructuredText
.. _chapter-modeling_faqs:
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.. default-domain:: cpp
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.. cpp:namespace:: ceres
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========
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Modeling
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========
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Use analytical/automatic derivatives
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====================================
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This is the single most important piece of advice we can give to you. It is
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tempting to take the easy way out and use numeric differentiation. This is a bad
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idea. Numeric differentiation is slow, ill-behaved, hard to get right, and
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results in poor convergence behaviour.
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Ceres allows the user to define templated functors which will be automatically
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differentiated. For most situations this is enough and we recommend using this
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facility. In some cases the derivatives are simple enough or the performance
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considerations are such that the overhead of automatic differentiation is too
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much. In such cases, analytic derivatives are recommended.
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The use of numerical derivatives should be a measure of last resort, where it is
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simply not possible to write a templated implementation of the cost function.
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In many cases it is not possible to do analytic or automatic differentiation of
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the entire cost function, but it is generally the case that it is possible to
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decompose the cost function into parts that need to be numerically
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differentiated and parts that can be automatically or analytically
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differentiated.
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To this end, Ceres has extensive support for mixing analytic, automatic and
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numeric differentiation. See :class:`CostFunctionToFunctor`.
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When using Quaternions, consider using :class:`QuaternionManifold`
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==================================================================
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`Quaternions <https://en.wikipedia.org/wiki/Quaternion>`_ are a four dimensional
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parameterization of the space of three dimensional rotations :math:`SO(3)`.
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However, the :math:`SO(3)` is a three dimensional set, and so is the tangent
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space of a Quaternion. Therefore, it is sometimes (not always) beneficial to
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associate a local parameterization with parameter blocks representing a
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Quaternion. Assuming that the order of entries in your parameter block is
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:math:`w,x,y,z`, you can use :class:`QuaternionManifold`.
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.. NOTE::
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If you are using `Eigen's Quaternion
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<http://eigen.tuxfamily.org/dox/classEigen_1_1Quaternion.html>`_
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object, whose layout is :math:`x,y,z,w`, then you should use
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:class:`EigenQuaternionManifold`.
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How do I solve problems with general linear & non-linear **inequality** constraints with Ceres Solver?
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======================================================================================================
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Currently, Ceres Solver only supports upper and lower bounds constraints on the
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parameter blocks.
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A crude way of dealing with inequality constraints is have one or more of your
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cost functions check if the inequalities you are interested in are satisfied,
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and if not return false instead of true. This will prevent the solver from ever
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stepping into an infeasible region.
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This requires that the starting point for the optimization be a feasible point.
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You also risk pre-mature convergence using this method.
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How do I solve problems with general linear & non-linear **equality** constraints with Ceres Solver?
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====================================================================================================
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There is no built in support in ceres for solving problems with equality
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constraints. Currently, Ceres Solver only supports upper and lower bounds
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constraints on the parameter blocks.
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The trick described above for dealing with inequality constraints will **not**
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work for equality constraints.
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How do I set one or more components of a parameter block constant?
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==================================================================
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Using :class:`SubsetManifold`.
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