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