87 lines
4.2 KiB
ReStructuredText
87 lines
4.2 KiB
ReStructuredText
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========
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Features
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========
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.. _chapter-features:
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* **Code Quality** - Ceres Solver has been used in production at
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Google for more than four years now. It is clean, extensively tested
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and well documented code that is actively developed and supported.
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* **Modeling API** - It is rarely the case that one starts with the
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exact and complete formulation of the problem that one is trying to
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solve. Ceres's modeling API has been designed so that the user can
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easily build and modify the objective function, one term at a
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time. And to do so without worrying about how the solver is going to
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deal with the resulting changes in the sparsity/structure of the
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underlying problem.
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- **Derivatives** Supplying derivatives is perhaps the most tedious
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and error prone part of using an optimization library. Ceres
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ships with `automatic`_ and `numeric`_ differentiation. So you
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never have to compute derivatives by hand (unless you really want
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to). Not only this, Ceres allows you to mix automatic, numeric and
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analytical derivatives in any combination that you want.
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- **Robust Loss Functions** Most non-linear least squares problems
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involve data. If there is data, there will be outliers. Ceres
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allows the user to *shape* their residuals using a
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:class:`LossFunction` to reduce the influence of outliers.
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- **Local Parameterization** In many cases, some parameters lie on a
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manifold other than Euclidean space, e.g., rotation matrices. In
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such cases, the user can specify the geometry of the local tangent
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space by specifying a :class:`LocalParameterization` object.
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* **Solver Choice** Depending on the size, sparsity structure, time &
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memory budgets, and solution quality requiremnts, different
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optimization algorithms will suit different needs. To this end,
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Ceres Solver comes with a variety of optimization algorithms:
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- **Trust Region Solvers** - Ceres supports Levenberg-Marquardt,
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Powell's Dogleg, and Subspace dogleg methods. The key
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computational cost in all of these methods is the solution of a
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linear system. To this end Ceres ships with a variety of linear
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solvers - dense QR and dense Cholesky factorization (using
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`Eigen`_ or `LAPACK`_) for dense problems, sparse Cholesky
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factorization (`SuiteSparse`_, `CXSparse`_ or `Eigen`_) for large
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sparse problems custom Schur complement based dense, sparse, and
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iterative linear solvers for `bundle adjustment`_ problems.
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- **Line Search Solvers** - When the problem size is so large that
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storing and factoring the Jacobian is not feasible or a low
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accuracy solution is required cheaply, Ceres offers a number of
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line search based algorithms. This includes a number of variants
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of Non-linear Conjugate Gradients, BFGS and LBFGS.
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* **Speed** - Ceres Solver has been extensively optimized, with C++
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templating, hand written linear algebra routines and OpenMP based
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multithreading of the Jacobian evaluation and the linear solvers.
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* **Solution Quality** Ceres is the `best performing`_ solver on the NIST
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problem set used by Mondragon and Borchers for benchmarking
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non-linear least squares solvers.
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* **Covariance estimation** - Evaluate the sensitivity/uncertainty of
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the solution by evaluating all or part of the covariance
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matrix. Ceres is one of the few solvers that allows you to to do
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this analysis at scale.
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* **Community** Since its release as an open source software, Ceres
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has developed an active developer community that contributes new
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features, bug fixes and support.
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* **Portability** - Runs on *Linux*, *Windows*, *Mac OS X*, *Android*
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*and iOS*.
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* **BSD Licensed** The BSD license offers the flexibility to ship your
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application
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.. _best performing: https://groups.google.com/forum/#!topic/ceres-solver/UcicgMPgbXw
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.. _bundle adjustment: http://en.wikipedia.org/wiki/Bundle_adjustment
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.. _SuiteSparse: http://www.cise.ufl.edu/research/sparse/SuiteSparse/
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.. _Eigen: http://eigen.tuxfamily.org/
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.. _LAPACK: http://www.netlib.org/lapack/
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.. _CXSparse: https://www.cise.ufl.edu/research/sparse/CXSparse/
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.. _automatic: http://en.wikipedia.org/wiki/Automatic_differentiation
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.. _numeric: http://en.wikipedia.org/wiki/Numerical_differentiation
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