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