|  | .. default-domain:: cpp | 
|  |  | 
|  | .. cpp:namespace:: ceres | 
|  |  | 
|  | ==== | 
|  | Why? | 
|  | ==== | 
|  | .. _chapter-features: | 
|  |  | 
|  | * **Code Quality** - Ceres Solver has been used in production at | 
|  | Google for more than four years now. 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. | 
|  |  | 
|  | - **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 a | 
|  | :class:`LossFunction` to reduce the influence of outliers. | 
|  |  | 
|  | - **Manifolds** 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 :class:`Manifold` object. | 
|  |  | 
|  | * **Solver Choice** Depending on the size, sparsity structure, time & | 
|  | memory budgets, and solution quality requirements, different | 
|  | optimization algorithms will suit different needs. To this end, | 
|  | Ceres Solver comes with a variety of optimization algorithms: | 
|  |  | 
|  | - **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`_, `LAPACK`_ or `CUDA`_) for dense problems, sparse | 
|  | Cholesky factorization (`SuiteSparse`_, `Apple's Accelerate`_, | 
|  | `CXSparse`_ `Eigen`_) 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 Solver has been extensively optimized, with C++ | 
|  | templating, hand written linear algebra routines and OpenMP or | 
|  | modern C++ threads based multithreading of the Jacobian evaluation | 
|  | and the linear solvers. | 
|  |  | 
|  | * **GPU Acceleration** If your system supports `CUDA`_ then Ceres | 
|  | Solver can use the Nvidia GPU on your system to speed up the solver. | 
|  |  | 
|  | * **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 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 | 
|  |  | 
|  | .. _best performing: 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 | 
|  | .. _CUDA : https://developer.nvidia.com/cuda-toolkit | 
|  | .. _Apple's Accelerate: https://developer.apple.com/documentation/accelerate/sparse_solvers |