| | .. 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/ |
| | .. _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 |
| |
|
