| .. default-domain:: cpp |
| |
| .. cpp:namespace:: ceres |
| |
| ==== |
| Why? |
| ==== |
| .. _chapter-features: |
| |
| * **Code Quality** - Ceres Solver has been used in production at |
| Google since 2011. 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`_, |
| `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 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/ |
| .. _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 |