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Ceres Solver
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1.13
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Why?
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Installation
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Tutorial
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On Derivatives
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Modeling Non-linear Least Squares
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Solving Non-linear Least Squares
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Covariance Estimation
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General Unconstrained Minimization
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FAQS, Tips & Tricks
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Users
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Docs »
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Why?
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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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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 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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