| // Ceres Solver - A fast non-linear least squares minimizer |
| // Copyright 2010, 2011, 2012 Google Inc. All rights reserved. |
| // http://code.google.com/p/ceres-solver/ |
| // |
| // Redistribution and use in source and binary forms, with or without |
| // modification, are permitted provided that the following conditions are met: |
| // |
| // * Redistributions of source code must retain the above copyright notice, |
| // this list of conditions and the following disclaimer. |
| // * Redistributions in binary form must reproduce the above copyright notice, |
| // this list of conditions and the following disclaimer in the documentation |
| // and/or other materials provided with the distribution. |
| // * Neither the name of Google Inc. nor the names of its contributors may be |
| // used to endorse or promote products derived from this software without |
| // specific prior written permission. |
| // |
| // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" |
| // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE |
| // LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR |
| // CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF |
| // SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS |
| // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN |
| // CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE |
| // POSSIBILITY OF SUCH DAMAGE. |
| // |
| // Author: sameeragarwal@google.com (Sameer Agarwal) |
| // |
| // Helpers for making CostFunctions as needed by the least squares framework, |
| // with Jacobians computed via automatic differentiation. For more information |
| // on automatic differentation, see the wikipedia article at |
| // http://en.wikipedia.org/wiki/Automatic_differentiation |
| // |
| // To get an auto differentiated cost function, you must define a class with a |
| // templated operator() (a functor) that computes the cost function in terms of |
| // the template parameter T. The autodiff framework substitutes appropriate |
| // "jet" objects for T in order to compute the derivative when necessary, but |
| // this is hidden, and you should write the function as if T were a scalar type |
| // (e.g. a double-precision floating point number). |
| // |
| // The function must write the computed value in the last argument (the only |
| // non-const one) and return true to indicate success. |
| // |
| // For example, consider a scalar error e = k - x'y, where both x and y are |
| // two-dimensional column vector parameters, the prime sign indicates |
| // transposition, and k is a constant. The form of this error, which is the |
| // difference between a constant and an expression, is a common pattern in least |
| // squares problems. For example, the value x'y might be the model expectation |
| // for a series of measurements, where there is an instance of the cost function |
| // for each measurement k. |
| // |
| // The actual cost added to the total problem is e^2, or (k - x'k)^2; however, |
| // the squaring is implicitly done by the optimization framework. |
| // |
| // To write an auto-differentiable cost function for the above model, first |
| // define the object |
| // |
| // class MyScalarCostFunction { |
| // MyScalarCostFunction(double k): k_(k) {} |
| // |
| // template <typename T> |
| // bool operator()(const T* const x , const T* const y, T* e) const { |
| // e[0] = T(k_) - x[0] * y[0] + x[1] * y[1]; |
| // return true; |
| // } |
| // |
| // private: |
| // double k_; |
| // }; |
| // |
| // Note that in the declaration of operator() the input parameters x and y come |
| // first, and are passed as const pointers to arrays of T. If there were three |
| // input parameters, then the third input parameter would come after y. The |
| // output is always the last parameter, and is also a pointer to an array. In |
| // the example above, e is a scalar, so only e[0] is set. |
| // |
| // Then given this class definition, the auto differentiated cost function for |
| // it can be constructed as follows. |
| // |
| // CostFunction* cost_function |
| // = new AutoDiffCostFunction<MyScalarCostFunction, 1, 2, 2>( |
| // new MyScalarCostFunction(1.0)); ^ ^ ^ |
| // | | | |
| // Dimension of residual ------+ | | |
| // Dimension of x ----------------+ | |
| // Dimension of y -------------------+ |
| // |
| // In this example, there is usually an instance for each measumerent of k. |
| // |
| // In the instantiation above, the template parameters following |
| // "MyScalarCostFunction", "1, 2, 2", describe the functor as computing a |
| // 1-dimensional output from two arguments, both 2-dimensional. |
| // |
| // The autodiff cost function also supports cost functions with a |
| // runtime-determined number of residuals. For example: |
| // |
| // CostFunction* cost_function |
| // = new AutoDiffCostFunction<MyScalarCostFunction, DYNAMIC, 2, 2>( |
| // new CostFunctionWithDynamicNumResiduals(1.0), ^ ^ ^ |
| // runtime_number_of_residuals); <----+ | | | |
| // | | | | |
| // | | | | |
| // Actual number of residuals ------+ | | | |
| // Indicate dynamic number of residuals ---------+ | | |
| // Dimension of x -------------------------------------+ | |
| // Dimension of y ----------------------------------------+ |
| // |
| // The framework can currently accommodate cost functions of up to 6 independent |
| // variables, and there is no limit on the dimensionality of each of them. |
| // |
| // WARNING #1: Since the functor will get instantiated with different types for |
| // T, you must to convert from other numeric types to T before mixing |
| // computations with other variables of type T. In the example above, this is |
| // seen where instead of using k_ directly, k_ is wrapped with T(k_). |
| // |
| // WARNING #2: A common beginner's error when first using autodiff cost |
| // functions is to get the sizing wrong. In particular, there is a tendency to |
| // set the template parameters to (dimension of residual, number of parameters) |
| // instead of passing a dimension parameter for *every parameter*. In the |
| // example above, that would be <MyScalarCostFunction, 1, 2>, which is missing |
| // the last '2' argument. Please be careful when setting the size parameters. |
| |
| #ifndef CERES_PUBLIC_AUTODIFF_COST_FUNCTION_H_ |
| #define CERES_PUBLIC_AUTODIFF_COST_FUNCTION_H_ |
| |
| #include <glog/logging.h> |
| #include "ceres/internal/autodiff.h" |
| #include "ceres/internal/scoped_ptr.h" |
| #include "ceres/sized_cost_function.h" |
| #include "ceres/types.h" |
| |
| namespace ceres { |
| |
| // A cost function which computes the derivative of the cost with respect to |
| // the parameters (a.k.a. the jacobian) using an autodifferentiation framework. |
| // The first template argument is the functor object, described in the header |
| // comment. The second argument is the dimension of the residual (or |
| // ceres::DYNAMIC to indicate it will be set at runtime), and subsequent |
| // arguments describe the size of the Nth parameter, one per parameter. |
| // |
| // The constructors take ownership of the cost functor. |
| // |
| // If the number of residuals (argument "M" below) is ceres::DYNAMIC, then the |
| // two-argument constructor must be used. The second constructor takes a number |
| // of residuals (in addition to the templated number of residuals). This allows |
| // for varying the number of residuals for a single autodiff cost function at |
| // runtime. |
| template <typename CostFunctor, |
| int M, // Number of residuals, or ceres::DYNAMIC. |
| int N0, // Number of parameters in block 0. |
| int N1 = 0, // Number of parameters in block 1. |
| int N2 = 0, // Number of parameters in block 2. |
| int N3 = 0, // Number of parameters in block 3. |
| int N4 = 0, // Number of parameters in block 4. |
| int N5 = 0, // Number of parameters in block 5. |
| int N6 = 0, // Number of parameters in block 6. |
| int N7 = 0, // Number of parameters in block 7. |
| int N8 = 0, // Number of parameters in block 8. |
| int N9 = 0> // Number of parameters in block 9. |
| class AutoDiffCostFunction : |
| public SizedCostFunction<M, N0, N1, N2, N3, N4, N5, N6, N7, N8, N9> { |
| public: |
| // Takes ownership of functor. Uses the template-provided value for the |
| // number of residuals ("M"). |
| explicit AutoDiffCostFunction(CostFunctor* functor) |
| : functor_(functor) { |
| CHECK_NE(M, DYNAMIC) << "Can't run the fixed-size constructor if the " |
| << "number of residuals is set to ceres::DYNAMIC."; |
| } |
| |
| // Takes ownership of functor. Ignores the template-provided number of |
| // residuals ("M") in favor of the "num_residuals" argument provided. |
| // |
| // This allows for having autodiff cost functions which return varying |
| // numbers of residuals at runtime. |
| AutoDiffCostFunction(CostFunctor* functor, int num_residuals) |
| : functor_(functor) { |
| CHECK_EQ(M, DYNAMIC) << "Can't run the dynamic-size constructor if the " |
| << "number of residuals is not ceres::DYNAMIC."; |
| SizedCostFunction<M, N0, N1, N2, N3, N4, N5, N6, N7, N8, N9> |
| ::set_num_residuals(num_residuals); |
| } |
| |
| virtual ~AutoDiffCostFunction() {} |
| |
| // Implementation details follow; clients of the autodiff cost function should |
| // not have to examine below here. |
| // |
| // To handle varardic cost functions, some template magic is needed. It's |
| // mostly hidden inside autodiff.h. |
| virtual bool Evaluate(double const* const* parameters, |
| double* residuals, |
| double** jacobians) const { |
| if (!jacobians) { |
| return internal::VariadicEvaluate< |
| CostFunctor, double, N0, N1, N2, N3, N4, N5, N6, N7, N8, N9> |
| ::Call(*functor_, parameters, residuals); |
| } |
| return internal::AutoDiff<CostFunctor, double, |
| N0, N1, N2, N3, N4, N5, N6, N7, N8, N9>::Differentiate( |
| *functor_, |
| parameters, |
| SizedCostFunction<M, N0, N1, N2, N3, N4, N5, N6, N7, N8, N9> |
| ::num_residuals(), |
| residuals, |
| jacobians); |
| } |
| |
| private: |
| internal::scoped_ptr<CostFunctor> functor_; |
| }; |
| |
| } // namespace ceres |
| |
| #endif // CERES_PUBLIC_AUTODIFF_COST_FUNCTION_H_ |
