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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2015 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
// 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)
//
// Create 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. Please see cost_function.h for details on how the return
// value maybe used to impose simple constraints on the parameter
// block.
//
// 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 MyScalarCostFunctor {
// MyScalarCostFunctor(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<MyScalarCostFunctor, 1, 2, 2>(
// new MyScalarCostFunctor(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
// "MyScalarCostFunctor", "1, 2, 2", describe the functor as computing a
// 1-dimensional output from two arguments, both 2-dimensional.
//
// AutoDiffCostFunction also supports cost functions with a
// runtime-determined number of residuals. For example:
//
// CostFunction* cost_function
// = new AutoDiffCostFunction<MyScalarCostFunctor, DYNAMIC, 2, 2>(
// new CostFunctorWithDynamicNumResiduals(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 10
// 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 <MyScalarCostFunctor, 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 <memory>
#include "ceres/internal/autodiff.h"
#include "ceres/sized_cost_function.h"
#include "ceres/types.h"
#include "glog/logging.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 kNumResiduals 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 kNumResiduals, // 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<kNumResiduals,
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 ("kNumResiduals").
explicit AutoDiffCostFunction(CostFunctor* functor)
: functor_(functor) {
CHECK_NE(kNumResiduals, 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
// kNumResiduals 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(kNumResiduals, DYNAMIC)
<< "Can't run the dynamic-size constructor if the "
<< "number of residuals is not ceres::DYNAMIC.";
SizedCostFunction<kNumResiduals,
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 variadic 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<kNumResiduals,
N0, N1, N2, N3, N4,
N5, N6, N7, N8, N9>::num_residuals(),
residuals,
jacobians);
}
private:
std::unique_ptr<CostFunctor> functor_;
};
} // namespace ceres
#endif // CERES_PUBLIC_AUTODIFF_COST_FUNCTION_H_