include/ceres/numeric_diff_cost_function.h - ceres-solver - Git at Google


            
            // 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: keir@google.com (Keir Mierle)

            
            //         sameeragarwal@google.com (Sameer Agarwal)

            
            //

            
            // Create CostFunctions as needed by the least squares framework with jacobians

            
            // computed via numeric (a.k.a. finite) differentiation. For more details see

            
            // http://en.wikipedia.org/wiki/Numerical_differentiation.

            
            //

            
            // To get an numerically differentiated cost function, you must define

            
            // a class with a operator() (a functor) that computes the residuals.

            
            //

            
            // 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 numerically-differentiable cost function for the above model, first

            
            // define the object

            
            //

            
            //   class MyScalarCostFunctor {

            
            //     MyScalarCostFunctor(double k): k_(k) {}

            
            //

            
            //     bool operator()(const double* const x,

            
            //                     const double* const y,

            
            //                     double* residuals) const {

            
            //       residuals[0] = 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

            
            // doubles. 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,

            
            // the residual is a scalar, so only residuals[0] is set.

            
            //

            
            // Then given this class definition, the numerically differentiated

            
            // cost function with central differences used for computing the

            
            // derivative can be constructed as follows.

            
            //

            
            //   CostFunction* cost_function

            
            //       = new NumericDiffCostFunction<MyScalarCostFunctor, CENTRAL, 1, 2, 2>(

            
            //           new MyScalarCostFunctor(1.0));                    ^     ^  ^  ^

            
            //                                                             |     |  |  |

            
            //                                 Finite Differencing Scheme -+     |  |  |

            
            //                                 Dimension of residual ------------+  |  |

            
            //                                 Dimension of x ----------------------+  |

            
            //                                 Dimension of y -------------------------+

            
            //

            
            // In this example, there is usually an instance for each measurement 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.

            
            //

            
            // NumericDiffCostFunction also supports cost functions with a

            
            // runtime-determined number of residuals. For example:

            
            //

            
            //   CostFunction* cost_function

            
            //       = new NumericDiffCostFunction<MyScalarCostFunctor, CENTRAL, DYNAMIC, 2, 2>(

            
            //           new CostFunctorWithDynamicNumResiduals(1.0),               ^     ^  ^

            
            //           TAKE_OWNERSHIP,                                            |     |  |

            
            //           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.

            
            //

            
            // The central difference method is considerably more accurate at the cost of

            
            // twice as many function evaluations than forward difference. Consider using

            
            // central differences begin with, and only after that works, trying forward

            
            // difference to improve performance.

            
            //

            
            // WARNING #1: A common beginner's error when first using

            
            // NumericDiffCostFunction 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.

            
            //

            
            ////////////////////////////////////////////////////////////////////////////

            
            ////////////////////////////////////////////////////////////////////////////

            
            //

            
            // ALTERNATE INTERFACE

            
            //

            
            // For a variety of reasons, including compatibility with legacy code,

            
            // NumericDiffCostFunction can also take CostFunction objects as

            
            // input. The following describes how.

            
            //

            
            // To get a numerically differentiated cost function, define a

            
            // subclass of CostFunction such that the Evaluate() function ignores

            
            // the jacobian parameter. The numeric differentiation wrapper will

            
            // fill in the jacobian parameter if necessary by repeatedly calling

            
            // the Evaluate() function with small changes to the appropriate

            
            // parameters, and computing the slope. For performance, the numeric

            
            // differentiation wrapper class is templated on the concrete cost

            
            // function, even though it could be implemented only in terms of the

            
            // virtual CostFunction interface.

            
            //

            
            // The numerically differentiated version of a cost function for a cost function

            
            // can be constructed as follows:

            
            //

            
            //   CostFunction* cost_function

            
            //       = new NumericDiffCostFunction<MyCostFunction, CENTRAL, 1, 4, 8>(

            
            //           new MyCostFunction(...), TAKE_OWNERSHIP);

            
            //

            
            // where MyCostFunction has 1 residual and 2 parameter blocks with sizes 4 and 8

            
            // respectively. Look at the tests for a more detailed example.

            
            //

            
            // TODO(keir): Characterize accuracy; mention pitfalls; provide alternatives.


            #ifndef CERES_PUBLIC_NUMERIC_DIFF_COST_FUNCTION_H_

            
            #define CERES_PUBLIC_NUMERIC_DIFF_COST_FUNCTION_H_


            #include "Eigen/Dense"

            
            #include "ceres/cost_function.h"

            
            #include "ceres/internal/numeric_diff.h"

            
            #include "ceres/internal/scoped_ptr.h"

            
            #include "ceres/numeric_diff_options.h"

            
            #include "ceres/sized_cost_function.h"

            
            #include "ceres/types.h"

            
            #include "glog/logging.h"


            namespace ceres {


            template <typename CostFunctor,

            
                      NumericDiffMethodType method = CENTRAL,

            
                      int kNumResiduals = 0,  // Number of residuals, or ceres::DYNAMIC

            
                      int N0 = 0,   // 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 NumericDiffCostFunction

            
                : public SizedCostFunction<kNumResiduals,

            
                                           N0, N1, N2, N3, N4,

            
                                           N5, N6, N7, N8, N9> {

            
             public:

            
              NumericDiffCostFunction(

            
                  CostFunctor* functor,

            
                  Ownership ownership = TAKE_OWNERSHIP,

            
                  int num_residuals = kNumResiduals,

            
                  const NumericDiffOptions& options = NumericDiffOptions())

            
                  : functor_(functor),

            
                    ownership_(ownership),

            
                    options_(options) {

            
                if (kNumResiduals == DYNAMIC) {

            
                  SizedCostFunction<kNumResiduals,

            
                                    N0, N1, N2, N3, N4,

            
                                    N5, N6, N7, N8, N9>

            
                      ::set_num_residuals(num_residuals);

            
                }

            
              }


              ~NumericDiffCostFunction() {

            
                if (ownership_ != TAKE_OWNERSHIP) {

            
                  functor_.release();

            
                }

            
              }


              virtual bool Evaluate(double const* const* parameters,

            
                                    double* residuals,

            
                                    double** jacobians) const {

            
                using internal::FixedArray;

            
                using internal::NumericDiff;


                const int kNumParameters = N0 + N1 + N2 + N3 + N4 + N5 + N6 + N7 + N8 + N9;

            
                const int kNumParameterBlocks =

            
                    (N0 > 0) + (N1 > 0) + (N2 > 0) + (N3 > 0) + (N4 > 0) +

            
                    (N5 > 0) + (N6 > 0) + (N7 > 0) + (N8 > 0) + (N9 > 0);


                // Get the function value (residuals) at the the point to evaluate.

            
                if (!internal::EvaluateImpl<CostFunctor,

            
                                            N0, N1, N2, N3, N4, N5, N6, N7, N8, N9>(

            
                                                functor_.get(),

            
                                                parameters,

            
                                                residuals,

            
                                                functor_.get())) {

            
                  return false;

            
                }


                if (jacobians == NULL) {

            
                  return true;

            
                }


                // Create a copy of the parameters which will get mutated.

            
                FixedArray<double> parameters_copy(kNumParameters);

            
                FixedArray<double*> parameters_reference_copy(kNumParameterBlocks);


                parameters_reference_copy[0] = parameters_copy.get();

            
                if (N1) parameters_reference_copy[1] = parameters_reference_copy[0] + N0;

            
                if (N2) parameters_reference_copy[2] = parameters_reference_copy[1] + N1;

            
                if (N3) parameters_reference_copy[3] = parameters_reference_copy[2] + N2;

            
                if (N4) parameters_reference_copy[4] = parameters_reference_copy[3] + N3;

            
                if (N5) parameters_reference_copy[5] = parameters_reference_copy[4] + N4;

            
                if (N6) parameters_reference_copy[6] = parameters_reference_copy[5] + N5;

            
                if (N7) parameters_reference_copy[7] = parameters_reference_copy[6] + N6;

            
                if (N8) parameters_reference_copy[8] = parameters_reference_copy[7] + N7;

            
                if (N9) parameters_reference_copy[9] = parameters_reference_copy[8] + N8;


            #define CERES_COPY_PARAMETER_BLOCK(block)                               \

            
              if (N ## block) memcpy(parameters_reference_copy[block],              \

            
                                     parameters[block],                             \

            
                                     sizeof(double) * N ## block);  // NOLINT


                CERES_COPY_PARAMETER_BLOCK(0);

            
                CERES_COPY_PARAMETER_BLOCK(1);

            
                CERES_COPY_PARAMETER_BLOCK(2);

            
                CERES_COPY_PARAMETER_BLOCK(3);

            
                CERES_COPY_PARAMETER_BLOCK(4);

            
                CERES_COPY_PARAMETER_BLOCK(5);

            
                CERES_COPY_PARAMETER_BLOCK(6);

            
                CERES_COPY_PARAMETER_BLOCK(7);

            
                CERES_COPY_PARAMETER_BLOCK(8);

            
                CERES_COPY_PARAMETER_BLOCK(9);


            #undef CERES_COPY_PARAMETER_BLOCK


            #define CERES_EVALUATE_JACOBIAN_FOR_BLOCK(block)                        \

            
                if (N ## block && jacobians[block] != NULL) {                       \

            
                  if (!NumericDiff<CostFunctor,                                     \

            
                                   method,                                          \

            
                                   kNumResiduals,                                   \

            
                                   N0, N1, N2, N3, N4, N5, N6, N7, N8, N9,          \

            
                                   block,                                           \

            
                                   N ## block >::EvaluateJacobianForParameterBlock( \

            
                                       functor_.get(),                              \

            
                                       residuals,                                   \

            
                                       options_,                                    \

            
                                      SizedCostFunction<kNumResiduals,              \

            
                                       N0, N1, N2, N3, N4,                          \

            
                                       N5, N6, N7, N8, N9>::num_residuals(),        \

            
                                       block,                                       \

            
                                       N ## block,                                  \

            
                                       parameters_reference_copy.get(),             \

            
                                       jacobians[block])) {                         \

            
                    return false;                                                   \

            
                  }                                                                 \

            
                }


                CERES_EVALUATE_JACOBIAN_FOR_BLOCK(0);

            
                CERES_EVALUATE_JACOBIAN_FOR_BLOCK(1);

            
                CERES_EVALUATE_JACOBIAN_FOR_BLOCK(2);

            
                CERES_EVALUATE_JACOBIAN_FOR_BLOCK(3);

            
                CERES_EVALUATE_JACOBIAN_FOR_BLOCK(4);

            
                CERES_EVALUATE_JACOBIAN_FOR_BLOCK(5);

            
                CERES_EVALUATE_JACOBIAN_FOR_BLOCK(6);

            
                CERES_EVALUATE_JACOBIAN_FOR_BLOCK(7);

            
                CERES_EVALUATE_JACOBIAN_FOR_BLOCK(8);

            
                CERES_EVALUATE_JACOBIAN_FOR_BLOCK(9);


            #undef CERES_EVALUATE_JACOBIAN_FOR_BLOCK


                return true;

            
              }


             private:

            
              internal::scoped_ptr<CostFunctor> functor_;

            
              Ownership ownership_;

            
              NumericDiffOptions options_;

            
            };


            }  // namespace ceres


            #endif  // CERES_PUBLIC_NUMERIC_DIFF_COST_FUNCTION_H_
	// 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: keir@google.com (Keir Mierle)
	// sameeragarwal@google.com (Sameer Agarwal)
	//
	// Create CostFunctions as needed by the least squares framework with jacobians
	// computed via numeric (a.k.a. finite) differentiation. For more details see
	// http://en.wikipedia.org/wiki/Numerical_differentiation.
	//
	// To get an numerically differentiated cost function, you must define
	// a class with a operator() (a functor) that computes the residuals.
	//
	// 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 numerically-differentiable cost function for the above model, first
	// define the object
	//
	// class MyScalarCostFunctor {
	// MyScalarCostFunctor(double k): k_(k) {}
	//
	// bool operator()(const double* const x,
	// const double* const y,
	// double* residuals) const {
	// residuals[0] = 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
	// doubles. 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,
	// the residual is a scalar, so only residuals[0] is set.
	//
	// Then given this class definition, the numerically differentiated
	// cost function with central differences used for computing the
	// derivative can be constructed as follows.
	//
	// CostFunction* cost_function
	// = new NumericDiffCostFunction<MyScalarCostFunctor, CENTRAL, 1, 2, 2>(
	// new MyScalarCostFunctor(1.0)); ^ ^ ^ ^
	// \| \| \| \|
	// Finite Differencing Scheme -+ \| \| \|
	// Dimension of residual ------------+ \| \|
	// Dimension of x ----------------------+ \|
	// Dimension of y -------------------------+
	//
	// In this example, there is usually an instance for each measurement 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.
	//
	// NumericDiffCostFunction also supports cost functions with a
	// runtime-determined number of residuals. For example:
	//
	// CostFunction* cost_function
	// = new NumericDiffCostFunction<MyScalarCostFunctor, CENTRAL, DYNAMIC, 2, 2>(
	// new CostFunctorWithDynamicNumResiduals(1.0), ^ ^ ^
	// TAKE_OWNERSHIP, \| \| \|
	// 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.
	//
	// The central difference method is considerably more accurate at the cost of
	// twice as many function evaluations than forward difference. Consider using
	// central differences begin with, and only after that works, trying forward
	// difference to improve performance.
	//
	// WARNING #1: A common beginner's error when first using
	// NumericDiffCostFunction 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.
	//
	////////////////////////////////////////////////////////////////////////////
	////////////////////////////////////////////////////////////////////////////
	//
	// ALTERNATE INTERFACE
	//
	// For a variety of reasons, including compatibility with legacy code,
	// NumericDiffCostFunction can also take CostFunction objects as
	// input. The following describes how.
	//
	// To get a numerically differentiated cost function, define a
	// subclass of CostFunction such that the Evaluate() function ignores
	// the jacobian parameter. The numeric differentiation wrapper will
	// fill in the jacobian parameter if necessary by repeatedly calling
	// the Evaluate() function with small changes to the appropriate
	// parameters, and computing the slope. For performance, the numeric
	// differentiation wrapper class is templated on the concrete cost
	// function, even though it could be implemented only in terms of the
	// virtual CostFunction interface.
	//
	// The numerically differentiated version of a cost function for a cost function
	// can be constructed as follows:
	//
	// CostFunction* cost_function
	// = new NumericDiffCostFunction<MyCostFunction, CENTRAL, 1, 4, 8>(
	// new MyCostFunction(...), TAKE_OWNERSHIP);
	//
	// where MyCostFunction has 1 residual and 2 parameter blocks with sizes 4 and 8
	// respectively. Look at the tests for a more detailed example.
	//
	// TODO(keir): Characterize accuracy; mention pitfalls; provide alternatives.

	#ifndef CERES_PUBLIC_NUMERIC_DIFF_COST_FUNCTION_H_
	#define CERES_PUBLIC_NUMERIC_DIFF_COST_FUNCTION_H_

	#include "Eigen/Dense"
	#include "ceres/cost_function.h"
	#include "ceres/internal/numeric_diff.h"
	#include "ceres/internal/scoped_ptr.h"
	#include "ceres/numeric_diff_options.h"
	#include "ceres/sized_cost_function.h"
	#include "ceres/types.h"
	#include "glog/logging.h"

	namespace ceres {

	template <typename CostFunctor,
	NumericDiffMethodType method = CENTRAL,
	int kNumResiduals = 0, // Number of residuals, or ceres::DYNAMIC
	int N0 = 0, // 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 NumericDiffCostFunction
	: public SizedCostFunction<kNumResiduals,
	N0, N1, N2, N3, N4,
	N5, N6, N7, N8, N9> {
	public:
	NumericDiffCostFunction(
	CostFunctor* functor,
	Ownership ownership = TAKE_OWNERSHIP,
	int num_residuals = kNumResiduals,
	const NumericDiffOptions& options = NumericDiffOptions())
	: functor_(functor),
	ownership_(ownership),
	options_(options) {
	if (kNumResiduals == DYNAMIC) {
	SizedCostFunction<kNumResiduals,
	N0, N1, N2, N3, N4,
	N5, N6, N7, N8, N9>
	::set_num_residuals(num_residuals);
	}
	}

	~NumericDiffCostFunction() {
	if (ownership_ != TAKE_OWNERSHIP) {
	functor_.release();
	}
	}

	virtual bool Evaluate(double const* const* parameters,
	double* residuals,
	double** jacobians) const {
	using internal::FixedArray;
	using internal::NumericDiff;

	const int kNumParameters = N0 + N1 + N2 + N3 + N4 + N5 + N6 + N7 + N8 + N9;
	const int kNumParameterBlocks =
	(N0 > 0) + (N1 > 0) + (N2 > 0) + (N3 > 0) + (N4 > 0) +
	(N5 > 0) + (N6 > 0) + (N7 > 0) + (N8 > 0) + (N9 > 0);

	// Get the function value (residuals) at the the point to evaluate.
	if (!internal::EvaluateImpl<CostFunctor,
	N0, N1, N2, N3, N4, N5, N6, N7, N8, N9>(
	functor_.get(),
	parameters,
	residuals,
	functor_.get())) {
	return false;
	}

	if (jacobians == NULL) {
	return true;
	}

	// Create a copy of the parameters which will get mutated.
	FixedArray<double> parameters_copy(kNumParameters);
	FixedArray<double*> parameters_reference_copy(kNumParameterBlocks);

	parameters_reference_copy[0] = parameters_copy.get();
	if (N1) parameters_reference_copy[1] = parameters_reference_copy[0] + N0;
	if (N2) parameters_reference_copy[2] = parameters_reference_copy[1] + N1;
	if (N3) parameters_reference_copy[3] = parameters_reference_copy[2] + N2;
	if (N4) parameters_reference_copy[4] = parameters_reference_copy[3] + N3;
	if (N5) parameters_reference_copy[5] = parameters_reference_copy[4] + N4;
	if (N6) parameters_reference_copy[6] = parameters_reference_copy[5] + N5;
	if (N7) parameters_reference_copy[7] = parameters_reference_copy[6] + N6;
	if (N8) parameters_reference_copy[8] = parameters_reference_copy[7] + N7;
	if (N9) parameters_reference_copy[9] = parameters_reference_copy[8] + N8;

	#define CERES_COPY_PARAMETER_BLOCK(block) \
	if (N ## block) memcpy(parameters_reference_copy[block], \
	parameters[block], \
	sizeof(double) * N ## block); // NOLINT

	CERES_COPY_PARAMETER_BLOCK(0);
	CERES_COPY_PARAMETER_BLOCK(1);
	CERES_COPY_PARAMETER_BLOCK(2);
	CERES_COPY_PARAMETER_BLOCK(3);
	CERES_COPY_PARAMETER_BLOCK(4);
	CERES_COPY_PARAMETER_BLOCK(5);
	CERES_COPY_PARAMETER_BLOCK(6);
	CERES_COPY_PARAMETER_BLOCK(7);
	CERES_COPY_PARAMETER_BLOCK(8);
	CERES_COPY_PARAMETER_BLOCK(9);

	#undef CERES_COPY_PARAMETER_BLOCK

	#define CERES_EVALUATE_JACOBIAN_FOR_BLOCK(block) \
	if (N ## block && jacobians[block] != NULL) { \
	if (!NumericDiff<CostFunctor, \
	method, \
	kNumResiduals, \
	N0, N1, N2, N3, N4, N5, N6, N7, N8, N9, \
	block, \
	N ## block >::EvaluateJacobianForParameterBlock( \
	functor_.get(), \
	residuals, \
	options_, \
	SizedCostFunction<kNumResiduals, \
	N0, N1, N2, N3, N4, \
	N5, N6, N7, N8, N9>::num_residuals(), \
	block, \
	N ## block, \
	parameters_reference_copy.get(), \
	jacobians[block])) { \
	return false; \
	} \
	}

	CERES_EVALUATE_JACOBIAN_FOR_BLOCK(0);
	CERES_EVALUATE_JACOBIAN_FOR_BLOCK(1);
	CERES_EVALUATE_JACOBIAN_FOR_BLOCK(2);
	CERES_EVALUATE_JACOBIAN_FOR_BLOCK(3);
	CERES_EVALUATE_JACOBIAN_FOR_BLOCK(4);
	CERES_EVALUATE_JACOBIAN_FOR_BLOCK(5);
	CERES_EVALUATE_JACOBIAN_FOR_BLOCK(6);
	CERES_EVALUATE_JACOBIAN_FOR_BLOCK(7);
	CERES_EVALUATE_JACOBIAN_FOR_BLOCK(8);
	CERES_EVALUATE_JACOBIAN_FOR_BLOCK(9);

	#undef CERES_EVALUATE_JACOBIAN_FOR_BLOCK

	return true;
	}

	private:
	internal::scoped_ptr<CostFunctor> functor_;
	Ownership ownership_;
	NumericDiffOptions options_;
	};

	} // namespace ceres

	#endif // CERES_PUBLIC_NUMERIC_DIFF_COST_FUNCTION_H_