include/ceres/problem.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: sameeragarwal@google.com (Sameer Agarwal)
 //         keir@google.com (Keir Mierle)
 //
 // The Problem object is used to build and hold least squares problems.

 #ifndef CERES_PUBLIC_PROBLEM_H_
 #define CERES_PUBLIC_PROBLEM_H_

 #include <cstddef>
 #include <map>
 #include <memory>
 #include <set>
 #include <vector>

 #include "ceres/context.h"
 #include "ceres/internal/disable_warnings.h"
 #include "ceres/internal/port.h"
 #include "ceres/types.h"
 #include "glog/logging.h"

 namespace ceres {

 class CostFunction;
 class LossFunction;
 class LocalParameterization;
 class Solver;
 struct CRSMatrix;

 namespace internal {
 class Preprocessor;
 class ProblemImpl;
 class ParameterBlock;
 class ResidualBlock;
 }  // namespace internal

 // A ResidualBlockId is an opaque handle clients can use to remove residual
 // blocks from a Problem after adding them.
 typedef internal::ResidualBlock* ResidualBlockId;

 // A class to represent non-linear least squares problems. Such
 // problems have a cost function that is a sum of error terms (known
 // as "residuals"), where each residual is a function of some subset
 // of the parameters. The cost function takes the form
 //
 //    N    1
 //   SUM  --- loss( || r_i1, r_i2,..., r_ik ||^2  ),
 //   i=1   2
 //
 // where
 //
 //   r_ij     is residual number i, component j; the residual is a
 //            function of some subset of the parameters x1...xk. For
 //            example, in a structure from motion problem a residual
 //            might be the difference between a measured point in an
 //            image and the reprojected position for the matching
 //            camera, point pair. The residual would have two
 //            components, error in x and error in y.
 //
 //   loss(y)  is the loss function; for example, squared error or
 //            Huber L1 loss. If loss(y) = y, then the cost function is
 //            non-robustified least squares.
 //
 // This class is specifically designed to address the important subset
 // of "sparse" least squares problems, where each component of the
 // residual depends only on a small number number of parameters, even
 // though the total number of residuals and parameters may be very
 // large. This property affords tremendous gains in scale, allowing
 // efficient solving of large problems that are otherwise
 // inaccessible.
 //
 // The canonical example of a sparse least squares problem is
 // "structure-from-motion" (SFM), where the parameters are points and
 // cameras, and residuals are reprojection errors. Typically a single
 // residual will depend only on 9 parameters (3 for the point, 6 for
 // the camera).
 //
 // To create a least squares problem, use the AddResidualBlock() and
 // AddParameterBlock() methods, documented below. Here is an example least
 // squares problem containing 3 parameter blocks of sizes 3, 4 and 5
 // respectively and two residual terms of size 2 and 6:
 //
 //   double x1[] = { 1.0, 2.0, 3.0 };
 //   double x2[] = { 1.0, 2.0, 3.0, 5.0 };
 //   double x3[] = { 1.0, 2.0, 3.0, 6.0, 7.0 };
 //
 //   Problem problem;
 //
 //   problem.AddResidualBlock(new MyUnaryCostFunction(...), x1);
 //   problem.AddResidualBlock(new MyBinaryCostFunction(...), x2, x3);
 //
 // Please see cost_function.h for details of the CostFunction object.
 class CERES_EXPORT Problem {
  public:
   struct CERES_EXPORT Options {
     // These flags control whether the Problem object owns the cost
     // functions, loss functions, and parameterizations passed into
     // the Problem. If set to TAKE_OWNERSHIP, then the problem object
     // will delete the corresponding cost or loss functions on
     // destruction. The destructor is careful to delete the pointers
     // only once, since sharing cost/loss/parameterizations is
     // allowed.
     Ownership cost_function_ownership = TAKE_OWNERSHIP;
     Ownership loss_function_ownership = TAKE_OWNERSHIP;
     Ownership local_parameterization_ownership = TAKE_OWNERSHIP;

     // If true, trades memory for faster RemoveResidualBlock() and
     // RemoveParameterBlock() operations.
     //
     // By default, RemoveParameterBlock() and RemoveResidualBlock() take time
     // proportional to the size of the entire problem.  If you only ever remove
     // parameters or residuals from the problem occassionally, this might be
     // acceptable.  However, if you have memory to spare, enable this option to
     // make RemoveParameterBlock() take time proportional to the number of
     // residual blocks that depend on it, and RemoveResidualBlock() take (on
     // average) constant time.
     //
     // The increase in memory usage is twofold: an additonal hash set per
     // parameter block containing all the residuals that depend on the parameter
     // block; and a hash set in the problem containing all residuals.
     bool enable_fast_removal = false;

     // By default, Ceres performs a variety of safety checks when constructing
     // the problem. There is a small but measurable performance penalty to
     // these checks, typically around 5% of construction time. If you are sure
     // your problem construction is correct, and 5% of the problem construction
     // time is truly an overhead you want to avoid, then you can set
     // disable_all_safety_checks to true.
     //
     // WARNING: Do not set this to true, unless you are absolutely sure of what
     // you are doing.
     bool disable_all_safety_checks = false;

     // A Ceres global context to use for solving this problem. This may help to
     // reduce computation time as Ceres can reuse expensive objects to create.
     // The context object can be NULL, in which case Ceres may create one.
     //
     // Ceres does NOT take ownership of the pointer.
     Context* context = nullptr;
   };

   // The default constructor is equivalent to the
   // invocation Problem(Problem::Options()).
   Problem();
   explicit Problem(const Options& options);
   Problem(const Problem&) = delete;
   void operator=(const Problem&) = delete;

   ~Problem();

   // Add a residual block to the overall cost function. The cost
   // function carries with it information about the sizes of the
   // parameter blocks it expects. The function checks that these match
   // the sizes of the parameter blocks listed in parameter_blocks. The
   // program aborts if a mismatch is detected. loss_function can be
   // NULL, in which case the cost of the term is just the squared norm
   // of the residuals.
   //
   // The user has the option of explicitly adding the parameter blocks
   // using AddParameterBlock. This causes additional correctness
   // checking; however, AddResidualBlock implicitly adds the parameter
   // blocks if they are not present, so calling AddParameterBlock
   // explicitly is not required.
   //
   // The Problem object by default takes ownership of the
   // cost_function and loss_function pointers. These objects remain
   // live for the life of the Problem object. If the user wishes to
   // keep control over the destruction of these objects, then they can
   // do this by setting the corresponding enums in the Options struct.
   //
   // Note: Even though the Problem takes ownership of cost_function
   // and loss_function, it does not preclude the user from re-using
   // them in another residual block. The destructor takes care to call
   // delete on each cost_function or loss_function pointer only once,
   // regardless of how many residual blocks refer to them.
   //
   // Example usage:
   //
   //   double x1[] = {1.0, 2.0, 3.0};
   //   double x2[] = {1.0, 2.0, 5.0, 6.0};
   //   double x3[] = {3.0, 6.0, 2.0, 5.0, 1.0};
   //
   //   Problem problem;
   //
   //   problem.AddResidualBlock(new MyUnaryCostFunction(...), NULL, x1);
   //   problem.AddResidualBlock(new MyBinaryCostFunction(...), NULL, x2, x1);
   //
   ResidualBlockId AddResidualBlock(
       CostFunction* cost_function,
       LossFunction* loss_function,
       const std::vector<double*>& parameter_blocks);

   // Convenience methods for adding residuals with a small number of
   // parameters. This is the common case. Instead of specifying the
   // parameter block arguments as a vector, list them as pointers.
   ResidualBlockId AddResidualBlock(CostFunction* cost_function,
                                    LossFunction* loss_function,
                                    double* x0);
   ResidualBlockId AddResidualBlock(CostFunction* cost_function,
                                    LossFunction* loss_function,
                                    double* x0, double* x1);
   ResidualBlockId AddResidualBlock(CostFunction* cost_function,
                                    LossFunction* loss_function,
                                    double* x0, double* x1, double* x2);
   ResidualBlockId AddResidualBlock(CostFunction* cost_function,
                                    LossFunction* loss_function,
                                    double* x0, double* x1, double* x2,
                                    double* x3);
   ResidualBlockId AddResidualBlock(CostFunction* cost_function,
                                    LossFunction* loss_function,
                                    double* x0, double* x1, double* x2,
                                    double* x3, double* x4);
   ResidualBlockId AddResidualBlock(CostFunction* cost_function,
                                    LossFunction* loss_function,
                                    double* x0, double* x1, double* x2,
                                    double* x3, double* x4, double* x5);
   ResidualBlockId AddResidualBlock(CostFunction* cost_function,
                                    LossFunction* loss_function,
                                    double* x0, double* x1, double* x2,
                                    double* x3, double* x4, double* x5,
                                    double* x6);
   ResidualBlockId AddResidualBlock(CostFunction* cost_function,
                                    LossFunction* loss_function,
                                    double* x0, double* x1, double* x2,
                                    double* x3, double* x4, double* x5,
                                    double* x6, double* x7);
   ResidualBlockId AddResidualBlock(CostFunction* cost_function,
                                    LossFunction* loss_function,
                                    double* x0, double* x1, double* x2,
                                    double* x3, double* x4, double* x5,
                                    double* x6, double* x7, double* x8);
   ResidualBlockId AddResidualBlock(CostFunction* cost_function,
                                    LossFunction* loss_function,
                                    double* x0, double* x1, double* x2,
                                    double* x3, double* x4, double* x5,
                                    double* x6, double* x7, double* x8,
                                    double* x9);

   // Add a parameter block with appropriate size to the problem.
   // Repeated calls with the same arguments are ignored. Repeated
   // calls with the same double pointer but a different size results
   // in undefined behaviour.
   void AddParameterBlock(double* values, int size);

   // Add a parameter block with appropriate size and parameterization
   // to the problem. Repeated calls with the same arguments are
   // ignored. Repeated calls with the same double pointer but a
   // different size results in undefined behaviour.
   void AddParameterBlock(double* values,
                          int size,
                          LocalParameterization* local_parameterization);

   // Remove a parameter block from the problem. The parameterization of the
   // parameter block, if it exists, will persist until the deletion of the
   // problem (similar to cost/loss functions in residual block removal). Any
   // residual blocks that depend on the parameter are also removed, as
   // described above in RemoveResidualBlock().
   //
   // If Problem::Options::enable_fast_removal is true, then the
   // removal is fast (almost constant time). Otherwise, removing a parameter
   // block will incur a scan of the entire Problem object.
   //
   // WARNING: Removing a residual or parameter block will destroy the implicit
   // ordering, rendering the jacobian or residuals returned from the solver
   // uninterpretable. If you depend on the evaluated jacobian, do not use
   // remove! This may change in a future release.
   void RemoveParameterBlock(double* values);

   // Remove a residual block from the problem. Any parameters that the residual
   // block depends on are not removed. The cost and loss functions for the
   // residual block will not get deleted immediately; won't happen until the
   // problem itself is deleted.
   //
   // WARNING: Removing a residual or parameter block will destroy the implicit
   // ordering, rendering the jacobian or residuals returned from the solver
   // uninterpretable. If you depend on the evaluated jacobian, do not use
   // remove! This may change in a future release.
   void RemoveResidualBlock(ResidualBlockId residual_block);

   // Hold the indicated parameter block constant during optimization.
   void SetParameterBlockConstant(double* values);

   // Allow the indicated parameter block to vary during optimization.
   void SetParameterBlockVariable(double* values);

   // Returns true if a parameter block is set constant, and false otherwise.
   bool IsParameterBlockConstant(double* values) const;

   // Set the local parameterization for one of the parameter blocks.
   // The local_parameterization is owned by the Problem by default. It
   // is acceptable to set the same parameterization for multiple
   // parameters; the destructor is careful to delete local
   // parameterizations only once. The local parameterization can only
   // be set once per parameter, and cannot be changed once set.
   void SetParameterization(double* values,
                            LocalParameterization* local_parameterization);

   // Get the local parameterization object associated with this
   // parameter block. If there is no parameterization object
   // associated then NULL is returned.
   const LocalParameterization* GetParameterization(double* values) const;

   // Set the lower/upper bound for the parameter with position "index".
   void SetParameterLowerBound(double* values, int index, double lower_bound);
   void SetParameterUpperBound(double* values, int index, double upper_bound);

   // Number of parameter blocks in the problem. Always equals
   // parameter_blocks().size() and parameter_block_sizes().size().
   int NumParameterBlocks() const;

   // The size of the parameter vector obtained by summing over the
   // sizes of all the parameter blocks.
   int NumParameters() const;

   // Number of residual blocks in the problem. Always equals
   // residual_blocks().size().
   int NumResidualBlocks() const;

   // The size of the residual vector obtained by summing over the
   // sizes of all of the residual blocks.
   int NumResiduals() const;

   // The size of the parameter block.
   int ParameterBlockSize(const double* values) const;

   // The size of local parameterization for the parameter block. If
   // there is no local parameterization associated with this parameter
   // block, then ParameterBlockLocalSize = ParameterBlockSize.
   int ParameterBlockLocalSize(const double* values) const;

   // Is the given parameter block present in this problem or not?
   bool HasParameterBlock(const double* values) const;

   // Fills the passed parameter_blocks vector with pointers to the
   // parameter blocks currently in the problem. After this call,
   // parameter_block.size() == NumParameterBlocks.
   void GetParameterBlocks(std::vector<double*>* parameter_blocks) const;

   // Fills the passed residual_blocks vector with pointers to the
   // residual blocks currently in the problem. After this call,
   // residual_blocks.size() == NumResidualBlocks.
   void GetResidualBlocks(std::vector<ResidualBlockId>* residual_blocks) const;

   // Get all the parameter blocks that depend on the given residual block.
   void GetParameterBlocksForResidualBlock(
       const ResidualBlockId residual_block,
       std::vector<double*>* parameter_blocks) const;

   // Get the CostFunction for the given residual block.
   const CostFunction* GetCostFunctionForResidualBlock(
       const ResidualBlockId residual_block) const;

   // Get the LossFunction for the given residual block. Returns NULL
   // if no loss function is associated with this residual block.
   const LossFunction* GetLossFunctionForResidualBlock(
       const ResidualBlockId residual_block) const;

   // Get all the residual blocks that depend on the given parameter block.
   //
   // If Problem::Options::enable_fast_removal is true, then
   // getting the residual blocks is fast and depends only on the number of
   // residual blocks. Otherwise, getting the residual blocks for a parameter
   // block will incur a scan of the entire Problem object.
   void GetResidualBlocksForParameterBlock(
       const double* values,
       std::vector<ResidualBlockId>* residual_blocks) const;

   // Options struct to control Problem::Evaluate.
   struct EvaluateOptions {
     // The set of parameter blocks for which evaluation should be
     // performed. This vector determines the order that parameter
     // blocks occur in the gradient vector and in the columns of the
     // jacobian matrix. If parameter_blocks is empty, then it is
     // assumed to be equal to vector containing ALL the parameter
     // blocks.  Generally speaking the parameter blocks will occur in
     // the order in which they were added to the problem. But, this
     // may change if the user removes any parameter blocks from the
     // problem.
     //
     // NOTE: This vector should contain the same pointers as the ones
     // used to add parameter blocks to the Problem. These parameter
     // block should NOT point to new memory locations. Bad things will
     // happen otherwise.
     std::vector<double*> parameter_blocks;

     // The set of residual blocks to evaluate. This vector determines
     // the order in which the residuals occur, and how the rows of the
     // jacobian are ordered. If residual_blocks is empty, then it is
     // assumed to be equal to the vector containing ALL the residual
     // blocks. Generally speaking the residual blocks will occur in
     // the order in which they were added to the problem. But, this
     // may change if the user removes any residual blocks from the
     // problem.
     std::vector<ResidualBlockId> residual_blocks;

     // Even though the residual blocks in the problem may contain loss
     // functions, setting apply_loss_function to false will turn off
     // the application of the loss function to the output of the cost
     // function. This is of use for example if the user wishes to
     // analyse the solution quality by studying the distribution of
     // residuals before and after the solve.
     bool apply_loss_function = true;

     int num_threads = 1;
   };

   // Evaluate Problem. Any of the output pointers can be NULL. Which
   // residual blocks and parameter blocks are used is controlled by
   // the EvaluateOptions struct above.
   //
   // Note 1: The evaluation will use the values stored in the memory
   // locations pointed to by the parameter block pointers used at the
   // time of the construction of the problem. i.e.,
   //
   //   Problem problem;
   //   double x = 1;
   //   problem.AddResidualBlock(new MyCostFunction, NULL, &x);
   //
   //   double cost = 0.0;
   //   problem.Evaluate(Problem::EvaluateOptions(), &cost, NULL, NULL, NULL);
   //
   // The cost is evaluated at x = 1. If you wish to evaluate the
   // problem at x = 2, then
   //
   //    x = 2;
   //    problem.Evaluate(Problem::EvaluateOptions(), &cost, NULL, NULL, NULL);
   //
   // is the way to do so.
   //
   // Note 2: If no local parameterizations are used, then the size of
   // the gradient vector (and the number of columns in the jacobian)
   // is the sum of the sizes of all the parameter blocks. If a
   // parameter block has a local parameterization, then it contributes
   // "LocalSize" entries to the gradient vector (and the number of
   // columns in the jacobian).
   //
   // Note 3: This function cannot be called while the problem is being
   // solved, for example it cannot be called from an IterationCallback
   // at the end of an iteration during a solve.
   bool Evaluate(const EvaluateOptions& options,
                 double* cost,
                 std::vector<double>* residuals,
                 std::vector<double>* gradient,
                 CRSMatrix* jacobian);

  private:
   friend class Solver;
   friend class Covariance;
   std::unique_ptr<internal::ProblemImpl> problem_impl_;
 };

 }  // namespace ceres

 #include "ceres/internal/reenable_warnings.h"

 #endif  // CERES_PUBLIC_PROBLEM_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: sameeragarwal@google.com (Sameer Agarwal)
	// keir@google.com (Keir Mierle)
	//
	// The Problem object is used to build and hold least squares problems.

	#ifndef CERES_PUBLIC_PROBLEM_H_
	#define CERES_PUBLIC_PROBLEM_H_

	#include <cstddef>
	#include <map>
	#include <memory>
	#include <set>
	#include <vector>

	#include "ceres/context.h"
	#include "ceres/internal/disable_warnings.h"
	#include "ceres/internal/port.h"
	#include "ceres/types.h"
	#include "glog/logging.h"

	namespace ceres {

	class CostFunction;
	class LossFunction;
	class LocalParameterization;
	class Solver;
	struct CRSMatrix;

	namespace internal {
	class Preprocessor;
	class ProblemImpl;
	class ParameterBlock;
	class ResidualBlock;
	} // namespace internal

	// A ResidualBlockId is an opaque handle clients can use to remove residual
	// blocks from a Problem after adding them.
	typedef internal::ResidualBlock* ResidualBlockId;

	// A class to represent non-linear least squares problems. Such
	// problems have a cost function that is a sum of error terms (known
	// as "residuals"), where each residual is a function of some subset
	// of the parameters. The cost function takes the form
	//
	// N 1
	// SUM --- loss( \|\| r_i1, r_i2,..., r_ik \|\|^2 ),
	// i=1 2
	//
	// where
	//
	// r_ij is residual number i, component j; the residual is a
	// function of some subset of the parameters x1...xk. For
	// example, in a structure from motion problem a residual
	// might be the difference between a measured point in an
	// image and the reprojected position for the matching
	// camera, point pair. The residual would have two
	// components, error in x and error in y.
	//
	// loss(y) is the loss function; for example, squared error or
	// Huber L1 loss. If loss(y) = y, then the cost function is
	// non-robustified least squares.
	//
	// This class is specifically designed to address the important subset
	// of "sparse" least squares problems, where each component of the
	// residual depends only on a small number number of parameters, even
	// though the total number of residuals and parameters may be very
	// large. This property affords tremendous gains in scale, allowing
	// efficient solving of large problems that are otherwise
	// inaccessible.
	//
	// The canonical example of a sparse least squares problem is
	// "structure-from-motion" (SFM), where the parameters are points and
	// cameras, and residuals are reprojection errors. Typically a single
	// residual will depend only on 9 parameters (3 for the point, 6 for
	// the camera).
	//
	// To create a least squares problem, use the AddResidualBlock() and
	// AddParameterBlock() methods, documented below. Here is an example least
	// squares problem containing 3 parameter blocks of sizes 3, 4 and 5
	// respectively and two residual terms of size 2 and 6:
	//
	// double x1[] = { 1.0, 2.0, 3.0 };
	// double x2[] = { 1.0, 2.0, 3.0, 5.0 };
	// double x3[] = { 1.0, 2.0, 3.0, 6.0, 7.0 };
	//
	// Problem problem;
	//
	// problem.AddResidualBlock(new MyUnaryCostFunction(...), x1);
	// problem.AddResidualBlock(new MyBinaryCostFunction(...), x2, x3);
	//
	// Please see cost_function.h for details of the CostFunction object.
	class CERES_EXPORT Problem {
	public:
	struct CERES_EXPORT Options {
	// These flags control whether the Problem object owns the cost
	// functions, loss functions, and parameterizations passed into
	// the Problem. If set to TAKE_OWNERSHIP, then the problem object
	// will delete the corresponding cost or loss functions on
	// destruction. The destructor is careful to delete the pointers
	// only once, since sharing cost/loss/parameterizations is
	// allowed.
	Ownership cost_function_ownership = TAKE_OWNERSHIP;
	Ownership loss_function_ownership = TAKE_OWNERSHIP;
	Ownership local_parameterization_ownership = TAKE_OWNERSHIP;

	// If true, trades memory for faster RemoveResidualBlock() and
	// RemoveParameterBlock() operations.
	//
	// By default, RemoveParameterBlock() and RemoveResidualBlock() take time
	// proportional to the size of the entire problem. If you only ever remove
	// parameters or residuals from the problem occassionally, this might be
	// acceptable. However, if you have memory to spare, enable this option to
	// make RemoveParameterBlock() take time proportional to the number of
	// residual blocks that depend on it, and RemoveResidualBlock() take (on
	// average) constant time.
	//
	// The increase in memory usage is twofold: an additonal hash set per
	// parameter block containing all the residuals that depend on the parameter
	// block; and a hash set in the problem containing all residuals.
	bool enable_fast_removal = false;

	// By default, Ceres performs a variety of safety checks when constructing
	// the problem. There is a small but measurable performance penalty to
	// these checks, typically around 5% of construction time. If you are sure
	// your problem construction is correct, and 5% of the problem construction
	// time is truly an overhead you want to avoid, then you can set
	// disable_all_safety_checks to true.
	//
	// WARNING: Do not set this to true, unless you are absolutely sure of what
	// you are doing.
	bool disable_all_safety_checks = false;

	// A Ceres global context to use for solving this problem. This may help to
	// reduce computation time as Ceres can reuse expensive objects to create.
	// The context object can be NULL, in which case Ceres may create one.
	//
	// Ceres does NOT take ownership of the pointer.
	Context* context = nullptr;
	};

	// The default constructor is equivalent to the
	// invocation Problem(Problem::Options()).
	Problem();
	explicit Problem(const Options& options);
	Problem(const Problem&) = delete;
	void operator=(const Problem&) = delete;

	~Problem();

	// Add a residual block to the overall cost function. The cost
	// function carries with it information about the sizes of the
	// parameter blocks it expects. The function checks that these match
	// the sizes of the parameter blocks listed in parameter_blocks. The
	// program aborts if a mismatch is detected. loss_function can be
	// NULL, in which case the cost of the term is just the squared norm
	// of the residuals.
	//
	// The user has the option of explicitly adding the parameter blocks
	// using AddParameterBlock. This causes additional correctness
	// checking; however, AddResidualBlock implicitly adds the parameter
	// blocks if they are not present, so calling AddParameterBlock
	// explicitly is not required.
	//
	// The Problem object by default takes ownership of the
	// cost_function and loss_function pointers. These objects remain
	// live for the life of the Problem object. If the user wishes to
	// keep control over the destruction of these objects, then they can
	// do this by setting the corresponding enums in the Options struct.
	//
	// Note: Even though the Problem takes ownership of cost_function
	// and loss_function, it does not preclude the user from re-using
	// them in another residual block. The destructor takes care to call
	// delete on each cost_function or loss_function pointer only once,
	// regardless of how many residual blocks refer to them.
	//
	// Example usage:
	//
	// double x1[] = {1.0, 2.0, 3.0};
	// double x2[] = {1.0, 2.0, 5.0, 6.0};
	// double x3[] = {3.0, 6.0, 2.0, 5.0, 1.0};
	//
	// Problem problem;
	//
	// problem.AddResidualBlock(new MyUnaryCostFunction(...), NULL, x1);
	// problem.AddResidualBlock(new MyBinaryCostFunction(...), NULL, x2, x1);
	//
	ResidualBlockId AddResidualBlock(
	CostFunction* cost_function,
	LossFunction* loss_function,
	const std::vector<double*>& parameter_blocks);

	// Convenience methods for adding residuals with a small number of
	// parameters. This is the common case. Instead of specifying the
	// parameter block arguments as a vector, list them as pointers.
	ResidualBlockId AddResidualBlock(CostFunction* cost_function,
	LossFunction* loss_function,
	double* x0);
	ResidualBlockId AddResidualBlock(CostFunction* cost_function,
	LossFunction* loss_function,
	double* x0, double* x1);
	ResidualBlockId AddResidualBlock(CostFunction* cost_function,
	LossFunction* loss_function,
	double* x0, double* x1, double* x2);
	ResidualBlockId AddResidualBlock(CostFunction* cost_function,
	LossFunction* loss_function,
	double* x0, double* x1, double* x2,
	double* x3);
	ResidualBlockId AddResidualBlock(CostFunction* cost_function,
	LossFunction* loss_function,
	double* x0, double* x1, double* x2,
	double* x3, double* x4);
	ResidualBlockId AddResidualBlock(CostFunction* cost_function,
	LossFunction* loss_function,
	double* x0, double* x1, double* x2,
	double* x3, double* x4, double* x5);
	ResidualBlockId AddResidualBlock(CostFunction* cost_function,
	LossFunction* loss_function,
	double* x0, double* x1, double* x2,
	double* x3, double* x4, double* x5,
	double* x6);
	ResidualBlockId AddResidualBlock(CostFunction* cost_function,
	LossFunction* loss_function,
	double* x0, double* x1, double* x2,
	double* x3, double* x4, double* x5,
	double* x6, double* x7);
	ResidualBlockId AddResidualBlock(CostFunction* cost_function,
	LossFunction* loss_function,
	double* x0, double* x1, double* x2,
	double* x3, double* x4, double* x5,
	double* x6, double* x7, double* x8);
	ResidualBlockId AddResidualBlock(CostFunction* cost_function,
	LossFunction* loss_function,
	double* x0, double* x1, double* x2,
	double* x3, double* x4, double* x5,
	double* x6, double* x7, double* x8,
	double* x9);

	// Add a parameter block with appropriate size to the problem.
	// Repeated calls with the same arguments are ignored. Repeated
	// calls with the same double pointer but a different size results
	// in undefined behaviour.
	void AddParameterBlock(double* values, int size);

	// Add a parameter block with appropriate size and parameterization
	// to the problem. Repeated calls with the same arguments are
	// ignored. Repeated calls with the same double pointer but a
	// different size results in undefined behaviour.
	void AddParameterBlock(double* values,
	int size,
	LocalParameterization* local_parameterization);

	// Remove a parameter block from the problem. The parameterization of the
	// parameter block, if it exists, will persist until the deletion of the
	// problem (similar to cost/loss functions in residual block removal). Any
	// residual blocks that depend on the parameter are also removed, as
	// described above in RemoveResidualBlock().
	//
	// If Problem::Options::enable_fast_removal is true, then the
	// removal is fast (almost constant time). Otherwise, removing a parameter
	// block will incur a scan of the entire Problem object.
	//
	// WARNING: Removing a residual or parameter block will destroy the implicit
	// ordering, rendering the jacobian or residuals returned from the solver
	// uninterpretable. If you depend on the evaluated jacobian, do not use
	// remove! This may change in a future release.
	void RemoveParameterBlock(double* values);

	// Remove a residual block from the problem. Any parameters that the residual
	// block depends on are not removed. The cost and loss functions for the
	// residual block will not get deleted immediately; won't happen until the
	// problem itself is deleted.
	//
	// WARNING: Removing a residual or parameter block will destroy the implicit
	// ordering, rendering the jacobian or residuals returned from the solver
	// uninterpretable. If you depend on the evaluated jacobian, do not use
	// remove! This may change in a future release.
	void RemoveResidualBlock(ResidualBlockId residual_block);

	// Hold the indicated parameter block constant during optimization.
	void SetParameterBlockConstant(double* values);

	// Allow the indicated parameter block to vary during optimization.
	void SetParameterBlockVariable(double* values);

	// Returns true if a parameter block is set constant, and false otherwise.
	bool IsParameterBlockConstant(double* values) const;

	// Set the local parameterization for one of the parameter blocks.
	// The local_parameterization is owned by the Problem by default. It
	// is acceptable to set the same parameterization for multiple
	// parameters; the destructor is careful to delete local
	// parameterizations only once. The local parameterization can only
	// be set once per parameter, and cannot be changed once set.
	void SetParameterization(double* values,
	LocalParameterization* local_parameterization);

	// Get the local parameterization object associated with this
	// parameter block. If there is no parameterization object
	// associated then NULL is returned.
	const LocalParameterization* GetParameterization(double* values) const;

	// Set the lower/upper bound for the parameter with position "index".
	void SetParameterLowerBound(double* values, int index, double lower_bound);
	void SetParameterUpperBound(double* values, int index, double upper_bound);

	// Number of parameter blocks in the problem. Always equals
	// parameter_blocks().size() and parameter_block_sizes().size().
	int NumParameterBlocks() const;

	// The size of the parameter vector obtained by summing over the
	// sizes of all the parameter blocks.
	int NumParameters() const;

	// Number of residual blocks in the problem. Always equals
	// residual_blocks().size().
	int NumResidualBlocks() const;

	// The size of the residual vector obtained by summing over the
	// sizes of all of the residual blocks.
	int NumResiduals() const;

	// The size of the parameter block.
	int ParameterBlockSize(const double* values) const;

	// The size of local parameterization for the parameter block. If
	// there is no local parameterization associated with this parameter
	// block, then ParameterBlockLocalSize = ParameterBlockSize.
	int ParameterBlockLocalSize(const double* values) const;

	// Is the given parameter block present in this problem or not?
	bool HasParameterBlock(const double* values) const;

	// Fills the passed parameter_blocks vector with pointers to the
	// parameter blocks currently in the problem. After this call,
	// parameter_block.size() == NumParameterBlocks.
	void GetParameterBlocks(std::vector<double> parameter_blocks) const;

	// Fills the passed residual_blocks vector with pointers to the
	// residual blocks currently in the problem. After this call,
	// residual_blocks.size() == NumResidualBlocks.
	void GetResidualBlocks(std::vector<ResidualBlockId>* residual_blocks) const;

	// Get all the parameter blocks that depend on the given residual block.
	void GetParameterBlocksForResidualBlock(
	const ResidualBlockId residual_block,
	std::vector<double> parameter_blocks) const;

	// Get the CostFunction for the given residual block.
	const CostFunction* GetCostFunctionForResidualBlock(
	const ResidualBlockId residual_block) const;

	// Get the LossFunction for the given residual block. Returns NULL
	// if no loss function is associated with this residual block.
	const LossFunction* GetLossFunctionForResidualBlock(
	const ResidualBlockId residual_block) const;

	// Get all the residual blocks that depend on the given parameter block.
	//
	// If Problem::Options::enable_fast_removal is true, then
	// getting the residual blocks is fast and depends only on the number of
	// residual blocks. Otherwise, getting the residual blocks for a parameter
	// block will incur a scan of the entire Problem object.
	void GetResidualBlocksForParameterBlock(
	const double* values,
	std::vector<ResidualBlockId>* residual_blocks) const;

	// Options struct to control Problem::Evaluate.
	struct EvaluateOptions {
	// The set of parameter blocks for which evaluation should be
	// performed. This vector determines the order that parameter
	// blocks occur in the gradient vector and in the columns of the
	// jacobian matrix. If parameter_blocks is empty, then it is
	// assumed to be equal to vector containing ALL the parameter
	// blocks. Generally speaking the parameter blocks will occur in
	// the order in which they were added to the problem. But, this
	// may change if the user removes any parameter blocks from the
	// problem.
	//
	// NOTE: This vector should contain the same pointers as the ones
	// used to add parameter blocks to the Problem. These parameter
	// block should NOT point to new memory locations. Bad things will
	// happen otherwise.
	std::vector<double*> parameter_blocks;

	// The set of residual blocks to evaluate. This vector determines
	// the order in which the residuals occur, and how the rows of the
	// jacobian are ordered. If residual_blocks is empty, then it is
	// assumed to be equal to the vector containing ALL the residual
	// blocks. Generally speaking the residual blocks will occur in
	// the order in which they were added to the problem. But, this
	// may change if the user removes any residual blocks from the
	// problem.
	std::vector<ResidualBlockId> residual_blocks;

	// Even though the residual blocks in the problem may contain loss
	// functions, setting apply_loss_function to false will turn off
	// the application of the loss function to the output of the cost
	// function. This is of use for example if the user wishes to
	// analyse the solution quality by studying the distribution of
	// residuals before and after the solve.
	bool apply_loss_function = true;

	int num_threads = 1;
	};

	// Evaluate Problem. Any of the output pointers can be NULL. Which
	// residual blocks and parameter blocks are used is controlled by
	// the EvaluateOptions struct above.
	//
	// Note 1: The evaluation will use the values stored in the memory
	// locations pointed to by the parameter block pointers used at the
	// time of the construction of the problem. i.e.,
	//
	// Problem problem;
	// double x = 1;
	// problem.AddResidualBlock(new MyCostFunction, NULL, &x);
	//
	// double cost = 0.0;
	// problem.Evaluate(Problem::EvaluateOptions(), &cost, NULL, NULL, NULL);
	//
	// The cost is evaluated at x = 1. If you wish to evaluate the
	// problem at x = 2, then
	//
	// x = 2;
	// problem.Evaluate(Problem::EvaluateOptions(), &cost, NULL, NULL, NULL);
	//
	// is the way to do so.
	//
	// Note 2: If no local parameterizations are used, then the size of
	// the gradient vector (and the number of columns in the jacobian)
	// is the sum of the sizes of all the parameter blocks. If a
	// parameter block has a local parameterization, then it contributes
	// "LocalSize" entries to the gradient vector (and the number of
	// columns in the jacobian).
	//
	// Note 3: This function cannot be called while the problem is being
	// solved, for example it cannot be called from an IterationCallback
	// at the end of an iteration during a solve.
	bool Evaluate(const EvaluateOptions& options,
	double* cost,
	std::vector<double>* residuals,
	std::vector<double>* gradient,
	CRSMatrix* jacobian);

	private:
	friend class Solver;
	friend class Covariance;
	std::unique_ptr<internal::ProblemImpl> problem_impl_;
	};

	} // namespace ceres

	#include "ceres/internal/reenable_warnings.h"

	#endif // CERES_PUBLIC_PROBLEM_H_