// 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.

// Copyright 2007 Google Inc. All Rights Reserved.

//

// Authors: wjr@google.com (William Rucklidge),

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

//          dgossow@google.com (David Gossow)

#ifndef CERES_PUBLIC_GRADIENT_CHECKER_H_

#define CERES_PUBLIC_GRADIENT_CHECKER_H_

#include <vector>

#include <string>

#include "ceres/cost_function.h"

#include "ceres/dynamic_numeric_diff_cost_function.h"

#include "ceres/internal/eigen.h"

#include "ceres/internal/fixed_array.h"

#include "ceres/internal/macros.h"

#include "ceres/internal/scoped_ptr.h"

#include "ceres/local_parameterization.h"

#include "glog/logging.h"

namespace ceres {

// GradientChecker compares the Jacobians returned by a cost function against

// derivatives estimated using finite differencing.

//

// The condition enforced is that

//

//    (J_actual(i, j) - J_numeric(i, j))

//   ------------------------------------  <  relative_precision

//   max(J_actual(i, j), J_numeric(i, j))

//

// where J_actual(i, j) is the jacobian as computed by the supplied cost

// function (by the user) multiplied by the local parameterization Jacobian

// and J_numeric is the jacobian as computed by finite differences, multiplied

// by the local parameterization Jacobian as well.

//

// How to use: Fill in an array of pointers to parameter blocks for your

// CostFunction, and then call Probe(). Check that the return value is 'true'.

class CERES_EXPORT GradientChecker {

 public:

  // This will not take ownership of the cost function or local

  // parameterizations.

  //

  // function: The cost function to probe.

  // local_parameterization: A vector of local parameterizations for each

  // parameter. May be NULL or contain NULL pointers to indicate that the

  // respective parameter does not have a local parameterization.

  // options: Options to use for numerical differentiation.

  GradientChecker(

      const CostFunction* function,

      const std::vector<const LocalParameterization*>* local_parameterizations,

      const NumericDiffOptions& options);

  // Contains results from a call to Probe for later inspection.

  struct CERES_EXPORT ProbeResults {

    // The return value of the cost function.

    bool return_value;

    // Computed residual vector.

    Vector residuals;

    // The sizes of the Jacobians below are dictated by the cost function's

    // parameter block size and residual block sizes. If a parameter block

    // has a local parameterization associated with it, the size of the "local"

    // Jacobian will be determined by the local parameterization dimension and

    // residual block size, otherwise it will be identical to the regular

    // Jacobian.

    // Derivatives as computed by the cost function.

    std::vector<Matrix> jacobians;

    // Derivatives as computed by the cost function in local space.

    std::vector<Matrix> local_jacobians;

    // Derivatives as computed by nuerical differentiation in local space.

    std::vector<Matrix> numeric_jacobians;

    // Derivatives as computed by nuerical differentiation in local space.

    std::vector<Matrix> local_numeric_jacobians;

    // Contains the maximum relative error found in the local Jacobians.

    double maximum_relative_error;

    // If an error was detected, this will contain a detailed description of

    // that error.

    std::string error_log;

  };

  // Call the cost function, compute alternative Jacobians using finite

  // differencing and compare results. If local parameterizations are given,

  // the Jacobians will be multiplied by the local parameterization Jacobians

  // before performing the check, which effectively means that all errors along

  // the null space of the local parameterization will be ignored.

  // Returns false if the Jacobians don't match, the cost function return false,

  // or if the cost function returns different residual when called with a

  // Jacobian output argument vs. calling it without. Otherwise returns true.

  //

  // parameters: The parameter values at which to probe.

  // relative_precision: A threshold for the relative difference between the

  // Jacobians. If the Jacobians differ by more than this amount, then the

  // probe fails.

  // results: On return, the Jacobians (and other information) will be stored

  // here. May be NULL.

  //

  // Returns true if no problems are detected and the difference between the

  // Jacobians is less than error_tolerance.

  bool Probe(double const* const* parameters,

             double relative_precision,

             ProbeResults* results) const;

 private:

  CERES_DISALLOW_IMPLICIT_CONSTRUCTORS(GradientChecker);

  std::vector<const LocalParameterization*> local_parameterizations_;

  const CostFunction* function_;

  internal::scoped_ptr<CostFunction> finite_diff_cost_function_;

};

}  // namespace ceres

#endif  // CERES_PUBLIC_GRADIENT_CHECKER_H_