Add an example for EvaluationCallback

Change-Id: Ia488f8b181118c8d07861149c4bd52f7217336ce
diff --git a/docs/source/nnls_modeling.rst b/docs/source/nnls_modeling.rst
index 4b558dd..e393148 100644
--- a/docs/source/nnls_modeling.rst
+++ b/docs/source/nnls_modeling.rst
@@ -2478,7 +2478,10 @@
    to use a global shared variable (discouraged; bug-prone).  As far
    as Ceres is concerned, it is evaluating cost functions like any
    other; it just so happens that behind the scenes the cost functions
-   reuse pre-computed data to execute faster.
+   reuse pre-computed data to execute faster. See
+   `examples/evaluation_callback_example.cc
+   <https://ceres-solver.googlesource.com/ceres-solver/+/master/examples/evaluation_callback_example.cc>`_
+   for an example.
 
    See ``evaluation_callback_test.cc`` for code that explicitly
    verifies the preconditions between
diff --git a/examples/CMakeLists.txt b/examples/CMakeLists.txt
index 3be34a1..8af2077 100644
--- a/examples/CMakeLists.txt
+++ b/examples/CMakeLists.txt
@@ -78,6 +78,9 @@
 add_executable(iteration_callback_example iteration_callback_example.cc)
 target_link_libraries(iteration_callback_example PRIVATE Ceres::ceres)
 
+add_executable(evaluation_callback_example evaluation_callback_example.cc)
+target_link_libraries(evaluation_callback_example PRIVATE Ceres::ceres)
+
 if (GFLAGS)
   add_executable(powell powell.cc)
   target_link_libraries(powell PRIVATE Ceres::ceres gflags)
diff --git a/examples/evaluation_callback_example.cc b/examples/evaluation_callback_example.cc
new file mode 100644
index 0000000..579fca3
--- /dev/null
+++ b/examples/evaluation_callback_example.cc
@@ -0,0 +1,253 @@
+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2023 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)
+//
+// This example illustrates the use of the EvaluationCallback, which can be used
+// to perform high performance computation of the residual and Jacobians outside
+// Ceres (in this case using Eigen's vectorized code) and then the CostFunctions
+// just copy these computed residuals and Jacobians appropriately and pass them
+// to Ceres Solver.
+//
+// The results of running this example should be identical to the results
+// obtained by running curve_fitting.cc. The only difference between the two
+// examples is how the residuals and Jacobians are computed.
+//
+// The observant reader will note that both here and curve_fitting.cc instead of
+// creating one ResidualBlock for each observation one can just do one
+// ResidualBlock/CostFunction for the entire problem. The reason for keeping one
+// residual per observation is that it is what is needed if and when we need to
+// introduce a loss function which is what we do in robust_curve_fitting.cc
+
+#include "Eigen/Core"
+#include "ceres/ceres.h"
+#include "glog/logging.h"
+
+// Data generated using the following octave code.
+//   randn('seed', 23497);
+//   m = 0.3;
+//   c = 0.1;
+//   x=[0:0.075:5];
+//   y = exp(m * x + c);
+//   noise = randn(size(x)) * 0.2;
+//   y_observed = y + noise;
+//   data = [x', y_observed'];
+
+const int kNumObservations = 67;
+// clang-format off
+const double data[] = {
+  0.000000e+00, 1.133898e+00,
+  7.500000e-02, 1.334902e+00,
+  1.500000e-01, 1.213546e+00,
+  2.250000e-01, 1.252016e+00,
+  3.000000e-01, 1.392265e+00,
+  3.750000e-01, 1.314458e+00,
+  4.500000e-01, 1.472541e+00,
+  5.250000e-01, 1.536218e+00,
+  6.000000e-01, 1.355679e+00,
+  6.750000e-01, 1.463566e+00,
+  7.500000e-01, 1.490201e+00,
+  8.250000e-01, 1.658699e+00,
+  9.000000e-01, 1.067574e+00,
+  9.750000e-01, 1.464629e+00,
+  1.050000e+00, 1.402653e+00,
+  1.125000e+00, 1.713141e+00,
+  1.200000e+00, 1.527021e+00,
+  1.275000e+00, 1.702632e+00,
+  1.350000e+00, 1.423899e+00,
+  1.425000e+00, 1.543078e+00,
+  1.500000e+00, 1.664015e+00,
+  1.575000e+00, 1.732484e+00,
+  1.650000e+00, 1.543296e+00,
+  1.725000e+00, 1.959523e+00,
+  1.800000e+00, 1.685132e+00,
+  1.875000e+00, 1.951791e+00,
+  1.950000e+00, 2.095346e+00,
+  2.025000e+00, 2.361460e+00,
+  2.100000e+00, 2.169119e+00,
+  2.175000e+00, 2.061745e+00,
+  2.250000e+00, 2.178641e+00,
+  2.325000e+00, 2.104346e+00,
+  2.400000e+00, 2.584470e+00,
+  2.475000e+00, 1.914158e+00,
+  2.550000e+00, 2.368375e+00,
+  2.625000e+00, 2.686125e+00,
+  2.700000e+00, 2.712395e+00,
+  2.775000e+00, 2.499511e+00,
+  2.850000e+00, 2.558897e+00,
+  2.925000e+00, 2.309154e+00,
+  3.000000e+00, 2.869503e+00,
+  3.075000e+00, 3.116645e+00,
+  3.150000e+00, 3.094907e+00,
+  3.225000e+00, 2.471759e+00,
+  3.300000e+00, 3.017131e+00,
+  3.375000e+00, 3.232381e+00,
+  3.450000e+00, 2.944596e+00,
+  3.525000e+00, 3.385343e+00,
+  3.600000e+00, 3.199826e+00,
+  3.675000e+00, 3.423039e+00,
+  3.750000e+00, 3.621552e+00,
+  3.825000e+00, 3.559255e+00,
+  3.900000e+00, 3.530713e+00,
+  3.975000e+00, 3.561766e+00,
+  4.050000e+00, 3.544574e+00,
+  4.125000e+00, 3.867945e+00,
+  4.200000e+00, 4.049776e+00,
+  4.275000e+00, 3.885601e+00,
+  4.350000e+00, 4.110505e+00,
+  4.425000e+00, 4.345320e+00,
+  4.500000e+00, 4.161241e+00,
+  4.575000e+00, 4.363407e+00,
+  4.650000e+00, 4.161576e+00,
+  4.725000e+00, 4.619728e+00,
+  4.800000e+00, 4.737410e+00,
+  4.875000e+00, 4.727863e+00,
+  4.950000e+00, 4.669206e+00,
+};
+// clang-format on
+
+// This implementation of the EvaluationCallback interface also stores the
+// residuals and Jacobians that the CostFunction copies their values from.
+class MyEvaluationCallback : public ceres::EvaluationCallback {
+ public:
+  MyEvaluationCallback(const double& m, const double& c) : m_(m), c_(c) {
+    x_ = Eigen::VectorXd::Zero(kNumObservations);
+    y_ = Eigen::VectorXd::Zero(kNumObservations);
+    residuals_ = Eigen::VectorXd::Zero(kNumObservations);
+    jacobians_ = Eigen::MatrixXd::Zero(kNumObservations, 2);
+    for (int i = 0; i < kNumObservations; ++i) {
+      x_[i] = data[2 * i];
+      y_[i] = data[2 * i + 1];
+    }
+    PrepareForEvaluation(true, true);
+  }
+
+  void PrepareForEvaluation(bool evaluate_jacobians,
+                            bool new_evaluation_point) final {
+    if (new_evaluation_point) {
+      ComputeResidualAndJacobian(evaluate_jacobians);
+      jacobians_are_stale_ = !evaluate_jacobians;
+    } else {
+      if (evaluate_jacobians && jacobians_are_stale_) {
+        ComputeResidualAndJacobian(evaluate_jacobians);
+        jacobians_are_stale_ = false;
+      }
+    }
+  }
+
+  const Eigen::VectorXd& residuals() const { return residuals_; }
+  const Eigen::MatrixXd& jacobians() const { return jacobians_; }
+  bool jacobians_are_stale() const { return jacobians_are_stale_; }
+
+ private:
+  void ComputeResidualAndJacobian(bool evaluate_jacobians) {
+    residuals_ = -(m_ * x_.array() + c_).exp();
+    if (evaluate_jacobians) {
+      jacobians_.col(0) = residuals_.array() * x_.array();
+      jacobians_.col(1) = residuals_;
+    }
+    residuals_ += y_;
+  }
+
+  const double& m_;
+  const double& c_;
+  Eigen::VectorXd x_;
+  Eigen::VectorXd y_;
+  Eigen::VectorXd residuals_;
+  Eigen::MatrixXd jacobians_;
+
+  // jacobians_are_stale_ keeps track of whether the jacobian matrix matches the
+  // residuals or not, we only compute it if we know that Solver is going to
+  // need access to it.
+  bool jacobians_are_stale_ = true;
+};
+
+// As the name implies this CostFunction does not do any computation, it just
+// copies the appropriate residual and Jacobian from the matrices stored in
+// MyEvaluationCallback.
+class CostAndJacobianCopyingCostFunction
+    : public ceres::SizedCostFunction<1, 1, 1> {
+ public:
+  CostAndJacobianCopyingCostFunction(
+      int index, const MyEvaluationCallback& evaluation_callback)
+      : index_(index), evaluation_callback_(evaluation_callback) {}
+  ~CostAndJacobianCopyingCostFunction() = default;
+
+  bool Evaluate(double const* const* parameters,
+                double* residuals,
+                double** jacobians) const final {
+    residuals[0] = evaluation_callback_.residuals()(index_);
+    if (!jacobians) return true;
+
+    // Ensure that we are not using stale Jacobians.
+    CHECK(!evaluation_callback_.jacobians_are_stale());
+
+    if (jacobians[0] != nullptr)
+      jacobians[0][0] = evaluation_callback_.jacobians()(index_, 0);
+    if (jacobians[1] != nullptr)
+      jacobians[1][0] = evaluation_callback_.jacobians()(index_, 1);
+    return true;
+  }
+
+ private:
+  int index_ = -1;
+  const MyEvaluationCallback& evaluation_callback_;
+};
+
+int main(int argc, char** argv) {
+  google::InitGoogleLogging(argv[0]);
+
+  const double initial_m = 0.0;
+  const double initial_c = 0.0;
+  double m = initial_m;
+  double c = initial_c;
+
+  MyEvaluationCallback evaluation_callback(m, c);
+  ceres::Problem::Options problem_options;
+  problem_options.evaluation_callback = &evaluation_callback;
+  ceres::Problem problem(problem_options);
+  for (int i = 0; i < kNumObservations; ++i) {
+    problem.AddResidualBlock(
+        new CostAndJacobianCopyingCostFunction(i, evaluation_callback),
+        nullptr,
+        &m,
+        &c);
+  }
+
+  ceres::Solver::Options options;
+  options.max_num_iterations = 25;
+  options.linear_solver_type = ceres::DENSE_QR;
+  options.minimizer_progress_to_stdout = true;
+
+  ceres::Solver::Summary summary;
+  ceres::Solve(options, &problem, &summary);
+  std::cout << summary.BriefReport() << "\n";
+  std::cout << "Initial m: " << initial_m << " c: " << initial_c << "\n";
+  std::cout << "Final   m: " << m << " c: " << c << "\n";
+  return 0;
+}
diff --git a/include/ceres/evaluation_callback.h b/include/ceres/evaluation_callback.h
index 81fe29d..e582dc8 100644
--- a/include/ceres/evaluation_callback.h
+++ b/include/ceres/evaluation_callback.h
@@ -66,8 +66,12 @@
 
   // Called before Ceres requests residuals or jacobians for a given setting of
   // the parameters. User parameters (the double* values provided to the cost
-  // functions) are fixed until the next call to PrepareForEvaluation(). If
-  // new_evaluation_point == true, then this is a new point that is different
+  // functions) are fixed until the next call to PrepareForEvaluation().
+  //
+  // If evaluate_jacobians == true, then the user provided CostFunctions will be
+  // asked to evaluate one or more of their Jacobians.
+  //
+  // If new_evaluation_point == true, then this is a new point that is different
   // from the last evaluated point. Otherwise, it is the same point that was
   // evaluated previously (either jacobian or residual) and the user can use
   // cached results from previous evaluations.