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+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2015 Google Inc. All rights reserved.
+// http://ceres-solver.org/
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are met:
+//
+// * Redistributions of source code must retain the above copyright notice,
+// this list of conditions and the following disclaimer.
+// * Redistributions in binary form must reproduce the above copyright notice,
+// this list of conditions and the following disclaimer in the documentation
+// and/or other materials provided with the distribution.
+// * Neither the name of Google Inc. nor the names of its contributors may be
+// used to endorse or promote products derived from this software without
+// specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+// POSSIBILITY OF SUCH DAMAGE.
+//
+// Author: keir@google.com (Keir Mierle)
+//
+// A simple example of using the Ceres minimizer.
+//
+// Minimize 0.5 (10 - x)^2 using analytic jacobian matrix.
+
+#include <vector>
+#include "ceres/ceres.h"
+#include "glog/logging.h"
+
+using ceres::CostFunction;
+using ceres::SizedCostFunction;
+using ceres::Problem;
+using ceres::Solver;
+using ceres::Solve;
+
+// A CostFunction implementing analytically derivatives for the
+// function f(x) = 10 - x.
+class QuadraticCostFunction
+ : public SizedCostFunction<1 /* number of residuals */,
+ 1 /* size of first parameter */> {
+ public:
+ virtual ~QuadraticCostFunction() {}
+
+ virtual bool Evaluate(double const* const* parameters,
+ double* residuals,
+ double** jacobians) const {
+ double x = parameters[0][0];
+
+ // f(x) = 10 - x.
+ residuals[0] = 10 - x;
+
+ // f'(x) = -1. Since there's only 1 parameter and that parameter
+ // has 1 dimension, there is only 1 element to fill in the
+ // jacobians.
+ //
+ // Since the Evaluate function can be called with the jacobians
+ // pointer equal to NULL, the Evaluate function must check to see
+ // if jacobians need to be computed.
+ //
+ // For this simple problem it is overkill to check if jacobians[0]
+ // is NULL, but in general when writing more complex
+ // CostFunctions, it is possible that Ceres may only demand the
+ // derivatives w.r.t. a subset of the parameter blocks.
+ if (jacobians != NULL && jacobians[0] != NULL) {
+ jacobians[0][0] = -1;
+ }
+
+ return true;
+ }
+};
+
+int main(int argc, char** argv) {
+ google::InitGoogleLogging(argv[0]);
+
+ // The variable to solve for with its initial value. It will be
+ // mutated in place by the solver.
+ double x = 0.5;
+ const double initial_x = x;
+
+ // Build the problem.
+ Problem problem;
+
+ // Set up the only cost function (also known as residual).
+ CostFunction* cost_function = new QuadraticCostFunction;
+ problem.AddResidualBlock(cost_function, NULL, &x);
+
+ // Run the solver!
+ Solver::Options options;
+ options.minimizer_progress_to_stdout = true;
+ Solver::Summary summary;
+ Solve(options, &problem, &summary);
+
+ std::cout << summary.BriefReport() << "\n";
+ std::cout << "x : " << initial_x
+ << " -> " << x << "\n";
+
+ return 0;
+}