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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2023 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
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// modification, are permitted provided that the following conditions are met:
//
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//
// 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 <iostream>
#include "Eigen/Core"
#include "absl/log/check.h"
#include "absl/log/initialize.h"
#include "ceres/ceres.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:
// m and c are passed by reference so that we have access to their values as
// they evolve over time through the course of optimization.
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() override = 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) {
absl::InitializeLog();
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;
}