1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257
|
// 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 <iostream>
#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:
// 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) {
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;
}
|