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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)
//
// An example program that minimizes Powell's singular function.
//
// F = 1/2 (f1^2 + f2^2 + f3^2 + f4^2)
//
// f1 = x1 + 10*x2;
// f2 = sqrt(5) * (x3 - x4)
// f3 = (x2 - 2*x3)^2
// f4 = sqrt(10) * (x1 - x4)^2
//
// The starting values are x1 = 3, x2 = -1, x3 = 0, x4 = 1.
// The minimum is 0 at (x1, x2, x3, x4) = 0.
//
// From: Testing Unconstrained Optimization Software by Jorge J. More, Burton S.
// Garbow and Kenneth E. Hillstrom in ACM Transactions on Mathematical Software,
// Vol 7(1), March 1981.
#include <iostream>
#include <string>
#include "absl/flags/flag.h"
#include "absl/flags/parse.h"
#include "absl/log/initialize.h"
#include "absl/log/log.h"
#include "ceres/ceres.h"
struct F1 {
template <typename T>
bool operator()(const T* const x1, const T* const x2, T* residual) const {
// f1 = x1 + 10 * x2;
residual[0] = x1[0] + 10.0 * x2[0];
return true;
}
};
struct F2 {
template <typename T>
bool operator()(const T* const x3, const T* const x4, T* residual) const {
// f2 = sqrt(5) (x3 - x4)
residual[0] = sqrt(5.0) * (x3[0] - x4[0]);
return true;
}
};
struct F3 {
template <typename T>
bool operator()(const T* const x2, const T* const x3, T* residual) const {
// f3 = (x2 - 2 x3)^2
residual[0] = (x2[0] - 2.0 * x3[0]) * (x2[0] - 2.0 * x3[0]);
return true;
}
};
struct F4 {
template <typename T>
bool operator()(const T* const x1, const T* const x4, T* residual) const {
// f4 = sqrt(10) (x1 - x4)^2
residual[0] = sqrt(10.0) * (x1[0] - x4[0]) * (x1[0] - x4[0]);
return true;
}
};
ABSL_FLAG(std::string,
minimizer,
"trust_region",
"Minimizer type to use, choices are: line_search & trust_region");
int main(int argc, char** argv) {
absl::InitializeLog();
absl::ParseCommandLine(argc, argv);
double x1 = 3.0;
double x2 = -1.0;
double x3 = 0.0;
double x4 = 1.0;
ceres::Problem problem;
// Add residual terms to the problem using the autodiff
// wrapper to get the derivatives automatically. The parameters, x1 through
// x4, are modified in place.
problem.AddResidualBlock(
new ceres::AutoDiffCostFunction<F1, 1, 1, 1>(), nullptr, &x1, &x2);
problem.AddResidualBlock(
new ceres::AutoDiffCostFunction<F2, 1, 1, 1>(), nullptr, &x3, &x4);
problem.AddResidualBlock(
new ceres::AutoDiffCostFunction<F3, 1, 1, 1>(), nullptr, &x2, &x3);
problem.AddResidualBlock(
new ceres::AutoDiffCostFunction<F4, 1, 1, 1>(), nullptr, &x1, &x4);
ceres::Solver::Options options;
LOG_IF(FATAL,
!ceres::StringToMinimizerType(absl::GetFlag(FLAGS_minimizer),
&options.minimizer_type))
<< "Invalid minimizer: " << absl::GetFlag(FLAGS_minimizer)
<< ", valid options are: trust_region and line_search.";
options.max_num_iterations = 100;
options.linear_solver_type = ceres::DENSE_QR;
options.minimizer_progress_to_stdout = true;
// clang-format off
std::cout << "Initial x1 = " << x1
<< ", x2 = " << x2
<< ", x3 = " << x3
<< ", x4 = " << x4
<< "\n";
// clang-format on
// Run the solver!
ceres::Solver::Summary summary;
ceres::Solve(options, &problem, &summary);
std::cout << summary.FullReport() << "\n";
// clang-format off
std::cout << "Final x1 = " << x1
<< ", x2 = " << x2
<< ", x3 = " << x3
<< ", x4 = " << x4
<< "\n";
// clang-format on
return 0;
}