Ceres Solver简介及使用

      Ceres Solver是一个开源的C++库，用于建模和解决大型、复杂的优化问题。它是一个成熟、功能丰富且高性能的库，自2010年以来一直在Google生产中使用。最新发布版本为2.1.0,license为BSD,它支持在Windows、Linux、Mac、Android、iOS上编译，源码地址：https://ceres-solver.googlesource.com/ceres-solver 
      Ceres Solver可用于解决两类问题：
      (1).具有边界约束的非线性最小二乘(Non-linear Least Squares)问题;
      (2).一般无约束优化问题。
      Ceres Solver依赖项：
      (1).必须的：CMake、Eigen、glog、gflags；
      (2).可选的：SuiteSparse、BLAS and LAPACK、CUDA。
      Ceres Solver在Ubuntu 20.04上编译：eigen, glog, gflags, ceres-solver都在/home/spring/Soft目录下

      (1).clone eigen源码：这里使用3.3.7版本，依次执行如下命令：

git clone https://gitlab.com/libeigen/eigen.git
cd eigen
git checkout 3.3.7

      编译eigen，在eigen目录下执行build_eigen.sh，其内容如下：

#! /bin/bash
 
if [[ ! -d "build" ]]; then
    mkdir build
    cd build
else
    cd build
fi
 
cmake \
    -DCMAKE_CXX_FLAGS=-fPIC \
    -DCMAKE_C_FLAGS=-fPIC \
    -DCMAKE_BUILD_TYPE=Release \
    -DCMAKE_INSTALL_PREFIX=../install \
    ..
make -j2
make install

      (2).clone glog源码：这里使用v0.4.0版本，依次执行如下命令：

git clone https://github.com/google/glog.git
cd glog
git checkout v0.4.0

      编译glog，在glog目录下直接执行build_glog.sh，其内容与build_eigen.sh完全一致。

      (3).clone gflags源码：这里使用v2.2.2版本，依次执行如下命令:

git clone https://github.com/gflags/gflags.git
cd gflags
git checkout v2.2.2

      编译gflags,在gflags目录执行build_gflags.sh，其内容与build_eigen.sh完全一致。

      (4).clone Ceres Solver源码：这里使用1.14.0版本，依次执行如下命令:

git clone https://ceres-solver.googlesource.com/ceres-solver
cd ceres-solver
git checkout 1.14.0

      编译ceres-solver,在ceres-solver目录执行build_ceres-solver.sh，其内容如下：

#! /bin/bash
 
if [[ ! -d "build" ]]; then
    mkdir build
    cd build
else
    cd build
fi
 
path=/home/spring/Soft
 
cmake \
    -DCMAKE_CXX_FLAGS=-fPIC \
    -DCMAKE_C_FLAGS=-fPIC \
    -DCMAKE_BUILD_TYPE=Release \
    -DCMAKE_INSTALL_PREFIX=../install \
    -DEigen3_DIR=${path}/eigen/install/share/eigen3/cmake \
    -Dglog_DIR=${path}/glog/install/lib/cmake/glog \
    -Dgflags_DIR=${path}/gflags/install/lib/cmake/gflags \
    ..
make -j2
make install

      Ceres Solver调用：在/home/spring/Soft目录下新建test目录,此目录内文件内容依次如下

      (1).main.cpp:

#include 
#include 
#include 
 
using namespace ceres;
 
struct CostFunctor {
    template <typename T>
    bool operator()(const T* const x, T* residual) const {
        residual[0] = 10.0 - x[0];
        return true;
    }
};
 
int main(int argc, char** argv)
{
    // reference: http://ceres-solver.org/nnls_tutorial.html
    google::InitGoogleLogging(argv[0]);
 
    // The variable to solve for with its initial value.
    double initial_x = 5.0;
    double x = initial_x;
 
    // Build the problem.
    Problem problem;
 
    // Set up the only cost function (also known as residual). This uses
    // auto-differentiation to obtain the derivative (jacobian).
    CostFunction* cost_function = new AutoDiffCostFunction1, 1>(new CostFunctor);
    problem.AddResidualBlock(cost_function, nullptr, &x);
 
    // Run the solver!
    Solver::Options options;
    options.linear_solver_type = ceres::DENSE_QR;
    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;
}

      (2).build.sh:

#! /bin/bash
 
if [[ ! -d "build" ]]; then
    mkdir build
    cd build
else
    cd build
fi
 
path=/home/spring/Soft
 
cp ${path}/glog/install/lib/libglog.a .
cp ${path}/gflags/install/lib/libgflags.a .
cp ${path}/ceres-solver/install/lib/libceres.a .
 
cmake ..
make

      (3).CMakeLists.txt:

cmake_minimum_required(VERSION 3.15)
project(test_ceres-solver)
 
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -fopenmp")
 
include_directories(
    ${CMAKE_CURRENT_SOURCE_DIR}/../eigen/install/include/eigen3
    ${CMAKE_CURRENT_SOURCE_DIR}/../glog/install/include
    ${CMAKE_CURRENT_SOURCE_DIR}/../gflags/install/include
    ${CMAKE_CURRENT_SOURCE_DIR}/../ceres-solver/install/include
)
 
add_executable(${CMAKE_PROJECT_NAME} ${CMAKE_CURRENT_SOURCE_DIR}/main.cpp)
target_link_directories(${CMAKE_PROJECT_NAME} PRIVATE ${CMAKE_CURRENT_SOURCE_DIR}/build)
target_link_libraries(${CMAKE_PROJECT_NAME} ceres glog gflags pthread)

      执行：

      首先执行：./build.sh

      然后执行：./build/test_ceres-solver ,结果如下图所示：