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‎.gitignore

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cmake-build-debug

‎.idea/.gitignore

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‎.idea/material_theme_project_new.xml

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‎CMakeLists.txt

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cmake_minimum_required(VERSION 3.29)
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project(CasADi_tutorial)
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set(CMAKE_CXX_STANDARD 20)
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find_package(casadi REQUIRED)
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find_library(CASADI_LIBRARY
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NAMES casadi
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HINTS ${CASADI_INCLUDE_DIR}/../lib $ENV{CASADI_PREFIX}/lib)
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if(CASADI_LIBRARY)
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set(CASADI_LIBRARIES ${CASADI_LIBRARIES} ${CASADI_LIBRARY})
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endif()
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include_directories(include
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${casadi_INCLUDE_DIRS}
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)
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add_executable(chapter1 chapter1-SX.cpp)
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add_executable(chapter2 chapter2-DM.cpp)
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add_executable(chapter3 chapter3-Function.cpp)
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add_executable(chapter4 chapter4-OptimalProblem.cpp)
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add_executable(chapter5 chapter5-GenCode.cpp)
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target_link_libraries(chapter1 ${CASADI_LIBRARIES})
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target_link_libraries(chapter2 ${CASADI_LIBRARIES})
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target_link_libraries(chapter3 ${CASADI_LIBRARIES})
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target_link_libraries(chapter4 ${CASADI_LIBRARIES})
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target_link_libraries(chapter5 ${CASADI_LIBRARIES})

‎chapter1-SX.cpp

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#include <iostream>
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#include <string>
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#include <casadi/casadi.hpp>
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using namespace casadi;
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int main(){
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// 创建符号变量
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casadi::SX q = casadi::SX::sym("q",7);
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std::cout<<"q: "<<q<<std::endl;
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SX q2 = SX::sym("q2",7);
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std::cout<<"q2: "<<q2<<std::endl;
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// 拼接符号变量
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// vertcat 垂直拼接 horzcat 水平拼接
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SX qh = SX::horzcat({q,q2});
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SX qv = SX::vertcat({q,q2});
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std::cout<<"qh: "<<qh<<std::endl;
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std::cout<<"qv: "<<qv<<std::endl;
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// 转置符号变量
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SX qt = qh.T();
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std::cout<<"transpose of qh: " <<qt <<std::endl;
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// 修改创建的符号变量的值
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SX t1 = SX::sym("t1",3);
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std::cout<<"t1 before: "<<t1<<std::endl;
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t1(0) = 3;
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t1(1) = 1;
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t1(2) = 4;
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std::cout<<"t1 after: "<<t1<<std::endl;
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SX t2 = SX::ones(3,1);
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t2(1) = 3;
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t2(2) = 1;
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std::cout<<"t2: "<<t2<<std::endl;
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SX T01 = casadi::SX::zeros(4,4);
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T01(Slice(0,3,1),3) = t1;
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T01(3,3) = 1;
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T01(2,2) = -1;
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T01(0,0) = cos(q(0));
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T01(0,1) = -sin(q(0));
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T01(1,0) = -sin(q(0));
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T01(1,1) = -cos(q(0));
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std::cout<<"T01: "<<T01<<std::endl;
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auto T12 = SX::zeros(4,4);
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T12(Slice(0,3),3) = t2;
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T12(3,3) = 1;
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T12(0,0) = cos(q(1));
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T12(0,1) = -sin(q(1));
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T12(2,0) = sin(q(1));
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T12(2,1) = cos(q(1));
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std::cout<<"T12: "<<T12<<std::endl;
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// 矩阵乘法
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casadi::SX A = SX::zeros(2,2);
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A(0,0) = 100;
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A(0,1) = 50;
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A(1,0) = -1;
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A(0,1) = -2;
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casadi::SX B = SX::zeros(2,2);
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B(0,0) = 0.5;
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B(0,1) = 0.1;
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B(1,0) = 0.2;
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B(0,1) = 0.4;
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std::cout<< "test matrix multiplication: "<<std::endl;
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std::cout<< "A: "<<A<<std::endl;
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std::cout<< "B: "<<B<<std::endl;
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std::cout<< "element multiplication: "<<A*B<<std::endl;
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std::cout<< "matrix multiplication: "<<SX::mtimes(A,B)<<std::endl;
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return 0;
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};

‎chapter2-DM.cpp

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//
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// Created by lock on 2024/10/11.
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//
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// DM ： Dense Matrix
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#include "iostream"
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#include "string"
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#include "casadi/casadi.hpp"
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using namespace casadi;
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void print(const std::string name,DM dm){
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std::cout<<name<<": \n"<<dm<<std::endl;
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}
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void print(const std::string name,SX sx){
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std::cout<<name<<": \n"<<sx<<std::endl;
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}
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int main(){
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// 创建稠密矩阵，以及基本的操作
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DM q = DM::ones(7,1);
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print("q",q);
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DM q2 = DM::rand(7,1);
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print("q2",q2);
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auto qh = DM::horzcat({q, q2});
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print("qh",qh);
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auto qv = DM::vertcat({q, q2});
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print("qv",qv);
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DM qt = qh.T();
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print("qt",qt);
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// 修改稠密矩阵的变量
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DM t1 = DM::zeros(3,1);
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DM t2 = DM::ones(3,1);
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print("t1 before",t1);
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print("t2 before",t2);
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t1(0) = 0;
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t1(1) = 0;
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t1(2) = 0.214;
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t2(1) = 0.15;
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t2(2) = -0.2314;
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print("t1 after",t1);
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print("t2 after",t2);
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DM T01 = DM::zeros(4,4);
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T01(Slice(0,3),3) = t1;
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casadi::DM A = DM::zeros(2,2);
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A(0,0) = 100;
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A(0,1) = 50;
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A(1,0) = -1;
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A(0,1) = -2;
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casadi::DM B = DM::zeros(2,2);
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B(0,0) = 0.5;
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B(0,1) = 0.1;
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B(1,0) = 0.2;
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B(0,1) = 0.4;
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std::cout<< "test matrix multiplication: "<<std::endl;
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std::cout<< "A: "<<A<<std::endl;
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std::cout<< "B: "<<B<<std::endl;
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std::cout<< "element multiplication: "<<A*B<<std::endl;
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std::cout<< "matrix multiplication: "<<DM::mtimes(A,B)<<std::endl;
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return 0;
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}

‎chapter3-Function.cpp

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//
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// Created by lock on 2024/10/11.
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//
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#include <casadi/casadi.hpp>
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#include <iostream>
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using namespace casadi;
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void print(const std::string name,DM dm){
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std::cout<<name<<": \n"<<dm<<std::endl;
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}
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void print(const std::string name,SX sx){
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std::cout<<name<<": \n"<<sx<<std::endl;
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}
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void print(const std::string name,Function f){
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std::cout<<name<<": \n"<<f<<std::endl;
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}
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int main() {
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/*
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* 如何创建Function
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* a.使用符号表达式
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* b.使用字典构建（后面结尾再说）
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* */
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// 定义输入
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SX x = SX::sym("x",1);
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SX y = SX::sym("y",1);
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// 定义输出
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SX f = SX::sym("f");
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// 建立关系
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f = x*x+y*y;
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SX f2 = SX::sym("f2");
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f2 = x+y;
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Function myFunction = Function("myFunction",{x,y},{f,f2});
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print("myFunction",myFunction);
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/*
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* Function的调用
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* a.计算函数值
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* b.替换得到符号表达式
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* */
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std::vector<DM> input = {2,3};
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std::vector<DM> output = myFunction(input);
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std::cout<<output[0]<<std::endl;
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/*
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* 多输出的Function
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* 取得
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* */
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std::cout<<output[1]<<std::endl;
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/*
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* Function的自带的函数
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* 求导，Jacobian
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* */
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Function jac = myFunction.jacobian();
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print("jac",jac);
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std::vector<DM> jacInput = {DM::zeros(1,1),DM::ones(1,1),DM::ones(1,1),DM::ones(1,1)};
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auto jacOut = jac(jacInput);
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std::cout<<jacOut<<std::endl;
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/*
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* 嵌套Function
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* */
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Function cosFunction = Function("cosFunction",{x},{cos(x)});
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Function sinFunction = Function("sinFunction",{x},{sin(x)});
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Function inheritFunction = Function("inheritFunction",{x},sinFunction(cosFunction(x)[0]));
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print("inheritFunction",inheritFunction);
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DM inheritIn = DM::ones(1,1);
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DM inheritOut = inheritFunction({inheritIn})[0];
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print("inheritOut",inheritOut);
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/*
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* 使用字典构建Function（引出求解器构建）
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* */
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return 0;
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}

‎chapter4-OptimalProblem.cpp

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//
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// Created by lock on 2024/10/11.
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//
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#include <iostream>
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#include <casadi/casadi.hpp>
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using namespace casadi;
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/*
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* test problem:
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* min x0^2 + x1^2
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* s.t. x0+x1-10 = 0
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* */
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int main() {
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// auto x= SX::sym("x",2);
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// auto obj = pow(x(0),2)+ pow(x(1),2);
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// auto g = x(0)+x(1)-10;
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//
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// SXDict nlp = {{"x",x},{"f",obj},{"g",g}};
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// Function solver = nlpsol("solver","ipopt",nlp);
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// std::map<std::string,DM> arg,res;
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// arg["lbx"] = -DM::inf(2);
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// arg["ubx"] = DM::inf(2);
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// arg["lbg"] = 0;
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// arg["ubg"] = 0;
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//
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// arg["x0"] = DM::zeros(2);
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//
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// res = solver(arg);
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//
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// std::cout<<"----------"<<std::endl;
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// std::cout<<"obj in solution = " <<res.at("f")<<std::endl;
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// std::cout<<"primal solution = " << res.at("x")<<std::endl;
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// std::cout<<"dual solution(x) =" <<res.at("lam_x")<<std::endl;
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// std::cout<<"dual solution(g) =" <<res.at("lam_g")<<std::endl;
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/*
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* test problem 2
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* max 2x+y
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* s.t x+y <=40
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* 4x-y>=10
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* 2x+y<=50
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* x,y>0
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* */
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// auto x = SX::sym("x", 2);
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// auto obj = 2 * x(0) + x(1);
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// auto g = SX::vertcat(
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// {x(0) + x(1),
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// 4 * x(0) - x(1),
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// 2 * (x(0) + x(1))});
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//
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// SXDict nlp = {{"x", x},
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// {"f", obj},
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// {"g", g}};
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// Function solver = nlpsol("solver", "ipopt", nlp);
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// std::map<std::string, DM> arg, res;
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// arg["lbx"] = 0;
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// arg["ubx"] = DM::inf(2);
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// arg["lbg"] = DM::vertcat({-DM::inf(), 10, -DM::inf()});
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// arg["ubg"] = DM::vertcat({40, DM::inf(), 50});
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//
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// arg["x0"] = DM::zeros(2);
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//
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// res = solver(arg);
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//
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// std::cout << "----------" << std::endl;
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// std::cout << "obj in solution = " << res.at("f") << std::endl;
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// std::cout << "primal solution = " << res.at("x") << std::endl;
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// std::cout << "dual solution(x) =" << res.at("lam_x") << std::endl;
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// std::cout << "dual solution(g) =" << res.at("lam_g") << std::endl;
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/*
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* Nonlinear optimization problem
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*
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* min (x-2)^2 + (y-1)^2
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* s.t x^2+y^2<=4
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* x*y>=1
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* x+y>=1
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*
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* */
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auto x = SX::sym("x", 2);
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auto obj = pow(x(0)-2,2) + pow(x(1)-1,2);
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auto g = SX::vertcat(
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{pow(x(0),2) + pow(x(1),2),
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x(0)*x(1),
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x(0)+x(1)});
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SXDict nlp = {{"x", x},
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{"f", obj},
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{"g", g}};
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Function solver = nlpsol("solver", "ipopt", nlp);
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std::map<std::string, DM> arg, res;
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arg["lbx"] = -DM::inf(2);
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arg["ubx"] = DM::inf(2);
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arg["lbg"] = DM::vertcat({-DM::inf(), 1, 1});
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arg["ubg"] = DM::vertcat({4, DM::inf(), DM::inf()});
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arg["x0"] = DM::zeros(2);
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res = solver(arg);
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std::cout << "----------" << std::endl;
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std::cout << "obj in solution = " << res.at("f") << std::endl;
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std::cout << "primal solution = " << res.at("x") << std::endl;
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std::cout << "dual solution(x) =" << res.at("lam_x") << std::endl;
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std::cout << "dual solution(g) =" << res.at("lam_g") << std::endl;
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return 0;
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}

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