【云藏山鹰代数信息系统】云藏山鹰逻辑学与云藏山鹰逻辑系统代码浅析

【云藏山鹰代数信息系统】云藏山鹰逻辑学与云藏山鹰逻辑系统代码浅析云藏山鹰圆上的傅里叶变换的逻辑类型与逻辑实现架构设计改进CRTP模式优化策略克隆C++20 Concepts约束模板参数策略工厂模式性能优化（关键）FFT算法数值稳定性优化角度规范化数值稳定性数学正确性特征标计算优化添加群论操作功能扩展建议窗函数实现示例代码质量异常处理与边界检查单元测试框架文档完善优先级排序附录 云藏山鹰代数信息系统（YUDST Algebra Information System）进阶阅读云藏山鹰圆上的傅里叶变换的逻辑类型与逻辑实现#define_USE_MATH_DEFINES#includeiostream#includecmath#includememory#includeutility#includevector#includecomplex#includealgorithm#includenumeric#includestring// ==================== 基础数据结构 ====================// 定义圆上的点（极坐标）structPoint{doubletheta;// 角度（弧度）doubler;// 半径Point(doubletheta=0.0,doubler=1.0):theta(theta),r(r){// 规范化角度到 [0, 2π)normalize();}voidnormalize(){while(theta0)theta+=2*M_PI;while(theta=2*M_PI)theta-=2*M_PI;}// 转换为笛卡尔坐标std::pairdouble,doubletoCartesian()const{return{r*std::cos(theta),r*std::sin(theta)};}// 从笛卡尔坐标创建staticPointfromCartesian(doublex,doubley){doubler=std::sqrt(x*x+y*y);doubletheta=std::atan2(y,x);if(theta0)theta+=2*M_PI;returnPoint(theta,r);}voidprint()const{std::cout"(θ="theta" ("theta*180/M_PI"°), r="r")";}};// 复数类型别名（用于傅里叶变换）usingComplex=std::complexdouble;// ==================== 策略接口 ====================// 策略接口：定义逻辑操作行为classLogicStrategy{public:virtualPointexecute(constPointp)const=0;virtualstd::stringname()const=0;virtualstd::unique_ptrLogicStrategyclone()const=0;virtual~LogicStrategy()=default;};// 逻辑映射策略接口classTruthMappingStrategy{public:virtualintmap(constPointp)const=0;virtualstd::stringname()const=0;virtual~TruthMappingStrategy()=default;};// ==================== C(2)群策略 ====================classC2IdentityStrategy:publicLogicStrategy{public:Pointexecute(constPointp)constoverride{returnp;// 恒等映射}std::stringname()constoverride{return"C2_E (恒等)";}std::unique_ptrLogicStrategyclone()constoverride{returnstd::make_uniqueC2IdentityStrategy(*this);}};classC2RotationStrategy:publicLogicStrategy{public:Pointexecute(constPointp)constoverride{Pointresult(p.theta+M_PI,p.r);// 旋转180度result.normalize();returnresult;}std::stringname()constoverride{return"C2_C2 (180°旋转)";}std::unique_ptrLogicStrategyclone()constoverride{returnstd::make_uniqueC2RotationStrategy(*this);}};// ==================== C(3)群策略 ====================classC3Rotation0Strategy:publicLogicStrategy{public:Pointexecute(constPointp)constoverride{returnp;// 0度旋转}std::stringname()constoverride{return"C3_E (0°)";}std::unique_ptrLogicStrategyclone()constoverride{returnstd::make_uniqueC3Rotation0Strategy(*this);}};classC3Rotation120Strategy:publicLogicStrategy{public:Pointexecute(constPointp)constoverride{Pointresult(p.theta+2*M_PI/3,p.r);// 旋转120度result.normalize();returnresult;}std::stringname()constoverride{return"C3_C3 (120°)";}std::unique_ptrLogicStrategyclone()constoverride{returnstd::make_uniqueC3Rotation120Strategy(*this);}};classC3Rotation240Strategy:publicLogicStrategy{public:Pointexecute(constPointp)constoverride{Pointresult(p.theta+4*M_PI/3,p.r);// 旋转240度result.normalize();returnresult;}std::stringname()constoverride{return"C3_C3² (240°)";}std::unique_ptrLogicStrategyclone()constoverride{returnstd::make_uniqueC3Rotation240Strategy(*this);}};// ==================== C(7,r)群策略（7阶循环群） ====================// C7群是7阶循环群，有7个元素：{E, C7, C7², C7³, C7⁴, C7⁵, C7⁶}// 每个元素对应旋转 k * 360°/7 = k * 51.42857...°classC7RotationStrategy:publicLogicStrategy{protected:intk;// 旋转次数（0-6）staticconstexprintN=7;staticconstexprdoubleANGLE=2*M_PI/N;// 2π/7public:explicitC7RotationStrategy(introtation_k):k(rotation_k%N){if(k0)k+=N;}Pointexecute(constPointp)constoverride{Pointresult(p.theta+k*ANGLE,p.r);result.normalize();returnresult;}std::stringname()constoverride{if(k==0)return"C7_E (恒等)";return"C7_"+std::to_string(k)+" ("+std::to_string(static_castint(k*360.0/N+0.5))+"°)";}std::unique_ptrLogicStrategyclone()constoverride{returnstd::make_uniqueC7RotationStrategy(*this);}intgetK()const{returnk;}staticintgetOrder(){returnN;}};// 为每个C7元素创建具体类（便于策略模式使用）classC7_E:publicC7RotationStrategy{public:C7_E():C7RotationStrategy(0){}std::unique_ptrLogicStrategyclone()constoverride{returnstd::make_uniqueC7_E(*this);}};classC7_C1:publicC7RotationStrategy{public:C7_C1():C7RotationStrategy(1){}std::unique_ptrLogicStrategyclone()constoverride{returnstd::make_uniqueC7_C1(*this);}};classC7_C2:publicC7RotationStrategy{public:C7_C2():C7RotationStrategy(2){}std::unique_ptrLogicStrategyclone()constoverride{returnstd::make_uniqueC7_C2(*this);}};classC7_C3:publicC7RotationStrategy{public:C7_C3():C7RotationStrategy(3){}std::unique_ptrLogicStrategyclone()constoverride{returnstd::make_uniqueC7_C3(*this);}};classC7_C4:publicC7RotationStrategy{public:C7_C4():C7RotationStrategy(4){}std::unique_ptrLogicStrategyclone()constoverride{returnstd::make_uniqueC7_C4(*this);}};classC7_C5:publicC7RotationStrategy{public:C7_C5():C7RotationStrategy(5){}std::unique_ptrLogicStrategyclone()constoverride{returnstd::make_uniqueC7_C5(*this);}};classC7_C6:publicC7RotationStrategy{public:C7_C6():C7RotationStrategy(6){}std::unique_ptrLogicSt