360网站推广官网怎么优化,网站平台开发要注意什么问题,200平方办公室装修设计,网页升级跳转自动刷新这是我的课程作业#xff0c;用了 Eigen 库#xff0c;最后的输出是 latex 的表格的一部分 具体内容就是 梯度下降法 精确线搜索#xff08;单峰区间搜索 黄金分割#xff09; 从书本的 Matlab 代码转译过来的其实#xff0c;所以应该是一看就懂了 这里定义了两个测试…这是我的课程作业用了 Eigen 库最后的输出是 latex 的表格的一部分 具体内容就是 梯度下降法 精确线搜索单峰区间搜索 黄金分割 从书本的 Matlab 代码转译过来的其实所以应该是一看就懂了 这里定义了两个测试函数 fun 和 fun2 整个最优化方法包装在 SteepestDescent 类里面 用了模板封装类这样应该是 double 和 Eigne 的 Vector 都可以支持的 用了 tuple 返回值用了 functional 接受函数形参所以应该要 C11 以上进行编译 #include 3rdparty/Eigen/Eigen/Dense#include cstdint #include fstream #include functional #include iostream #include string #include tuple#ifndef DEBUG # define DEBUG 0 #endifusing namespace Eigen;templateclass YClass, class XClass class SteepestDescent { public:SteepestDescent(std::functionYClass(XClass) const fun,std::functionXClass(XClass) const gfun,double delta,double epsilon): m_fun(fun), m_gfun(gfun), m_delta(delta), m_epsilon(epsilon) {};/*** brief Find single peak interval.** It will stop if the number of iterations exceeds the given upper limit.** param fun Target function.* param alpha0 Start point.* param h Search direction.** return XClass Left end of single peak interval.* return XClass Right end of single peak interval.* return XClass Inner point of single peak interval.* 1 represents same direction w.r.t. h, -1 represents reversed direction w.r.t. h.*/std::tupleXClass, XClass, XClass ForwardBackward(XClass alpha0, XClass h);/*** brief Find a minimum of a function inside a specified interval.** param fun Target function.* param a Left end of interval.* param b Right end of interval.* param delta Tolerable error of input variable.* param epsilon Tolerable error of target function value.** return bool Is early stop. Let interpolation points to be p, q, if fun(a) fun(p) and fun(q) fun(b)* return XClass Minimum point.* return YClass Function value of minimum point.*/std::tuplebool, XClass, YClass GoldenSectionSearch(XClass a, XClass b);/*** brief Run Forward Backward and Golden Section Search** param fun Target function.* param gfun Gredient of target function.* param x0 Start point.* param h Search direction.* param delta Tolerable error of input variable.* param epsilon Tolerable error of target function value.* return std::tupleYClass, YClass, uint32_t*/std::tupleXClass, YClass, uint32_t ForwardBackwardAndGoldenSectionSearch(XClass x0);/*** brief Run Armijo Search** param fun Target function.* param gfun Gredient of target function.* param x0 Start point.* param h Search direction.* param delta Tolerable error of input variable.* param epsilon Tolerable error of target function value.* return std::tupleYClass, YClass, uint32_t*/std::tupleXClass, YClass, uint32_t ArmijoSearch(XClass x0);private:std::functionYClass(XClass) m_fun;std::functionXClass(XClass) m_gfun;double m_delta;double m_epsilon; };templateclass YClass, class XClass std::tupleXClass, XClass, XClass SteepestDescentYClass, XClass::ForwardBackward(XClass alpha0, XClass h) {uint32_t k 0, max_k 500;bool reversed false;XClass alpha1 alpha0, alpha alpha0;YClass phi0 m_fun(alpha0), phi1 m_fun(alpha0);double t 1e-2;while (k max_k){alpha1 alpha0 t * h;phi1 m_fun(alpha1);// forward searchif (phi1 phi0){t 2.0 * t;alpha alpha0;alpha0 alpha1;phi0 phi1;}else{// backward searchif (k 0){t -t;alpha alpha1;}// find another endelse{break;}}k;}#if DEBUGstd::cout ForwardBackward total iteration std::endl;std::cout k std::endl; #endifXClass left t 0.0 ? alpha : alpha1;XClass right t 0.0 ? alpha : alpha1;return {left, right, alpha0}; }templateclass YClass, class XClass std::tuplebool, XClass, YClass SteepestDescentYClass, XClass::GoldenSectionSearch(XClass a, XClass b) {uint32_t k 0, max_k 500;double t (sqrt(5) - 1.0) / 2.0;XClass h b - a;XClass p a (1 - t) * h, q a t * h;YClass phia m_fun(a), phib m_fun(b);YClass phip m_fun(p), phiq m_fun(q);bool is_early_stop false;if (phia phip phiq phib){is_early_stop true;#if DEBUGstd::cout GoldenSectionSearch total it eration std::endl;std::cout k std::endl; #endifreturn {is_early_stop, a, phia};}while (((abs(phip - phia) m_epsilon) || (h.norm() m_delta)) k max_k){if (phip phiq){b q;q p;phib phiq;phiq phip;h b - a;p a (1 - t) * h;phip m_fun(p);}else{a p;p q;phia phip;phip phiq;h b - a;q a t * h;phiq m_fun(q);}k;}#if DEBUGstd::cout GoldenSectionSearch total iteration std::endl;std::cout k std::endl; #endifif (phip phiq){return {is_early_stop, p, phip};}else{return {is_early_stop, q, phiq};} }templateclass YClass, class XClass std::tupleXClass, YClass, uint32_t SteepestDescentYClass, XClass::ForwardBackwardAndGoldenSectionSearch(XClass x0) {uint32_t k 0, max_k 5000;YClass phi_min m_fun(x0);#if DEBUG// file pointerstd::fstream fout;// opens an existing csv file or creates a new file.fout.open(SteepestDescent.csv, std::ios::out | std::ios::trunc);// Insert the data to filefout x0[0] , x0[1] , phi_min \n; #endifwhile (k max_k){Vector2d h -m_gfun(x0);if (h.norm() m_epsilon){return {x0, phi_min, k};}auto [left, right, inner] ForwardBackward(x0, h);auto [is_early_stop, x1, phix1] GoldenSectionSearch(left, right);if (is_early_stop){x1 inner;phix1 m_fun(x1);}x0 x1;phi_min phix1;k;#if DEBUGstd::cout iteration k : std::endl;std::cout h std::endl;std::cout h std::endl;std::cout left pointer std::endl;std::cout left std::endl;std::cout right pointer std::endl;std::cout right std::endl;std::cout inner pointer std::endl;std::cout inner std::endl;std::cout current point std::endl;std::cout x1 std::endl;std::cout current evaluation std::endl;std::cout phix1 std::endl;// Insert the data to filefout x0[0] , x0[1] , phi_min \n; #endif}return {x0, phi_min, k}; }templateclass YClass, class XClass std::tupleXClass, YClass, uint32_t SteepestDescentYClass, XClass::ArmijoSearch(XClass x0) {uint32_t k 0, max_k 5000;YClass phi_min m_fun(x0);double rho 0.5;double sigma 0.4;while (k max_k){Vector2d h -m_gfun(x0);if (h.norm() m_epsilon){return {x0, phi_min, k};}uint32_t m 0;uint32_t mk 0;while (m 20) // Armijo Search{phi_min m_fun(x0 pow(rho, m) * h);if (phi_min m_fun(x0) sigma * pow(rho, m) * (-pow(h.norm(), 2.0))){mk m;break;}m m 1;}x0 x0 pow(rho, mk) * h;k;}return {x0, phi_min, k}; }double fun(Vector2d x) { return 100.0 * pow(pow(x[0], 2.0) - x[1], 2.0) pow(x[0] - 1, 2.0); }Vector2d gfun(Vector2d x) {return Vector2d(400.0 * x[0] * (pow(x[0], 2.0) - x[1]) 2.0 * (x[0] - 1.0), -200.0 * (pow(x[0], 2.0) - x[1])); }double fun2(Vector2d x) { return 3.0 * pow(x[0], 2.0) 2.0 * pow(x[1], 2.0) - 4.0 * x[0] - 6.0 * x[1]; }Vector2d gfun2(Vector2d x) { return Vector2d(6.0 * x[0] - 4.0, 4.0 * x[1] - 6.0); }int main() {std::vectorVector2d points {Vector2d(0.0, 0.0),Vector2d(2.0, 1.0),Vector2d(1.0, -1.0),Vector2d(-1.0, -1.0),Vector2d(-1.2, 1.0),Vector2d(10.0, 10.0)};SteepestDescentdouble, Vector2d sd(fun, gfun, 1e-4, 1e-5);std::fstream fout_result_1, fout_result_2;fout_result_1.open(ForwardBackwardAndGoldenSectionSearch_Result.csv, std::ios::out | std::ios::trunc);fout_result_2.open(ArmijoSearch_Result.csv, std::ios::out | std::ios::trunc);fout_result_1 初始点 ($x_0$) 目标函数值 ($f(x_k)$) 迭代次数 ($k$) \\\\ \n;fout_result_1 \\midrule \n;fout_result_2 初始点 ($x_0$) 目标函数值 ($f(x_k)$) 迭代次数 ($k$) \\\\ \n;fout_result_2 \\midrule \n;for (size_t i 0; i points.size(); i){auto [x, val, k] sd.ForwardBackwardAndGoldenSectionSearch(points[i]);fout_result_1 $( points[i][0] , points[i][1] )^T$ val k \\\\ \n;auto [x2, val2, k2] sd.ArmijoSearch(points[i]);fout_result_2 $( points[i][0] , points[i][1] )^T$ val2 k2 \\\\ \n;}fout_result_1.close();fout_result_2.close(); }