我可以使用不同的循环来执行此操作，以及如何使其成为函数？

Question

足球踢球运动

目标函数是(2 * (v0)^2 * sind(a) * cosd(a)) / g)

使用黄金搜索法 我们必须通过以下结构为任何用户定义的初始速度选择一个角度来创建一个最大化 x 距离的程序：

给定a = [theta]

最大化x(a)

这样

0 < theta < 90
x > 0
y > 0

至少使用以下输入创建函数：v0 和 x(a)

clc
clear

%gravity
g = 9.81;

%objective function

func = @(v0,a) ((2 * (v0)^2 * sind(a) * cosd(a)) / g);

%angle bounds (degrees)  0 < xa < 90 

Xup = 85;

Xlo = 1;

%golden ratio = ((1 + sqrt(5))/2

G = 1.618;

%iteration

d  = (G - 1)*(Xup - Xlo);

x1 = (Xup - d);

x2 = (Xlo + d);

%error tolerance

et = 10^-2;  

%error limit

error = inf;

%v0 is a user input

v0 = input('input intial velocity:')

% at end points

f_up = func(v0,Xup);   %-8.1667

f_lo = func(v0,Xlo);    %2.0525

%function iterations

f1 = func(v0,x1);

f2 = func(v0,x2);


while error > et

    if f1 > f2

        Xup = x2;

        f_upper = f2;

        x2 = x1;

        f2 = f1;

        d = (G - 1)*(Xup - Xlo);

        Xlo = Xup - d;

        f1 = func(v0,x1);

    elseif f1 < f2

        Xlo = x1;

        f_lower = f1;

        x1 = x2;

        f1 = f2;

        d = (G - 1)*(Xup - Xlo);

        x2 = Xlo + d;

    else

        Xlo = (x1 + x2)/2;

        Xup = Xlo;

    end

    %calculating absolute error determining convergence

    error = abs(Xup - Xlo);

end


a = (x1 + x2)/2

distance = func(v0,a)

在调用函数前应输入初始速度v0，答案应始终显示45为角度，同时显示以该角度计算的距离。

Answer 1

通读 cmets，this 链接对于实现 黄金搜索 也很有用。

---

最大化给定目标的函数

function gold(v0)
% given data
g = 9.81;

Xup = 85;
Xlo = 1;
et = 10^-2;
% since v0 is a user define, it is considered as constant in function func
% minimize the opposite of the objective is equivalent to maximization
func = @(a) -1*((2 * (v0)^2 * sind(a) * cosd(a)) / g);
% make a call to  goldSearch
[angle, negative_dist] = goldSearch(func, Xlo, Xup, et);

% since we minimize the opposite, to find the real value, multiple by -1
distance = -negative_dist;

% display result
fprintf('Angle : %f\nDistance: %f\n',angle,distance);



            % goldSearch minimize the function  
            function [ xMin, fMin] = goldSearch(funcname, a, b, tol) 

            % a is the lower bound, b is the upper bound
            % default tolerance 
            if nargin <4 
                tol=1.0e-6; 
            end

            % golden ratio value
            R=(sqrt(5)-1)/2; 
            C=1 - R; 

            % initial try and error
            x1=R*a+ C*b; 
            x2=C*a +R*b; 

            % get their function evaluation
            f1=feval(funcname,x1); 
            f2=feval(funcname,x2); 


            while (b-a)>tol
               % update upper bound 
               if f1>f2 
                   a = x1; x1 = x2; f1 = f2; 
                   x2 = C*a + R*b; 
                   f2= feval(funcname,x2); 
               else 
               % update lower bound
                   b = x2; x2 = x1; f2 = f1; 
                   x1= R*a + C*b; 
                   f1= feval(funcname,x1); 
               end
            end

                if f1< f2 
                   fMin=f1; xMin=x1; 
                else 
                   fMin=f2; xMin=x2; 
                end 



            end 

end

---

测试功能

format short g
v0 = input('input intial velocity:');
gold(v0)

---

结果

input intial velocity:25
Angle : 45.000154
Distance: 63.710499