Matlab 抛物线法

%v1.0 author: liuxi BIT

%best_x为最优的x值，best_fx为最优的函数值，y为函数，x为函数y的变量，x1,x0,x2为已知的三点且满足f1>f0function[best_x best_fx]=paowuxianfa(y,x,x1,x0,x2,epsilon1,epsilon2)

if nargin==5

    epsilon1=0.0000001;

    epsilon2=0.0000001;

end

%求f(x1),f(x0),f(x2)

f1=subs(y,x,x1);

f0=subs(y,x,x0);

f2=subs(y,x,x2);

k=0;

while abs(x1-x2)>epsilon1&&abs((x2-x0)*f1+(x1-x2)*f0+(x0-x1)*f2)>epsilon2%step1 step2

    x3=0.5*((x2^2-x0^2)*f1+(x1^2-x2^2)*f0+(x0^2-x1^2)*f2)/((x2-x0)*f1+(x1-x2)*f0+(x0-x1)*f2);%step3   x3对应算法中的x一拔，就是x上面有一个“—”

    f3=subs(y,x,x3);

if f0-f3<0%转step6

if x0            x2=x3;f2=f3;

        else

            x1=x3;f1=f3;

end%if x0    elseif f0-f3==0%转step7

if x0            x1=x0;x2=x3;x0=0.5*(x1+x2);

            f1=f0;f2=f3;f0=subs(y,x,x0);

        elseif x0==x3%转step8

            x4=0.5*(x1+x0);f4=subs(y,x,x4);%x4对应算法中的x一冒，就是x上面有一个“^”

if f4                x2=x0;x0=x4;f2=f0;f0=f4;

            elseif f4==f0

                x1=x4;x2=x0;x0=0.5*(x1+x2);

                f1=f4;f2=f0;f0=subs(y,x,x0);

            else

                x1=x4;f1=f4;

end%if f4        else%转step9

            x1=x3;x2=x0;x0=0.5*(x1+x2);

             f1=f3;f2=f0;f0=subs(y,x,x0);

end% if x0    else %转step5

if x0>x3

            x2=x0;x0=x3;f2=f0;f0=f3;

        else

            x1=x0;x0=x3;f1=f0;f0=f3;

        end

end%if f0-f3<0

    k=k+1;

end%while

best_x=x0;

best_fx=f0;