斐波那契法求極小值

   功能：用斐波那契法求f(x)在區(qū)間[a,b]上的近似極小值。當且僅當f(x)在[a,b]上為單峰時次方法適用

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function X=fibonacci(f,a,b,tol,e)

% input  - f is the object function input as a string 'f'

%        - a and b are the end points of the interval

%        - tol : length of uncertainy

%        - e :distinguishability of constant

% output - X : x and y coordinates of minimum

%   note : this function calls the m-file fib.m while had been edited 


i=1;

F=1;

while F<=(b-a)/tol

      F=fib(i);

      i=i+1;

end

n=i-1;

A=zeros(1,n-2);B=zeros(1,n-2);

A(1)=a;

B(1)=b;

c=A(1)+(fib(n-2)/fib(n))*(B(1)-A(1));

d=A(1)+(fib(n-1)/fib(n))*(B(1)-A(1));

k=1;

while k=n-3

      if feval(f,c)>feval(f,d)

         A(k+1)=c;

         B(k+1)=B(k);

         c=d;

         d=A(k+1)+(fib(n-k-1)/fib(n-k))*(B(k+1)-A(k+1));

      else

         A(k+1)=A(k);

         B(k+1)=d;

         d=c;

         c=A(k+1)+(fib(n-k-2)/fib(n-k))*(B(k+1)-A(k+1));

      end

      k=k+1;

end

if feval(f,c)>feval(f,d)

   A(n-2)=c;

   B(n-2)=B(n-3);

   c=d;

   d=A(n-2)+(0.5+e)*(B(n-2)-A(n-2));

else 

   A(n-2)=A(N-3);

   B(n-2)=d;

   d=c;

   c=A(n-2)+(0.5+e)*(B(n-2)-A(n-2));

end

if feval(f,c)>feval(f,d)

   a=c;

   b=B(n-2);

else

   a=A(n-2);

   b=d;

end

X=[(a+b)/2 feval(f,(a+b)/2)];

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% 下面的程序用來生成斐波那契數(shù)

function y=fib(n)

fz(1)=1;

fz(2)=1;

for k=3:n

    fz(k)=fz(k-1)+fz(k-1);

end

y=fz(n);