function [V0,y0,dV,dy]=nelder(F,V,min1,max1,epsilon,show)%Input    - F is the object function input as a string 'F'%         - V is a 3xn matrix containing starting simplex%         - min1 & max1 are minimum and maximum number of iterations%         - epsilon is the tolerance%         - show == 1 displays iterations (P and Q)%Output   - V0 is the vertex forthe minimum%         - y0 is the function value F(V0)%         - dV is the size of the final simplex%         - dy is the error bound for the minimum%         - P is a matrix containing the vertex iterations%         - Q is an array containing the iterations for F(P)%  NUMERICAL METHODS: Matlab Programs% (c) 2004 by John H. Mathews and Kurtis D. Fink%  Complementary Software to accompany the textbook:%  NUMERICAL METHODS: Using Matlab, Fourth Edition%  ISBN: 0-13-065248-2%  Prentice-Hall Pub. Inc.%  One Lake Street%  Upper Saddle River, NJ 07458if nargin==5,   show=0;end[mm n]=size(V);% Order the verticesfor j=1:n+1   Z=V(j,1:n);   Y(j)=feval(F,Z);end[mm lo]=min(Y);[mm hi]=max(Y);li=hi;ho=lo;for j=1:n+1   if(j~=lo&j~=hi&Y(j)<=Y(li))      li=j;   end   if (j~=hi&j~=lo&Y(j)>=Y(ho))      ho=j;   endendcnt=0;%  Start of Nelder-Mead algorithmwhile (Y(hi)>Y(lo)+epsilon&cnt<max1)|cnt<min1   S=zeros(1,1:n);   for j=1:n+1      S=S+V(j,1:n);   end   M=(S-V(hi,1:n))/n;   R=2*M-V(hi,1:n);   yR=feval(F,R);   if (yR<Y(ho))      if (Y(li)<yR)         V(hi,1:n)=R;         Y(hi)=yR;      else         E=2*R-M;         yE=feval(F,E);         if (yE<Y(li))            V(hi,1:n)=E;            Y(hi)=yE;         else            V(hi,1:n)=R;            Y(hi)=yR;         end      end   else      if (yR<Y(hi))         V(hi,1:n)=R;         Y(hi)=yR;      end      C=(V(hi,1:n)+M)/2;      yC=feval(F,C);      C2=(M+R)/2;      yC2=feval(F,C2);      if (yC2<yC)         C=C2;         yC=yC2;      end      if (yC<Y(hi))         V(hi,1:n)=C;         Y(hi)=yC;      else         for j=1:n+1            if (j~=lo)               V(j,1:n)=(V(j,1:n)+V(lo,1:n))/2;               Z=V(j,1:n);               Y(j)=feval(F,Z);            end         end      end   end   [mm lo]=min(Y);   [mm hi]=max(Y);   li=hi;   ho=lo;   for j=1:n+1      if (j~=lo&j~=hi&Y(j)<=Y(li))         li=j;      end      if (j~=hi&j~=lo&Y(j)>=Y(ho))         ho=j;      end   end   cnt=cnt+1;   P(cnt,:)=V(lo,:);   Q(cnt)=Y(lo);end% End of Nelder-Mead algorithm%Determine size of simplexsnorm=0;for j=1:n+1   s=norm(V(j)-V(lo));   if(s>=snorm)      snorm=s;   endendQ=Q';V0=V(lo,1:n);y0=Y(lo);dV=snorm;dy=abs(Y(hi)-Y(lo));if (show==1)   disp(P);   disp(Q);end