針對1個變量繪製3個變量

Question

我有一個計算最大值的代碼。這個代碼由四個變量組成www是a，b和c的函數，分別表示xx，yy和zz，所以我的問題是如何將www映射爲xx，yy和zz？感謝您的幫助

objfun文件

function f=W4qubit(x,a,b,c,d) 
c1=-cos(x(1))*(cos(x(5))*(cos(x(9))*(cos(x(13))-cos(x(15)))-cos(x(11))*(cos(x(13))+cos(x(15))))+... 
    cos(x(7))*(cos(x(11))*(cos(x(15))-cos(x(13)))-cos(x(9))*(cos(x(13))+cos(x(15)))))-... 
    cos(x(3))*(cos(x(5))*(cos(x(11))*(cos(x(15))-cos(x(13)))-cos(x(9))*(cos(x(13))+cos(x(15))))-... 
    cos(x(7))*(cos(x(9))*(cos(x(13))-cos(x(15)))-cos(x(11))*(cos(x(13))+cos(x(15))))); 
c2=cos(x(1))*(cos(x(5))*(sin(x(9))*(sin(x(13))*cos(x(10)-x(14))-sin(x(15))*cos(x(10)-x(16)))-... 
    sin(x(11))*(sin(x(13))*cos(x(12)-x(14))+sin(x(15))*cos(x(12)-x(16))))+... 
    cos(x(7))*(sin(x(11))*(sin(x(15))*cos(x(12)-x(16))-sin(x(13))*cos(x(12)-x(14)))-... 
    sin(x(9))*(sin(x(13))*cos(x(10)-x(14))+sin(x(15))*cos(x(10)-x(16)))))+... 
    cos(x(3))*(cos(x(5))*(sin(x(11))*(sin(x(15))*cos(x(12)-x(16))-sin(x(13))*cos(x(12)-x(14)))-... 
    sin(x(9))*(sin(x(13))*cos(x(10)-x(14))+sin(x(15))*cos(x(10)-x(16))))-... 
    cos(x(7))*(sin(x(9))*(sin(x(13))*cos(x(10)-x(14))-sin(x(15))*cos(x(10)-x(16)))-... 
    sin(x(11))*(sin(x(13))*cos(x(12)-x(14))+sin(x(15))*cos(x(12)-x(16))))); 
c3=cos(x(1))*(sin(x(5))*(cos(x(9))*(sin(x(13))*cos(x(6)-x(14))-sin(x(15))*cos(x(6)-x(16)))-... 
    cos(x(11))*(sin(x(13))*cos(x(6)-x(14))+sin(x(15))*cos(x(6)-x(16))))+... 
    sin(x(7))*(cos(x(11))*(sin(x(15))*cos(x(8)-x(16))-sin(x(13))*cos(x(8)-x(14)))-... 
    cos(x(9))*(sin(x(13))*cos(x(8)-x(14))+sin(x(15))*cos(x(8)-x(16)))))+... 
    cos(x(3))*(sin(x(5))*(cos(x(11))*(sin(x(15))*cos(x(6)-x(16))-sin(x(13))*cos(x(6)-x(14)))-... 
    cos(x(9))*(sin(x(13))*cos(x(6)-x(14))+sin(x(15))*cos(x(6)-x(16))))-... 
    sin(x(7))*(cos(x(9))*(sin(x(13))*cos(x(8)-x(14))-sin(x(15))*cos(x(8)-x(16)))-... 
    cos(x(11))*(sin(x(13))*cos(x(8)-x(14))+sin(x(15))*cos(x(8)-x(16))))); 
c4=cos(x(1))*(sin(x(5))*(sin(x(9))*cos(x(6)-x(10))*(cos(x(13))-cos(x(15)))-sin(x(11))*cos(x(6)-x(12))*(cos(x(13))+cos(x(15))))+... 
    sin(x(7))*(sin(x(11))*cos(x(8)-x(12))*(cos(x(15))-cos(x(13)))-sin(x(9))*cos(x(8)-x(10))*(cos(x(13))+cos(x(15)))))+... 
    cos(x(3))*(sin(x(5))*(sin(x(11))*cos(x(6)-x(12))*(cos(x(15))-cos(x(13)))-sin(x(9))*cos(x(6)-x(10))*(cos(x(13))+cos(x(15))))-... 
    sin(x(7))*(sin(x(9))*cos(x(8)-x(10))*(cos(x(13))-cos(x(15)))-sin(x(11))*cos(x(8)-x(12))*(cos(x(13))+cos(x(15))))); 
c5=sin(x(1))*(cos(x(5))*(cos(x(9))*(sin(x(13))*cos(x(2)-x(14))-sin(x(15))*cos(x(2)-x(16)))-... 
    cos(x(11))*(sin(x(13))*cos(x(2)-x(14))+sin(x(15))*cos(x(2)-x(16))))+... 
    cos(x(7))*(cos(x(11))*(sin(x(15))*cos(x(2)-x(16))-sin(x(13))*cos(x(2)-x(14)))-... 
    cos(x(9))*(sin(x(13))*cos(x(2)-x(14))+sin(x(15))*cos(x(2)-x(16)))))+... 
    sin(x(3))*(cos(x(5))*(cos(x(11))*(sin(x(15))*cos(x(4)-x(16))-sin(x(13))*cos(x(4)-x(14)))-... 
    cos(x(9))*(sin(x(13))*cos(x(4)-x(14))+sin(x(15))*cos(x(4)-x(16))))-... 
    cos(x(7))*(cos(x(9))*(sin(x(13))*cos(x(4)-x(14))-sin(x(15))*cos(x(4)-x(16)))-... 
    cos(x(11))*(sin(x(13))*cos(x(4)-x(14))+sin(x(15))*cos(x(4)-x(16))))); 
c6=sin(x(1))*(cos(x(5))*(sin(x(9))*cos(x(2)-x(10))*(cos(x(13))-cos(x(15)))-sin(x(11))*cos(x(2)-x(12))*(cos(x(13))+cos(x(15))))+... 
    cos(x(7))*(sin(x(11))*cos(x(2)-x(12))*(cos(x(15))-cos(x(13)))-sin(x(9))*cos(x(2)-x(10))*(cos(x(13))+cos(x(15)))))+... 
    sin(x(3))*(cos(x(5))*(sin(x(11))*cos(x(4)-x(12))*(cos(x(15))-cos(x(13)))-sin(x(9))*cos(x(4)-x(10))*(cos(x(13))+cos(x(15))))-... 
    cos(x(7))*(sin(x(9))*cos(x(4)-x(10))*(cos(x(13))-cos(x(15)))-sin(x(11))*cos(x(4)-x(12))*(cos(x(13))+cos(x(15))))); 
c7=sin(x(1))*(sin(x(5))*cos(x(2)-x(6))*(cos(x(9))*(cos(x(13))-cos(x(15)))-cos(x(11))*(cos(x(13))+cos(x(15))))-... 
    sin(x(7))*cos(x(2)-x(8))*(cos(x(11))*(cos(x(15))-cos(x(13)))-cos(x(9))*(cos(x(13))+cos(x(15)))))+... 
    sin(x(3))*(sin(x(5))*cos(x(4)-x(6))*(cos(x(11))*(cos(x(15))-cos(x(13)))-cos(x(9))*(cos(x(13))+cos(x(15))))-... 
    sin(x(7))*cos(x(4)-x(8))*(cos(x(9))*(cos(x(13))-cos(x(15)))-cos(x(11))*(cos(x(13))+cos(x(15))))); 
A2=2*a*b; 
A3=2*a*c; 
A4=2*b*c; 
A5=2*a*d; 
A6=2*b*d; 
A7=2*c*d; 
f1=c1+A2*c2+A3*c3+A4*c4+A5*c5+A6*c6+A7*c7; 
f=-(f1^2); 

我主要的代碼

clear 
close 
clc 
%x=[x(1),x(2),x(3),x(4),x(5),x(6),x(7),x(8),x(9),x(10),x(11),x(12),x(13),x(14),x(15),x(16)]; % angles; 

lb=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
ub=[pi,2*pi,pi,2*pi,pi,2*pi,pi,2*pi,pi,2*pi,pi,2*pi,pi,2*pi,pi,2*pi]; 
options = optimoptions(@fmincon,'TolX',10^-12,'MaxIter',1500,'MaxFunEvals',10^8,'Algorithm','sqp','TolFun',10^-8); 
a=0:0.1:1; 
b=0:0.1:1; 
c=0:0.1:1; 
w=NaN(length(a),length(b),length(c)); 
ww=NaN(length(a),length(b),length(c)); 
www=NaN(length(a),length(c)); 
for k=1:100 
    x0=rand([1,16]).*ub*.9986;%7976 

for i=1:length(a) 
for j=1:length(b) 
for l=1:length(c) 
dhelp=1-(a(i)^2)-(b(j)^2)-(c(l)^2); 
if (dhelp>0 || dhelp==0) 
    d=sqrt(dhelp); 
     [~,fval]=fmincon(@(x)W4qubit(x,a(i),b(j),c(l),d),x0,[],[],[],[],lb,ub,[],options); 
w(i,j,l)=sqrt(-fval); 
else 
    w(i,j,l)=nan; 
end 
ww=max(w,ww); 
end 
end 
end 
end 
www=max(ww,[],3); 
yy=b.^2;xx=a.^2;zz=c.^2; 
meshc(xx,yy,www) 
grid on 
zlabel('\fontname{Times New Roman} M_{max}') 
xlabel('\fontname{Times New Roman}\alpha^2') 
ylabel('\fontname{Times New Roman}\gamma^2') 
%title('fontname{Times New Roman} Maximum of the Svetlichny operator. Method 1 (alpha|0001>+beta|0010>+gamma|1000>)') 

Answer 1

不知道的文件，但不

plot(www,[xx;yy;zz]); 

做的工作爲你？我沒有優化工具箱，所以我無法測試您的腳本。但原則上，這應該起作用。