Plotting a Piecewise function Dg?
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Hello community I look to get the figure of Dg, please verifiy if the definition of Piecewise function Dg is correct and Thank you
clc
clear all
x=[]; y=[]; z=[];
for n=1:1001
x1=0.01*(n-1);
x2=4;
B=[0,x1,4,x2;
x1,3,x2,x2;
x1,0,5,x2;
0,5,x2,x1];
%{
Pd=eig(B);
if max(real(Pd))<0
disp('fail');
disp(n);
end
%}
B11=[B(1,1),B(1,2);B(2,1),B(2,2)];
B22=[B(3,3),B(3,4);B(4,3),B(4,4)];
B12=[B(1,3),B(1,4);B(2,3),B(2,4)];
V1_2=[B11,B12;B12',B22];
A1=det(B11);
B1=det(B22);
C1=det(B12);
D1=det(V1_2);
Sum=det(B11)+det(B22)+2.*det(B12);
nup=sqrt(Sum+sqrt(Sum.^2-4.*det(V1_2)))./sqrt(2);
nun=sqrt(Sum-sqrt(Sum.^2-4.*det(V1_2)))./sqrt(2);
%defin quantum discord
fmp=(nup+1)/2*log((nup+1)/2)-(nup-1)/2*log((nup-1)/2);
fmn=(nun+1)/2*log((nun+1)/2)-(nun-1)/2*log((nun-1)/2);
fB1=(sqrt(B1)+1)/2*log((sqrt(B1)+1)/2)-(sqrt(B1)-1)/2*log((sqrt(B1)-1)/2);
Dg1=fB1-fmp-fmn;
%inf epsilon
G1=(2*C1^2+(B1-1)*(D1-A1)+2*abs(C1)*sqrt(C1^2+(-1+B1)*(-A1+D1)))/(B1-1)^2;%val1
G2=(A1*B1-C1^2+D1-sqrt(C1^4+(-A1*B1+D1)^2-2*C1*(A1*B1+D1)))/2*B1;%val2
G3=(D1-A1*B1)^2-(1+B1)*C1^2*(A1+D1);%<=0 condition
DgG1=(sqrt(G1)+1)/2*log((sqrt(G1)+1)/2)-(sqrt(G1)-1)/2*log((sqrt(G1)-1)/2); %val if %G3<=0 condition
DgG2=(sqrt(G2)+1)/2*log((sqrt(G2)+1)/2)-(sqrt(G2)-1)/2*log((sqrt(G2)-1)/2); %else G3>0
if G3 <= 0
Dg = real(DgG1+Dg1);
else
Dg = real(DgG2+Dg1);
end
x(n)=x1; y(n)=Dg;
n=n+1;
end
plot(x,y)
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