mmpp2_fit.m

function MAP=mmpp2_fit(E1,E2,E3,ACFLAG1)
%  mmpp2_fit fits the moments and lag-1 acf with a MMPP2
%
%   MAP=mmpp2_fit(E1,E2,E3,ACFLAG1) returns a MMPP2 with prescribed first three
%   moments and lag-1 acf
%
%   Input:
%       E1   = the first moment
%       E2   = the second moment
%       E3   = the third moment
%       ACFLAG1 = lag-1 acf *note MMPP2 can fit only ACFLAG1 in [0,0.5]
%
%   Output:
%       MAP = a map in the form of {D0,D1} with the given moments of E1, E2,
%       E3 and the autocorrelation parameter G2
SCV=(E2-E1^2)/E1^2;
G2=ACFLAG1/((1-1/SCV)/2);
if (G2<1e-6) || (G2==0)
    % if G2 is not symbolic and G2 is very close to zeros, fit the moments
    % and autocorrelations with a MAP(1)
    mu00=2*(6*E1^3*SCV-E3)/E1/(6*E1^3*SCV+3*E1^3*SCV^2+3*E1^3-2*E3);
    mu11=0;
    q01= 9*E1^5*(SCV-1)*(SCV^2-2*SCV+1)/(6*E1^3*SCV-E3)/(6*E1^3*SCV+3*E1^3*SCV^2+3*E1^3-2*E3);
    q10=-3*(SCV-1)*E1^2/(6*E1^3*SCV-E3);
else
    % if G2 is not close to 1, fit with a MMPP(2)
    mu00=G2*(-4*E3*G2+4*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*E3*G2-18*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*G2-18*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*G2*SCV^2-12*E1^3*G2^2-12*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*G2^2*SCV+12*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*G2*SCV+12*E1^3*G2*SCV^2-9*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*SCV+3*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)+12*E1^3*G2^2*SCV+9*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*SCV^2+12*E1^3*G2+12*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*G2^2-3*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*SCV^3)/(12*E1^3*G2^3*SCV+3*E1^3*SCV^3*G2-12*E1^3*G2^3+18*E1^3*G2^2*SCV^2-3*E1^3*G2+27*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*G2*SCV^2-9*E1^3*G2*SCV^2+18*E1^3*G2^2-12*E1^3*G2^2*SCV+9*E1^3*G2*SCV-12*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*G2^3*SCV-9*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*SCV^3*G2-24*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*G2^2*SCV^2-(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*E3*SCV^2+4*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*E3*G2^2+12*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*G2^3-(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*E3+2*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*E3*SCV+9*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*G2+24*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*G2^2*SCV-27*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*G2*SCV+6*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*SCV-12*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*SCV^2-24*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*G2^2+6*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*SCV^3-4*E3*G2^2)/E1;
    mu11=(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/E1/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3);
    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6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))*E1^5/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*SCV^2+45*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))*E1^5/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*G2*SCV-12*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))*E1^2/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*SCV*E3-3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))*E1^2/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*G2*E3+9*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))*E1^5/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*G2*SCV^3+36*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))*E1^5/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*G2^2*SCV^2-6*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))*E1^2/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*G2^2*E3+18*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))*E1^5/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*G2^3*SCV-18*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))*E1^5/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*G2^3-9*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))*E1^5/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*G2);
    q10=3*(-3*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*SCV^3-3*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*G2*SCV^2+6*E1^3*SCV^2+3*E1^3*G2*SCV^2+3*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*SCV^2+6*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*G2*SCV-E3*SCV-6*E1^3*SCV+(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*E3*SCV-6*E1^3*G2*SCV-3*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*SCV-(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*E3+3*E1^3*G2-3*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)*G2+3*E1^3*(-3*E1^3*G2+3*E1^3*G2*SCV-6*E1^3*SCV+E3+(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2)^(1/2))/(-3*E1^3*SCV^2-6*E1^3*SCV-3*E1^3+2*E3)+E3)*E1^2*(-1+G2)/(E3^2-12*E1^3*SCV*E3+6*E1^3*G2*E3-6*G2*SCV*E1^3*E3+18*G2*SCV^3*E1^6-18*E1^6*G2*SCV^2+9*E1^6*G2^2+36*E1^6*SCV^2+18*E1^6*G2*SCV-18*E1^6*SCV*G2^2+9*E1^6*SCV^2*G2^2-18*E1^6*G2);
end
D0=[ -mu00-q01,       q01;
    q10, -mu11-q10];
D1=[ mu00,   0;
    0, mu11];
MAP={D0,D1};
end