function output = ModelT6(x,x0,del,param)



% \[Mu]1[x1_,x2_,x3_] = a1*(b1-x1); 
% \[Mu]2[x1_,x2_,x3_] = a21*(b1-x1) + a2*(b2-x2); 
% \[Mu]3[x1_,x2_,x3_] = a31*(b1-x1) + a32*(b2-x2) + a3*(b3-x3); 

% \[Sigma]11[x1_,x2_,x3_] = Sqrt[x1]; 
% \[Sigma]22[x1_,x2_,x3_] = g22*Sqrt[x1]; 
% \[Sigma]33[x1_,x2_,x3_] = g33;
% \[Sigma]12[x1_,x2_,x3_] = 0;
% \[Sigma]13[x1_,x2_,x3_] = 0; 
% \[Sigma]21[x1_,x2_,x3_] = g21*Sqrt[x1];
% \[Sigma]23[x1_,x2_,x3_] = 0;
% \[Sigma]31[x1_,x2_,x3_] = g31*Sqrt[x1];
% \[Sigma]32[x1_,x2_,x3_] = g32*Sqrt[x1];

% Dv[x1_,x2_,x3_] = Log[g22] + Log[g33] + Log[x1];


x1 = x(1);
x2 = x(2);
x3 = x(3);
x10 = x0(1);
x20 = x0(2);
x30 = x0(3);


a1 = param(1);
b1 = param(2);
a21 = param(3);
a2 = param(4);
b2 = param(5);
a31 = param(6);
a32 = param(7);
a3 = param(8);
b3 = param(9);
g21 = param(10);
g22 = param(11);
g31 = param(12);
g32 = param(13);
g33 = param(14);


Dv = log(g22) + log(g33) + log(x1); 


cm1 = ((g21^4 - 14*g21^2*g22^2 - 15*g22^4)*(x1 - x10)^4)/(96*g22^4*x10^3) + ((g21^2 + g22^2)*(x1 - x10)^3)/(4*g22^2*x10^2) - ((g21^3 - 7*g21*g22^2)*(x1 - x10)^3*(x2 - x20))/(24*g22^4*x10^3) - (g21*(x1 - x10)^2*(x2 - x20))/(2*g22^2*x10^2) + ((3*g21^2 - 7*g22^2)*(x1 - x10)^2*(x2 - x20)^2)/(48*g22^4*x10^3) + ((x1 - x10)*(x2 - x20)^2)/(4*g22^2*x10^2) - (g21*(x1 - x10)*(x2 - x20)^3)/(24*g22^4*x10^3) + (x2 - x20)^4/(96*g22^4*x10^3) - (1/(2*g22^2*g33^2*x10))*(g21^2*(x1 - x10)^2*(g33^2 + g32^2*x10) + (g33^2 + g32^2*x10)*(x2 - x20)^2 - 2*g22*g32*x10*(x2 - x20)*(g31*(-x1 + x10) + x3 - x30) - 2*g21*(x1 - x10)*((g33^2 + g32^2*x10)*(x2 - x20) + g22*g32*x10*(g31*(x1 - x10) - x3 + x30)) + g22^2*(g33^2*(x1 - x10)^2 + x10*(g31*(x1 - x10) - x3 + x30)^2));


c0 = -((1/(24*g22^2*g33^2*x10^2))*((x1 - x10)^2*(g21^2*g33^2 + 12*a1*b1*g21^2*g33^2 + g22^2*g33^2 + 12*a1*b1*g22^2*g33^2 - 12*a31*g22^2*g31*x10^2 + 12*a1*g22^2*g31^2*x10^2 + 12*a31*g21*g22*g32*x10^2 - 24*a1*g21*g22*g31*g32*x10^2 + 12*a1*g21^2*g32^2*x10^2 - 12*a21*(b1*g21*g33^2 + g32*((-g22)*g31 + g21*g32)*x10^2) - 12*a2*g21*g33^2*(b2 - x20)))) + ((12*g32*(a32*g22 - a2*g32)*x10^2 - g33^2*(1 + 12*a2*x10))*(x2 - x20)^2)/(24*g22^2*g33^2*x10^2) + (1/(12*g22^2*g33^2*x10^2))*((x1 - x10)*(x2 - x20)*(g21*g33^2 + 6*a1*b1*g21*g33^2 + 6*a32*g22^2*g31*x10^2 + 6*a31*g22*g32*x10^2 - 6*a32*g21*g22*g32*x10^2 - 6*a1*g22*g31*g32*x10^2 + 6*a1*g21*g32^2*x10^2 - 6*a21*(b1*g33^2 + g32^2*x10^2) + 6*a2*((-b2)*g33^2 - g22*g31*g32*x10^2 + g21*x10*(g33^2 + g32^2*x10) + g33^2*x20))) + (((-a31)*g22 + a1*g22*g31 + a3*g22*g31 + a21*g32 - a1*g21*g32 - a3*g21*g32)*(x1 - x10)*(x3 - x30))/(2*g22*g33^2) + (((-a32)*g22 + (a2 + a3)*g32)*(x2 - x20)*(x3 - x30))/(2*g22*g33^2) - (a3*(x3 - x30)^2)/(2*g33^2) + ((x3 - x30)*(a3*b3*g22 - a1*b1*g22*g31 - a21*b1*g32 - a2*b2*g32 + a1*b1*g21*g32 + a31*g22*(b1 - x10) + a1*g22*g31*x10 + a21*g32*x10 - a1*g21*g32*x10 + a32*g22*(b2 - x20) + a2*g32*x20 - a3*g22*x30))/(g22*g33^2) + (1/(g22^2*g33^2*x10))*(x2 - x20)*((-a1)*b1*g21*g33^2 - a31*b1*g22*g32*x10 - a32*b2*g22*g32*x10 - a3*b3*g22*g32*x10 + a1*b1*g22*g31*g32*x10 - a1*b1*g21*g32^2*x10 + a1*g21*g33^2*x10 + a31*g22*g32*x10^2 - a1*g22*g31*g32*x10^2 + a1*g21*g32^2*x10^2 + a21*(b1 - x10)*(g33^2 + g32^2*x10) + a2*(g33^2 + g32^2*x10)*(b2 - x20) + a32*g22*g32*x10*x20 + a3*g22*g32*x10*x30) + (1/(g22^2*g33^2*x10))*(x1 - x10)*(a1*b1*g21^2*g33^2 + a1*b1*g22^2*g33^2 - a31*b1*g22^2*g31*x10 - a32*b2*g22^2*g31*x10 - a3*b3*g22^2*g31*x10 + a1*b1*g22^2*g31^2*x10 + a31*b1*g21*g22*g32*x10 + a32*b2*g21*g22*g32*x10 + a3*b3*g21*g22*g32*x10 - 2*a1*b1*g21*g22*g31*g32*x10 + a1*b1*g21^2*g32^2*x10 - a1*g21^2*g33^2*x10 - a1*g22^2*g33^2*x10 + a31*g22^2*g31*x10^2 - a1*g22^2*g31^2*x10^2 - a31*g21*g22*g32*x10^2 + 2*a1*g21*g22*g31*g32*x10^2 - a1*g21^2*g32^2*x10^2 + a21*(b1 - x10)*(g22*g31*g32*x10 - g21*(g33^2 + g32^2*x10)) + a2*(g22*g31*g32*x10 - g21*(g33^2 + g32^2*x10))*(b2 - x20) + a32*g22^2*g31*x10*x20 - a32*g21*g22*g32*x10*x20 + a3*g22^2*g31*x10*x30 - a3*g21*g22*g32*x10*x30);



c1 = (-(1/(12*g22^2*g33^2*x10)))*(6*a1^2*b1^2*g21^2*g33^2 + g22^2*g33^2 - 6*a1*b1*g22^2*g33^2 + 6*a1^2*b1^2*g22^2*g33^2 + 6*a31^2*b1^2*g22^2*x10 + 12*a31*a32*b1*b2*g22^2*x10 + 6*a32^2*b2^2*g22^2*x10 + 12*a3*a31*b1*b3*g22^2*x10 + 12*a3*a32*b2*b3*g22^2*x10 + 6*a3^2*b3^2*g22^2*x10 - 12*a1*a31*b1^2*g22^2*g31*x10 - 12*a1*a32*b1*b2*g22^2*g31*x10 - 12*a1*a3*b1*b3*g22^2*g31*x10 + 6*a1^2*b1^2*g22^2*g31^2*x10 + 12*a1*a31*b1^2*g21*g22*g32*x10 + 12*a1*a32*b1*b2*g21*g22*g32*x10 + 12*a1*a3*b1*b3*g21*g22*g32*x10 - 12*a1^2*b1^2*g21*g22*g31*g32*x10 + 6*a1^2*b1^2*g21^2*g32^2*x10 - 12*a1^2*b1*g21^2*g33^2*x10 - 6*a3*g22^2*g33^2*x10 - 12*a1^2*b1*g22^2*g33^2*x10 - 12*a31^2*b1*g22^2*x10^2 - 12*a31*a32*b2*g22^2*x10^2 - 12*a3*a31*b3*g22^2*x10^2 + 24*a1*a31*b1*g22^2*g31*x10^2 + 12*a1*a32*b2*g22^2*g31*x10^2 + 12*a1*a3*b3*g22^2*g31*x10^2 - 12*a1^2*b1*g22^2*g31^2*x10^2 - 24*a1*a31*b1*g21*g22*g32*x10^2 - 12*a1*a32*b2*g21*g22*g32*x10^2 - 12*a1*a3*b3*g21*g22*g32*x10^2 + 24*a1^2*b1*g21*g22*g31*g32*x10^2 - 12*a1^2*b1*g21^2*g32^2*x10^2 + 6*a1^2*g21^2*g33^2*x10^2 + 6*a1^2*g22^2*g33^2*x10^2 + 6*a31^2*g22^2*x10^3 - 12*a1*a31*g22^2*g31*x10^3 + 6*a1^2*g22^2*g31^2*x10^3 + 12*a1*a31*g21*g22*g32*x10^3 - 12*a1^2*g21*g22*g31*g32*x10^3 + 6*a1^2*g21^2*g32^2*x10^3 + 6*a21^2*(b1 - x10)^2*(g33^2 + g32^2*x10) + 6*a2^2*(g33^2 + g32^2*x10)*(b2 - x20)^2 - 12*a31*a32*b1*g22^2*x10*x20 - 12*a32^2*b2*g22^2*x10*x20 - 12*a3*a32*b3*g22^2*x10*x20 + 12*a1*a32*b1*g22^2*g31*x10*x20 - 12*a1*a32*b1*g21*g22*g32*x10*x20 + 12*a31*a32*g22^2*x10^2*x20 - 12*a1*a32*g22^2*g31*x10^2*x20 + 12*a1*a32*g21*g22*g32*x10^2*x20 + 6*a32^2*g22^2*x10*x20^2 - 12*a3*a31*b1*g22^2*x10*x30 - 12*a3*a32*b2*g22^2*x10*x30 - 12*a3^2*b3*g22^2*x10*x30 + 12*a1*a3*b1*g22^2*g31*x10*x30 - 12*a1*a3*b1*g21*g22*g32*x10*x30 + 12*a3*a31*g22^2*x10^2*x30 - 12*a1*a3*g22^2*g31*x10^2*x30 + 12*a1*a3*g21*g22*g32*x10^2*x30 + 12*a3*a32*g22^2*x10*x20*x30 + 6*a3^2*g22^2*x10*x30^2 + 12*a21*(b1 - x10)*(a1*(b1 - x10)*(g22*g31*g32*x10 - g21*(g33^2 + g32^2*x10)) + a2*(g33^2 + g32^2*x10)*(b2 - x20) + g22*g32*x10*((-a32)*b2 - a3*b3 + a31*(-b1 + x10) + a32*x20 + a3*x30)) - 6*a2*(2*a1*(b1 - x10)*((-g22)*g31*g32*x10 + g21*(g33^2 + g32^2*x10))*(b2 - x20) + g22*x10*(2*a3*b2*b3*g32 + g22*g33^2 + 2*a31*g32*(b1 - x10)*(b2 - x20) + 2*a32*g32*(b2 - x20)^2 - 2*a3*b3*g32*x20 - 2*a3*b2*g32*x30 + 2*a3*g32*x20*x30)));


output = (-3/2)*log(2*pi*del) - Dv + cm1/del + c0 + c1*del; 



