// vectorized version
void diffPDF_nu_tCopula_new_vec(double* u, double* v, int* n, double* par, double* par2, int* copula, double* out)
{
int nn = 1;
double* ipars = (double *) malloc(2*sizeof(double));
for (int i = 0; i < (*n); ++i) {
ipars[0] = par[i];
ipars[1] = par2[i];
diffPDF_nu_tCopula_new(&u[i], &v[i], &nn, ipars, &copula[i], &out[i]);
};
free(ipars);
}
void diff2PDF_nu_u_tCopula_new(double* u, double* v, int* n, double* param, int* copula, double* out)
{
double x1, x2;
int j=0, k=1;
double t1, t2, t3, t4, t6, t7, t8, t9, t10, t11, t12, t13, M, c=0, out1=0, out2=0, diffPDF=0, diff_dt=0, diff_dt2=0, diff_dt3=0, M_nu=0;
double t14, t15, t16, t17;
double rho = param[0];
double nu = param[1];
t1=nu+2.0;
t3=(nu+1.0)/nu;
t14=rho*rho;
t4=1.0-t14;
t17=nu*nu;
for(j=0;j<*n;j++)
{
LL(copula, &k, &u[j], &v[j], &rho, &nu, &c);
c=exp(c);
x1=qt(u[j],nu,1,0);
x2=qt(v[j],nu,1,0);
t15=x1*x1;
t16=x2*x2;
M = ( nu*t4 + t15 + t16 - 2.0*rho*x1*x2 );
t2=dt(x1,nu,0);
diffPDF_nu_tCopula_new(&u[j], &v[j], &k, param, copula, &diffPDF);
diff_dt_nu(&x1, &nu, &diff_dt);
diff_dt_u(&x1, &nu, &diff_dt2);
diff_dt_x(&x1, &nu, &diff_dt3);
diffX_nu_tCopula(&x1, param, &out1);
diffX_nu_tCopula(&x2, param, &out2);
t8=(x1*out2+out1*x2);
M_nu=t4+2.0*x1*out1+2.0*x2*out2-2.0*rho*t8;
t6=1.0+t15/nu;
t7=x1-rho*x2;
t9=-diffPDF/t2 + c/t2/t2*(diff_dt+diff_dt3*out1);
t10=t1*t7/M + diff_dt2;
t11=c/t2;
t12=t7/M - t1*t7/M/M*M_nu + t1*(out1-rho*out2)/M;
t13=-out1*t3/t6 + x1/(t17+nu*t15) + x1*t3/t6/t6 * (2.0*x1*out1/nu - t15/t17);
out[j]=t9*t10 - t11*(t12+t13);
}
}
void diff2PDF_rho_nu_tCopula_new(double* u, double* v, int* n, double* param, int* copula, double* out)
{
double out1=0, out2=0, x1, x2;
int j=0, k=1;
double t3, t4, t5, t6, t7, t8, t9, t10, t11, M_rho, M_nu, M, c;
double rho = param[0];
double nu = param[1];
t4=1.0-rho*rho;
t3=rho/t4;
t5=nu+2.0;
for(j=0;j<*n;j++)
{
LL(copula, &k, &u[j], &v[j], &rho, &nu, &c);
c=exp(c);
x1=qt(u[j],nu,1,0);
x2=qt(v[j],nu,1,0);
diffX_nu_tCopula(&x1, param, &out1);
diffX_nu_tCopula(&x2, param, &out2);
t10=x1*x1;
t11=x2*x2;
M = ( nu*t4 + t10 + t11 - 2.0*rho*x1*x2 );
diffPDF_rho_tCopula(&u[j], &v[j], &k, param, copula, &t6);
diffPDF_nu_tCopula_new(&u[j], &v[j], &k, param, copula, &t7);
M_rho=-2.0*(nu*rho+x1*x2);
t8=(x1*out2+out1*x2);
M_nu=t4+2.0*x1*out1+2.0*x2*out2-2.0*rho*t8;
t9=-t3+t5/M*(rho+t8+0.5*M_nu*M_rho/M)-0.5*M_rho/M;
out[j]=c*t9+t6*t7/c;
}
}
void VineLogLikRvineDeriv(int* T, int* d, int* family, int* kk, int* ii, int* maxmat, int* matrix, int* condirect, int* conindirect, double* par, double* par2, double* data,
double* out, double* ll, double* vv, double* vv2, int* calcupdate, double* tilde_vdirect, double* tilde_vindirect, double* tilde_value, int* tcop, int* margin)
{
int i, j, k, t, m, **fam, **calc;
double sumloglik=0.0, **theta, **nu, ***tildevdirect, ***tildevindirect, *zr1, *zr2, *tildezr1, *tildezr2, *cop;
double *handle1;
double param[2];
zr1=(double*) Calloc(*T,double);
zr2=(double*) Calloc(*T,double);
handle1=(double*) Calloc(*T,double);
tildezr1=(double*) Calloc(*T,double);
tildezr2=(double*) Calloc(*T,double);
cop=(double*) Calloc(*T,double);
double ***tildevalue;
tildevalue=create_3darray(*d,*d,*T);
//Allocate memory
tildevdirect = create_3darray(*d,*d,*T);
tildevindirect = create_3darray(*d,*d,*T);
theta=create_matrix(*d,*d);
nu=create_matrix(*d,*d);
fam=create_intmatrix(*d,*d);
calc=create_intmatrix(*d,*d);
//Initialize
k=0;
for(i=0;i<(*d);i++)
{
for(j=0;j<(*d);j++)
{
theta[i][j]=par[(i+1)+(*d)*j-1] ;
nu[i][j]=par2[(i+1)+(*d)*j-1] ;
fam[i][j]=family[(i+1)+(*d)*j-1] ;
calc[i][j]=calcupdate[(i+1)+(*d)*j-1] ;
}
}
for(i=0;i<(*d);i++)
{
for(j=0;j<(*d);j++)
{
for(t=0;t<*T;t++ )
{
tildevdirect[i][j][t]=0;
tildevindirect[i][j][t]=0;
tildevalue[i][j][t]=0;
}
}
}
m=maxmat[*kk+(*d)*(*ii-1)-1];
for(t=0;t<*T;t++ )
{
zr1[t]=vv[*kk+(*d)*(*ii-1)+(*d)*(*d)*t-1];
cop[t]=exp(ll[*kk+(*d)*(*ii-1)+(*d)*(*d)*t-1]);
}
if(m == matrix[*kk+*d*(*ii-1)-1])
{
for(t=0;t<*T;t++ )
{
zr2[t]=vv[*kk+(*d)*(*d-m)+(*d)*(*d)*t-1];
}
}
else
{
for(t=0;t<*T;t++)
{
zr2[t]=vv2[*kk+(*d)*(*d-m)+(*d)*(*d)*t-1];
}
}
param[0]=theta[*kk-1][*ii-1];
param[1]=nu[*kk-1][*ii-1];
if(*tcop==1) //For the t-copula (first parameter)
{
diffhfunc_rho_tCopula(zr1,zr2,T,param,&fam[*kk-1][*ii-1],tildevdirect[*kk-2][*ii-1]);
diffhfunc_rho_tCopula(zr2,zr1,T,param,&fam[*kk-1][*ii-1],tildevindirect[*kk-2][*ii-1]);
diffPDF_rho_tCopula(zr1,zr2,T,param,&fam[*kk-1][*ii-1],tildevalue[*kk-1][*ii-1]);
for(t=0;t<*T;t++ )
{
tildevalue[*kk-1][*ii-1][t]=tildevalue[*kk-1][*ii-1][t]/cop[t];
}
}
else if(*tcop==2) // for the t-copula (second parameter)
{
diffhfunc_nu_tCopula_new(zr1,zr2,T,param,&fam[*kk-1][*ii-1],tildevdirect[*kk-2][*ii-1]);
diffhfunc_nu_tCopula_new(zr2,zr1,T,param,&fam[*kk-1][*ii-1],tildevindirect[*kk-2][*ii-1]);
diffPDF_nu_tCopula_new(zr1,zr2,T,param,&fam[*kk-1][*ii-1],tildevalue[*kk-1][*ii-1]);
for(t=0;t<*T;t++ )
{
tildevalue[*kk-1][*ii-1][t]=tildevalue[*kk-1][*ii-1][t]/cop[t];
}
}
else
{
if( *margin == 0 ) //Das ist unser bisheriger Fall mit stetigen Variablen (ohne t-copula)
{
diffhfunc_mod(zr1,zr2,T,&theta[*kk-1][*ii-1],&fam[*kk-1][*ii-1],tildevdirect[*kk-2][*ii-1]);
diffhfunc_mod2(zr2,zr1,T,&theta[*kk-1][*ii-1],&fam[*kk-1][*ii-1],tildevindirect[*kk-2][*ii-1]);
diffPDF_mod(zr1,zr2,T,&theta[*kk-1][*ii-1],&fam[*kk-1][*ii-1],tildevalue[*kk-1][*ii-1]);
for(t=0;t<*T;t++ )
{
tildevalue[*kk-1][*ii-1][t]=tildevalue[*kk-1][*ii-1][t]/cop[t];
}
}
else if( *margin== 1) // Ableitung nach dem ersten Argument = margin1
{
diffhfunc_v_mod2(zr2,zr1,T,&theta[*kk-1][*ii-1],&fam[*kk-1][*ii-1],tildevindirect[*kk-2][*ii-1]);
diffPDF_u_mod(zr1,zr2,T,&theta[*kk-1][*ii-1],&fam[*kk-1][*ii-1],tildevalue[*kk-1][*ii-1]); // hier k?nnte difflPDF stehen
for(t=0;t<*T;t++ )
{
tildevdirect[*kk-2][*ii-1][t]=cop[t];
tildevalue[*kk-1][*ii-1][t]=tildevalue[*kk-1][*ii-1][t]/cop[t];
}
}
else // Ableitung nach dem zweiten Argument = margin2
{
diffhfunc_v_mod(zr1,zr2,T,&theta[*kk-1][*ii-1],&fam[*kk-1][*ii-1],tildevdirect[*kk-2][*ii-1]);
diffPDF_v_mod(zr1,zr2,T,&theta[*kk-1][*ii-1],&fam[*kk-1][*ii-1],tildevalue[*kk-1][*ii-1]); // hier k?nnte difflPDF stehen
for(t=0;t<*T;t++ )
{
tildevindirect[*kk-2][*ii-1][t]=cop[t];
tildevalue[*kk-1][*ii-1][t]=tildevalue[*kk-1][*ii-1][t]/cop[t];
}
}
}
// add up for the final derivative
for(t=0;t<*T;t++ )
{
sumloglik+=tildevalue[*kk-1][*ii-1][t];
}
for(i=*ii-1; i>-1; i--)
{
for(k=*kk-2;k>i;k--)
{
if(calc[k][i]==1)
{
m=maxmat[(k+1)+*d*i-1];
for(t=0;t<*T;t++ )
{
zr1[t]=vv[(k+1)+(*d)*i+(*d)*(*d)*t-1];
tildezr1[t]=tildevdirect[k][i][t];
cop[t]=exp(ll[(k+1)+(*d)*i+(*d)*(*d)*t-1]);
}
if(m == matrix[(k+1)+*d*i-1])
{
for(t=0;t<*T;t++ )
{
zr2[t]=vv[(k+1)+(*d)*(*d-m)+(*d)*(*d)*t-1];
tildezr2[t]=tildevdirect[k][(*d-m)][t];
}
}
else
{
for(t=0;t<*T;t++ )
{
zr2[t]=vv2[(k+1)+(*d)*(*d-m)+(*d)*(*d)*t-1];
tildezr2[t]=tildevindirect[k][(*d-m)][t];
}
}
for(t=0;t<*T;t++ )
{
tildevdirect[k-1][i][t]=0;
tildevindirect[k-1][i][t]=0;
tildevalue[k][i][t]=0;
}
if(calc[k+1][i]==1)
{
param[0]=theta[k][i];
param[1]=nu[k][i];
if(fam[k][i]==2) //For the t-copula
{
diffPDF_u_tCopula_new(zr1,zr2,T,param,&fam[k][i],handle1);
}
else
{
diffPDF_u_mod(zr1,zr2,T,&theta[k][i],&fam[k][i],handle1);
}
for(t=0;t<*T;t++ )
{
tildevalue[k][i][t]+=handle1[t]/cop[t]*tildezr1[t];
}
if(condirect[k+(*d)*i-1]==1)
{
for(t=0;t<*T;t++ )
{
tildevdirect[k-1][i][t]+=cop[t]*tildezr1[t];
}
}
if(conindirect[k+(*d)*i-1]==1)
{
param[0]=theta[k][i];
param[1]=nu[k][i];
if(fam[k][i]==2) //For the t-copula
{
diffhfunc_v_tCopula_new(zr2,zr1,T,param,&fam[k][i],handle1);
}
else
{
diffhfunc_v_mod2(zr2,zr1,T,&theta[k][i],&fam[k][i],handle1);
}
for(t=0;t<*T;t++ )
{
tildevindirect[k-1][i][t]+=handle1[t]*tildezr1[t];
}
}
}
if(calc[k+1][(*d-m)]==1)
{
param[0]=theta[k][i];
param[1]=nu[k][i];
if(fam[k][i]==2) //For the t-copula
{
diffPDF_u_tCopula_new(zr2,zr1,T,param,&fam[k][i],handle1);
}
else
{
diffPDF_v_mod(zr1,zr2,T,&theta[k][i],&fam[k][i],handle1);
}
for(t=0;t<*T;t++ )
{
tildevalue[k][i][t]+=handle1[t]/cop[t]*tildezr2[t];
}
if(condirect[k+(*d)*i-1]==1)
{
param[0]=theta[k][i];
param[1]=nu[k][i];
if(fam[k][i]==2) //For the t-copula
{
diffhfunc_v_tCopula_new(zr1,zr2,T,param,&fam[k][i],handle1);
}
else
{
diffhfunc_v_mod(zr1,zr2,T,&theta[k][i],&fam[k][i],handle1);
}
for(t=0;t<*T;t++ )
{
tildevdirect[k-1][i][t]+=handle1[t]*tildezr2[t];
}
}
if(conindirect[k+(*d)*i-1]==1)
{
for(t=0;t<*T;t++ )
{
tildevindirect[k-1][i][t]+=cop[t]*tildezr2[t];
}
}
}
}
for(t=0;t<*T;t++ )
{
sumloglik += tildevalue[k][i][t];
}
}
}//for loops closed
*out = sumloglik;
for(i=0;i<(*d);i++)
{
for(j=0;j<(*d);j++)
{
for(t=0;t<*T;t++ )
{
tilde_vdirect[(i+1)+(*d)*j+(*d)*(*d)*t-1]=tildevdirect[i][j][t];
tilde_vindirect[(i+1)+(*d)*j+(*d)*(*d)*t-1]=tildevindirect[i][j][t];
tilde_value[(i+1)+(*d)*j+(*d)*(*d)*t-1]=tildevalue[i][j][t];
}
}
}
//Free memory:
free_matrix(theta,*d); free_matrix(nu,*d); free_intmatrix(fam,*d);
free_intmatrix(calc, *d);
free_3darray(tildevindirect,*d,*d);
free_3darray(tildevdirect,*d,*d);
free_3darray(tildevalue,*d,*d);
Free(zr1); Free(zr2); Free(tildezr1); Free(tildezr2); Free(handle1); Free(cop);
}
void diff2PDF_nu_tCopula_new(double* u, double* v, int* n, double* param, int* copula, double* out)
{
double out1=0, out2=0, out3=0, out4=0, x1, x2, diff_nu=0;
int j=0, k=1;
double t1, t2, t3, t4, t5, t6, t8, t9, t10, t11, t12, t13, t14, t15, t16, t17, t18, t19, t20, t21, t22, t23, t24, t25, M_nu, M, M_nu_nu, c;
double rho = param[0];
double nu = param[1];
t1=(nu+1.0)/2.0;
t2=nu/2.0;
t23=nu*nu;
t3=1.0/t23;
t4=1.0/(2.0*nu);
t5=0.5*trigamma(t1);
t6=(1.0-rho*rho);
t9=0.5*trigamma(t2);
t10=-t5+t9-t3-t4;
for(j=0;j<*n;j++)
{
LL(copula, &k, &u[j], &v[j], &rho, &nu, &c);
c=exp(c);
x1=qt(u[j],nu,1,0);
x2=qt(v[j],nu,1,0);
diffX_nu_tCopula(&x1, param, &out1);
diffX_nu_tCopula(&x2, param, &out2);
M = ( nu*t6 + x1*x1 + x2*x2 - 2.0*rho*x1*x2 );
t8=(x1*out2+out1*x2);
M_nu=t6+2.0*x1*out1+2.0*x2*out2-2.0*rho*t8;
t24=x1*x1;
t25=x2*x2;
t11=1.0+2.0*x1*out1;
t12=nu+t24;
t13=t11/t12;
t14=1.0+2.0*x2*out2;
t15=nu+t25;
t16=t14/t15;
diff2_x_nu(&x1,&nu,&out3);
diff2_x_nu(&x2,&nu,&out4);
t17=2.0*out1*out1 + 2.0*x1*out3;
t18=t17/t12;
t19=2.0*out2*out2 + 2.0*x2*out4;
t20=t19/t15;
t21=t13*t13;
t22=t16*t16;
M_nu_nu=2.0*out1*out1 + 2.0*x1*out3 + 2.0*out2*out2 + 2.0*x2*out4 - 4.0*rho*out1*out2 - 2.0*rho*(x2*out3 + x1*out4);
diffPDF_nu_tCopula_new(&u[j], &v[j], &k, param, copula, &diff_nu);
out[j]=c*( t10+0.5*(t13+t16) + t1*(t18-t21+t20-t22) + 0.5*t13 + 0.5*t16 - M_nu/M - (nu/2.0+1.0)*(M_nu_nu/M-M_nu*M_nu/M/M )) + diff_nu*diff_nu/c;
}
}
