// Compute the gradient vector of the conditional log likelihood for a Gaussian-Binary model :
void Grad_Cond_Bin(double rho,double pij, double p,int *flag, double *gradcor, double *grad,
int *npar, double *nuis, double *thr, double u, double v)
{
// Initialization variables:
double dpij=0.0, dij=0.0, rvar=0.0, dpdm=0.0, f=0.0;
double q1=0.0, q2=0.0, q3=0.0, sh=0.0, vario=0.0, z=0;
int h=0, i=0, j=0;
//init variables:
z=(nuis[0]-*thr)/sqrt(nuis[2]+nuis[1]);
rvar=nuis[2]/(nuis[2]+nuis[1]);
//set derivatives components:
q1=dnorm(z,0,1,0);//stand normal pdf
q2=pnorm(z*sqrt((1-rvar*rho)/(1+rvar*rho)),0,1,1,0);// stand norm cdf
q3=d2norm(z,z,rvar*rho);// biv stand norm pdf
//derivatives:
dpdm=q1/sqrt(nuis[2]+nuis[1]);/*dp/dmu*/
dpij=2*dpdm*q2;/*dpij/dmu*/
f=-(0.5*(nuis[0]-*thr)*dpdm)/(nuis[2]+nuis[1]);/* dp/dsill*/
dij=2*f*q2;/* dpij/dsill*/
vario=2*(p-pij);//variogramma binario!!!
sh=1/(1-2*p+pij);
// Derivative of the difference respect with the mean
if(flag[0]==1) { grad[i]=(dpij-2*dpdm)*(1-((u+v)*nij(dpij,dpdm,pij,p)+
(u*v)*mij(dpij,dpdm,pij,p)))*sh+dpdm*(1-(u+v)/(2*p))/(1-p); i++; }
// Derivative of the difference respect with the nugget
if(flag[1]==1) { grad[i]=1; i++; }
// Derivative of the difference respect with the sill
if(flag[2]==1) { grad[i]=(dij-2*f)*(1-((u+v)*nij(dij,f,pij,p)+
(u*v)*mij(dij,f,pij,p)))*sh+f*(1-(u+v)/(2*p))/(1-p); i++; }
// Derivatives with respect to the correlation parameters
for(j=i;j<*npar;j++) { grad[j]=gradcor[j]*q3*rvar*(1-((u+v)*2*(p-1)/vario +
(u*v)*2*(pij-2*pow(p,2)+p)/(vario*pij)))*sh; h++; }
return;
}
double LCOrbits::ArmVelocity(int em, int rec, double trec)
{
LCVector ri(MT), rj(MT), vi(MT), vj(MT), rij(MT), nij(MT), n(MT);
ri = position(rec, trec);
vi = velocity(rec, trec);
rj = position(em, trec);
vj = velocity(em, trec);
rij = rj-ri;
nij = rij.unit();
n = nij * (-1.);
return(vj*n-vi*n);
}
double LCOrbits::ArmCompute(int em, int rec, double trec)
{
double tA(0.), tij;
if ((em<1)||(em>NARMMAX)||((rec<1)&&(rec>NARMMAX))){
std::cerr << "ERROR in LCOrbits::ArmCompute : Spacecraft number must be in [0," << NARMMAX << "] ! " << Endl;
throw std::invalid_argument ("ERROR in LCOrbits::ArmCompute : Spacecraft number must be in [0,NARMMAX] ! ");
}
/*
if(OrderArm != -10)
OrderArm = order_default;
if ((OrderArm<-2)||(OrderArm>2))
throw std::invalid_argument ("ERROR in LCOrbits::ArmCompute : Order must be 0 (for 0), 1 (for 1/2), 2 (for 1) or -1 (for analytical MLDC eccentric formulation)");
*/
if(OrderArm >= 0){
LCVector ri(MT), rj(MT), vi(MT), vj(MT), rij(MT), nij(MT), n(MT);
/*! **** Read positions and velocities and compute related quantities
* Index i refers to receiver and j to emitter
* \f{eqnarray*}{
* \vec{r}_{ij} & = & \vec{r}_j - \vec{r}_i = \vec{r}_{em} - \vec{r}_{rec} \\
* \vec{n}_{ij} & = & \vec{r}_{ij} / | \vec{r}_{ij} | \\
* \hat{n} & = & - \vec{n}_{ij} \\
* t_{ij} & = & - | \vec{r}_{ij} | / c = - | \vec{r}_{em} - \vec{r}_{rec} | / c
* \f}
*/
ri = position(rec, trec);
vi = velocity(rec, trec);
vi = vi/LC::c_SI;
rj = position(em, trec);
vj = velocity(em, trec);
vj = vj/LC::c_SI;
/*
ri.p[0] = 5.e9;
ri.p[1] = 0.;
ri.p[2] = 0.;
rj.p[0] = -1.e-5;
rj.p[1] = 0.;
rj.p[2] = 0.;
rij = rj-ri;
*/
rij = rj-ri;
nij = rij.unit();
n = nij*(-1.);
tij = rij.norm()/LC::c_SI;
tij = -tij;
/*
MT->o->precision(16);
Cout << "em = " << em << " -> rec = " << rec << " : " << rij.norm() << " ==> " << tij << Endl;
for(int i=0; i<3; i++)
Cout << "\t\t" << ri.p[i] << "\t\t" << rj.p[i] << "\t\t" << rij.p[i] << Endl;
*/
if (OrderArm>=0)
tA += ArmOrderContrib(0, tij, ri, rj, vi, vj, rij, nij, n);
if (OrderArm>=1)
tA += ArmOrderContrib(1, tij, ri, rj, vi, vj, rij, nij, n);
if (OrderArm>=2)
tA += ArmOrderContrib(2, tij, ri, rj, vi, vj, rij, nij, n);
return (tA);
}else{
return( ArmSpecific(em, rec, trec) );
}
}
