bool DSphere::randomPoint(const Vector3 &viewpoint, const Vector2 &seed, float time, Vector3 &light_point, Vector3 &N, float &pdf, Color &radiance) const {
float d = (viewpoint - getCenter(0)).magnitude();
if (d < radius) {return false;}
float r = radius;
//internal angle of cone surrounding light seen from viewpoint
float sin_alpha_max = r / d;
float cos_alpha_max = sqrt(1 - sin_alpha_max * sin_alpha_max);
float q = 1.0 / (2*M_PI*(1 - cos_alpha_max));
float cos_alpha = 1 + seed.x() * (cos_alpha_max - 1);
float sin_alpha = sqrt(1 - cos_alpha * cos_alpha);
float phi = 2*M_PI*seed.y();
float cos_phi = cos(phi);
float sin_phi = sin(phi);
Vector3 k_i(cos_phi * sin_alpha, sin_phi * sin_alpha, cos_alpha);
//construct local coordinate system UVW where viewpoint at origin and sphere at (0,0,d) in UVW
ONB UVW;
UVW.initFromW(getCenter(0) - viewpoint);
Ray to_light(viewpoint, k_i.x() * UVW.u() + k_i.y() * UVW.v() + k_i.z() * UVW.w());
IntersectRecord rec;
if (this -> intersect(to_light, 0.00001, FLT_MAX, time, rec)) {
light_point = rec.intersection;
float cos_theta_prime = -dot(rec.uvw.w(), to_light.direction());
pdf = q * cos_theta_prime / (light_point - viewpoint).squaredMagnitude();
N = rec.uvw.w();
radiance = mptr -> emittedRadiance(rec.uvw, -to_light.direction(), light_point, rec.uv);
return true;
}
return false;
}
Type objective_function<Type>::operator() () {
// data:
DATA_MATRIX(x_ij);
DATA_VECTOR(y_i);
DATA_IVECTOR(k_i); // vector of IDs
DATA_INTEGER(n_k); // number of IDs
// parameters:
PARAMETER_VECTOR(b_j)
PARAMETER_VECTOR(sigma_j);
PARAMETER(log_b0_sigma);
PARAMETER_VECTOR(b0_k);
int n_data = y_i.size(); // get number of data points to loop over
// Linear predictor
vector<Type> linear_predictor_i(n_data);
vector<Type> linear_predictor_sigma_i(n_data);
linear_predictor_i = x_ij*b_j;
linear_predictor_sigma_i = sqrt(exp(x_ij*sigma_j));
Type nll = 0.0; // initialize negative log likelihood
for(int i = 0; i < n_data; i++){
nll -= dnorm(y_i(i), b0_k(k_i(i)) + linear_predictor_i(i) , linear_predictor_sigma_i(i), true);
}
for(int k = 0; k < n_k; k++){
nll -= dnorm(b0_k(k), Type(0.0), exp(log_b0_sigma), true);
}
REPORT( b0_k );
REPORT(b_j );
ADREPORT( b0_k );
ADREPORT( b_j );
return nll;
}
Type objective_function<Type>::operator() () {
// data:
DATA_MATRIX(x_ij);
DATA_VECTOR(y_i);
DATA_IVECTOR(k_i); // vector of IDs
DATA_INTEGER(n_k); // number of IDs
DATA_INTEGER(n_j); // number of IDs
DATA_VECTOR(b1_cov_re_i); // predictor data for random slope
DATA_VECTOR(sigma1_cov_re_i); // predictor data for random slope
//DATA_VECTOR(sigma2_cov_re_i); // predictor data for random slope
// parameters:
PARAMETER_VECTOR(b_j)
PARAMETER_VECTOR(sigma_j);
PARAMETER(log_b0_sigma);
PARAMETER_VECTOR(b0_k);
PARAMETER(log_b1_sigma);
PARAMETER_VECTOR(b1_k);
PARAMETER(log_sigma0_sigma);
PARAMETER(log_sigma1_sigma);
PARAMETER_VECTOR(sigma0_k);
PARAMETER_VECTOR(sigma1_k);
int n_data = y_i.size(); // get number of data points to loop over
// Linear predictor
vector<Type> linear_predictor_i(n_data);
vector<Type> linear_predictor_sigma_i(n_data);
linear_predictor_i = x_ij*b_j;
linear_predictor_sigma_i = x_ij*sigma_j;
Type nll = 0.0; // initialize negative log likelihood
for(int i = 0; i < n_data; i++){
nll -= dnorm(
y_i(i),
b0_k(k_i(i)) + b1_k(k_i(i)) * b1_cov_re_i(i) +
linear_predictor_i(i),
sqrt(exp(
sigma0_k(k_i(i)) +
sigma1_k(k_i(i)) * sigma1_cov_re_i(i) +
linear_predictor_sigma_i(i))),
true);
}
for(int k = 0; k < n_k; k++){
nll -= dnorm(b0_k(k), Type(0.0), exp(log_b0_sigma), true);
nll -= dnorm(b1_k(k), Type(0.0), exp(log_b1_sigma), true);
nll -= dnorm(sigma0_k(k), Type(0.0), exp(log_sigma0_sigma), true);
nll -= dnorm(sigma1_k(k), Type(0.0), exp(log_sigma1_sigma), true);
//nll -= dnorm(sigma2_k(k), Type(0.0), exp(log_sigma2_sigma), true);
}
// Reporting
Type b0_sigma = exp(log_b0_sigma);
Type b1_sigma = exp(log_b1_sigma);
Type sigma0_sigma = exp(log_sigma0_sigma);
Type sigma1_sigma = exp(log_sigma1_sigma);
//Type sigma2_sigma = exp(log_sigma2_sigma);
vector<Type> b1_b1_k(n_k);
vector<Type> sigma1_sigma1_k(n_k);
for(int k = 0; k < n_k; k++){
// these are fixed-effect slopes + random-effect slopes
b1_b1_k(k) = b_j(n_j) + b1_k(k);
sigma1_sigma1_k(k) = sigma_j(n_j) + sigma1_k(k);
}
REPORT( b0_k );
REPORT( b1_k );
REPORT( b_j );
REPORT( sigma0_k );
REPORT( sigma1_k );
//REPORT( sigma2_k );
REPORT(b0_sigma);
REPORT(b1_sigma);
REPORT(sigma0_sigma);
REPORT(sigma1_sigma);
//REPORT(sigma2_sigma);
REPORT(b1_b1_k);
REPORT(sigma1_sigma1_k);
//ADREPORT( b0_k );
//ADREPORT( b1_k );
//ADREPORT( b_j );
//ADREPORT( sigma0_k );
//ADREPORT( sigma1_k );
//ADREPORT( sigma2_k );
//ADREPORT(b0_sigma);
//ADREPORT(b1_sigma);
//ADREPORT(sigma0_sigma);
//ADREPORT(sigma1_sigma);
//ADREPORT(sigma2_sigma);
//ADREPORT(b1_b1_k);
//ADREPORT(sigma1_sigma1_k);
return nll;
}
