Float SHVector::eval(Float theta, Float phi) const {
Float result = 0;
Float cosTheta = std::cos(theta);
Float *sinPhi = (Float *) alloca(sizeof(Float)*m_bands),
*cosPhi = (Float *) alloca(sizeof(Float)*m_bands);
for (int m=0; m<m_bands; ++m) {
sinPhi[m] = std::sin((m+1) * phi);
cosPhi[m] = std::cos((m+1) * phi);
}
for (int l=0; l<m_bands; ++l) {
for (int m=1; m<=l; ++m) {
Float L = legendreP(l, m, cosTheta) * normalization(l, m);
result += operator()(l, -m) * SQRT_TWO * sinPhi[m-1] * L;
result += operator()(l, m) * SQRT_TWO * cosPhi[m-1] * L;
}
result += operator()(l, 0) * legendreP(l, 0, cosTheta) * normalization(l, 0);
}
return result;
}
Float *SHSampler::legendreIntegrals(Float a, Float b) {
Float *P = new Float[m_bands*(m_bands+1)/2];
m_dataSize += m_bands*(m_bands+1)/2;
P[I(0, 0)] = b-a;
if (m_bands == 1)
return P;
Float *Pa = new Float[m_bands*(m_bands+1)/2];
Float *Pb = new Float[m_bands*(m_bands+1)/2];
for (int l=0; l<m_bands; ++l) {
for (int m=0; m<=l; ++m) {
Pa[I(l,m)] = legendreP(l, m, a);
Pb[I(l,m)] = legendreP(l, m, b);
}
}
P[I(1,0)] = (b*b - a*a)/2;
P[I(1,1)] = .5f * (-b*std::sqrt(1-b*b) - std::asin(b) + a*std::sqrt(1-a*a) + std::asin(a));
for (int l=2; l<m_bands; ++l) {
for (int m=0; m<=l-2; ++m) {
Float ga = (2*l-1)*(1-a*a) * Pa[I(l-1,m)];
Float gb = (2*l-1)*(1-b*b) * Pb[I(l-1,m)];
P[I(l, m)] = ((l-2)*(l-1+m)*P[I(l-2, m)]-gb+ga)/((l+1)*(l-m));
}
P[I(l, l-1)] = (2*l-1)/(Float)(l+1) * ((1-a*a)*Pa[I(l-1, l-1)] - (1-b*b)*Pb[I(l-1, l-1)]);
P[I(l, l)] = 1/(Float)(l+1) * (l*(2*l-3)*(2*l-1) * P[I(l-2, l-2)] + b*Pb[I(l,l)] - a*Pa[I(l, l)]);
}
delete[] Pa;
delete[] Pb;
return P;
}
Float SHVector::eval(const Vector &v) const {
Float result = 0;
Float cosTheta = v.z, phi = std::atan2(v.y, v.x);
if (phi < 0) phi += 2*M_PI;
Float *sinPhi = (Float *) alloca(sizeof(Float)*m_bands),
*cosPhi = (Float *) alloca(sizeof(Float)*m_bands);
for (int m=0; m<m_bands; ++m) {
sinPhi[m] = std::sin((m+1) * phi);
cosPhi[m] = std::cos((m+1) * phi);
}
for (int l=0; l<m_bands; ++l) {
for (int m=1; m<=l; ++m) {
Float L = legendreP(l, m, cosTheta) * normalization(l, m);
result += operator()(l, -m) * SQRT_TWO * sinPhi[m-1] * L;
result += operator()(l, m) * SQRT_TWO * cosPhi[m-1] * L;
}
result += operator()(l, 0) * legendreP(l, 0, cosTheta) * normalization(l, 0);
}
return result;
}
int BinlessEmbedComp(struct options_binless *opts,
double **warped,
int *n_vec,
int N,
int R,
double **embedded)
{
int idx,q,h;
double temp;
for(idx=0;idx<N;idx++)
for(h=0;h<R;h++)
{
temp=0;
if(opts->rec_tag==0) /* episodic data */
for(q=0;q<n_vec[idx];q++)
temp+=legendreP(h,warped[idx][q]);
else if(opts->rec_tag==1) /* continuous data */
for(q=0;q<n_vec[idx];q++)
temp += warped[idx][q]*legendreP(h,opts->w_start+q*(opts->w_end-opts->w_start)/(n_vec[idx]-1));
embedded[idx][h] = sqrt(2*h+1)*temp;
}
return EXIT_SUCCESS;
}
Float SHVector::evalAzimuthallyInvariant(const Vector &v) const {
Float result = 0, cosTheta = v.z;
for (int l=0; l<m_bands; ++l)
result += operator()(l, 0) * legendreP(l, 0, cosTheta) * normalization(l, 0);
return result;
}
Float SHVector::evalAzimuthallyInvariant(Float theta, Float phi) const {
Float result = 0, cosTheta = std::cos(theta);
for (int l=0; l<m_bands; ++l)
result += operator()(l, 0) * legendreP(l, 0, cosTheta) * normalization(l, 0);
return result;
}
