double AiryInfoObs::chord(double r, double h, double rsq, double hsq) const
{
if (r==0.)
return 0.;
#ifdef AIRY_DEBUG
else if (r<h)
throw SBError("Airy calculation r<h");
else if (h < 0.)
throw SBError("Airy calculation h<0");
#endif
else
return rsq*std::asin(h/r) - h*sqrt(rsq-hsq);
}
double MoffatCalculateScaleRadiusFromHLR(double re, double rm, double beta)
{
dbg<<"Start MoffatCalculateScaleRadiusFromHLR\n";
// The basic equation that is relevant here is the flux of a Moffat profile
// out to some radius.
// flux(R) = int( (1+r^2/rd^2 )^(-beta) 2pi r dr, r=0..R )
// = (pi rd^2 / (beta-1)) (1 - (1+R^2/rd^2)^(1-beta) )
// For now, we can ignore the first factor. We call the second factor fluxfactor below,
// or in this function f(R).
//
// We are given two values of R for which we know that the ratio of their fluxes is 1/2:
// f(re) = 0.5 * f(rm)
//
if (rm == 0.) {
// If rm = infinity (which we actually indicate with rm=0), then we can solve for
// rd analytically:
//
// f(rm) = 1
// f(re) = 0.5 = 1 - (1+re^2/rd^2)^(1-beta)
// re^2/rd^2 = 0.5^(1/(1-beta)) - 1
double rerd = std::sqrt( std::pow(0.5, 1./(1.-beta)) - 1.);
dbg<<"rm = 0, so analytic.\n";
xdbg<<"rd = re/rerd = "<<re<<" / "<<rerd<<" = "<<re/rerd<<std::endl;
return re / rerd;
} else {
// If trunc < infinity, then the equations are slightly circular:
// f(rm) = 1 - (1 + rm^2/rd^2)^(1-beta)
// 2*f(re) = 2 - 2*(1 + re^2/rd^2)^(1-beta)
// 2*(1+re^2/rd^2)^(1-beta) = 1 + (1+rm^2/rd^2)^(1-beta)
//
// As rm decreases, rd increases.
// Eventually rd increases to infinity. When does that happen:
// Take the limit as rd->infinity in the above equation:
// 2 + 2*(1-beta) re^2/rd^2) = 1 + 1 + (1-beta) rm^2/rd^2
// 2 re^2 = rm^2
// rm = sqrt(2) * re
// So this is the limit for how low rm is allowed to be for a given re
if (rm <= std::sqrt(2.) * re)
throw SBError("Moffat truncation radius must be > sqrt(2) * half_light_radius.");
dbg<<"rm != 0, so not analytic.\n";
MoffatScaleRadiusFunc func(re,rm,beta);
// For the lower bound of rd, we can use the untruncated value:
double r1 = re / std::sqrt( std::pow(0.5, 1./(1.-beta)) - 1.);
xdbg<<"r1 = "<<r1<<std::endl;
// For the upper bound, we don't really have a good choice, so start with 2*r1
// and we'll expand it if necessary.
double r2 = 2. * r1;
xdbg<<"r2 = "<<r2<<std::endl;
Solve<MoffatScaleRadiusFunc> solver(func,r1,r2);
solver.setMethod(Brent);
solver.bracketUpper();
xdbg<<"After bracket, range is "<<solver.getLowerBound()<<" .. "<<
solver.getUpperBound()<<std::endl;
double rd = solver.root();
xdbg<<"Root is "<<rd<<std::endl;
return rd;
}
}
void SBConvolve::SBConvolveImpl::add(const SBProfile& rhs)
{
dbg<<"Start SBConvolveImpl::add. Adding item # "<<_plist.size()+1<<std::endl;
// Add new terms(s) to the _plist:
assert(GetImpl(rhs));
const SBProfileImpl* p = GetImpl(rhs);
const SBConvolveImpl* sbc = dynamic_cast<const SBConvolveImpl*>(p);
const SBAutoConvolve::SBAutoConvolveImpl* sbc2 =
dynamic_cast<const SBAutoConvolve::SBAutoConvolveImpl*>(p);
const SBAutoCorrelate::SBAutoCorrelateImpl* sbc3 =
dynamic_cast<const SBAutoCorrelate::SBAutoCorrelateImpl*>(p);
if (sbc) {
dbg<<" (Item is really "<<sbc->_plist.size()<<" items.)"<<std::endl;
// If rhs is an SBConvolve, copy its list here
for (ConstIter pptr = sbc->_plist.begin(); pptr!=sbc->_plist.end(); ++pptr) {
if (!pptr->isAnalyticK() && !_real_space)
throw SBError("SBConvolve requires members to be analytic in k");
if (!pptr->isAnalyticX() && _real_space)
throw SBError("Real_space SBConvolve requires members to be analytic in x");
_plist.push_back(*pptr);
}
} else if (sbc2) {
dbg<<" (Item is really AutoConvolve.)"<<std::endl;
// If rhs is an SBAutoConvolve, put two of its item here:
const SBProfile& obj = sbc2->getAdaptee();
if (!obj.isAnalyticK() && !_real_space)
throw SBError("SBConvolve requires members to be analytic in k");
if (!obj.isAnalyticX() && _real_space)
throw SBError("Real_space SBConvolve requires members to be analytic in x");
_plist.push_back(obj);
_plist.push_back(obj);
} else if (sbc3) {
dbg<<" (Item is really AutoCorrelate items.)"<<std::endl;
// If rhs is an SBAutoCorrelate, put its item and 180 degree rotated verion here:
const SBProfile& obj = sbc3->getAdaptee();
if (!obj.isAnalyticK() && !_real_space)
throw SBError("SBConvolve requires members to be analytic in k");
if (!obj.isAnalyticX() && _real_space)
throw SBError("Real_space SBConvolve requires members to be analytic in x");
_plist.push_back(obj);
SBProfile temp = obj;
temp.applyRotation(180. * degrees);
_plist.push_back(temp);
} else {
if (!rhs.isAnalyticK() && !_real_space)
throw SBError("SBConvolve requires members to be analytic in k");
if (!rhs.isAnalyticX() && _real_space)
throw SBError("Real-space SBConvolve requires members to be analytic in x");
_plist.push_back(rhs);
}
}
void SBConvolve::SBConvolveImpl::add(const SBProfile& sbp)
{
dbg<<"Start SBConvolveImpl::add. Adding item # "<<_plist.size()+1<<std::endl;
// Add new terms(s) to the _plist:
assert(GetImpl(sbp));
const SBProfileImpl* p = GetImpl(sbp);
const SBConvolveImpl* sbc = dynamic_cast<const SBConvolveImpl*>(p);
const SBAutoConvolve::SBAutoConvolveImpl* sbc2 =
dynamic_cast<const SBAutoConvolve::SBAutoConvolveImpl*>(p);
const SBAutoCorrelate::SBAutoCorrelateImpl* sbc3 =
dynamic_cast<const SBAutoCorrelate::SBAutoCorrelateImpl*>(p);
if (sbc) {
dbg<<" (Item is really "<<sbc->_plist.size()<<" items.)"<<std::endl;
// If sbp is an SBConvolve, copy its list here
for (ConstIter pptr = sbc->_plist.begin(); pptr!=sbc->_plist.end(); ++pptr) add(*pptr);
} else if (sbc2) {
dbg<<" (Item is really AutoConvolve.)"<<std::endl;
// If sbp is an SBAutoConvolve, put two of its item here:
const SBProfile& obj = sbc2->getAdaptee();
add(obj);
add(obj);
} else if (sbc3) {
dbg<<" (Item is really AutoCorrelate items.)"<<std::endl;
// If sbp is an SBAutoCorrelate, put its item and 180 degree rotated verion here:
const SBProfile& obj = sbc3->getAdaptee();
add(obj);
SBProfile temp = obj.rotate(180. * degrees);
add(temp);
} else {
if (!sbp.isAnalyticK() && !_real_space)
throw SBError("SBConvolve requires members to be analytic in k");
if (!sbp.isAnalyticX() && _real_space)
throw SBError("Real-space SBConvolve requires members to be analytic in x");
_plist.push_back(sbp);
}
_x0 += sbp.centroid().x;
_y0 += sbp.centroid().y;
_isStillAxisymmetric = _isStillAxisymmetric && sbp.isAxisymmetric();
_fluxProduct *= sbp.getFlux();
}
SpergelInfo::SpergelInfo(double nu, const GSParamsPtr& gsparams) :
_nu(nu), _gsparams(gsparams),
_gamma_nup1(boost::math::tgamma(_nu+1.0)),
_gamma_nup2(_gamma_nup1 * (_nu+1)),
_xnorm0((_nu > 0.) ? _gamma_nup1 / (2. * _nu) * std::pow(2., _nu) : INFINITY),
_maxk(0.), _stepk(0.), _re(0.)
{
dbg<<"Start SpergelInfo constructor for nu = "<<_nu<<std::endl;
if (_nu < sbp::minimum_spergel_nu || _nu > sbp::maximum_spergel_nu)
throw SBError("Requested Spergel index out of range");
}
double AiryInfoNoObs::kValue(double ksq_over_pisq) const
{
if (ksq_over_pisq >= 4.) return 0.;
if (ksq_over_pisq == 0.) return M_PI;
/* in between we calculate half-height at intersection */
double hsq = 1. - ksq_over_pisq/4.;
#ifdef AIRY_DEBUG
if (hsq<0.) throw SBError("Airy calculation half-height invalid");
#endif
double h = sqrt(hsq);
return 2. * (std::asin(h) - h*sqrt(1.-hsq));
}
/* area inside intersection of 2 circles both with radius r, seperated by t*/
double AiryInfoObs::circle_intersection(
double r, double rsq, double tsq) const
{
assert(r >= 0.);
if (tsq >= 4.*rsq) return 0.;
if (tsq == 0.) return M_PI*rsq;
/* in between we calculate half-height at intersection */
double hsq = rsq - tsq/4.;
#ifdef AIRY_DEBUG
if (hsq<0.) throw SBError("Airy calculation half-height invalid");
#endif
double h = sqrt(hsq);
return 2.*chord(r,h,rsq,hsq);
}
boost::shared_ptr<PhotonArray> SBConvolve::SBConvolveImpl::shoot(int N, UniformDeviate u) const
{
dbg<<"Convolve shoot: N = "<<N<<std::endl;
dbg<<"Target flux = "<<getFlux()<<std::endl;
std::list<SBProfile>::const_iterator pptr = _plist.begin();
if (pptr==_plist.end())
throw SBError("Cannot shoot() for empty SBConvolve");
boost::shared_ptr<PhotonArray> result = pptr->shoot(N, u);
// It may be necessary to shuffle when convolving because we do
// do not have a gaurantee that the convolvee's photons are
// uncorrelated, e.g. they might both have their negative ones
// at the end.
// However, this decision is now made by the convolve method.
for (++pptr; pptr != _plist.end(); ++pptr)
result->convolve(*pptr->shoot(N, u), u);
dbg<<"Convolve Realized flux = "<<result->getTotalFlux()<<std::endl;
return result;
}
void SBConvolve::SBConvolveImpl::shoot(PhotonArray& photons, UniformDeviate ud) const
{
const int N = photons.size();
dbg<<"Convolve shoot: N = "<<N<<std::endl;
dbg<<"Target flux = "<<getFlux()<<std::endl;
std::list<SBProfile>::const_iterator pptr = _plist.begin();
if (pptr==_plist.end())
throw SBError("Cannot shoot() for empty SBConvolve");
pptr->shoot(photons, ud);
// It may be necessary to shuffle when convolving because we do
// do not have a gaurantee that the convolvee's photons are
// uncorrelated, e.g. they might both have their negative ones
// at the end.
// However, this decision is now made by the convolve method.
for (++pptr; pptr != _plist.end(); ++pptr) {
PhotonArray temp(N);
pptr->shoot(temp, ud);
photons.convolve(temp, ud);
}
dbg<<"Convolve Realized flux = "<<photons.getTotalFlux()<<std::endl;
}
double SBConvolve::SBConvolveImpl::xValue(const Position<double>& pos) const
{
// Perform a direct calculation of the convolution at a particular point by
// doing the real-space integral.
// Note: This can only really be done one pair at a time, so it is
// probably rare that this will be more efficient if N > 2.
// For now, we don't bother implementing this for N > 2.
if (_plist.size() == 2) {
const SBProfile& p1 = _plist.front();
const SBProfile& p2 = _plist.back();
if (p2.isAxisymmetric())
return RealSpaceConvolve(p2,p1,pos,_fluxProduct,this->gsparams);
else
return RealSpaceConvolve(p1,p2,pos,_fluxProduct,this->gsparams);
} else if (_plist.empty())
return 0.;
else if (_plist.size() == 1)
return _plist.front().xValue(pos);
else
throw SBError("Real-space integration of more than 2 profiles is not implemented.");
}
/* area inside intersection of 2 circles radii r & s, seperated by t*/
double AiryInfoObs::circle_intersection(
double r, double s, double rsq, double ssq, double tsq) const
{
assert(r >= s);
assert(s >= 0.);
double rps_sq = (r+s)*(r+s);
if (tsq >= rps_sq) return 0.;
double rms_sq = (r-s)*(r-s);
if (tsq <= rms_sq) return M_PI*ssq;
/* in between we calculate half-height at intersection */
double hsq = 0.5*(rsq + ssq) - (tsq*tsq + rps_sq*rms_sq)/(4.*tsq);
#ifdef AIRY_DEBUG
if (hsq<0.) throw SBError("Airy calculation half-height invalid");
#endif
double h = sqrt(hsq);
if (tsq < rsq - ssq)
return M_PI*ssq - chord(s,h,ssq,hsq) + chord(r,h,rsq,hsq);
else
return chord(s,h,ssq,hsq) + chord(r,h,rsq,hsq);
}
SBMoffat::SBMoffatImpl::SBMoffatImpl(double beta, double size, RadiusType rType,
double trunc, double flux,
const GSParamsPtr& gsparams) :
SBProfileImpl(gsparams),
_beta(beta), _flux(flux), _trunc(trunc),
_ft(Table<double,double>::spline),
_re(0.), // initially set to zero, may be updated by size or getHalfLightRadius().
_stepk(0.), // calculated by stepK() and stored.
_maxk(0.) // calculated by maxK() and stored.
{
xdbg<<"Start SBMoffat constructor: \n";
xdbg<<"beta = "<<_beta<<"\n";
xdbg<<"flux = "<<_flux<<"\n";
xdbg<<"trunc = "<<_trunc<<"\n";
if (_trunc == 0. && beta <= 1.1)
throw SBError("Moffat profiles with beta <= 1.1 must be truncated.");
if (_trunc < 0.)
throw SBError("Invalid negative truncation radius provided to SBMoffat.");
// First, relation between FWHM and rD:
double FWHMrD = 2.* std::sqrt(std::pow(2., 1./_beta)-1.);
xdbg<<"FWHMrD = "<<FWHMrD<<"\n";
// Set size of this instance according to type of size given in constructor:
switch (rType) {
case FWHM:
_rD = size / FWHMrD;
break;
case HALF_LIGHT_RADIUS:
{
_re = size;
// This is a bit complicated, so break it out into its own function.
_rD = MoffatCalculateScaleRadiusFromHLR(_re,_trunc,_beta);
}
break;
case SCALE_RADIUS:
_rD = size;
break;
default:
throw SBError("Unknown SBMoffat::RadiusType");
}
_rD_sq = _rD * _rD;
_inv_rD = 1./_rD;
_inv_rD_sq = _inv_rD*_inv_rD;
if (_trunc > 0.) {
_maxRrD = _trunc * _inv_rD;
xdbg<<"maxRrD = "<<_maxRrD<<"\n";
// Analytic integration of total flux:
_fluxFactor = 1. - std::pow( 1+_maxRrD*_maxRrD, (1.-_beta));
} else {
_fluxFactor = 1.;
// Set maxRrD to the radius where missing fractional flux is xvalue_accuracy
// (1+R^2)^(1-beta) = xvalue_accuracy
_maxRrD = std::sqrt(std::pow(this->gsparams->xvalue_accuracy, 1. / (1. - _beta))- 1.);
xdbg<<"Not truncated. Calculated maxRrD = "<<_maxRrD<<"\n";
}
_FWHM = FWHMrD * _rD;
_maxR = _maxRrD * _rD;
_maxR_sq = _maxR * _maxR;
_maxRrD_sq = _maxRrD * _maxRrD;
_norm = _flux * (_beta-1.) / (M_PI * _fluxFactor * _rD_sq);
_knorm = _flux;
dbg << "Moffat rD " << _rD << " fluxFactor " << _fluxFactor
<< " norm " << _norm << " maxR " << _maxR << std::endl;
if (std::abs(_beta-1) < this->gsparams->xvalue_accuracy)
_pow_beta = &SBMoffatImpl::pow_1;
else if (std::abs(_beta-1.5) < this->gsparams->xvalue_accuracy)
_pow_beta = &SBMoffatImpl::pow_15;
else if (std::abs(_beta-2) < this->gsparams->xvalue_accuracy)
_pow_beta = &SBMoffatImpl::pow_2;
else if (std::abs(_beta-2.5) < this->gsparams->xvalue_accuracy)
_pow_beta = &SBMoffatImpl::pow_25;
else if (std::abs(_beta-3) < this->gsparams->xvalue_accuracy)
_pow_beta = &SBMoffatImpl::pow_3;
else if (std::abs(_beta-3.5) < this->gsparams->xvalue_accuracy)
_pow_beta = &SBMoffatImpl::pow_35;
else if (std::abs(_beta-4) < this->gsparams->xvalue_accuracy)
_pow_beta = &SBMoffatImpl::pow_4;
else _pow_beta = &SBMoffatImpl::pow_gen;
if (_trunc > 0.) _kV = &SBMoffatImpl::kV_trunc;
else if (std::abs(_beta-1.5) < this->gsparams->kvalue_accuracy)
_kV = &SBMoffatImpl::kV_15;
else if (std::abs(_beta-2) < this->gsparams->kvalue_accuracy)
_kV = &SBMoffatImpl::kV_2;
else if (std::abs(_beta-2.5) < this->gsparams->kvalue_accuracy)
_kV = &SBMoffatImpl::kV_25;
else if (std::abs(_beta-3) < this->gsparams->kvalue_accuracy) {
_kV = &SBMoffatImpl::kV_3; _knorm /= 2.;
} else if (std::abs(_beta-3.5) < this->gsparams->kvalue_accuracy) {
_kV = &SBMoffatImpl::kV_35; _knorm /= 3.;
} else if (std::abs(_beta-4) < this->gsparams->kvalue_accuracy) {
_kV = &SBMoffatImpl::kV_4; _knorm /= 8.;
} else {
_kV = &SBMoffatImpl::kV_gen;
_knorm *= 4. / (boost::math::tgamma(beta-1.) * std::pow(2.,beta));
}
}