contrib/brl/bbas/bsta/bsta_gaussian_sphere.h

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// This is brl/bbas/bsta/bsta_gaussian_sphere.h
#ifndef bsta_gaussian_sphere_h_
#define bsta_gaussian_sphere_h_
//:
// \file
// \brief A (hyper-)spherical Gaussian distribution (i.e. single variance)
// \author Matt Leotta (mleotta@lems.brown.edu)
// \date January 25, 2006
//
// \verbatim
//  Modifications
//   Jan 21 2008 - Matt Leotta - Rename probability to prob_density and
//                               add probability integration over a box
// \endverbatim

#include "bsta_gaussian.h"
#include <vcl_iostream.h>
#include <vnl/vnl_random.h>

//: A (hyper-)spherical Gaussian distribution
// Thus, the covariance matrix is the identity times a scalar variance
template <class T, unsigned n>
class bsta_gaussian_sphere : public bsta_gaussian<T,n>
{
 public:
  typedef typename bsta_gaussian<T,n>::vector_type vector_;
  typedef  T covar_type;
  //: Constructor
  bsta_gaussian_sphere()
  : bsta_gaussian<T,n>(), var_(T(0)), det_covar_(T(0)) {}

  //: Constructor
  bsta_gaussian_sphere(const vector_& mean,
                       const covar_type& var)
  : bsta_gaussian<T,n>(mean), var_(var), det_covar_(T(-1))
  { compute_det(); }

  //: The variance of the distribution
  const covar_type& var() const { return var_; }

  //: Set the variance of the distribution
  void set_var(const covar_type& var) { var_ = var; compute_det(); }

  //: generic access to covariance or variance across Gaussians
  const covar_type& covar() const {return var_;}

  //: generic set covariance across Gaussian subtypes
  void set_covar(const covar_type& covar) {this->set_var(covar);}

  //: The probability density at this sample given square mahalanobis distance
  T dist_prob_density(const T& sqr_mahal_dist) const
  {
    if (det_covar_ <= 0)
      return T(0);
    return static_cast<T>(vcl_sqrt(1/(det_covar_*two_pi_power<n>::value()))
         * vcl_exp(-sqr_mahal_dist/2));
  }

  //: The probability density at this sample
  T prob_density(const vector_& pt) const
  {
    return dist_prob_density(sqr_mahalanobis_dist(pt));
  }

  //: The probability integrated over a box
  T probability(const vector_& min_pt,
                const vector_& max_pt) const;

  //: The squared Mahalanobis distance to this point
  T sqr_mahalanobis_dist(const vector_& pt) const;

  //: Compute the determinant of the covariance matrix
  T det_covar() const { return det_covar_; }

  //: sample from the distribution
  vector_ sample(vnl_random& rng) const;

 protected:
  //: The variance
  covar_type var_;

  //: The cached covariance determinant
  T det_covar_;

 private:
  //: compute the determinant of the covariance
  void compute_det();
};

template <class T , unsigned n>
inline vcl_ostream& operator<< (vcl_ostream& os,
                                bsta_gaussian_sphere<T, n> const& g)
{
  os << "gauss_sphere:mean(" << g.mean() << ")\n"
     << "gauss_sphere:var(" << g.var() << ")\n";
  return os;
}

#endif // bsta_gaussian_sphere_h_