vonMisesSufficient.h

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/**
 *  \file IMP/isd/vonMisesSufficient.h    \brief Normal distribution of Function
 *
 *  Copyright 2007-2014 IMP Inventors. All rights reserved.
 */

#ifndef IMPISD_VON_MISES_SUFFICIENT_H
#define IMPISD_VON_MISES_SUFFICIENT_H

#include <IMP/isd/isd_config.h>
#include <IMP/macros.h>
#include <IMP/kernel/Model.h>
#include <IMP/constants.h>
#include <math.h>
#include <boost/math/special_functions/bessel.hpp>

IMPISD_BEGIN_NAMESPACE

//! vonMisesSufficient
/** Probability density function and -log(p) of von Mises distribution
    of N iid von Mises observations, provided through their sufficient
    statistics.
    This is much more efficient than multiplying N von Mises densities.
    \f[ f(\chi|N, R_0, \chi_{exp}, \kappa) =
       \frac{\exp \left(R_0 \kappa \cos (\chi - \chi_{exp})\right)}
       {2\pi I_0(\kappa)^N} \f]
    where
    \f[ R = \sqrt{\left(\sum_{i=1}^N \cos \chi_{exp}^i\right)^2
                  + \left(\sum_{i=1}^N \cos \chi_{exp}^i\right)^2} \f]
    \f[ \exp (i \chi_{exp}) = \frac{1}{R} \sum_{j=1}^N \exp(i \chi_{exp}^j) \f]
    If \f$N=1\f$ and \f$\mu_1=\mu_2\f$ this reduces to the original von Mises
    distribution with known mean and concentration.
    \note derivative with respect to the mean \f$\chi_{exp}\f$ is not provided.
 */

class vonMisesSufficient : public base::Object {
 public:
  /** compute von Mises given the sufficient statistics
    \param[in] chi
    \param[in] N number of observations
    \param[in] R0 component of N observations on the x axis (\f$R_0\f$)
    \param[in] chiexp mean (\f$\chi_{exp}\f$)
    \param[in] kappa concentration
  */
  vonMisesSufficient(double chi, unsigned N, double R0, double chiexp,
                     double kappa)
      : base::Object("von Mises sufficient %1%"),
        x_(chi),
        R0_(R0),
        chiexp_(chiexp) {
    N_ = N;
    force_set_kappa(kappa);
  }

  /** compute von Mises given the raw observations
   * this is equivalent to calling get_sufficient_statistics and then the other
   * constructor.
    \param[in] chi
    \param[in] obs a list of observed angles (in radians).
    \param[in] kappa concentration
  */
  vonMisesSufficient(double chi, Floats obs, double kappa)
      : base::Object("von Mises sufficient %1%"), x_(chi) {
    Floats stats = get_sufficient_statistics(obs);
    N_ = (unsigned)stats[0];
    R0_ = stats[1];
    chiexp_ = stats[2];
    force_set_kappa(kappa);
  }

  /* energy (score) functions, aka -log(p) */
  virtual double evaluate() const {
    return logterm_ - R0_ * kappa_ * cos(x_ - chiexp_);
  }

  virtual double evaluate_derivative_x() const {
    return R0_ * kappa_ * sin(x_ - chiexp_);
  }

  virtual double evaluate_derivative_kappa() const {
    return -R0_ * cos(x_ - chiexp_) + double(N_) * I1_ / I0_;
  }

  /* probability density function */
  virtual double density() const {
    return exp(R0_ * kappa_ * cos(x_ - chiexp_)) / (2 * IMP::PI * I0N_);
  }

  /* getting parameters */
  double get_x() { return x_; }
  double get_R0() { return R0_; }
  double get_chiexp() { return chiexp_; }
  double get_N() { return N_; }
  double get_kappa() { return kappa_; }

  /* change of parameters */
  void set_x(double x) { x_ = x; }

  void set_R0(double R0) { R0_ = R0; }

  void set_chiexp(double chiexp) { chiexp_ = chiexp; }

  void set_N(unsigned N) {
    N_ = N;
    I0N_ = pow(I0_, static_cast<int>(N_));
    logterm_ = log(2 * IMP::PI * I0N_);
  }

  void set_kappa(double kappa) {
    if (kappa_ != kappa) {
      force_set_kappa(kappa);
    }
  }

  //! Compute sufficient statistics from a list of observations.
  /** See Mardia and El-Atoum, "Bayesian inference for the von Mises-Fisher
      distribution ", Biometrika, 1967.
      \return the number of observations, \f$R_0\f$ (the component on the
              x axis) and \f$\chi_{exp}\f$
   */
  static Floats get_sufficient_statistics(Floats data) {
    unsigned N = data.size();
    // mean cosine
    double cosbar = 0;
    double sinbar = 0;
    for (unsigned i = 0; i < N; ++i) {
      cosbar += cos(data[i]);
      sinbar += sin(data[i]);
    }
    double R = sqrt(cosbar * cosbar + sinbar * sinbar);
    double chi = acos(cosbar / R);
    if (sinbar < 0) chi = -chi;
    Floats retval(3);
    retval[0] = N;
    retval[1] = R;
    retval[2] = chi;
    return retval;
  }

  IMP_OBJECT_METHODS(vonMisesSufficient);
  /*IMP_OBJECT_INLINE(vonMisesSufficient, out << "vonMisesSufficient: " << x_
                    << ", " << N_ << ", " << R0_ << ", " << chiexp_
                    << ", " << kappa_  <<std::endl, {});*/

 private:
  double x_, R0_, chiexp_, kappa_, I0_, I1_, logterm_, I0N_;
  unsigned N_;
  void force_set_kappa(double kappa) {
    kappa_ = kappa;
    I0_ = double(boost::math::cyl_bessel_i(0, kappa));
    I1_ = double(boost::math::cyl_bessel_i(1, kappa));
    I0N_ = pow(I0_, static_cast<int>(N_));
    logterm_ = log(2 * IMP::PI * I0N_);
  }
};

IMPISD_END_NAMESPACE

#endif /* IMPISD_VON_MISES_SUFFICIENT_H */