JQuantile.hh

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#ifndef __JTOOLS__JQUANTILE__
#define __JTOOLS__JQUANTILE__

#include <ostream>
#include <iomanip>
#include <cmath>
#include <limits>
#include <algorithm>
#include <map>
#include <iterator>

#include "JLang/JException.hh"
#include "JLang/JTitle.hh"
#include "JLang/JVectorize.hh"
#include "JLang/JManip.hh"
#include "JMath/JMath.hh"


/**
 * \author mdejong
 */

namespace JTOOLS {}
namespace JPP { using namespace JTOOLS; }

namespace JTOOLS {

  using JMATH::JMath;
  using JLANG::JTitle;
  using JLANG::JDivisionByZero;
  using JLANG::JNoValue;
  using JLANG::array_type;
  using JLANG::make_array;


  /**
   * Auxiliary data structure for quantiles.
   */
  struct JQuantile_t :
    public JTitle
  {
    /**
     * Constructor.
     *
     * \param  title            title
     * \param  quantiles        quantiles
     */
    JQuantile_t(const JTitle& title     = "",
                const bool    quantiles = false) :
      JTitle   (title),
      quantiles(quantiles)
    {
      reset();
    }


    /**
     * Reset.
     */
    void reset()
    {
      sum = 0.0;
      rms = 0.0;
      tot = 0.0;
      num = 0;
      min = std::numeric_limits<double>::max();
      max = std::numeric_limits<double>::lowest();

      buffer.clear();
    }

  protected:
    double        sum;
    double        rms;
    double        tot;
    double        min;
    double        max;
    long long int num;
    bool          quantiles;
    std::multimap<double, double> buffer;
  };


  /**
   * Quantile calculator.\n
   * This class acts as a zero-dimensional histogram.
   */
  struct JQuantile :
    public JQuantile_t,
    public JMath<JQuantile>
  {
    /**
     * Constructor.
     *
     * \param  title            title
     * \param  quantiles        quantiles
     */
    JQuantile(const JTitle& title  = "",
              const bool    quantiles = false) :
      JQuantile_t(title, quantiles)
    {}


    /**
     * Constructor.
     *
     * \param  title            title
     * \param  __begin          begin of data
     * \param  __end            end   of data
     * \param  quantiles        quantiles
     * \param  w                weight
     */
    template<class iterator_type>
    JQuantile(const JTitle& title,
              iterator_type __begin,
              iterator_type __end,
              const bool    quantiles = false,
              const double  w         = 1.0) :
      JQuantile_t(title, quantiles)
    {
      put(__begin, __end, w);
    }


    /**
     * Constructor.
     *
     * \param  title            title
     * \param  buffer           input data
     * \param  quantiles        quantiles
     * \param  w                weight
     */
    template<class JElement_t, class JAllocator_t>
    JQuantile(const JTitle& title,
              const array_type<JElement_t, JAllocator_t>& buffer,
              const bool    quantiles = false,
              const double  w         = 1.0) :
      JQuantile_t(title, quantiles)
    {
      put(buffer, w);
    }


    /**
     * Add quantile.
     *
     * \param  Q           quantile
     * \return             this quantile
     */
    JQuantile& add(const JQuantile& Q)
    {
      sum += Q.sum;
      rms += Q.rms;
      tot += Q.tot;
      num += Q.num;
      min  = std::min(min, Q.min);
      max  = std::max(max, Q.max);

      if (quantiles) {
        std::copy(Q.buffer.begin(), Q.buffer.end(), std::inserter(buffer, buffer.end()));
      }

      return *this;
    }


    /**
     * Put value.
     *
     * \param  x           value
     * \param  w           weight
     */
    void put(const double x, const double w = 1.0)
    {
      sum += w*x;
      rms += w*x*x;
      tot += w;
      num += 1;
      min  = std::min(min, x);
      max  = std::max(max, x);

      if (quantiles) {
        buffer.insert(std::make_pair(x,w));
      }
    }


    /**
     * Put data.
     *
     * \param  __begin          begin of data
     * \param  __end            end   of data
     * \param  w                weight
     */
    template<class iterator_type>
    void put(iterator_type __begin,
             iterator_type __end,
             const double w = 1.0)
    {
      for (iterator_type i = __begin; i != __end; ++i) {
        put(*i, w);
      }
    }


    /**
     * Put data.
     *
     * \param  buffer           input data
     * \param  w                weight
     */
    template<class JElement_t, class JAllocator_t>
    void put(const array_type<JElement_t, JAllocator_t>& buffer,
             const double w = 1.0)
    {
      for (typename array_type<JElement_t, JAllocator_t>::const_iterator i = buffer.begin(); i != buffer.end(); ++i) {
        put(*i, w);
      }
    }


    /**
     * Get total count.
     *
     * \return             count
     */
    long long int getCount() const
    {
      return num;
    }


    /**
     * Get total weight.
     *
     * \return             weight
     */
    double getTotal() const
    {
      return tot;
    }


    /**
     * Get weighted sum.
     *
     * \return             weighted sum
     */
    double getSum() const
    {
      return sum;
    }


    /**
     * Get minimum.
     *
     * \return             minimum
     */
    double getMin() const
    {
      return min;
    }


    /**
     * Get maximum.
     *
     * \return             maximum
     */
    double getMax() const
    {
      return max;
    }


    /**
     * Get mean value.
     *
     * \return             mean value
     */
    double getMean() const
    {
      if (tot != 0.0)
        return sum / tot;
      else
        THROW(JDivisionByZero, "JQuantile::getMean()");
    }


    /**
     * Get RMS.
     *
     * \return             RMS
     */
    double getRMS() const
    {
      if (tot != 0.0)
        return sqrt(rms/tot);
      else
        THROW(JDivisionByZero, "JQuantile::getRMS()");
    }


    /**
     * Get standard deviation
     *
     * \return             standard deviation
     */
    double getSTDev() const
    {
      if (tot != 0.0)
        return sqrt(rms*tot - sum*sum)/tot;
      else
        THROW(JDivisionByZero, "JQuantile::getSTDev()");
    }


    /**
     * Get maximal deviation from average.
     *
     * \param  relative    if true, relative to average, else absolute
     * \return             deviation
     */
    double getDeviation(const bool relative = true) const
    {
      if (relative)
        return std::max(getMax() - getMean(), getMean() - getMin());
      else
        return getMax() - getMin();
    }


    /**
     * Test relative accuracy.
     *
     * \param  precision   relative precision
     * \return             true if reached accuracy; else false
     */
    bool hasAccuracy(const double precision) const
    {
      return getCount() > 3 && getSTDev() < precision * getMean();
    }


    /**
     * Get quantile.
     *
     * \param  Q           quantile 
     * \param  reverse     reverse
     * \return             value
     */
    double getQuantile(const double Q, const bool reverse = false) const
    {
      if (quantiles) {

        double W = 0.0;

        for (std::map<double, double>::const_iterator i = buffer.begin(); i != buffer.end(); ++i) {
          W += i->second;
        }

        if (reverse)
          return getQuantile(buffer.rbegin(), buffer.rend(), Q*W);
        else
          return getQuantile(buffer. begin(), buffer. end(), Q*W);
      }

      THROW(JNoValue, "Option 'quantiles' at JQuantile() incompatible with method getQuantile().");
    }


    /**
     * Print quantile.
     *
     * \param  out         output stream
     * \param  lpr         long print
     */
    std::ostream& print(std::ostream& out, bool lpr = true) const
    {
      using namespace std;

      const int nc = getTitle().size();

      if (lpr) {
        out << setw(nc) << left  << " "             << ' '
            << setw(10) << left  << "    mean"      << ' '
            << setw(10) << left  << "    STD"       << ' '
            << setw(10) << left  << "  deviation"   << endl;
      }

      out << setw(nc) << left << getTitle()          << ' '
          << SCIENTIFIC(10,2) << getMean()           << ' '
          << SCIENTIFIC(10,2) << getSTDev()          << ' '
          << SCIENTIFIC(10,2) << getDeviation(false) << endl;

      return out;
    }


    /**
     * Print quantile.
     *
     * \param  out           output stream
     * \param  quantile      quantile
     * \return               output stream
     */
    friend inline std::ostream& operator<<(std::ostream& out, const JQuantile& quantile)
    {
      return quantile.print(out, getLongprint(out));
    }

  protected:
    /**
     * Get quantile.
     *
     * \param  __begin     begin of data
     * \param  __end       end   of data
     * \param  W           weight
     * \return             value
     */
    template<class T>
    static double getQuantile(T __begin, T __end, const double W)
    {
      double w = 0.0;

      for (T i = __begin; i != __end; ++i) {

        w += i->second;

        if (w >= W) {
          return i->first;
        }
      }

      THROW(JNoValue, "Invalid weight " << W);
    }
  };
}

#endif