ceph/src/boost/boost/accumulators/statistics/p_square_cumul_dist.hpp

   1 ///////////////////////////////////////////////////////////////////////////////
   2 // p_square_cumulative_distribution.hpp
   3 //
   4 //  Copyright 2005 Daniel Egloff, Olivier Gygi. Distributed under the Boost
   5 //  Software License, Version 1.0. (See accompanying file
   6 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
   7
   8 #ifndef BOOST_ACCUMULATORS_STATISTICS_P_SQUARE_CUMUL_DIST_HPP_DE_01_01_2006
   9 #define BOOST_ACCUMULATORS_STATISTICS_P_SQUARE_CUMUL_DIST_HPP_DE_01_01_2006
  10
  11 #include <vector>
  12 #include <functional>
  13 #include <boost/parameter/keyword.hpp>
  14 #include <boost/range.hpp>
  15 #include <boost/mpl/placeholders.hpp>
  16 #include <boost/accumulators/accumulators_fwd.hpp>
  17 #include <boost/accumulators/framework/accumulator_base.hpp>
  18 #include <boost/accumulators/framework/extractor.hpp>
  19 #include <boost/accumulators/numeric/functional.hpp>
  20 #include <boost/accumulators/framework/parameters/sample.hpp>
  21 #include <boost/accumulators/statistics_fwd.hpp>
  22 #include <boost/accumulators/statistics/count.hpp>
  23
  24 namespace boost { namespace accumulators
  25 {
  26 ///////////////////////////////////////////////////////////////////////////////
  27 // num_cells named parameter
  28 //
  29 BOOST_PARAMETER_NESTED_KEYWORD(tag, p_square_cumulative_distribution_num_cells, num_cells)
  30
  31 BOOST_ACCUMULATORS_IGNORE_GLOBAL(p_square_cumulative_distribution_num_cells)
  32
  33 namespace impl
  34 {
  35     ///////////////////////////////////////////////////////////////////////////////
  36     // p_square_cumulative_distribution_impl
  37     //  cumulative_distribution calculation (as histogram)
  38     /**
  39         @brief Histogram calculation of the cumulative distribution with the \f$P^2\f$ algorithm
  40
  41         A histogram of the sample cumulative distribution is computed dynamically without storing samples
  42         based on the \f$ P^2 \f$ algorithm. The returned histogram has a specifiable amount (num_cells)
  43         equiprobable (and not equal-sized) cells.
  44
  45         For further details, see
  46
  47         R. Jain and I. Chlamtac, The P^2 algorithm for dynamic calculation of quantiles and
  48         histograms without storing observations, Communications of the ACM,
  49         Volume 28 (October), Number 10, 1985, p. 1076-1085.
  50
  51         @param p_square_cumulative_distribution_num_cells.
  52     */
  53     template<typename Sample>
  54     struct p_square_cumulative_distribution_impl
  55       : accumulator_base
  56     {
  57         typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
  58         typedef std::vector<float_type> array_type;
  59         typedef std::vector<std::pair<float_type, float_type> > histogram_type;
  60         // for boost::result_of
  61         typedef iterator_range<typename histogram_type::iterator> result_type;
  62
  63         template<typename Args>
  64         p_square_cumulative_distribution_impl(Args const &args)
  65           : num_cells(args[p_square_cumulative_distribution_num_cells])
  66           , heights(num_cells + 1)
  67           , actual_positions(num_cells + 1)
  68           , desired_positions(num_cells + 1)
  69           , positions_increments(num_cells + 1)
  70           , histogram(num_cells + 1)
  71           , is_dirty(true)
  72         {
  73             std::size_t b = this->num_cells;
  74
  75             for (std::size_t i = 0; i < b + 1; ++i)
  76             {
  77                 this->actual_positions[i] = i + 1.;
  78                 this->desired_positions[i] = i + 1.;
  79                 this->positions_increments[i] = numeric::fdiv(i, b);
  80             }
  81         }
  82
  83         template<typename Args>
  84         void operator ()(Args const &args)
  85         {
  86             this->is_dirty = true;
  87
  88             std::size_t cnt = count(args);
  89             std::size_t sample_cell = 1; // k
  90             std::size_t b = this->num_cells;
  91
  92             // accumulate num_cells + 1 first samples
  93             if (cnt <= b + 1)
  94             {
  95                 this->heights[cnt - 1] = args[sample];
  96
  97                 // complete the initialization of heights by sorting
  98                 if (cnt == b + 1)
  99                 {
 100                     std::sort(this->heights.begin(), this->heights.end());
 101                 }
 102             }
 103             else
 104             {
 105                 // find cell k such that heights[k-1] <= args[sample] < heights[k] and adjust extreme values
 106                 if (args[sample] < this->heights[0])
 107                 {
 108                     this->heights[0] = args[sample];
 109                     sample_cell = 1;
 110                 }
 111                 else if (this->heights[b] <= args[sample])
 112                 {
 113                     this->heights[b] = args[sample];
 114                     sample_cell = b;
 115                 }
 116                 else
 117                 {
 118                     typename array_type::iterator it;
 119                     it = std::upper_bound(
 120                         this->heights.begin()
 121                       , this->heights.end()
 122                       , args[sample]
 123                     );
 124
 125                     sample_cell = std::distance(this->heights.begin(), it);
 126                 }
 127
 128                 // increment positions of markers above sample_cell
 129                 for (std::size_t i = sample_cell; i < b + 1; ++i)
 130                 {
 131                     ++this->actual_positions[i];
 132                 }
 133
 134                 // update desired position of markers 2 to num_cells + 1
 135                 // (desired position of first marker is always 1)
 136                 for (std::size_t i = 1; i < b + 1; ++i)
 137                 {
 138                     this->desired_positions[i] += this->positions_increments[i];
 139                 }
 140
 141                 // adjust heights of markers 2 to num_cells if necessary
 142                 for (std::size_t i = 1; i < b; ++i)
 143                 {
 144                     // offset to desire position
 145                     float_type d = this->desired_positions[i] - this->actual_positions[i];
 146
 147                     // offset to next position
 148                     float_type dp = this->actual_positions[i + 1] - this->actual_positions[i];
 149
 150                     // offset to previous position
 151                     float_type dm = this->actual_positions[i - 1] - this->actual_positions[i];
 152
 153                     // height ds
 154                     float_type hp = (this->heights[i + 1] - this->heights[i]) / dp;
 155                     float_type hm = (this->heights[i - 1] - this->heights[i]) / dm;
 156
 157                     if ( ( d >= 1. && dp > 1. ) || ( d <= -1. && dm < -1. ) )
 158                     {
 159                         short sign_d = static_cast<short>(d / std::abs(d));
 160
 161                         // try adjusting heights[i] using p-squared formula
 162                         float_type h = this->heights[i] + sign_d / (dp - dm) * ( (sign_d - dm) * hp + (dp - sign_d) * hm );
 163
 164                         if ( this->heights[i - 1] < h && h < this->heights[i + 1] )
 165                         {
 166                             this->heights[i] = h;
 167                         }
 168                         else
 169                         {
 170                             // use linear formula
 171                             if (d>0)
 172                             {
 173                                 this->heights[i] += hp;
 174                             }
 175                             if (d<0)
 176                             {
 177                                 this->heights[i] -= hm;
 178                             }
 179                         }
 180                         this->actual_positions[i] += sign_d;
 181                     }
 182                 }
 183             }
 184         }
 185
 186         template<typename Args>
 187         result_type result(Args const &args) const
 188         {
 189             if (this->is_dirty)
 190             {
 191                 this->is_dirty = false;
 192
 193                 // creates a vector of std::pair where each pair i holds
 194                 // the values heights[i] (x-axis of histogram) and
 195                 // actual_positions[i] / cnt (y-axis of histogram)
 196
 197                 std::size_t cnt = count(args);
 198
 199                 for (std::size_t i = 0; i < this->histogram.size(); ++i)
 200                 {
 201                     this->histogram[i] = std::make_pair(this->heights[i], numeric::fdiv(this->actual_positions[i], cnt));
 202                 }
 203             }
 204             //return histogram;
 205             return make_iterator_range(this->histogram);
 206         }
 207
 208     private:
 209         std::size_t num_cells;            // number of cells b
 210         array_type  heights;              // q_i
 211         array_type  actual_positions;     // n_i
 212         array_type  desired_positions;    // n'_i
 213         array_type  positions_increments; // dn'_i
 214         mutable histogram_type histogram; // histogram
 215         mutable bool is_dirty;
 216     };
 217
 218 } // namespace detail
 219
 220 ///////////////////////////////////////////////////////////////////////////////
 221 // tag::p_square_cumulative_distribution
 222 //
 223 namespace tag
 224 {
 225     struct p_square_cumulative_distribution
 226       : depends_on<count>
 227       , p_square_cumulative_distribution_num_cells
 228     {
 229         /// INTERNAL ONLY
 230         ///
 231         typedef accumulators::impl::p_square_cumulative_distribution_impl<mpl::_1> impl;
 232     };
 233 }
 234
 235 ///////////////////////////////////////////////////////////////////////////////
 236 // extract::p_square_cumulative_distribution
 237 //
 238 namespace extract
 239 {
 240     extractor<tag::p_square_cumulative_distribution> const p_square_cumulative_distribution = {};
 241
 242     BOOST_ACCUMULATORS_IGNORE_GLOBAL(p_square_cumulative_distribution)
 243 }
 244
 245 using extract::p_square_cumulative_distribution;
 246
 247 // So that p_square_cumulative_distribution can be automatically substituted with
 248 // weighted_p_square_cumulative_distribution when the weight parameter is non-void
 249 template<>
 250 struct as_weighted_feature<tag::p_square_cumulative_distribution>
 251 {
 252     typedef tag::weighted_p_square_cumulative_distribution type;
 253 };
 254
 255 template<>
 256 struct feature_of<tag::weighted_p_square_cumulative_distribution>
 257   : feature_of<tag::p_square_cumulative_distribution>
 258 {
 259 };
 260
 261 }} // namespace boost::accumulators
 262
 263 #endif