source: trunk/yat/statistics/utility.h @ 1470

Last change on this file since 1470 was 1470, checked in by Peter, 13 years ago
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1#ifndef _theplu_yat_statistics_utility_
2#define _theplu_yat_statistics_utility_
3
4// $Id: utility.h 1470 2008-09-02 17:46:36Z peter $
5
6/*
7  Copyright (C) 2004 Jari Häkkinen, Peter Johansson
8  Copyright (C) 2005 Peter Johansson
9  Copyright (C) 2006 Jari Häkkinen, Peter Johansson, Markus Ringnér
10  Copyright (C) 2007 Jari Häkkinen, Peter Johansson
11  Copyright (C) 2008 Peter Johansson
12
13  This file is part of the yat library, http://dev.thep.lu.se/yat
14
15  The yat library is free software; you can redistribute it and/or
16  modify it under the terms of the GNU General Public License as
17  published by the Free Software Foundation; either version 2 of the
18  License, or (at your option) any later version.
19
20  The yat library is distributed in the hope that it will be useful,
21  but WITHOUT ANY WARRANTY; without even the implied warranty of
22  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
23  General Public License for more details.
24
25  You should have received a copy of the GNU General Public License
26  along with this program; if not, write to the Free Software
27  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
28  02111-1307, USA.
29*/
30
31#include "Percentiler.h"
32
33#include "yat/classifier/DataLookupWeighted1D.h"
34#include "yat/classifier/Target.h"
35#include "yat/utility/VectorBase.h"
36#include "yat/utility/yat_assert.h"
37
38#include <algorithm>
39#include <cmath>
40#include <stdexcept>
41#include <vector>
42
43#include <gsl/gsl_statistics_double.h>
44
45namespace theplu {
46namespace yat {
47namespace statistics { 
48
49  /**
50     \brief 50th percentile
51     @see Percentiler
52  */
53  template <class T> 
54  double median(T first, T last, const bool sorted=false); 
55
56  /**
57     \see Percentiler
58  */
59  template <class T>
60  double percentile(T first, T last, double p, bool sorted=false);
61 
62  /**
63     Adding a range [\a first, \a last) into an object of type T. The
64     requirements for the type T is to have an add(double, bool, double)
65     function.
66  */
67  template <typename T, typename ForwardIterator>
68  void add(T& o, ForwardIterator first, ForwardIterator last,
69           const classifier::Target& target)
70  {
71    for (size_t i=0; first!=last; ++i, ++first)
72      o.add(utility::iterator_traits<ForwardIterator>().data(first),
73            target.binary(i), 
74            utility::iterator_traits<ForwardIterator>().weight(first));
75  } 
76
77  ///
78  /// Calculates the probability to get \a k or smaller from a
79  /// hypergeometric distribution with parameters \a n1 \a n2 \a
80  /// t. Hypergeomtric situation you get in the following situation:
81  /// Let there be \a n1 ways for a "good" selection and \a n2 ways
82  /// for a "bad" selection out of a total of possibilities. Take \a
83  /// t samples without replacement and \a k of those are "good"
84  /// samples. \a k will follow a hypergeomtric distribution.
85  ///
86  /// @return cumulative hypergeomtric distribution functions P(k).
87  ///
88  double cdf_hypergeometric_P(unsigned int k, unsigned int n1, 
89                              unsigned int n2, unsigned int t);
90
91
92  /**
93     \brief one-sided p-value
94
95     This function uses the t-distribution to calculate the one-sided
96     p-value. Given that the true correlation is zero (Null
97     hypothesis) the estimated correlation, r, after a transformation
98     is t-distributed:
99
100     \f$ \sqrt{(n-2)} \frac{r}{\sqrt{(1-r^2)}} \in t(n-2) \f$
101
102     \return Probability that correlation is larger than \a r by
103     chance when having \a n samples.
104   */
105  double pearson_p_value(double r, unsigned int n);
106
107  ///
108  /// @brief Computes the kurtosis of the data in a vector.
109  ///
110  /// The kurtosis measures how sharply peaked a distribution is,
111  /// relative to its width. The kurtosis is normalized to zero for a
112  /// gaussian distribution.
113  ///
114  double kurtosis(const utility::VectorBase&);
115
116
117  ///
118  /// @brief Median absolute deviation from median
119  ///
120  /// Function is non-mutable function
121  ///
122  template <class T>
123  double mad(T first, T last, const bool sorted=false)
124  {
125    double m = median(first, last, sorted);
126    std::vector<double> ad;
127    ad.reserve(std::distance(first, last));
128    for( ; first!=last; ++first)
129      ad.push_back(fabs(*first-m));
130    std::sort(ad.begin(), ad.end());
131    return median(ad.begin(), ad.end(), true);
132  }
133 
134
135  ///
136  /// Median is defined to be value in the middle. If number of values
137  /// is even median is the average of the two middle values.  the
138  /// median value is given by p equal to 50. If \a sorted is false
139  /// (default), the range is copied, the copy is sorted, and then
140  /// used to calculate the median.
141  ///
142  /// Function is a non-mutable function, i.e., \a first and \a last
143  /// can be const_iterators.
144  ///
145  /// Requirements: T should be an iterator over a range of doubles (or
146  /// any type being convertable to double).
147  ///
148  /// @return median of range
149  ///
150  template <class T> 
151  double median(T first, T last, const bool sorted=false) 
152  { return percentile2(first, last, 50.0, sorted); }
153
154  /**
155     The percentile is determined by the \a p, a number between 0 and
156     100. The percentile is found by interpolation, using the formula
157     \f$ percentile = (1 - \delta) x_i + \delta x_{i+1} \f$ where \a
158     p is floor\f$((n - 1)p/100)\f$ and \f$ \delta \f$ is \f$
159     (n-1)p/100 - i \f$.Thus the minimum value of the vector is given
160     by p equal to zero, the maximum is given by p equal to 100 and
161     the median value is given by p equal to 50. If @a sorted
162     is false (default), the vector is copied, the copy is sorted,
163     and then used to calculate the median.
164
165     Function is a non-mutable function, i.e., \a first and \a last
166     can be const_iterators.
167     
168     Requirements: T should be an iterator over a range of doubles (or
169     any type being convertable to double).
170     
171     @return \a p'th percentile of range
172
173     \deprecated percentile2 will replace this function in the future
174
175     \note the definition of percentile used here is not identical to
176     that one used in percentile2 and Percentile. The difference is
177     smaller for large ranges.
178  */
179  template <class RandomAccessIterator>
180  double percentile(RandomAccessIterator first, RandomAccessIterator last, 
181                    double p, bool sorted=false)
182  {
183    // range is one value only is a special case
184    if (first+1 == last)
185      return utility::iterator_traits<RandomAccessIterator>().data(first);
186    if (sorted) {
187      // have to take care of this special case
188      if (p>=100)
189        return utility::iterator_traits<RandomAccessIterator>().data(--last);
190      double j = p/100 * (std::distance(first,last)-1);
191      int i = static_cast<int>(j);
192      return (1-j+floor(j))*first[i] + (j-floor(j))*first[i+1];
193    }
194
195    std::vector<typename std::iterator_traits<RandomAccessIterator>::value_type> 
196      v_copy;
197    v_copy.reserve(std::distance(first,last));
198    std::copy(first, last, std::back_inserter(v_copy));
199    size_t i = static_cast<size_t>(p/100 * (v_copy.size()-1));
200    if (i+2 < v_copy.size()) {
201      std::partial_sort(v_copy.begin(), v_copy.begin()+i+2, v_copy.end());
202    }
203    else
204      std::sort(v_copy.begin(), v_copy.end());
205    return percentile(v_copy.begin(), v_copy.end(), p, true);
206  }
207
208
209  /**
210     \see Percentiler
211     
212     \since new in yat 0.5
213   */
214  template <class RandomAccessIterator>
215  double percentile2(RandomAccessIterator first, RandomAccessIterator last, 
216                     double p, bool sorted=false)
217  {
218    Percentiler percentiler(p, sorted);
219    return percentiler(first, last);
220  }
221
222  ///
223  /// @brief Computes the skewness of the data in a vector.
224  ///
225  /// The skewness measures the asymmetry of the tails of a
226  /// distribution.
227  ///
228  double skewness(const utility::VectorBase&);
229 
230}}} // of namespace statistics, yat, and theplu
231
232#endif
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