NeoPZ
stats.py
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1 #! /usr/bin/env python2.7
2 #***************************************************************************
3 #* Copyright (C) 2013 by Edson Borin *
4 #* edson@ic.unicamp.br *
5 #* *
6 #* This program is free software; you can redistribute it and/or modify *
7 #* it under the terms of the GNU General Public License as published by *
8 #* the Free Software Foundation; either version 2 of the License, or *
9 #* (at your option) any later version. *
10 #* *
11 #* This program is distributed in the hope that it will be useful, *
12 #* but WITHOUT ANY WARRANTY; without even the implied warranty of *
13 #* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
14 #* GNU General Public License for more details. *
15 #* *
16 #* You should have received a copy of the GNU General Public License *
17 #* along with this program; if not, write to the *
18 #* Free Software Foundation, Inc., *
19 #* 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. *
20 #**************************************************************************/
21 
22 import math # sqrt
23 
24 # Provide statistics functions
25 # TODO: Improve the description...
26 
27 class StatsError(Exception):
28  def __init__(self, msg):
29  self.msg = msg
30  def __str__(self):
31  return self.msg
32 
33 def average(vlist) :
34  sz = len(vlist)
35  if sz == 0 :
36  return 0.0
37  else :
38  s=reduce(lambda x,y : float(x)+float(y), vlist, 0.0)
39  return s/sz
40 
41 def variance(vlist) :
42  size=len(vlist)
43  if size == 1 or size == 0:
44  raise StatsError("Cannot calculate variance for a sample of size "+str(size))
45  sum1=reduce(lambda x,y : float(x)+float(y), vlist, 0.0)
46  sum2=reduce(lambda x,y : float(x)+(float(y)*float(y)), vlist, 0.0)
47  v = (sum2-(pow(sum1,2)/float(size)))/float(size-1)
48  if v < 0.0 :
49  if v > -1.e-15 : # tolerate floating point rounding errors
50  return 0.0
51  else :
52  raise StatsError("Something went wrong while calculating the variance (result < 0.0)")
53  return v
54 
55 def stdev(vlist) :
56  var = variance(vlist)
57  return math.sqrt(var)
58 
59 def conf_int(vlist, conf_level) :
60  df=len(vlist) # Sample size
61  if df < 0:
62  raise StatsError("Sample size must be >= 2 in order to compute the confidence interval.")
63  std = stdev(vlist)
64  students_t_table = [['df/p', 20, 50, 80, 90, 95, 98, 99, 99.9],
65  [1, 0.324920, 1, 3.077684, 6.313752, 12.70620, 31.82052, 63.65674, 636.6192],
66  [2, 0.288675, 0.816497, 1.885618, 2.919986, 4.30265, 6.96456, 9.92484, 31.5991],
67  [3, 0.276671, 0.764892, 1.637744, 2.353363, 3.18245, 4.54070, 5.84091, 12.9240],
68  [4, 0.270722, 0.740697, 1.533206, 2.131847, 2.77645, 3.74695, 4.60409, 8.6103],
69  [5, 0.267181, 0.726687, 1.475884, 2.015048, 2.57058, 3.36493, 4.03214, 6.8688],
70  [6, 0.264835, 0.717558, 1.439756, 1.943180, 2.44691, 3.14267, 3.70743, 5.9588],
71  [7, 0.263167, 0.711142, 1.414924, 1.894579, 2.36462, 2.99795, 3.49948, 5.4079],
72  [8, 0.261921, 0.706387, 1.396815, 1.859548, 2.30600, 2.89646, 3.35539, 5.0413],
73  [9, 0.260955, 0.702722, 1.383029, 1.833113, 2.26216, 2.82144, 3.24984, 4.7809],
74  [10, 0.260185, 0.699812, 1.372184, 1.812461, 2.22814, 2.76377, 3.16927, 4.5869],
75  [11, 0.259556, 0.697445, 1.363430, 1.795885, 2.20099, 2.71808, 3.10581, 4.4370],
76  [12, 0.259033, 0.695483, 1.356217, 1.782288, 2.17881, 2.68100, 3.05454, 4.3178],
77  [13, 0.258591, 0.693829, 1.350171, 1.770933, 2.16037, 2.65031, 3.01228, 4.2208],
78  [14, 0.258213, 0.692417, 1.345030, 1.761310, 2.14479, 2.62449, 2.97684, 4.1405],
79  [15, 0.257885, 0.691197, 1.340606, 1.753050, 2.13145, 2.60248, 2.94671, 4.0728],
80  [16, 0.257599, 0.690132, 1.336757, 1.745884, 2.11991, 2.58349, 2.92078, 4.0150],
81  [17, 0.257347, 0.689195, 1.333379, 1.739607, 2.10982, 2.56693, 2.89823, 3.9651],
82  [18, 0.257123, 0.688364, 1.330391, 1.734064, 2.10092, 2.55238, 2.87844, 3.9216],
83  [19, 0.256923, 0.687621, 1.327728, 1.729133, 2.09302, 2.53948, 2.86093, 3.8834],
84  [20, 0.256743, 0.686954, 1.325341, 1.724718, 2.08596, 2.52798, 2.84534, 3.8495],
85  [21, 0.256580, 0.686352, 1.323188, 1.720743, 2.07961, 2.51765, 2.83136, 3.8193],
86  [22, 0.256432, 0.685805, 1.321237, 1.717144, 2.07387, 2.50832, 2.81876, 3.7921],
87  [23, 0.256297, 0.685306, 1.319460, 1.713872, 2.06866, 2.49987, 2.80734, 3.7676],
88  [24, 0.256173, 0.684850, 1.317836, 1.710882, 2.06390, 2.49216, 2.79694, 3.7454],
89  [25, 0.256060, 0.684430, 1.316345, 1.708141, 2.05954, 2.48511, 2.78744, 3.7251],
90  [26, 0.255955, 0.684043, 1.314972, 1.705618, 2.05553, 2.47863, 2.77871, 3.7066],
91  [27, 0.255858, 0.683685, 1.313703, 1.703288, 2.05183, 2.47266, 2.77068, 3.6896],
92  [28, 0.255768, 0.683353, 1.312527, 1.701131, 2.04841, 2.46714, 2.76326, 3.6739],
93  [29, 0.255684, 0.683044, 1.311434, 1.699127, 2.04523, 2.46202, 2.75639, 3.6594],
94  [30, 0.255605, 0.682756, 1.310415, 1.697261, 2.04227, 2.45726, 2.75000, 3.6460],
95  ['inf', 0.253347, 0.674490, 1.281552, 1.644854, 1.95996, 2.32635, 2.57583, 3.2905]]
96  col=1
97  while col < len(students_t_table[0]):
98  if students_t_table[0][col] == conf_level: break
99  col+=1
100  if col == len(students_t_table[0]):
101  raise StatsError("Confidence level = "+str(conf_level)+" is not supported.")
102  if df <= 30:
103  lin = 1
104  while lin < len(students_t_table):
105  if students_t_table[lin][0] == df:
106  tstar = students_t_table[lin][col]
107  break
108  lin+=1
109  if lin == len(students_t_table):
110  raise StatsError("Could not find T critical value.")
111  else:
112  tstar = students_t_table[31][col]
113  return tstar*(float(std)/float(math.sqrt(df+1)))
stats.stdev
def stdev(vlist)
Definition: stats.py:70
stats.StatsError.__init__
def __init__(self, msg)
Definition: stats.py:28
stats.average
def average(vlist)
Definition: stats.py:45
stats.variance
def variance(vlist)
Definition: stats.py:54
stats.conf_int
def conf_int(vlist, conf_level)
Definition: stats.py:59
pow
TPZFlopCounter pow(const TPZFlopCounter &orig, const TPZFlopCounter &xp)
Returns the power and increments the counter of the power.
Definition: pzreal.h:487
stats.StatsError.__str__
def __str__(self)
Definition: stats.py:30
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