1 # Copyright (C) 2009-2010 W. Trevor King <wking@drexel.edu>
3 # This program is free software: you can redistribute it and/or modify
4 # it under the terms of the GNU General Public License as published by
5 # the Free Software Foundation, either version 3 of the License, or
6 # (at your option) any later version.
8 # This program is distributed in the hope that it will be useful,
9 # but WITHOUT ANY WARRANTY; without even the implied warranty of
10 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
11 # GNU General Public License for more details.
13 # You should have received a copy of the GNU General Public License
14 # along with this program. If not, see <http://www.gnu.org/licenses/>.
16 # The author may be contacted at <wking@drexel.edu> on the Internet, or
17 # write to Trevor King, Drexel University, Physics Dept., 3141 Chestnut St.,
18 # Philadelphia PA 19104, USA.
20 """Histogram generation and comparison.
26 class Histogram (object):
27 """A histogram with a flexible comparison method, `residual()`.
31 def calculate_bin_edges(self, data, bin_width):
34 >>> h.calculate_bin_edges(numpy.array([-7.5, 18.2, 4]), 10)
35 array([-10., 0., 10., 20.])
36 >>> h.calculate_bin_edges(numpy.array([-7.5, 18.2, 4, 20]), 10)
37 array([-10., 0., 10., 20.])
38 >>> h.calculate_bin_edges(numpy.array([0, 18.2, 4, 20]), 10)
39 array([ 0., 10., 20.])
40 >>> h.calculate_bin_edges(numpy.array([18.2, 4, 20]), 10)
41 array([ 0., 10., 20.])
42 >>> h.calculate_bin_edges(numpy.array([18.2, 20]), 10)
47 bin_start = m - m % bin_width
48 return numpy.arange(bin_start, M+bin_width, bin_width, dtype=data.dtype)
50 def from_data(self, data, bin_edges):
51 """Initialize from `data`.
53 All bins should be of equal width (so we can calculate which
54 bin a data point belongs to).
56 `data` should be a numpy array.
59 self.bin_edges = bin_edges
60 bin_width = self.bin_edges[1] - self.bin_edges[0]
62 bin_is = numpy.floor((data - self.bin_edges[0])/bin_width)
64 for i in range(len(self.bin_edges)-1):
65 self.counts.append(sum(bin_is == i))
66 self.total = float(len(data)) # some data might be outside the bins
67 self.mean = data.mean()
68 self.std_dev = data.std()
71 def from_stream(self, stream):
72 """Initialize from `stream`.
76 # comment and blank lines ignored
77 <bin_edge><whitespace><count>
83 `<bin_edge>` should mark the left-hand side of the bin, and
84 all bins should be of equal width (so we know where the last
89 >>> h.from_stream(StringIO.StringIO('''# Force (N)\\tUnfolding events
95 ['Force (N)', 'Unfolding events']
100 >>> h.bin_edges # doctest: +ELLIPSIS
101 [1.5e-10, 2.000...e-10, 2.500...e-10, 3e-10]
102 >>> h.probabilities # doctest: +ELLIPSIS
103 [0.181..., 0.727..., 0.0909...]
108 for line in stream.readlines():
110 if len(line) == 0 or line.startswith('#'):
111 if self.headings == None and line.startswith('#'):
112 line = line[len('#'):]
113 self.headings = [x.strip() for x in line.split('\t')]
114 continue # ignore blank lines and comments
115 bin_edge,count = line.split()
116 self.bin_edges.append(float(bin_edge))
117 self.counts.append(float(count))
118 bin_width = self.bin_edges[1] - self.bin_edges[0]
119 self.bin_edges.append(self.bin_edges[-1]+bin_width)
120 self.total = float(sum(self.counts))
122 for bin,count in zip(self.bin_edges, self.counts):
123 bin += bin_width / 2.0
124 self.mean += bin * count
125 self.mean /= float(self.total)
127 for bin,count in zip(self.bin_edges, self.counts):
128 bin += bin_width / 2.0
129 variance += (bin - self.mean)**2 * count
130 self.std_dev = numpy.sqrt(variance)
133 def to_stream(self, stream):
134 """Write to `stream` with the same format as `from_stream()`.
138 >>> h.headings = ['Force (N)', 'Unfolding events']
139 >>> h.bin_edges = [1.5e-10, 2e-10, 2.5e-10, 3e-10]
140 >>> h.counts = [10, 40, 5]
141 >>> h.to_stream(sys.stdout)
142 ... # doctest: +NORMALIZE_WHITESPACE, +REPORT_UDIFF
143 # Force (N)\tUnfolding events
148 if self.headings != None:
149 stream.write('# %s\n' % '\t'.join(self.headings))
150 for bin,count in zip(self.bin_edges, self.counts):
151 stream.write('%g\t%g\n' % (bin, count))
154 self.total = float(self.total)
155 self.probabilities = [count/self.total for count in self.counts]
157 def mean_residual(self, other):
158 return abs(other.mean - self.mean)
160 def std_dev_residual(self, other):
161 return abs(other.std_dev - self.std_dev)
163 def chi_squared_residual(self, other):
164 assert self.bin_edges == other.bin_edges
166 for probA,probB in zip(self.probabilities, other.probabilities):
167 residual += (probA-probB)**2 / probB
170 def jensen_shannon_residual(self, other):
171 assert self.bin_edges == other.bin_edges
174 Kullback-Leibler divergence for a single bin, with the
175 exception that we return 0 if q==0, rather than
176 exploding like d_KL should. We can do this because
177 the way d_KL_term is used in the Jensen-Shannon
178 divergence, if q (really m) == 0, then p also == 0,
179 and the Jensen-Shannon divergence for the entire term
182 if p==0 or q==0 or p==q:
184 return p * numpy.log2(p/q)
186 for probA,probB in zip(self.probabilities, other.probabilities):
187 m = (probA+probB) / 2.0
188 residual += 0.5*(d_KL_term(probA,m) + d_KL_term(probB,m))
191 def _method_to_type(self, name):
192 return name[:-len('_residual')].replace('_', '-')
194 def _type_to_method(self, name):
195 return '%s_residual' % name.replace('-', '_')
198 """Return a list of supported residual types.
200 return sorted([self._method_to_type(x)
201 for x in dir(self) if x.endswith('_residual')])
203 def residual(self, other, type='jensen-shannon'):
204 """Compare this histogram with `other`.
206 Supported comparison `type`\s may be found with `types()`:
210 ['chi-squared', 'jensen-shannon', 'mean', 'std-dev']
212 Selecting an invalid `type` raises an exception.
214 >>> h.residual(other=None, type='invalid-type')
215 Traceback (most recent call last):
217 AttributeError: 'Histogram' object has no attribute 'invalid_type_residual'
219 For residual types where there is a convention, this histogram
220 is treated as the experimental histogram and the other
221 histogram is treated as the theoretical one.
223 r_method = getattr(self, self._type_to_method(type))
224 return r_method(other)