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.
28 _multiprocess_can_split_ = True
29 """Allow nosetests to split tests between processes.
33 class Histogram (object):
34 """A histogram with a flexible comparison method, `residual()`.
38 def calculate_bin_edges(self, data, bin_width):
41 >>> h.calculate_bin_edges(numpy.array([-7.5, 18.2, 4]), 10)
42 array([-10., 0., 10., 20.])
43 >>> h.calculate_bin_edges(numpy.array([-7.5, 18.2, 4, 20]), 10)
44 array([-10., 0., 10., 20.])
45 >>> h.calculate_bin_edges(numpy.array([0, 18.2, 4, 20]), 10)
46 array([ 0., 10., 20.])
47 >>> h.calculate_bin_edges(numpy.array([18.2, 4, 20]), 10)
48 array([ 0., 10., 20.])
49 >>> h.calculate_bin_edges(numpy.array([18.2, 20]), 10)
54 bin_start = m - m % bin_width
55 return numpy.arange(bin_start, M+bin_width, bin_width, dtype=data.dtype)
57 def from_data(self, data, bin_edges):
58 """Initialize from `data`.
60 All bins should be of equal width (so we can calculate which
61 bin a data point belongs to).
64 data = numpy.array(data)
65 self.bin_edges = numpy.array(bin_edges)
66 bin_width = self.bin_edges[1] - self.bin_edges[0]
68 bin_is = numpy.floor((data - self.bin_edges[0])/bin_width)
69 self.counts = numpy.zeros((len(self.bin_edges)-1,), dtype=numpy.int)
70 for i in range(len(self.counts)):
71 self.counts[i] = (bin_is == i).sum()
72 self.counts = numpy.array(self.counts)
73 self.total = float(len(data)) # some data might be outside the bins
74 self.mean = data.mean()
75 self.std_dev = data.std()
78 def from_stream(self, stream):
79 """Initialize from `stream`.
83 # comment and blank lines ignored
84 <bin_edge><whitespace><count>
87 `<bin_edge>` should mark the left-hand side of the bin, and
88 all bins should be of equal width (so we know where the last
93 >>> h.from_stream(StringIO.StringIO('''# Force (N)\\tUnfolding events
99 ['Force (N)', 'Unfolding events']
104 >>> h.bin_edges # doctest: +ELLIPSIS
105 [1.5e-10, 2.000...e-10, 2.500...e-10, 3e-10]
106 >>> h.probabilities # doctest: +ELLIPSIS
107 [0.181..., 0.727..., 0.0909...]
112 for line in stream.readlines():
114 if len(line) == 0 or line.startswith('#'):
115 if self.headings == None and line.startswith('#'):
116 line = line[len('#'):]
117 self.headings = [x.strip() for x in line.split('\t')]
118 continue # ignore blank lines and comments
120 bin_edge,count = line.split()
122 log().error('Unable to parse histogram line: "%s"' % line)
124 self.bin_edges.append(float(bin_edge))
125 self.counts.append(float(count))
126 bin_width = self.bin_edges[1] - self.bin_edges[0]
127 self.bin_edges.append(self.bin_edges[-1]+bin_width)
130 def to_stream(self, stream):
131 """Write to `stream` with the same format as `from_stream()`.
135 >>> h.headings = ['Force (N)', 'Unfolding events']
136 >>> h.bin_edges = [1.5e-10, 2e-10, 2.5e-10, 3e-10]
137 >>> h.counts = [10, 40, 5]
138 >>> h.to_stream(sys.stdout)
139 ... # doctest: +NORMALIZE_WHITESPACE, +REPORT_UDIFF
140 #Force (N)\tUnfolding events
145 if self.headings != None:
146 stream.write('#%s\n' % '\t'.join(self.headings))
147 for bin,count in zip(self.bin_edges, self.counts):
148 stream.write('%g\t%g\n' % (bin, count))
151 """Analyze `.counts` and `.bin_edges` if the raw data is missing.
153 Generate `.total`, `.mean`, and `.std_dev`, and run
156 bin_width = self.bin_edges[1] - self.bin_edges[0]
157 self.total = float(sum(self.counts))
159 for bin,count in zip(self.bin_edges, self.counts):
160 bin += bin_width / 2.0
161 self.mean += bin * count
162 self.mean /= float(self.total)
164 for bin,count in zip(self.bin_edges, self.counts):
165 bin += bin_width / 2.0
166 variance += (bin - self.mean)**2 * count
167 self.std_dev = numpy.sqrt(variance)
171 """Generate `.probabilities` from `.total` and `.counts`.
173 self.total = float(self.total)
174 self.probabilities = [count/self.total for count in self.counts]
176 def mean_residual(self, other):
177 return abs(other.mean - self.mean)
179 def std_dev_residual(self, other):
180 return abs(other.std_dev - self.std_dev)
182 def chi_squared_residual(self, other):
183 assert (self.bin_edges == other.bin_edges).all()
185 for probA,probB in zip(self.probabilities, other.probabilities):
186 residual += (probA-probB)**2 / probB
189 def jensen_shannon_residual(self, other):
190 assert (self.bin_edges == other.bin_edges).all()
193 Kullback-Leibler divergence for a single bin, with the
194 exception that we return 0 if q==0, rather than
195 exploding like d_KL should. We can do this because
196 the way d_KL_term is used in the Jensen-Shannon
197 divergence, if q (really m) == 0, then p also == 0,
198 and the Jensen-Shannon divergence for the entire term
201 if p==0 or q==0 or p==q:
203 return p * numpy.log2(p/q)
205 for probA,probB in zip(self.probabilities, other.probabilities):
206 m = (probA+probB) / 2.0
207 residual += 0.5*(d_KL_term(probA,m) + d_KL_term(probB,m))
210 def _method_to_type(self, name):
211 return name[:-len('_residual')].replace('_', '-')
213 def _type_to_method(self, name):
214 return '%s_residual' % name.replace('-', '_')
217 """Return a list of supported residual types.
219 return sorted([self._method_to_type(x)
220 for x in dir(self) if x.endswith('_residual')])
222 def residual(self, other, type='jensen-shannon'):
223 """Compare this histogram with `other`.
225 Supported comparison `type`\s may be found with `types()`:
229 ['chi-squared', 'jensen-shannon', 'mean', 'std-dev']
231 Selecting an invalid `type` raises an exception.
233 >>> h.residual(other=None, type='invalid-type')
234 Traceback (most recent call last):
236 AttributeError: 'Histogram' object has no attribute 'invalid_type_residual'
238 For residual types where there is a convention, this histogram
239 is treated as the experimental histogram and the other
240 histogram is treated as the theoretical one.
242 r_method = getattr(self, self._type_to_method(type))
243 return r_method(other)