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+# Copyright (c) 2023 Cisco and/or its affiliates.
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at:
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+"""Module holding BitCountingStats class."""
+
+import dataclasses
+import math
+import typing
+
+from .avg_stdev_stats import AvgStdevStats
+
+
+@dataclasses.dataclass
+class BitCountingStats(AvgStdevStats):
+ """Class for statistics which include information content of a group.
+
+ The information content is based on an assumption that the data
+ consists of independent random values from a normal distribution.
+
+ Instances are only statistics, the data itself is stored elsewhere.
+
+ The coding needs to know the previous average, and a maximal value
+ so both values are required as inputs.
+
+ This is a subclass of AvgStdevStats, even though all methods are overriden.
+ Only for_runs method calls the parent implementation, without using super().
+ """
+
+ max_value: float = None
+ """Maximal sample value (real or estimated).
+ Default value is there just for argument ordering reasons,
+ leaving None leads to exceptions."""
+ unit: float = 1.0
+ """Typical resolution of the values."""
+ prev_avg: typing.Optional[float] = None
+ """Population average of the previous group (if any)."""
+ bits: float = None
+ """The computed information content of the group.
+ It is formally an argument to init function, just to keep repr string
+ a valid call. ut the init value is ignored and always recomputed.
+ """
+
+ def __post_init__(self):
+ """Construct the stats object by computing from the values needed.
+
+ The None values are allowed for stats for zero size data,
+ but such stats can report arbitrary avg and max_value.
+ Stats for nonzero size data cannot contain None,
+ else ValueError is raised.
+
+ The max_value needs to be numeric for nonzero size,
+ but its relations to avg and prev_avg are not examined.
+
+ The bit count is not real, as that would depend on numeric precision
+ (number of significant bits in values).
+ The difference is assumed to be constant per value,
+ which is consistent with Gauss distribution
+ (but not with floating point mechanic).
+ The hope is the difference will have
+ no real impact on the classification procedure.
+ """
+ # Zero size should in principle have non-zero bits (coding zero size),
+ # but zero allows users to add empty groups without affecting bits.
+ self.bits = 0.0
+ if self.size < 1:
+ return
+ if self.max_value <= 0.0:
+ raise ValueError(f"Invalid max value: {self!r}")
+ max_value = self.max_value / self.unit
+ avg = self.avg / self.unit
+ # Length of the sequence must be also counted in bits,
+ # otherwise the message would not be decodable.
+ # Model: probability of k samples is 1/k - 1/(k+1) == 1/k/(k+1)
+ # This is compatible with zero size leading to zero bits.
+ self.bits += math.log(self.size * (self.size + 1), 2)
+ if self.prev_avg is None:
+ # Avg is considered to be uniformly distributed
+ # from zero to max_value.
+ self.bits += math.log(max_value + 1, 2)
+ else:
+ # Opposite triangle distribution with minimum.
+ prev_avg = self.prev_avg / self.unit
+ norm = prev_avg * prev_avg
+ norm -= (prev_avg - 1) * max_value
+ norm += max_value * max_value / 2
+ self.bits -= math.log((abs(avg - prev_avg) + 1) / norm, 2)
+ if self.size < 2:
+ return
+ stdev = self.stdev / self.unit
+ # Stdev is considered to be uniformly distributed
+ # from zero to max_value. That is quite a bad expectation,
+ # but resilient to negative samples etc.
+ self.bits += math.log(max_value + 1, 2)
+ # Now we know the samples lie on sphere in size-1 dimensions.
+ # So it is (size-2)-sphere, with radius^2 == stdev^2 * size.
+ # https://en.wikipedia.org/wiki/N-sphere
+ sphere_area_ln = math.log(2)
+ sphere_area_ln += math.log(math.pi) * ((self.size - 1) / 2)
+ sphere_area_ln -= math.lgamma((self.size - 1) / 2)
+ sphere_area_ln += math.log(stdev + 1) * (self.size - 2)
+ sphere_area_ln += math.log(self.size) * ((self.size - 2) / 2)
+ self.bits += sphere_area_ln / math.log(2)
+
+ @classmethod
+ def for_runs_and_params(
+ cls,
+ runs: typing.Iterable[typing.Union[float, AvgStdevStats]],
+ max_value: float,
+ unit: float = 1.0,
+ prev_avg: typing.Optional[float] = None,
+ ):
+ """Return new stats instance describing the sequence of runs.
+
+ If you want to append data to existing stats object,
+ you can simply use the stats object as the first run.
+
+ Instead of a verb, "for" is used to start this method name,
+ to signify the result contains less information than the input data.
+
+ The two optional values can come from outside of the runs provided.
+
+ The max_value cannot be None for non-zero size data.
+ The implementation does not check if no datapoint exceeds max_value.
+
+ TODO: Document the behavior for zero size result.
+
+ :param runs: Sequence of data to describe by the new metadata.
+ :param max_value: Maximal expected value.
+ :param unit: Typical resolution of the values.
+ :param prev_avg: Population average of the previous group, if any.
+ :type runs: Iterable[Union[float, AvgStdevStats]]
+ :type max_value: Union[float, NoneType]
+ :type unit: float
+ :type prev_avg: Union[float, NoneType]
+ :returns: The new stats instance.
+ :rtype: cls
+ """
+ asd = AvgStdevStats.for_runs(runs)
+ ret_obj = cls(
+ size=asd.size,
+ avg=asd.avg,
+ stdev=asd.stdev,
+ max_value=max_value,
+ unit=unit,
+ prev_avg=prev_avg,
+ )
+ return ret_obj