Add jumpavg

Signed-off-by: Tibor Frank <tifrank@cisco.com>
Change-Id: Ide837683569d1ec0e409565282c058264695640d

6 files changed, 738 insertions, 0 deletions

diff --git a/resources/libraries/python/jumpavg/AvgStdevStats.py b/resources/libraries/python/jumpavg/AvgStdevStats.py
new file mode 100644
index 0000000000..9a8decd932
--- /dev/null
+++ b/resources/libraries/python/jumpavg/AvgStdevStats.py
@@ -0,0 +1,113 @@
+# Copyright (c) 2019 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 AvgStdevStats class."""
+
+import math
+
+
+class AvgStdevStats:
+    """Class for statistics which include average and stdev of a group.
+
+    Contrary to other stats types, adding values to the group
+    is computationally light without any caching.
+
+    Instances are only statistics, the data itself is stored elsewhere.
+    """
+
+    def __init__(self, size=0, avg=0.0, stdev=0.0):
+        """Construct the stats object by storing the values needed.
+
+        Each value has to be numeric.
+        The values are not sanitized depending on size, wrong initialization
+        can cause delayed math errors.
+
+        :param size: Number of values participating in this group.
+        :param avg: Population average of the participating sample values.
+        :param stdev: Population standard deviation of the sample values.
+        :type size: int
+        :type avg: float
+        :type stdev: float
+        """
+        self.size = size
+        self.avg = avg
+        self.stdev = stdev
+
+    def __str__(self):
+        """Return string with human readable description of the group.
+
+        :returns: Readable description.
+        :rtype: str
+        """
+        return f"size={self.size} avg={self.avg} stdev={self.stdev}"
+
+    def __repr__(self):
+        """Return string executable as Python constructor call.
+
+        :returns: Executable constructor call.
+        :rtype: str
+        """
+        return (
+            f"AvgStdevStats(size={self.size!r},avg={self.avg!r}"
+            f",stdev={self.stdev!r})"
+        )
+
+    @classmethod
+    def for_runs(cls, runs):
+        """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.
+
+        Here, Run is a hypothetical abstract class, an union of float and cls.
+        Defining that as a real abstract class in Python 2 is too much hassle.
+
+        :param runs: Sequence of data to describe by the new metadata.
+        :type runs: Iterable[Union[float, cls]]
+        :returns: The new stats instance.
+        :rtype: cls
+        """
+        # Using Welford method to be more resistant to rounding errors.
+        # Adapted from code for sample standard deviation at:
+        # https://www.johndcook.com/blog/standard_deviation/
+        # The logic of plus operator is taken from
+        # https://www.johndcook.com/blog/skewness_kurtosis/
+        total_size = 0
+        total_avg = 0.0
+        moment_2 = 0.0
+        for run in runs:
+            if isinstance(run, (float, int)):
+                run_size = 1
+                run_avg = run
+                run_stdev = 0.0
+            else:
+                run_size = run.size
+                run_avg = run.avg
+                run_stdev = run.stdev
+            old_total_size = total_size
+            delta = run_avg - total_avg
+            total_size += run_size
+            total_avg += delta * run_size / total_size
+            moment_2 += run_stdev * run_stdev * run_size
+            moment_2 += delta * delta * old_total_size * run_size / total_size
+        if total_size < 1:
+            # Avoid division by zero.
+            return cls(size=0)
+        # TODO: Is it worth tracking moment_2 instead, and compute and cache
+        # stdev on demand, just to possibly save some sqrt calls?
+        total_stdev = math.sqrt(moment_2 / total_size)
+        ret_obj = cls(size=total_size, avg=total_avg, stdev=total_stdev)
+        return ret_obj
diff --git a/resources/libraries/python/jumpavg/BitCountingGroup.py b/resources/libraries/python/jumpavg/BitCountingGroup.py
new file mode 100644
index 0000000000..0c1aabba30
--- /dev/null
+++ b/resources/libraries/python/jumpavg/BitCountingGroup.py
@@ -0,0 +1,173 @@
+# Copyright (c) 2019 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 BitCountingGroup class."""
+
+import copy
+
+from .AvgStdevStats import AvgStdevStats
+from .BitCountingStats import BitCountingStats
+
+
+class BitCountingGroup:
+    # TODO: Inherit from collections.abc.Sequence in Python 3.
+    """Group of runs which tracks bit count in an efficient manner.
+
+    This class contains methods that mutate the internal state,
+    use copy() method to save the previous state.
+
+    The Sequence-like access is related to the list of runs,
+    for example group[0] returns the first run in the list.
+    Writable list-like methods are not implemented.
+
+    As the group bit count depends on previous average
+    and overall maximal value, those values are assumed
+    to be known beforehand (and immutable).
+
+    As the caller is allowed to divide runs into groups in any way,
+    a method to add a single run in an efficient manner is provided.
+    """
+
+    def __init__(self, run_list=None, stats=None, bits=None,
+                 max_value=None, prev_avg=None, comment="unknown"):
+        """Set the internal state and partially the stats.
+
+        A "group" stands for an Iterable of runs, where "run" is either
+        a float value, or a stats-like object (only size, avg and stdev
+        are accessed). Run is a hypothetical abstract class,
+        defining it in Python 2 is too much hassle.
+
+        Only a copy of the run list argument value is stored in the instance,
+        so it is not a problem if the value object is mutated afterwards.
+
+        It is not verified whether the user provided values are valid,
+        e.g. whether the stats and bits values reflect the runs.
+
+        :param run_list: List of run to compose into this group. Default: empty.
+        :param stats: Stats object used for computing bits.
+        :param bits: Cached value of information content.
+        :param max_value: Maximal sample value to be used for computing.
+        :param prev_avg: Average of the previous group, affects bits.
+        :param comment: Any string giving more info, e.g. "regression".
+        :type run_list: Iterable[Run]
+        :type stats: Optional[AvgStdevStats]
+        :type bits: Optional[float]
+        :type max_value: float
+        :type prev_avg: Optional[float]
+        :type comment: str
+        """
+        self.run_list = copy.deepcopy(run_list) if run_list else list()
+        self.stats = stats
+        self.cached_bits = bits
+        self.max_value = max_value
+        self.prev_avg = prev_avg
+        self.comment = comment
+        if self.stats is None:
+            self.stats = AvgStdevStats.for_runs(self.run_list)
+
+    def __str__(self):
+        """Return string with human readable description of the group.
+
+        :returns: Readable description.
+        :rtype: str
+        """
+        return f"stats={self.stats} bits={self.cached_bits}"
+
+    def __repr__(self):
+        """Return string executable as Python constructor call.
+
+        :returns: Executable constructor call.
+        :rtype: str
+        """
+        return (
+            f"BitCountingGroup(run_list={self.run_list!r},stats={self.stats!r}"
+            f",bits={self.cached_bits!r},max_value={self.max_value!r}"
+            f",prev_avg={self.prev_avg!r},comment={self.comment!r})"
+        )
+
+    def __getitem__(self, index):
+        """Return the run at the index.
+
+        :param index: Index of the run to return.
+        :type index: int
+        :returns: The run at the index.
+        :rtype: Run
+        """
+        return self.run_list[index]
+
+    def __len__(self):
+        """Return the number of runs in the group.
+
+        :returns: The Length of run_list.
+        :rtype: int
+        """
+        return len(self.run_list)
+
+    def copy(self):
+        """Return a new instance with copied internal state.
+
+        :returns: The copied instance.
+        :rtype: BitCountingGroup
+        """
+        stats = AvgStdevStats.for_runs([self.stats])
+        return self.__class__(
+            run_list=self.run_list, stats=stats, bits=self.cached_bits,
+            max_value=self.max_value, prev_avg=self.prev_avg,
+            comment=self.comment)
+
+    @property
+    def bits(self):
+        """Return overall bit content of the group list.
+
+        If not cached, compute from stats and cache.
+
+        :returns: The overall information content in bits.
+        :rtype: float
+        """
+        if self.cached_bits is None:
+            self.cached_bits = BitCountingStats.for_runs(
+                [self.stats], self.max_value, self.prev_avg).bits
+        return self.cached_bits
+
+    def append(self, run):
+        """Mutate to add the new run, return self.
+
+        Stats are updated, but old bits value is deleted from cache.
+
+        :param run: The run value to add to the group.
+        :type value: Run
+        :returns: The updated self.
+        :rtype: BitCountingGroup
+        """
+        self.run_list.append(run)
+        self.stats = AvgStdevStats.for_runs([self.stats, run])
+        self.cached_bits = None
+        return self
+
+    def extend(self, runs):
+        """Mutate to add the new runs, return self.
+
+        This is saves small amount of computation
+        compared to adding runs one by one in a loop.
+
+        Stats are updated, but old bits value is deleted from cache.
+
+        :param runs: The runs to add to the group.
+        :type value: Iterable[Run]
+        :returns: The updated self.
+        :rtype: BitCountingGroup
+        """
+        self.run_list.extend(runs)
+        self.stats = AvgStdevStats.for_runs([self.stats] + runs)
+        self.cached_bits = None
+        return self
diff --git a/resources/libraries/python/jumpavg/BitCountingGroupList.py b/resources/libraries/python/jumpavg/BitCountingGroupList.py
new file mode 100644
index 0000000000..bcc5e43267
--- /dev/null
+++ b/resources/libraries/python/jumpavg/BitCountingGroupList.py
@@ -0,0 +1,185 @@
+# Copyright (c) 2019 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 BitCountingGroupList class."""
+
+import copy
+
+from .BitCountingGroup import BitCountingGroup
+
+
+class BitCountingGroupList:
+    # TODO: Inherit from collections.abc.Sequence in Python 3.
+    """List of data groups which tracks overall bit count.
+
+    The Sequence-like access is related to the list of groups,
+    for example group_list[0] returns the first group in the list.
+    Writable list-like methods are not implemented.
+
+    The overall bit count is the sum of bit counts of each group.
+    Group is a sequence of data samples accompanied by their stats.
+    Different partitioning of data samples into the groups
+    results in different overall bit count.
+    This can be used to group samples in various contexts.
+
+    As the group bit count depends on previous average
+    and overall maximal value, order of groups is important.
+    Having the logic encapsulated here spares the caller
+    the effort to pass averages around.
+
+    The data can be only added, and there is some logic to skip
+    recalculations if the bit count is not needed.
+    """
+
+    def __init__(self, group_list=None, bits_except_last=0.0, max_value=None):
+        """Set the internal state without any calculations.
+
+        The group list argument is copied deeply, so it is not a problem
+        if the value object is mutated afterwards.
+
+        A "group" stands for an Iterable of runs, where "run" is either
+        a float value, or a stats-like object (only size, avg and stdev
+        are accessed). Run is a hypothetical abstract class,
+        defining it in Python 2 is too much hassle.
+
+        It is not verified whether the user provided values are valid,
+        e.g. whether the cached bits values make sense.
+
+        The max_value is required and immutable,
+        it is recommended the callers find their maximum beforehand.
+
+        :param group_list: List of groups to compose this group list (or empty).
+        :param bits_except_last: Partial sum of all but one group bits.
+        :param max_value: Maximal sample value to base bits computation on.
+        :type group_list: Iterable[BitCountingGroup]
+        :type bits_except_last: float
+        :type max_value: float
+        """
+        self.group_list = copy.deepcopy(group_list) if group_list else list()
+        self.bits_except_last = bits_except_last
+        self.max_value = max_value
+
+    def __str__(self):
+        """Return string with human readable description of the group list.
+
+        :returns: Readable description.
+        :rtype: str
+        """
+        return u"group_list={self.group_list} bits={self.bits}"
+
+    def __repr__(self):
+        """Return string executable as Python constructor call.
+
+        :returns: Executable constructor call.
+        :rtype: str
+        """
+        return (
+            f"BitCountingGroupList(group_list={self.group_list!r}"
+            f",bits_except_last={self.bits_except_last!r}"
+            f",max_value={self.max_value!r})"
+        )
+
+    def __getitem__(self, index):
+        """Return the group at the index.
+
+        :param index: Index of the group to return.
+        :type index: int
+        :returns: The group at the index.
+        :rtype: BitCountingGroup
+        """
+        return self.group_list[index]
+
+    def __len__(self):
+        """Return the length of the group list.
+
+        :returns: The Length of group_list.
+        :rtype: int
+        """
+        return len(self.group_list)
+
+    def copy(self):
+        """Return a new instance with copied internal state.
+
+        :returns: The copied instance.
+        :rtype: BitCountingGroupList
+        """
+        return self.__class__(
+            group_list=self.group_list, bits_except_last=self.bits_except_last,
+            max_value=self.max_value
+        )
+
+    @property
+    def bits(self):
+        """Return overall bit content of the group list.
+
+        :returns: The overall information content in bits.
+        :rtype: float
+        """
+        if not self.group_list:
+            return 0.0
+        # TODO: Is it worth to cache the overall result?
+        return self.bits_except_last + self.group_list[-1].bits
+
+    def append_group_of_runs(self, runs):
+        """Mutate to add a new group based on the runs, return self.
+
+        The argument is copied before adding to the group list,
+        so further edits do not affect the grup list.
+        The argument can also be a group, only runs from it are used.
+
+        :param runs: Runs to form the next group to be appended to self.
+        :type runs: Union[Iterable[Run], BitCountingGroup]
+        :returns: The updated self.
+        :rtype: BitCountingGroupList
+        """
+        prev_avg = self.group_list[-1].stats.avg if self.group_list else None
+        if isinstance(runs, BitCountingGroup):
+            # It is faster to avoid stats recalculation.
+            new_group = runs.copy()
+            new_group.max_value = self.max_value
+            new_group.prev_avg = prev_avg
+            new_group.cached_bits = None
+        else:
+            new_group = BitCountingGroup(
+                run_list=runs, max_value=self.max_value, prev_avg=prev_avg)
+        self.bits_except_last = self.bits
+        self.group_list.append(new_group)
+        return self
+
+    def append_run_to_to_last_group(self, run):
+        """Mutate to add new run at the end of the last group.
+
+        Basically a one-liner, only returning group list instead of last group.
+
+        :param run: The run value to add to the last group.
+        :type run: Run
+        :returns: The updated self.
+        :rtype: BitCountingGroupList
+        :raises IndexError: If group list is empty, no last group to add to.
+        """
+        self.group_list[-1].append(run)
+        return self
+
+    def extend_runs_to_last_group(self, runs):
+        """Mutate to add new runs to the end of the last group.
+
+        A faster alternative to appending runs one by one in a loop.
+
+        :param runs: The runs to add to the last group.
+        :type runs: Iterable[Run]
+        :returns: The updated self
+        :rtype: BitCountingGroupList
+        :raises IndexError: If group list is empty, no last group to add to.
+        """
+        self.group_list[-1].extend(runs)
+        return self
diff --git a/resources/libraries/python/jumpavg/BitCountingStats.py b/resources/libraries/python/jumpavg/BitCountingStats.py
new file mode 100644
index 0000000000..0addec013b
--- /dev/null
+++ b/resources/libraries/python/jumpavg/BitCountingStats.py
@@ -0,0 +1,169 @@
+# Copyright (c) 2019 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 math
+
+from .AvgStdevStats import AvgStdevStats
+
+
+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().
+    """
+
+    def __init__(
+            self, size=0, avg=None, stdev=0.0, max_value=None, prev_avg=None):
+        """Construct the stats object by computing from the values needed.
+
+        The values are not sanitized, faulty callers can cause math errors.
+
+        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.
+
+        :param size: Number of values participating in this group.
+        :param avg: Population average of the participating sample values.
+        :param stdev: Population standard deviation of the sample values.
+        :param max_value: Maximal expected value.
+            TODO: This might be more optimal,
+            but max-invariant algorithm will be nicer.
+        :param prev_avg: Population average of the previous group.
+            If None, no previous average is taken into account.
+            If not None, the given previous average is used to discourage
+            consecutive groups with similar averages
+            (opposite triangle distribution is assumed).
+        :type avg: float
+        :type size: int
+        :type stdev: float
+        :type max_value: Union[float, NoneType]
+        :type prev_avg: Union[float, NoneType]
+        """
+        self.avg = avg
+        self.size = size
+        self.stdev = stdev
+        self.max_value = max_value
+        self.prev_avg = prev_avg
+        # 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 avg is None:
+            raise ValueError(f"Avg is None: {self!r}")
+        if max_value is None or max_value <= 0.0:
+            raise ValueError(f"Invalid max value: {self!r}")
+        # 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(size * (size + 1), 2)
+        if prev_avg is None:
+            # Avg is considered to be uniformly distributed
+            # from zero to max_value.
+            self.bits += math.log(max_value + 1.0, 2)
+        else:
+            # Opposite triangle distribution with minimum.
+            self.bits += math.log(
+                max_value * (max_value + 1) / (abs(avg - prev_avg) + 1), 2)
+        if self.size < 2:
+            return
+        # 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 + 1.0, 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) + math.log(math.pi) * ((size - 1) / 2.0)
+        sphere_area_ln -= math.lgamma((size - 1) / 2.0)
+        sphere_area_ln += math.log(stdev + 1.0) * (size - 2)
+        sphere_area_ln += math.log(size) * ((size - 2) / 2.0)
+        self.bits += sphere_area_ln / math.log(2)
+
+    def __str__(self):
+        """Return string with human readable description of the group.
+
+        :returns: Readable description.
+        :rtype: str
+        """
+        return (
+            f"size={self.size} avg={self.avg} stdev={self.stdev}"
+            f" bits={self.bits}"
+        )
+
+    def __repr__(self):
+        """Return string executable as Python constructor call.
+
+        :returns: Executable constructor call.
+        :rtype: str
+        """
+        return (
+            f"BitCountingStats(size={self.size!r},avg={self.avg!r}"
+            f",stdev={self.stdev!r},max_value={self.max_value!r}"
+            f",prev_avg={self.prev_avg!r})"
+        )
+
+    @classmethod
+    def for_runs(cls, runs, max_value=None, prev_avg=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 prev_avg: Population average of the previous group, if any.
+        :type runs: Iterable[Union[float, AvgStdevStats]]
+        :type max_value: Union[float, NoneType]
+        :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, prev_avg=prev_avg)
+        return ret_obj
diff --git a/resources/libraries/python/jumpavg/__init__.py b/resources/libraries/python/jumpavg/__init__.py
new file mode 100644
index 0000000000..cb8b3df43d
--- /dev/null
+++ b/resources/libraries/python/jumpavg/__init__.py
@@ -0,0 +1,22 @@
+# Copyright (c) 2019 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.
+
+"""
+__init__ file for "jumpavg" Python package.
+"""
+
+from .AvgStdevStats import AvgStdevStats
+from .BitCountingStats import BitCountingStats
+from .BitCountingGroup import BitCountingGroup
+from .BitCountingGroupList import BitCountingGroupList
+from .classify import classify
diff --git a/resources/libraries/python/jumpavg/classify.py b/resources/libraries/python/jumpavg/classify.py
new file mode 100644
index 0000000000..5f5ce6160c
--- /dev/null
+++ b/resources/libraries/python/jumpavg/classify.py
@@ -0,0 +1,76 @@
+# Copyright (c) 2019 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 the classify function
+
+Classification os one of primary purposes of this package.
+
+Minimal message length principle is used
+for grouping results into the list of groups,
+assuming each group is a population of different Gaussian distribution.
+"""
+
+from .AvgStdevStats import AvgStdevStats
+from .BitCountingGroupList import BitCountingGroupList
+
+
+def classify(values):
+    """Return the values in groups of optimal bit count.
+
+    Here, a value is either a float, or an iterable of floats.
+    Such iterables represent an undivisible sequence of floats.
+
+    Internally, such sequence is replaced by AvgStdevStats
+    after maximal value is found.
+
+    :param values: Sequence of runs to classify.
+    :type values: Iterable[Union[float, Iterable[float]]]
+    :returns: Classified group list.
+    :rtype: BitCountingGroupList
+    """
+    processed_values = list()
+    max_value = 0.0
+    for value in values:
+        if isinstance(value, (float, int)):
+            if value > max_value:
+                max_value = value
+            processed_values.append(value)
+        else:
+            for subvalue in value:
+                if subvalue > max_value:
+                    max_value = subvalue
+            processed_values.append(AvgStdevStats.for_runs(value))
+    open_at = list()
+    closed_before = [BitCountingGroupList(max_value=max_value)]
+    for index, value in enumerate(processed_values):
+        newly_open = closed_before[index].copy()
+        newly_open.append_group_of_runs([value])
+        open_at.append(newly_open)
+        record_group_list = newly_open
+        for previous_index, old_open in enumerate(open_at[:index]):
+            new_open = old_open.copy().append_run_to_to_last_group(value)
+            open_at[previous_index] = new_open
+            if new_open.bits < record_group_list.bits:
+                record_group_list = new_open
+        closed_before.append(record_group_list)
+    partition = closed_before[-1]
+    previous_average = partition[0].stats.avg
+    for group in partition:
+        if group.stats.avg == previous_average:
+            group.comment = u"normal"
+        elif group.stats.avg < previous_average:
+            group.comment = u"regression"
+        elif group.stats.avg > previous_average:
+            group.comment = u"progression"
+        previous_average = group.stats.avg
+    return partition