Source code for apache_beam.transforms.stats

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"""This module has all statistic related transforms."""

from __future__ import absolute_import
from __future__ import division

import heapq
import itertools
import math
import sys
import typing
from builtins import round

from apache_beam import coders
from apache_beam import typehints
from apache_beam.transforms.core import *
from apache_beam.transforms.display import DisplayDataItem
from apache_beam.transforms.ptransform import PTransform

__all__ = [
    'ApproximateQuantiles',
    'ApproximateUnique',
]

# Type variables
T = typing.TypeVar('T')
K = typing.TypeVar('K')
V = typing.TypeVar('V')


[docs]class ApproximateUnique(object): """ Hashes input elements and uses those to extrapolate the size of the entire set of hash values by assuming the rest of the hash values are as densely distributed as the sample space. """ _NO_VALUE_ERR_MSG = 'Either size or error should be set. Received {}.' _MULTI_VALUE_ERR_MSG = 'Either size or error should be set. ' \ 'Received {size = %s, error = %s}.' _INPUT_SIZE_ERR_MSG = 'ApproximateUnique needs a size >= 16 for an error ' \ '<= 0.50. In general, the estimation error is about ' \ '2 / sqrt(sample_size). Received {size = %s}.' _INPUT_ERROR_ERR_MSG = 'ApproximateUnique needs an estimation error ' \ 'between 0.01 and 0.50. Received {error = %s}.'
[docs] @staticmethod def parse_input_params(size=None, error=None): """ Check if input params are valid and return sample size. :param size: an int not smaller than 16, which we would use to estimate number of unique values. :param error: max estimation error, which is a float between 0.01 and 0.50. If error is given, sample size will be calculated from error with _get_sample_size_from_est_error function. :return: sample size :raises: ValueError: If both size and error are given, or neither is given, or values are out of range. """ if None not in (size, error): raise ValueError(ApproximateUnique._MULTI_VALUE_ERR_MSG % (size, error)) elif size is None and error is None: raise ValueError(ApproximateUnique._NO_VALUE_ERR_MSG) elif size is not None: if not isinstance(size, int) or size < 16: raise ValueError(ApproximateUnique._INPUT_SIZE_ERR_MSG % (size)) else: return size else: if error < 0.01 or error > 0.5: raise ValueError(ApproximateUnique._INPUT_ERROR_ERR_MSG % (error)) else: return ApproximateUnique._get_sample_size_from_est_error(error)
@staticmethod def _get_sample_size_from_est_error(est_err): """ :return: sample size Calculate sample size from estimation error """ #math.ceil in python2.7 returns a float, while it returns an int in python3. return int(math.ceil(4.0 / math.pow(est_err, 2.0)))
[docs] @typehints.with_input_types(T) @typehints.with_output_types(int) class Globally(PTransform): """ Approximate.Globally approximate number of unique values""" def __init__(self, size=None, error=None): self._sample_size = ApproximateUnique.parse_input_params(size, error)
[docs] def expand(self, pcoll): coder = coders.registry.get_coder(pcoll) return pcoll \ | 'CountGlobalUniqueValues' \ >> (CombineGlobally(ApproximateUniqueCombineFn(self._sample_size, coder)))
[docs] @typehints.with_input_types(typing.Tuple[K, V]) @typehints.with_output_types(typing.Tuple[K, int]) class PerKey(PTransform): """ Approximate.PerKey approximate number of unique values per key""" def __init__(self, size=None, error=None): self._sample_size = ApproximateUnique.parse_input_params(size, error)
[docs] def expand(self, pcoll): coder = coders.registry.get_coder(pcoll) return pcoll \ | 'CountPerKeyUniqueValues' \ >> (CombinePerKey(ApproximateUniqueCombineFn(self._sample_size, coder)))
class _LargestUnique(object): """ An object to keep samples and calculate sample hash space. It is an accumulator of a combine function. """ _HASH_SPACE_SIZE = 2.0 * sys.maxsize def __init__(self, sample_size): self._sample_size = sample_size self._min_hash = sys.maxsize self._sample_heap = [] self._sample_set = set() def add(self, element): """ :param an element from pcoll. :return: boolean type whether the value is in the heap Adds a value to the heap, returning whether the value is (large enough to be) in the heap. """ if len(self._sample_heap) >= self._sample_size and element < self._min_hash: return False if element not in self._sample_set: self._sample_set.add(element) heapq.heappush(self._sample_heap, element) if len(self._sample_heap) > self._sample_size: temp = heapq.heappop(self._sample_heap) self._sample_set.remove(temp) self._min_hash = self._sample_heap[0] elif element < self._min_hash: self._min_hash = element return True def get_estimate(self): """ :return: estimation count of unique values If heap size is smaller than sample size, just return heap size. Otherwise, takes into account the possibility of hash collisions, which become more likely than not for 2^32 distinct elements. Note that log(1+x) ~ x for small x, so for sampleSize << maxHash log(1 - sample_size/sample_space) / log(1 - 1/sample_space) ~ sample_size and hence estimate ~ sample_size * hash_space / sample_space as one would expect. Given sample_size / sample_space = est / hash_space est = sample_size * hash_space / sample_space Given above sample_size approximate, est = log1p(-sample_size/sample_space) / log1p(-1/sample_space) * hash_space / sample_space """ if len(self._sample_heap) < self._sample_size: return len(self._sample_heap) else: sample_space_size = sys.maxsize - 1.0 * self._min_hash est = (math.log1p(-self._sample_size / sample_space_size) / math.log1p(-1 / sample_space_size) * self._HASH_SPACE_SIZE / sample_space_size) return round(est) class ApproximateUniqueCombineFn(CombineFn): """ ApproximateUniqueCombineFn computes an estimate of the number of unique values that were combined. """ def __init__(self, sample_size, coder): self._sample_size = sample_size self._coder = coder def create_accumulator(self, *args, **kwargs): return _LargestUnique(self._sample_size) def add_input(self, accumulator, element, *args, **kwargs): try: accumulator.add(hash(self._coder.encode(element))) return accumulator except Exception as e: raise RuntimeError("Runtime exception: %s", e) # created an issue https://issues.apache.org/jira/browse/BEAM-7285 to speed up # merge process. def merge_accumulators(self, accumulators, *args, **kwargs): merged_accumulator = self.create_accumulator() for accumulator in accumulators: for i in accumulator._sample_heap: merged_accumulator.add(i) return merged_accumulator @staticmethod def extract_output(accumulator): return accumulator.get_estimate() def display_data(self): return {'sample_size': self._sample_size}
[docs]class ApproximateQuantiles(object): """ PTransfrom for getting the idea of data distribution using approximate N-tile (e.g. quartiles, percentiles etc.) either globally or per-key. """ @staticmethod def _display_data(num_quantiles, key, reverse): return { 'num_quantiles': DisplayDataItem(num_quantiles, label="Quantile Count"), 'key': DisplayDataItem(key.__name__ if hasattr(key, '__name__') else key.__class__.__name__, label='Record Comparer Key'), 'reverse': DisplayDataItem(str(reverse), label='Is reversed') }
[docs] @typehints.with_input_types(T) @typehints.with_output_types(typing.List[T]) class Globally(PTransform): """ PTransform takes PCollection and returns a list whose single value is approximate N-tiles of the input collection globally. Args: num_quantiles: number of elements in the resulting quantiles values list. key: (optional) Key is a mapping of elements to a comparable key, similar to the key argument of Python's sorting methods. reverse: (optional) whether to order things smallest to largest, rather than largest to smallest """ def __init__(self, num_quantiles, key=None, reverse=False): self._num_quantiles = num_quantiles self._key = key self._reverse = reverse
[docs] def expand(self, pcoll): return pcoll | CombineGlobally(ApproximateQuantilesCombineFn.create( num_quantiles=self._num_quantiles, key=self._key, reverse=self._reverse))
[docs] def display_data(self): return ApproximateQuantiles._display_data( num_quantiles=self._num_quantiles, key=self._key, reverse=self._reverse)
[docs] @typehints.with_input_types(typing.Tuple[K, V]) @typehints.with_output_types(typing.Tuple[K, typing.List[V]]) class PerKey(PTransform): """ PTransform takes PCollection of KV and returns a list based on each key whose single value is list of approximate N-tiles of the input element of the key. Args: num_quantiles: number of elements in the resulting quantiles values list. key: (optional) Key is a mapping of elements to a comparable key, similar to the key argument of Python's sorting methods. reverse: (optional) whether to order things smallest to largest, rather than largest to smallest """ def __init__(self, num_quantiles, key=None, reverse=False): self._num_quantiles = num_quantiles self._key = key self._reverse = reverse
[docs] def expand(self, pcoll): return pcoll | CombinePerKey(ApproximateQuantilesCombineFn.create( num_quantiles=self._num_quantiles, key=self._key, reverse=self._reverse))
[docs] def display_data(self): return ApproximateQuantiles._display_data( num_quantiles=self._num_quantiles, key=self._key, reverse=self._reverse)
class _QuantileBuffer(object): """A single buffer in the sense of the referenced algorithm. (see http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.6.6513&rep=rep1 &type=pdf and ApproximateQuantilesCombineFn for further information)""" def __init__(self, elements, level=0, weight=1): self.elements = elements self.level = level self.weight = weight def __lt__(self, other): self.elements < other.elements def sized_iterator(self): class QuantileBufferIterator(object): def __init__(self, elem, weight): self._iter = iter(elem) self.weight = weight def __iter__(self): return self def __next__(self): value = next(self._iter) return (value, self.weight) next = __next__ # For Python 2 return QuantileBufferIterator(self.elements, self.weight) class _QuantileState(object): """ Compact summarization of a collection on which quantiles can be estimated. """ min_val = None # Holds smallest item in the list max_val = None # Holds largest item in the list def __init__(self, buffer_size, num_buffers, unbuffered_elements, buffers): self.buffer_size = buffer_size self.num_buffers = num_buffers self.buffers = buffers # The algorithm requires that the manipulated buffers always be filled to # capacity to perform the collapse operation. This operation can be extended # to buffers of varying sizes by introducing the notion of fractional # weights, but it's easier to simply combine the remainders from all shards # into new, full buffers and then take them into account when computing the # final output. self.unbuffered_elements = unbuffered_elements def is_empty(self): """Check if the buffered & unbuffered elements are empty or not.""" return not self.unbuffered_elements and not self.buffers class ApproximateQuantilesCombineFn(CombineFn): """ This combiner gives an idea of the distribution of a collection of values using approximate N-tiles. The output of this combiner is the list of size of the number of quantiles (num_quantiles), containing the input values of the minimum value item of the list, the intermediate values (n-tiles) and the maximum value item of the list, in the sort order provided via key (similar to the key argument of Python's sorting methods). If there are fewer values to combine than the number of quantile (num_quantiles), then the resulting list will contain all the values being combined, in sorted order. If no `key` is provided, then the results are sorted in the natural order. To evaluate the quantiles, we use the "New Algorithm" described here: [MRL98] Manku, Rajagopalan & Lindsay, "Approximate Medians and other Quantiles in One Pass and with Limited Memory", Proc. 1998 ACM SIGMOD, Vol 27, No 2, p 426-435, June 1998. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.6.6513&rep=rep1 &type=pdf The default error bound is (1 / N), though in practice the accuracy tends to be much better. Args: num_quantiles: Number of quantiles to produce. It is the size of the final output list, including the mininum and maximum value items. buffer_size: The size of the buffers, corresponding to k in the referenced paper. num_buffers: The number of buffers, corresponding to b in the referenced paper. key: (optional) Key is a mapping of elements to a comparable key, similar to the key argument of Python's sorting methods. reverse: (optional) whether to order things smallest to largest, rather than largest to smallest """ # For alternating between biasing up and down in the above even weight # collapse operation. _offset_jitter = 0 # The cost (in time and space) to compute quantiles to a given accuracy is a # function of the total number of elements in the data set. If an estimate is # not known or specified, we use this as an upper bound. If this is too low, # errors may exceed the requested tolerance; if too high, efficiency may be # non-optimal. The impact is logarithmic with respect to this value, so this # default should be fine for most uses. _MAX_NUM_ELEMENTS = 1e9 _qs = None # Refers to the _QuantileState def __init__(self, num_quantiles, buffer_size, num_buffers, key=None, reverse=False): if key: self._comparator = lambda a, b: (key(a) < key(b)) - (key(a) > key(b)) \ if reverse else (key(a) > key(b)) - (key(a) < key(b)) else: self._comparator = lambda a, b: (a < b) - (a > b) if reverse \ else (a > b) - (a < b) self._num_quantiles = num_quantiles self._buffer_size = buffer_size self._num_buffers = num_buffers self._key = key self._reverse = reverse @classmethod def create(cls, num_quantiles, epsilon=None, max_num_elements=None, key=None, reverse=False): """ Creates an approximate quantiles combiner with the given key and desired number of quantiles. Args: num_quantiles: Number of quantiles to produce. It is the size of the final output list, including the mininum and maximum value items. epsilon: (optional) The default error bound is `epsilon`, which holds as long as the number of elements is less than `_MAX_NUM_ELEMENTS`. Specifically, if one considers the input as a sorted list x_1, ..., x_N, then the distance between each exact quantile x_c and its approximation x_c' is bounded by `|c - c'| < epsilon * N`. Note that these errors are worst-case scenarios. In practice the accuracy tends to be much better. max_num_elements: (optional) The cost (in time and space) to compute quantiles to a given accuracy is a function of the total number of elements in the data set. key: (optional) Key is a mapping of elements to a comparable key, similar to the key argument of Python's sorting methods. reverse: (optional) whether to order things smallest to largest, rather than largest to smallest """ max_num_elements = max_num_elements or cls._MAX_NUM_ELEMENTS if not epsilon: epsilon = 1.0 / num_quantiles b = 2 while (b - 2) * (1 << (b - 2)) < epsilon * max_num_elements: b = b + 1 b = b - 1 k = max(2, math.ceil(max_num_elements / float(1 << (b - 1)))) return cls(num_quantiles=num_quantiles, buffer_size=k, num_buffers=b, key=key, reverse=reverse) def _add_unbuffered(self, qs, elem): """ Add a new buffer to the unbuffered list, creating a new buffer and collapsing if needed. """ qs.unbuffered_elements.append(elem) if len(qs.unbuffered_elements) == qs.buffer_size: qs.unbuffered_elements.sort(key=self._key, reverse=self._reverse) heapq.heappush(qs.buffers, _QuantileBuffer(elements=qs.unbuffered_elements)) qs.unbuffered_elements = [] self._collapse_if_needed(qs) def _offset(self, newWeight): """ If the weight is even, we must round up or down. Alternate between these two options to avoid a bias. """ if newWeight % 2 == 1: return (newWeight + 1) / 2 else: self._offset_jitter = 2 - self._offset_jitter return (newWeight + self._offset_jitter) / 2 def _collapse(self, buffers): new_level = 0 new_weight = 0 for buffer_elem in buffers: # As presented in the paper, there should always be at least two # buffers of the same (minimal) level to collapse, but it is possible # to violate this condition when combining buffers from independently # computed shards. If they differ we take the max. new_level = max([new_level, buffer_elem.level + 1]) new_weight = new_weight + buffer_elem.weight new_elements = self._interpolate(buffers, self._buffer_size, new_weight, self._offset(new_weight)) return _QuantileBuffer(new_elements, new_level, new_weight) def _collapse_if_needed(self, qs): while len(qs.buffers) > self._num_buffers: toCollapse = [] toCollapse.append(heapq.heappop(qs.buffers)) toCollapse.append(heapq.heappop(qs.buffers)) minLevel = toCollapse[1].level while len(qs.buffers) > 0 and qs.buffers[0].level == minLevel: toCollapse.append(heapq.heappop(qs.buffers)) heapq.heappush(qs.buffers, self._collapse(toCollapse)) def _interpolate(self, i_buffers, count, step, offset): """ Emulates taking the ordered union of all elements in buffers, repeated according to their weight, and picking out the (k * step + offset)-th elements of this list for `0 <= k < count`. """ iterators = [] new_elements = [] compare_key = None if self._key: compare_key = lambda x: self._key(x[0]) for buffer_elem in i_buffers: iterators.append(buffer_elem.sized_iterator()) # Python 3 `heapq.merge` support key comparison and returns an iterator and # does not pull the data into memory all at once. Python 2 does not # support comparison on its `heapq.merge` api, so we use the itertools # which takes the `key` function for comparison and creates an iterator # from it. if sys.version_info[0] < 3: sorted_elem = iter( sorted(itertools.chain.from_iterable(iterators), key=compare_key, reverse=self._reverse)) else: sorted_elem = heapq.merge(*iterators, key=compare_key, reverse=self._reverse) weighted_element = next(sorted_elem) current = weighted_element[1] j = 0 while j < count: target = j * step + offset j = j + 1 try: while current <= target: weighted_element = next(sorted_elem) current = current + weighted_element[1] except StopIteration: pass new_elements.append(weighted_element[0]) return new_elements def create_accumulator(self): self._qs = _QuantileState(buffer_size=self._buffer_size, num_buffers=self._num_buffers, unbuffered_elements=[], buffers=[]) return self._qs def add_input(self, quantile_state, element): """ Add a new element to the collection being summarized by quantile state. """ if quantile_state.is_empty(): quantile_state.min_val = quantile_state.max_val = element elif self._comparator(element, quantile_state.min_val) < 0: quantile_state.min_val = element elif self._comparator(element, quantile_state.max_val) > 0: quantile_state.max_val = element self._add_unbuffered(quantile_state, elem=element) return quantile_state def merge_accumulators(self, accumulators): """Merges all the accumulators (quantile state) as one.""" qs = self.create_accumulator() for accumulator in accumulators: if accumulator.is_empty(): continue if not qs.min_val or self._comparator(accumulator.min_val, qs.min_val) < 0: qs.min_val = accumulator.min_val if not qs.max_val or self._comparator(accumulator.max_val, qs.max_val) > 0: qs.max_val = accumulator.max_val for unbuffered_element in accumulator.unbuffered_elements: self._add_unbuffered(qs, unbuffered_element) qs.buffers.extend(accumulator.buffers) self._collapse_if_needed(qs) return qs def extract_output(self, accumulator): """ Outputs num_quantiles elements consisting of the minimum, maximum and num_quantiles - 2 evenly spaced intermediate elements. Returns the empty list if no elements have been added. """ if accumulator.is_empty(): return [] all_elems = accumulator.buffers total_count = len(accumulator.unbuffered_elements) for buffer_elem in all_elems: total_count = total_count + accumulator.buffer_size * buffer_elem.weight if accumulator.unbuffered_elements: accumulator.unbuffered_elements.sort(key=self._key, reverse=self._reverse) all_elems.append(_QuantileBuffer(accumulator.unbuffered_elements)) step = 1.0 * total_count / (self._num_quantiles - 1) offset = (1.0 * total_count - 1) / (self._num_quantiles - 1) quantiles = [accumulator.min_val] quantiles.extend( self._interpolate(all_elems, self._num_quantiles - 2, step, offset)) quantiles.append(accumulator.max_val) return quantiles