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A vectorized hash table written in C for fast set/dict
like operations on NumPy arrays.
Hirola provides fast indexing and de-duplication of keys. It can be used as an extension of numpy.unique() and a very light (20-30KB download size) and much faster alternative to pandas.Categorical(). Hirola obtains its speed in the same way that NumPy does – vectorising, translating into C and imposing the following constraints:
- Keys must all be of the same predetermined type and size.
- The maximum size of a table must be chosen in advance and managed explicitly.
- To get any performance boost, operations should be done in bulk.
- Elements can not be removed.
Install Hirola with pip:
pip install hirolaA HashTable can be though of as a dict but with only an enumeration for
values.
To construct an empty hash table:
import numpy as np
import hirola
table = hirola.HashTable(
20, # <--- Maximum size for the table - up to 20 keys.
"U10", # <--- NumPy dtype - strings of up to 10 characters.
)Keys may be added individually...
>>> table.add("cat")
0... But it's much more efficient to add in bulk. The return value is an enumeration of when each key was first added. Duplicate keys are not re-added.
>>> table.add(["dog", "cat", "moose", "gruffalo"])
array([1, 0, 2, 3])Multidimensional inputs give multidimensional outputs of matching shapes.
>>> table.add([["rabbit", "cat"],
... ["gruffalo", "moose"],
... ["werewolf", "gremlin"]])
array([[4, 0],
[3, 2],
[5, 6]])Inspect all keys added so far via the keys attribute.
(Note that, unlike dict.keys(), it's a property instead of a method.)
>>> table.keys
array(['cat', 'dog', 'moose', 'gruffalo', 'rabbit', 'werewolf', 'gremlin'],
dtype='<U10')Key indices can be retrieved with table.get(key) or just table[key].
Again, retrieval is NumPy vectorised and is much faster if given large arrays of
inputs rather than one at a time.
>>> table.get("dog")
1
>>> table[["moose", "gruffalo"]]
array([2, 3])Like the Python dict,
using table[key] raises a KeyError if keys are missing
but using table.get(key) returns a configurable default.
Unlike Python's dict, the default default is -1.
>>> table["tortoise"]
KeyError: "key = 'tortoise' is not in this table."
>>> table.get("tortoise")
-1
>>> table.get("tortoise", default=99)
99
>>> table.get(["cat", "bear", "tortoise"], default=[100, 101, 102])
array([ 0, 101, 102])Unlike Python's set and dict, Hirola does not manage its size
automatically (although it can be reconfigured to).
To prevent wasted resizing (which is what Python does under the hood),
you have full control of and responsibility for how much space the table uses.
Obviously the table has to be large enough to fit all the keys in it.
Additionally, when a hash table gets to close to full it becomes much slower.
Depending on how much you favour speed over memory you should add 20-50% extra
headroom.
If you intend to a lot of looking up of the same small set of values then it can
continue to run faster if you increase max to 2-3x its minimal size.
To indicate that an array axis should be considered as a single key,
use NumPy's structured dtypes.
In the following example, the data type (points.dtype, 3)
indicates that a 3D point - a triplet of floats -
should be considered as one object.
See help(hirola.HashTable.dtype) for more information of specifying dtypes.
Only the last axis or last axes may be thought of as single keys.
For other setups, first convert with numpy.transpose().
import numpy as np
import hirola
# Create a cloud of 3D points with duplicates. This is 3000 points in total,
# with up to 1000 unique points.
points = np.random.uniform(-30, 30, (1000, 3))[np.random.choice(1000, 3000)]
# Create an empty hash table.
# In practice, you generally don't know how many unique elements there are
# so we'll pretend we don't either an assume the worst case of all 3000 are
# unique. We'll also give 25% padding for speed.
table = hirola.HashTable(len(points) * 1.25, (points.dtype, 3))
# Add all points to the table.
ids = table.add(points)Duplicate-free contents can be accessed from table.keys:
>>> table.keys # <--- These are `points` but with no duplicates.
array([[ 3.47736554, -15.17112511, -9.51454466],
[ -6.46948046, 23.64504329, -16.25743105],
[-27.02527253, -16.1967225 , -10.11544157],
...,
[ 3.75972597, 1.24130412, -8.14337206],
[-13.62256791, 11.76551455, -13.31312988],
[ 0.19851678, 4.06221179, -22.69006592]])
>>> table.keys.shape
(954, 3)Each point's location in table.keys is returned by table.add(),
like numpy.unique(..., return_args=True).
>>> ids # <--- These are the indices in `table.keys` of each point in `points`.
array([ 0, 1, 2, ..., 290, 242, 669])
>>> np.array_equal(table.keys[ids], points)
TrueLookup the indices of points without adding them using table.get().
HashTables become very slow when almost full.
As of v0.3.0, an efficiency warning will notify you if a table exceeds 90% full.
This warning can be reconfigured into an error, silenced or set to resize the
table automatically to make more room.
These are demonstrated in the example constructors below:
# The default: Issue a warning when the table is 90% full.
hirola.HashTable(..., almost_full=(0.9, "warn"))
# Disable all "almost full" behaviours.
hirola.HashTable(..., almost_full=None)
# To consider a table exceeding 80% full as an error use:
hirola.HashTable(..., almost_full=(0.8, "raise"))
# To automatically triple in size whenever the table exceeds 80% full use:
hirola.HashTable(..., almost_full=(0.8, 3.0))Resizing tables is slow (it's only marginally optimized beyond creating a new
bigger table and .add()-ing the existing keys) which is why it's not
enabled by default. It should be avoided unless you really have no idea how big
your table will need to be and favour the memory savings of not overestimating
over raw speed.
A HashTable can be used to replicate a dict,
set or a collections.Counter.
These examples below might turn into their own proper classes in the future but
so far I've never come across a real use case where they would actually fit.
A dict can be imitated using a HashTable() with a second array for
values.
The output of HashTable.add() and HashTable.get() should be used as
indices of values:
import numpy as np
import hirola
# The `keys` - will be populated with names of countries.
countries = hirola.HashTable(40, (str, 20))
# The `values` - will be populated with the names of each country's capital city.
capitals = np.empty(countries.max, (str, 20))Add or set items using the pattern values[table.add(key)] = value:
capitals[countries.add("Algeria")] = "Al Jaza'ir"Or in bulk:
new_keys = ["Angola", "Botswana", "Burkina Faso"]
new_values = ["Luanda", "Gaborone", "Ouagadougou"]
capitals[countries.add(new_keys)] = new_valuesLike Python dicts, the syntax to overwrite values is exactly the same as to write them.
Retrieve values with values[table[key]]:
>>> capitals[countries["Botswana"]]
'Gaborone'
>>> capitals[countries["Botswana", "Algeria"]]
array(['Gaborone', "Al Jaza'ir"], dtype='<U20')View all keys and values with table.keys and values[:len(table)].
A HashTable remembers the order keys were first added so this dict is
automatically a sorted dict.
# keys
>>> countries.keys
array(['Algeria', 'Angola', 'Botswana', 'Burkina Faso'], dtype='<U20')
# values
>>> capitals[:len(countries)]
array(["Al Jaza'ir", 'Luanda', 'Gaborone', 'Ouagadougou'], dtype='<U20')Depending on the usage scenario,
it may or may not make sense to want an equivalent to dict.items().
If you do want an equivalent,
use numpy.rec.fromarrays([table.keys, values[:len(table)]]),
possibly adding a names= option:
>>> np.rec.fromarrays([countries.keys, capitals[:len(countries)]],
... names="countries,capitals")
rec.array([('Algeria', "Al Jaza'ir"), ('Angola', 'Luanda'),
('Botswana', 'Gaborone'), ('Burkina Faso', 'Ouagadougou')],
dtype=[('countries', '<U20'), ('capitals', '<U20')])If the keys and values have the same dtype then numpy.c_ works too.
>>> np.c_[countries.keys, capitals[:len(countries)]]
array([['Algeria', "Al Jaza'ir"],
['Angola', 'Luanda'],
['Botswana', 'Gaborone'],
['Burkina Faso', 'Ouagadougou']], dtype='<U20')To get set-like capabilities from a HashTable,
leverage the contains() method.
For these examples we will experiment with integer multiples of 3 and 7.
import numpy as np
of_3s = np.arange(0, 100, 3)
of_7s = np.arange(0, 100, 7)We'll only require one array to be converted into a hash table.
The other can remain as an array.
If both are hash tables, simply use one table's keys attribute as the array.
import hirola
table_of_3s = hirola.HashTable(len(of_3s) * 1.25, of_3s.dtype)
table_of_3s.add(of_3s)Use table.contains() as a vectorised version of in.
>>> table_of_3s.contains(of_7s)
array([ True, False, False, True, False, False, True, False, False,
True, False, False, True, False, False])From the above, the common set operations can be derived:
set.intersection()- Values in the array and in the set:
>>> of_7s[table_of_3s.contains(of_7s)]
array([ 0, 21, 42, 63, 84])- Set subtraction - Values in the array which are not in the set:
>>> of_7s[~table_of_3s.contains(of_7s)]
array([ 7, 14, 28, 35, 49, 56, 70, 77, 91, 98])set.union()- Values in either the table or in the tested array (with no duplicates):
>>> np.concatenate([table_of_3s.keys, of_7s[~table_of_3s.contains(of_7s)]], axis=0)
array([ 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48,
51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99,
7, 14, 28, 35, 49, 56, 70, 77, 91, 98])For this example,
let's give ourselves something a bit more substantial to work on.
Counting word frequencies in Shakespeare's Hamlet play is the
trendy example for collections.Counter and it's what we'll use too.
from urllib.request import urlopen
import re
import numpy as np
hamlet = urlopen("https://gist.githubusercontent.com/provpup/2fc41686eab7400b796b/raw/b575bd01a58494dfddc1d6429ef0167e709abf9b/hamlet.txt").read()
words = np.array(re.findall(rb"([\w']+)", hamlet))A counter is just a dict with integer values and a dict is just a hash
table with a separate array for values.
import hirola
word_table = hirola.HashTable(len(words), words.dtype)
counts = np.zeros(word_table.max, dtype=int)The only new functionality that is not defined in using a hash table as a dict is the ability to count keys as they are added.
To count new elements use the rather odd line
np.add(counts, table.add(keys), 1).
np.add.at(counts, word_table.add(words), 1)This line does what you might expect counts[word_table.add(words)] += 1 to
do but, due to the way NumPy works,
the latter form fails to increment each count more than once if words
contains duplicates.
Use NumPy's indirect sorting functions to get most or least common keys.
# Get the most common word.
>>> word_table.keys[counts[:len(word_table)].argmax()]
b'the'
# Get the top 10 most common words. Note that these are unsorted.
>>> word_table.keys[counts[:len(word_table)].argpartition(-10)[-10:]]
array([b'it', b'and', b'my', b'of', b'in', b'a', b'to', b'the', b'I',
b'you'], dtype='|S14')
# Get all words in ascending order of commonness.
>>> word_table.keys[counts[:len(word_table)].argsort()]
array([b'END', b'whereat', b"griev'd", ..., b'to', b'and', b'the'],
dtype='|S14')If a service adds keys from untrusted users to a hash table and a malicious user
can reverse the hash function used by the hash table, they can generate and
submit a near infinite number of inputs that have the same hash. This causes the
insertion and lookup times to go from O(1) to O(len(table)), congesting
the service until it's unusable. Reversing hashes is not particularly difficult
and to emphasise that point, code to break hirola's hashes is provided in
denial_of_service.py.
Like the builtin hash() used internally by Python's set and dict,
hirola randomises the seed value of its hash functions on startup. This seed
changes which combinations of keys produce the same hash so that, provided the
attacker isn't able to find out the seed, they shouldn't be able to predict hash
collisions.
The seed value can be overridden with the hirola.HashTable(..., seed=value)
option or with a HIROLA_HASH_SEED environment variable analogous to Python's
PYTHONHASHSEED environment variable. But hirola.HashTable() doesn't
change any outward behavior based on its seed value so, whilst setting
PYTHONHASHSEED can be used to to make the order of Python sets reproducible,
setting hirola's seed shouldn't be needed for anything beyond morbid curiosity.