Pandas pd.Series.isin performance with set versus array

Question

In Python generally, membership of a hashable collection is best tested via set. We know this because the use of hashing gives us O(1) lookup complexity versus

Answer 1

This might not be obvious, but pd.Series.isin uses O(1)-look up per element.

After an analysis, which proves the above statement, we will use its insights to create a Cython-prototype which can easily beat the fastest out-of-the-box-solution.

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Let's assume that the "set" has n elements and the "series" has m elements. The running time is then:

 T(n,m)=T_preprocess(n)+m*T_lookup(n)

For the pure-python version, that means:

• T_preprocess(n)=0 - no preprocessing needed
• T_lookup(n)=O(1) - well known behavior of python's set
• results in T(n,m)=O(m)

What happens for pd.Series.isin(x_arr)? Obviously, if we skip the preprocessing and search in linear time we will get O(n*m), which is not acceptable.

It is easy to see with help of a debugger or a profiler (I used valgrind-callgrind+kcachegrind), what is going on: the working horse is the function __pyx_pw_6pandas_5_libs_9hashtable_23ismember_int64. Its definition can be found here:

• In a preprocessing step, a hash-map (pandas uses khash from klib) is created out of n elements from x_arr, i.e. in running time O(n).
• m look-ups happen in O(1) each or O(m) in total in the constructed hash-map.
• results in T(n,m)=O(m)+O(n)

We must remember - the elements of numpy-array are raw-C-integers and not the Python-objects in the original set - so we cannot use the set as it is.

An alternative to converting the set of Python-objects to a set of C-ints, would be to convert the single C-ints to Python-object and thus be able to use the original set. That is what happens in [i in x_set for i in ser.values]-variant:

• No preprocessing.
• m look-ups happen in O(1) time each or O(m) in total, but the look-up is slower due to necessary creation of a Python-object.
• results in T(n,m)=O(m)

Clearly, you could speed-up this version a little bit by using Cython.

But enough theory, let's take a look at the running times for different ns with fixed ms:

We can see: the linear time of preprocessing dominates the numpy-version for big ns. The version with conversion from numpy to pure-python (numpy->python) has the same constant behavior as the pure-python version but is slower, because of the necessary conversion - this all in accordance with our analysis.

That cannot be seen well in the diagram: if n < m the numpy version becomes faster - in this case the faster look-up of khash-lib plays the most important role and not the preprocessing-part.

My take-aways from this analysis:

• n < m: pd.Series.isin should be taken because O(n)-preprocessing isn't that costly.

• n > m: (probably cythonized version of) [i in x_set for i in ser.values] should be taken and thus O(n) avoided.

• clearly there is a gray zone where n and m are approximately equal and it is hard to tell which solution is best without testing.

• If you have it under your control: The best thing would be to build the set directly as a C-integer-set (khash (already wrapped in pandas) or maybe even some c++-implementations), thus eliminating the need for preprocessing. I don't know, whether there is something in pandas you could reuse, but it is probably not a big deal to write the function in Cython.

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The problem is that the last suggestion doesn't work out of the box, as neither pandas nor numpy have a notion of a set (at least to my limited knowledge) in their interfaces. But having raw-C-set-interfaces would be best of both worlds:

• no preprocessing needed because values are already passed as a set
• no conversion needed because the passed set consists of raw-C-values

I've coded a quick and dirty Cython-wrapper for khash (inspired by the wrapper in pandas), which can be installed via pip install https://github.com/realead/cykhash/zipball/master and then used with Cython for a faster isin version:

%%cython
import numpy as np
cimport numpy as np

from cykhash.khashsets cimport Int64Set

def isin_khash(np.ndarray[np.int64_t, ndim=1] a, Int64Set b):
    cdef np.ndarray[np.uint8_t,ndim=1, cast=True] res=np.empty(a.shape[0],dtype=np.bool)
    cdef int i
    for i in range(a.size):
        res[i]=b.contains(a[i])
    return res

As a further possibility the c++'s unordered_map can be wrapped (see listing C), which has the disadvantage of needing c++-libraries and (as we will see) is slightly slower.

Comparing the approaches (see listing D for creating of timings):

khash is about factor 20 faster than the numpy->python, about factor 6 faster than the pure python (but pure-python is not what we want anyway) and even about factor 3 faster than the cpp's-version.

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Listings

1) profiling with valgrind:

#isin.py
import numpy as np
import pandas as pd

np.random.seed(0)

x_set = {i for i in range(2*10**6)}
x_arr = np.array(list(x_set))


arr = np.random.randint(0, 20000, 10000)
ser = pd.Series(arr)


for _ in range(10):
   ser.isin(x_arr)

and now:

>>> valgrind --tool=callgrind python isin.py
>>> kcachegrind

leads to the following call graph:

B: ipython code for producing the running times:

import numpy as np
import pandas as pd
%matplotlib inline
import matplotlib.pyplot as plt

np.random.seed(0)

x_set = {i for i in range(10**2)}
x_arr = np.array(list(x_set))
x_list = list(x_set)

arr = np.random.randint(0, 20000, 10000)
ser = pd.Series(arr)
lst = arr.tolist()

n=10**3
result=[]
while n<3*10**6:
    x_set = {i for i in range(n)}
    x_arr = np.array(list(x_set))
    x_list = list(x_set)

    t1=%timeit -o  ser.isin(x_arr) 
    t2=%timeit -o  [i in x_set for i in lst]
    t3=%timeit -o  [i in x_set for i in ser.values]

    result.append([n, t1.average, t2.average, t3.average])
    n*=2

#plotting result:
for_plot=np.array(result)
plt.plot(for_plot[:,0], for_plot[:,1], label='numpy')
plt.plot(for_plot[:,0], for_plot[:,2], label='python')
plt.plot(for_plot[:,0], for_plot[:,3], label='numpy->python')
plt.xlabel('n')
plt.ylabel('running time')
plt.legend()
plt.show()

C: cpp-wrapper:

%%cython --cplus -c=-std=c++11 -a

from libcpp.unordered_set cimport unordered_set

cdef class HashSet:
    cdef unordered_set[long long int] s
    cpdef add(self, long long int z):
        self.s.insert(z)
    cpdef bint contains(self, long long int z):
        return self.s.count(z)>0

import numpy as np
cimport numpy as np

cimport cython
@cython.boundscheck(False)
@cython.wraparound(False)

def isin_cpp(np.ndarray[np.int64_t, ndim=1] a, HashSet b):
    cdef np.ndarray[np.uint8_t,ndim=1, cast=True] res=np.empty(a.shape[0],dtype=np.bool)
    cdef int i
    for i in range(a.size):
        res[i]=b.contains(a[i])
    return res

D: plotting results with different set-wrappers:

import numpy as np
import pandas as pd
%matplotlib inline
import matplotlib.pyplot as plt
from cykhash import Int64Set

np.random.seed(0)

x_set = {i for i in range(10**2)}
x_arr = np.array(list(x_set))
x_list = list(x_set)


arr = np.random.randint(0, 20000, 10000)
ser = pd.Series(arr)
lst = arr.tolist()

n=10**3
result=[]
while n<3*10**6:
    x_set = {i for i in range(n)}
    x_arr = np.array(list(x_set))
    cpp_set=HashSet()
    khash_set=Int64Set()

    for i in x_set:
        cpp_set.add(i)
        khash_set.add(i)


    assert((ser.isin(x_arr).values==isin_cpp(ser.values, cpp_set)).all())
    assert((ser.isin(x_arr).values==isin_khash(ser.values, khash_set)).all())


    t1=%timeit -o  isin_khash(ser.values, khash_set)
    t2=%timeit -o  isin_cpp(ser.values, cpp_set) 
    t3=%timeit -o  [i in x_set for i in lst]
    t4=%timeit -o  [i in x_set for i in ser.values]

    result.append([n, t1.average, t2.average, t3.average, t4.average])
    n*=2

#ploting result:
for_plot=np.array(result)
plt.plot(for_plot[:,0], for_plot[:,1], label='khash')
plt.plot(for_plot[:,0], for_plot[:,2], label='cpp')
plt.plot(for_plot[:,0], for_plot[:,3], label='pure python')
plt.plot(for_plot[:,0], for_plot[:,4], label='numpy->python')
plt.xlabel('n')
plt.ylabel('running time')
ymin, ymax = plt.ylim()
plt.ylim(0,ymax)
plt.legend()
plt.show()