Cannot understand numpy argpartition output
Question:
I am trying to use arpgpartition from numpy, but it seems there is something going wrong and I cannot seem to figure it out. Here is what’s happening:
These are first 5 elements of the sorted array norms
np.sort(norms)[:5]
array([ 53.64759445, 54.91434479, 60.11617279, 64.09630585, 64.75318909], dtype=float32)
But when I use indices_sorted = np.argpartition(norms, 5)[:5]
norms[indices_sorted]
array([ 60.11617279, 64.09630585, 53.64759445, 54.91434479, 64.75318909], dtype=float32)
When I think I should get the same result as the sorted array?
It works just fine when I use 3 as the parameter indices_sorted = np.argpartition(norms, 3)[:3]
norms[indices_sorted]
array([ 53.64759445, 54.91434479, 60.11617279], dtype=float32)
This isn’t making much sense to me, hoping someone can offer some insight?
EDIT: Rephrasing this question as whether argpartition preserves order of the k partitioned elements makes more sense.
Answers:
We need to use list of indices that are to be kept in sorted order instead of feeding the kth param as a scalar. Thus, to maintain the sorted nature across the first 5 elements, instead of np.argpartition(a,5)[:5], simply do –
np.argpartition(a,range(5))[:5]
Here’s a sample run to make things clear –
In [84]: a = np.random.rand(10)
In [85]: a
Out[85]:
array([ 0.85017222, 0.19406266, 0.7879974 , 0.40444978, 0.46057793,
0.51428578, 0.03419694, 0.47708 , 0.73924536, 0.14437159])
In [86]: a[np.argpartition(a,5)[:5]]
Out[86]: array([ 0.19406266, 0.14437159, 0.03419694, 0.40444978, 0.46057793])
In [87]: a[np.argpartition(a,range(5))[:5]]
Out[87]: array([ 0.03419694, 0.14437159, 0.19406266, 0.40444978, 0.46057793])
Please note that argpartition makes sense on performance aspect, if we are looking to get sorted indices for a small subset of elements, let’s say k number of elems which is a small fraction of the total number of elems.
Let’s use a bigger dataset and try to get sorted indices for all elems to make the above mentioned point clear –
In [51]: a = np.random.rand(10000)*100
In [52]: %timeit np.argpartition(a,range(a.size-1))[:5]
10 loops, best of 3: 105 ms per loop
In [53]: %timeit a.argsort()
1000 loops, best of 3: 893 µs per loop
Thus, to sort all elems, np.argpartition isn’t the way to go.
Now, let’s say I want to get sorted indices for only the first 5 elems with that big dataset and also keep the order for those –
In [68]: a = np.random.rand(10000)*100
In [69]: np.argpartition(a,range(5))[:5]
Out[69]: array([1647, 942, 2167, 1371, 2571])
In [70]: a.argsort()[:5]
Out[70]: array([1647, 942, 2167, 1371, 2571])
In [71]: %timeit np.argpartition(a,range(5))[:5]
10000 loops, best of 3: 112 µs per loop
In [72]: %timeit a.argsort()[:5]
1000 loops, best of 3: 888 µs per loop
Very useful here!
Given the task of indirectly sorting a subset (the top k, top meaning first in sort order) there are two builtin solutions: argsort and argpartition cf. @Divakar’s answer.
If, however, performance is a consideration then it may (depending on the sizes of the data and the subset of interest) be well worth resisting the “lure of the one-liner”, investing one more line and applying argsort on the output of argpartition:
>>> def top_k_sort(a, k):
... return np.argsort(a)[:k]
...
>>> def top_k_argp(a, k):
... return np.argpartition(a, range(k))[:k]
...
>>> def top_k_hybrid(a, k):
... b = np.argpartition(a, k)[:k]
... return b[np.argsort(a[b])]
>>> k = 100
>>> timeit.timeit('f(a,k)', 'a=rng((100000,))', number = 1000, globals={'f': top_k_sort, 'rng': np.random.random, 'k': k})
8.348663672804832
>>> timeit.timeit('f(a,k)', 'a=rng((100000,))', number = 1000, globals={'f': top_k_argp, 'rng': np.random.random, 'k': k})
9.869098862167448
>>> timeit.timeit('f(a,k)', 'a=rng((100000,))', number = 1000, globals={'f': top_k_hybrid, 'rng': np.random.random, 'k': k})
1.2305558240041137
argsort is O(n log n), argpartition with range argument appears to be O(nk) (?), and argpartition + argsort is O(n + k log k)
Therefore in an interesting regime n >> k >> 1 the hybrid method is expected to be fastest
UPDATE: ND version:
import numpy as np
from timeit import timeit
def top_k_sort(A,k,axis=-1):
return A.argsort(axis=axis)[(*axis%A.ndim*(slice(None),),slice(k))]
def top_k_partition(A,k,axis=-1):
return A.argpartition(range(k),axis=axis)[(*axis%A.ndim*(slice(None),),slice(k))]
def top_k_hybrid(A,k,axis=-1):
B = A.argpartition(k,axis=axis)[(*axis%A.ndim*(slice(None),),slice(k))]
return np.take_along_axis(B,np.take_along_axis(A,B,axis).argsort(axis),axis)
A = np.random.random((100,10000))
k = 100
from timeit import timeit
for f in globals().copy():
if f.startswith("top_"):
print(f, timeit(f"{f}(A,k)",globals=globals(),number=10)*100)
Sample run:
top_k_sort 63.72379460372031
top_k_partition 99.30561298970133
top_k_hybrid 10.714635509066284
Let’s describe the partition method in a simplified way which helps a lot understand argpartition
Following the example in the picture if we execute C=numpy.argpartition(A, 3) C will be the resulting array of getting the position of every element in B with respect to the A array. ie:
Idx(z) = index of element z in array A
then C would be
C = [ Idx(B[0]), Idx(B[1]), Idx(B[2]), Idx(X), Idx(B[4]), ..... Idx(B[N]) ]
As previously mentioned this method is very helpful and comes very handy when you have a huge array and you are only interested in a selected group of ordered elements, not the whole array.
I am trying to use arpgpartition from numpy, but it seems there is something going wrong and I cannot seem to figure it out. Here is what’s happening:
These are first 5 elements of the sorted array norms
np.sort(norms)[:5]
array([ 53.64759445, 54.91434479, 60.11617279, 64.09630585, 64.75318909], dtype=float32)
But when I use indices_sorted = np.argpartition(norms, 5)[:5]
norms[indices_sorted]
array([ 60.11617279, 64.09630585, 53.64759445, 54.91434479, 64.75318909], dtype=float32)
When I think I should get the same result as the sorted array?
It works just fine when I use 3 as the parameter indices_sorted = np.argpartition(norms, 3)[:3]
norms[indices_sorted]
array([ 53.64759445, 54.91434479, 60.11617279], dtype=float32)
This isn’t making much sense to me, hoping someone can offer some insight?
EDIT: Rephrasing this question as whether argpartition preserves order of the k partitioned elements makes more sense.
We need to use list of indices that are to be kept in sorted order instead of feeding the kth param as a scalar. Thus, to maintain the sorted nature across the first 5 elements, instead of np.argpartition(a,5)[:5], simply do –
np.argpartition(a,range(5))[:5]
Here’s a sample run to make things clear –
In [84]: a = np.random.rand(10)
In [85]: a
Out[85]:
array([ 0.85017222, 0.19406266, 0.7879974 , 0.40444978, 0.46057793,
0.51428578, 0.03419694, 0.47708 , 0.73924536, 0.14437159])
In [86]: a[np.argpartition(a,5)[:5]]
Out[86]: array([ 0.19406266, 0.14437159, 0.03419694, 0.40444978, 0.46057793])
In [87]: a[np.argpartition(a,range(5))[:5]]
Out[87]: array([ 0.03419694, 0.14437159, 0.19406266, 0.40444978, 0.46057793])
Please note that argpartition makes sense on performance aspect, if we are looking to get sorted indices for a small subset of elements, let’s say k number of elems which is a small fraction of the total number of elems.
Let’s use a bigger dataset and try to get sorted indices for all elems to make the above mentioned point clear –
In [51]: a = np.random.rand(10000)*100
In [52]: %timeit np.argpartition(a,range(a.size-1))[:5]
10 loops, best of 3: 105 ms per loop
In [53]: %timeit a.argsort()
1000 loops, best of 3: 893 µs per loop
Thus, to sort all elems, np.argpartition isn’t the way to go.
Now, let’s say I want to get sorted indices for only the first 5 elems with that big dataset and also keep the order for those –
In [68]: a = np.random.rand(10000)*100
In [69]: np.argpartition(a,range(5))[:5]
Out[69]: array([1647, 942, 2167, 1371, 2571])
In [70]: a.argsort()[:5]
Out[70]: array([1647, 942, 2167, 1371, 2571])
In [71]: %timeit np.argpartition(a,range(5))[:5]
10000 loops, best of 3: 112 µs per loop
In [72]: %timeit a.argsort()[:5]
1000 loops, best of 3: 888 µs per loop
Very useful here!
Given the task of indirectly sorting a subset (the top k, top meaning first in sort order) there are two builtin solutions: argsort and argpartition cf. @Divakar’s answer.
If, however, performance is a consideration then it may (depending on the sizes of the data and the subset of interest) be well worth resisting the “lure of the one-liner”, investing one more line and applying argsort on the output of argpartition:
>>> def top_k_sort(a, k):
... return np.argsort(a)[:k]
...
>>> def top_k_argp(a, k):
... return np.argpartition(a, range(k))[:k]
...
>>> def top_k_hybrid(a, k):
... b = np.argpartition(a, k)[:k]
... return b[np.argsort(a[b])]
>>> k = 100
>>> timeit.timeit('f(a,k)', 'a=rng((100000,))', number = 1000, globals={'f': top_k_sort, 'rng': np.random.random, 'k': k})
8.348663672804832
>>> timeit.timeit('f(a,k)', 'a=rng((100000,))', number = 1000, globals={'f': top_k_argp, 'rng': np.random.random, 'k': k})
9.869098862167448
>>> timeit.timeit('f(a,k)', 'a=rng((100000,))', number = 1000, globals={'f': top_k_hybrid, 'rng': np.random.random, 'k': k})
1.2305558240041137
argsort is O(n log n), argpartition with range argument appears to be O(nk) (?), and argpartition + argsort is O(n + k log k)
Therefore in an interesting regime n >> k >> 1 the hybrid method is expected to be fastest
UPDATE: ND version:
import numpy as np
from timeit import timeit
def top_k_sort(A,k,axis=-1):
return A.argsort(axis=axis)[(*axis%A.ndim*(slice(None),),slice(k))]
def top_k_partition(A,k,axis=-1):
return A.argpartition(range(k),axis=axis)[(*axis%A.ndim*(slice(None),),slice(k))]
def top_k_hybrid(A,k,axis=-1):
B = A.argpartition(k,axis=axis)[(*axis%A.ndim*(slice(None),),slice(k))]
return np.take_along_axis(B,np.take_along_axis(A,B,axis).argsort(axis),axis)
A = np.random.random((100,10000))
k = 100
from timeit import timeit
for f in globals().copy():
if f.startswith("top_"):
print(f, timeit(f"{f}(A,k)",globals=globals(),number=10)*100)
Sample run:
top_k_sort 63.72379460372031
top_k_partition 99.30561298970133
top_k_hybrid 10.714635509066284
Let’s describe the partition method in a simplified way which helps a lot understand argpartition
Following the example in the picture if we execute C=numpy.argpartition(A, 3) C will be the resulting array of getting the position of every element in B with respect to the A array. ie:
Idx(z) = index of element z in array A
then C would be
C = [ Idx(B[0]), Idx(B[1]), Idx(B[2]), Idx(X), Idx(B[4]), ..... Idx(B[N]) ]
As previously mentioned this method is very helpful and comes very handy when you have a huge array and you are only interested in a selected group of ordered elements, not the whole array.