Colin Ji - 6 months ago 21

C++ Question

I want to implement Vantage Point Tree in the python, but it use the std::nth_element in the C++.

So I want to find the equivalent 'nth_element' function in Python or in numpy.

Notice, the nth_element would only partial order an array, and it's O(N).

`int the_array[10] = {4,5,7,3,6,0,1,2,9,8};`

std::vector<int> the_v(the_array,the_array+10);

std::nth_element (the_v.begin()+0, the_v.begin()+5, the_v.begin()+10);

And now the vector could be:

`3,0,2,1,4,5,6,7,9,8`

And I not only want to get the nth element, but also want to get the re-arrange the two part of list, [3,0,2,1,4] and [6,7,9,8].

Moreover, nth_element support accept a function that could compare the two elements, such as, in the below as, the vector is a vector op DataPoint, and the DistanceComparator function will compare the two points distance with the_v.begin():

`vector<DataPoint> the_v;`

for(int n = 0; n < N; n++) the_v[n] = DataPoint(D, n, X + n * D);

std::nth_element (the_v.begin()+0, the_v.begin()+5, the_v.begin()+10,

DistanceComparator(the_v.begin()));

I've used the bhuvan-venkatesh's answer, and write some code to test.

`partition_timer = timeit.Timer("numpy.partition(a, 10000)",`

"import numpy;numpy.random.seed(2);"+

"a = numpy.random.rand(10000000)")

print(partition_timer.timeit(10))

sort_timer = timeit.Timer("numpy.sort(a)",

"import numpy;numpy.random.seed(2);"+

"a = numpy.random.rand(10000000)")

print(sort_timer.timeit(10))

sorted_timer = timeit.Timer("sorted(a)",

"import numpy;numpy.random.seed(2);"+

"a = numpy.random.rand(10000000)")

print(sorted_timer.timeit(10))

and the result:

`2.2217168808`

17.0386350155

281.301710844

And then, I will do more test using C++ code.

But there is a problem, when using the numpy, it would always return a new array, it will waste a lot of memory, when my array is huge.

How can I handle it.

Or I just have to write a C++ extend for python.

@bhuvan-venkatesh Thanks for recommending the partition function.

I use partition like the below:

`import numpy`

@profile

def for_numpy():

numpy.random.seed(2)

a = numpy.random.rand(1e7)

for i in range(100):

a.partition(numpy.random.randint(1e6))

if __name__ == '__main__':

for_numpy()

and ran the profiler like:

`python -m memory_profiler profiler_test.py`

and the result is:

`Line # Mem usage Increment Line Contents`

================================================

25 23.613 MiB 0.000 MiB @profile

26 def for_numpy():

27 23.613 MiB 0.000 MiB numpy.random.seed(2)

28 99.934 MiB 76.320 MiB a = numpy.random.rand(1e7)

29 100.004 MiB 0.070 MiB for i in range(100):

30 100.004 MiB 0.000 MiB a.partition(numpy.random.randint(1e6))

And it would not copy the whole array like:

numpy.partition(a, 3)

Answer

http://docs.scipy.org/doc/numpy/reference/generated/numpy.partition.html

Just make sure that the numpy partition will create two new arrays, meaning that you will quickly make a lot of new arrays. They are more efficient than python lists but will not do the exact same thing as in c++.

If you want the exact element then you can do a filter search which will still be O(n)

```
array = np.array(...)
partition = np.partition(array, 5) # O(n)
element = np.where(partition==array[5]) # O(n)
left, right = partition[:element], partition[element+1:] # O(n)
```

So your new code is slower but that is the python-y way to do it.

*EDIT:*

So you need a comparator? Apart from writing a small function of your own there is no way -- in pure numpy as a keyword -- because each numpy operation is implemented in highly optimized c-code meaning that passing in a python function or a python lambda would force numpy to go to the object level every time and eval.

*numpy.vectorize* goes to the object level, but in the end you will have to write your own code; Rosetta code has the impelmentation if you want to create a more "optimized algorithm". (I put that in quotes because with python objects you will still be much slower than c or numpy code because of object level access). If speed is your true concern, but you want the python readability consider making an extension with cython.