[Numpy-discussion] array slicing questions
eat
e.antero.tammi at gmail.com
Tue Jul 31 11:28:49 EDT 2012
Hi,
On Tue, Jul 31, 2012 at 5:01 PM, Vlastimil Brom <vlastimil.brom at gmail.com>wrote:
> 2012/7/31 eat <e.antero.tammi at gmail.com>:
> > Hi,
> >
> > On Tue, Jul 31, 2012 at 10:23 AM, Vlastimil Brom <
> vlastimil.brom at gmail.com>
> > wrote:
> >>
> >> 2012/7/30 eat <e.antero.tammi at gmail.com>:
> >> > Hi,
> >> >
> >> > A partial answer to your questions:
> >> >
> >> > On Mon, Jul 30, 2012 at 10:33 PM, Vlastimil Brom
> >> > <vlastimil.brom at gmail.com>
> >> > wrote:
> >> >>
> >> >> Hi all,
> >> >> I'd like to ask for some hints or advice regarding the usage of
> >> >> numpy.array and especially slicing.
> >> >>
> >> >> I only recently tried numpy and was impressed by the speedup in some
> >> >> parts of the code, hence I suspect, that I might miss some other
> >> >> oportunities in this area.
> >> >>
> >> >> I currently use the following code for a simple visualisation of the
> >> >> search matches within the text, the arrays are generally much larger
> >> >> than the sample - the texts size is generally hundreds of kilobytes
> up
> >> >> to a few MB - with an index position for each character.
> >> >> First there is a list of spans(obtained form the regex match
> objects),
> >> >> the respective character indices in between these slices should be
> set
> >> >> to 1:
> >> >>
> >> >> >>> import numpy
> >> >> >>> characters_matches = numpy.zeros(10)
> >> >> >>> matches_spans = numpy.array([[2,4], [5,9]])
> >> >> >>> for start, stop in matches_spans:
> >> >> ... characters_matches[start:stop] = 1
> >> >> ...
> >> >> >>> characters_matches
> >> >> array([ 0., 0., 1., 1., 0., 1., 1., 1., 1., 0.])
> >> >>
> >> >> Is there maybe a way tu achieve this in a numpy-only way - without
> the
> >> >> python loop?
> >> >> (I got the impression, the powerful slicing capabilities could make
> it
> >> >> possible, bud haven't found this kind of solution.)
> >> >>
> >> >>
> >> >> In the next piece of code all the character positions are evaluated
> >> >> with their "neighbourhood" and a kind of running proportions of the
> >> >> matched text parts are computed (the checks_distance could be
> >> >> generally up to the order of the half the text length, usually less :
> >> >>
> >> >> >>>
> >> >> >>> check_distance = 1
> >> >> >>> floating_checks_proportions = []
> >> >> >>> for i in numpy.arange(len(characters_matches)):
> >> >> ... lo = i - check_distance
> >> >> ... if lo < 0:
> >> >> ... lo = None
> >> >> ... hi = i + check_distance + 1
> >> >> ... checked_sublist = characters_matches[lo:hi]
> >> >> ... proportion = (checked_sublist.sum() / (check_distance * 2 +
> >> >> 1.0))
> >> >> ... floating_checks_proportions.append(proportion)
> >> >> ...
> >> >> >>> floating_checks_proportions
> >> >> [0.0, 0.33333333333333331, 0.66666666666666663, 0.66666666666666663,
> >> >> 0.66666666666666663, 0.66666666666666663, 1.0, 1.0,
> >> >> 0.66666666666666663, 0.33333333333333331]
> >> >> >>>
> >> >
> >> > Define a function for proportions:
> >> >
> >> > from numpy import r_
> >> >
> >> > from numpy.lib.stride_tricks import as_strided as ast
> >> >
> >> > def proportions(matches, distance= 1):
> >> >
> >> > cd, cd2p1, s= distance, 2* distance+ 1, matches.strides[0]
> >> >
> >> > # pad
> >> >
> >> > m= r_[[0.]* cd, matches, [0.]* cd]
> >> >
> >> > # create a suitable view
> >> >
> >> > m= ast(m, shape= (m.shape[0], cd2p1), strides= (s, s))
> >> >
> >> > # average
> >> >
> >> > return m[:-2* cd].sum(1)/ cd2p1
> >> > and use it like:
> >> > In []: matches
> >> > Out[]: array([ 0., 0., 1., 1., 0., 1., 1., 1., 1., 0.])
> >> >
> >> > In []: proportions(matches).round(2)
> >> > Out[]: array([ 0. , 0.33, 0.67, 0.67, 0.67, 0.67, 1. , 1. ,
> >> > 0.67,
> >> > 0.33])
> >> > In []: proportions(matches, 5).round(2)
> >> > Out[]: array([ 0.27, 0.36, 0.45, 0.55, 0.55, 0.55, 0.55, 0.55,
> >> > 0.45,
> >> > 0.36])
> >> >>
> >> >>
> >> >> I'd like to ask about the possible better approaches, as it doesn't
> >> >> look very elegant to me, and I obviously don't know the implications
> >> >> or possible drawbacks of numpy arrays in some scenarios.
> >> >>
> >> >> the pattern
> >> >> for i in range(len(...)): is usually considered inadequate in python,
> >> >> but what should be used in this case as the indices are primarily
> >> >> needed?
> >> >> is something to be gained or lost using (x)range or np.arange as the
> >> >> python loop is (probably?) inevitable anyway?
> >> >
> >> > Here np.arange(.) will create a new array and potentially wasting
> memory
> >> > if
> >> > it's not otherwise used. IMO nothing wrong looping with xrange(.) (if
> >> > you
> >> > really need to loop ;).
> >> >>
> >> >> Is there some mor elegant way to check for the "underflowing" lower
> >> >> bound "lo" to replace with None?
> >> >>
> >> >> Is it significant, which container is used to collect the results of
> >> >> the computation in the python loop - i.e. python list or a numpy
> >> >> array?
> >> >> (Could possibly matplotlib cooperate better with either container?)
> >> >>
> >> >> And of course, are there maybe other things, which should be made
> >> >> better/differently?
> >> >>
> >> >> (using Numpy 1.6.2, python 2.7.3, win XP)
> >> >
> >> >
> >> > My 2 cents,
> >> > -eat
> >> >>
> >> >> Thanks in advance for any hints or suggestions,
> >> >> regards,
> >> >> Vlastimil Brom
> >> >> _______________________________________________
> >> >> NumPy-Discussion mailing list
> >> >> NumPy-Discussion at scipy.org
> >> >> http://mail.scipy.org/mailman/listinfo/numpy-discussion
> >> >
> >> Hi,
> >> thank you very much for your suggestions!
> >>
> >> do I understand it correctly, that I have to special-case the function
> >> for distance = 0 (which should return the matches themselves without
> >> recalculation)?
> >
> > Yes.
> >>
> >>
> >> However, more importantly, I am getting a ValueError for some larger,
> >> (but not completely unreasonable) "distance"
> >>
> >> >>> proportions(matches, distance= 8190)
> >> Traceback (most recent call last):
> >> File "<input>", line 1, in <module>
> >> File "<input>", line 11, in proportions
> >> File "C:\Python27\lib\site-packages\numpy\lib\stride_tricks.py",
> >> line 28, in as_strided
> >> return np.asarray(DummyArray(interface, base=x))
> >> File "C:\Python27\lib\site-packages\numpy\core\numeric.py", line
> >> 235, in asarray
> >> return array(a, dtype, copy=False, order=order)
> >> ValueError: array is too big.
> >> >>>
> >>
> >> the distance= 8189 was the largest which worked in this snippet,
> >> however, it might be data-dependent, as I got this error as well e.g.
> >> for distance=4529 for a 20k text.
> >>
> >> Is this implementation-limited, or could it be solved in some
> >> alternative way which wouldn't have such limits (up to the order of,
> >> say, millions)?
> >
> > Apparently ast(.) does not return a view of the original matches rather a
> > copy of size (n* (2* distance+ 1)), thus you may run out of memory.
> >
> > Surely it can be solved up to millions of matches, but perhaps much
> slower
> > speed.
> >
> >
> > Regards,
> > -eat
> >>
> >>
> >> Thanks again
> >> regards
> >> vbr
> >>
> >> _______________________________________________
> >> NumPy-Discussion mailing list
> >> NumPy-Discussion at scipy.org
> >> http://mail.scipy.org/mailman/listinfo/numpy-discussion
> >
>
> Thank you for the confirmation,
> I'll wait and see, whether the current speed isn't actually already
> acceptable for the most cases...
> I could already gain a speedup by using the array.sum() and other
> features, maybe I will find yet other possibilities.
>
I just cooked up some pure pyhton and running sum based solution, which
actually may be faster and it scales quite well up to millions of matches:
def proportions_p(matches, distance= 1):
cd, cd2p1= distance, 2* distance+ 1
m, r= [0]* cd+ matches+ [0]* (cd+ 1), [0]* len(matches)
s= sum(m[:cd2p1])
for k in xrange(len(matches)):
r[k]= s/ cd2p1
s-= m[k]
s+= m[cd2p1+ k]
return r
Some verification and timings:
In []: a= arange(1, 100000, dtype= float)
In []: allclose(proportions(a, 1000), proportions_p(a.tolist(), 1000))
Out[]: True
In []: %timeit proportions(a, 1000)
1 loops, best of 3: 288 ms per loop
In []: %timeit proportions_p(a.tolist(), 1000)
10 loops, best of 3: 66.2 ms per loop
In []: a= arange(1, 1000000, dtype= float)
In []: %timeit proportions(a, 10000)
------------------------------------------------------------
Traceback (most recent call last):
[snip]
ValueError: array is too big.
In []: %timeit proportions_p(a.tolist(), 10000)
1 loops, best of 3: 680 ms per loop
Regards,
-eat
>
> regards,
> vbr
> _______________________________________________
> NumPy-Discussion mailing list
> NumPy-Discussion at scipy.org
> http://mail.scipy.org/mailman/listinfo/numpy-discussion
>
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