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I'm looking for a method in Python and/or Numpy vectorization to eliminate use of a for-loop for the following:

for i in list_range_values: v[list_list_values[i]] += list_comp_values[i]

where:

  • list_range_values is a Python list of integer values eg. [1, 3, 5], drawn from the range(0, R-1, 1)

  • list_comp_values is a Python list of numeric values eg. [0.7, 9.8, 1.2, 5, 10, 11.7, 6, 0.2] such that len(list_comp_values) = R

  • v is a numpy vector of length V such that R can be <, =, > than V

  • list_list_values is a Python list of lists (each list containing a different number of integer values eg. [[3, 6, 7], [5, 7, 11, 25, 99], [8, 45], [4, 7, 8], [0, 1], [21, 31, 41], [9, 11, 22, 33, 44], [17, 19]]) drawn from the range(0, V-1, 1) and with len(list_list_values) = R

Eg.

for i in list_range_values (= [1, 3, 5]): i=1: v[[5, 7, 11, 25, 99]] += list_comp_values[1] (= 9.8) i=3: v[[4, 7, 8]] += list_comp_values[3] (= 5) i=5: v[[21, 31, 41]] += list_comp_values[5] (= 11.7)

Is there a method available that allows eliminating the for-loop?

Cython, Scipy/Weave/Blitz and a C module are alternative solutions but want to make sure if there is a Numpy vectorization answer first.

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  • This is re-formulation of previous question at stackoverflow.com/questions/8695806/… which will be deleted later today. Commented Jan 2, 2012 at 13:05
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    Why do you want to get rid of the loop? It seems very appropriate to me. Commented Jan 2, 2012 at 14:16
  • I had figured out a way for your previous question (using numpy.bincount), but for this one, where you need arbitrary weights for each set if list_list_values, I don't think there's a way Commented Jan 2, 2012 at 14:19
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    @Niklas Baumstark. The for-loop is appropriate but not for delivering performance when the data sizes of the lists and lists of lists are millions of items long. Commented Jan 2, 2012 at 14:25
  • @dbv: I see. Maybe it would be easiest to write that loop in C if numpy does not provide the needed functionality (which I don't know). Commented Jan 2, 2012 at 14:27

3 Answers 3

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While it often results in a massive speedup to eliminate for loops and take advantage of numpy built-ins/vectorization. I would just point out that it is not always the case. Timing the simple for loop vs the much more involved vectorization, does not give you a large speedup and is much more verbose. Just something to consider:

from timeit import Timer setstr="""import numpy as np import itertools import random Nlists = 1000 total_lists = 5000 outsz = 100 maxsublistsz = 100 # create random list of lists list_range_values = random.sample(xrange(total_lists),Nlists) list_list_values = [random.sample(xrange(outsz),np.random.randint(1,maxsublistsz)) for k in xrange(total_lists)] list_comp_values = 10*np.random.uniform(size=(total_lists,)) v = np.zeros((outsz,)) def indices(start, end): lens = end - start np.cumsum(lens, out=lens) i = np.ones(lens[-1], dtype=int) i[0] = start[0] i[lens[:-1]] += start[1:] i[lens[:-1]] -= end[:-1] np.cumsum(i, out=i) return i def sum_by_group(values, groups): order = np.argsort(groups) groups = groups[order] values = values[order] values.cumsum(out=values) index = np.ones(len(groups), 'bool') index[:-1] = groups[1:] != groups[:-1] values = values[index] groups = groups[index] values[1:] = np.diff(values) return values, groups """ method1=""" list_list_lens = np.array(map(len, list_list_values)) comp_vals_expanded = np.repeat(list_comp_values, list_list_lens) list_vals_flat = np.fromiter(itertools.chain.from_iterable(list_list_values),dtype=int) list_list_starts = np.concatenate(([0], np.cumsum(list_list_lens)[:-1])) toadd = indices(list_list_starts[list_range_values],(list_list_starts + list_list_lens)[list_range_values]) v[list_vals_flat[toadd]] += comp_vals_expanded[toadd] """ method2=""" for k in list_range_values: v[list_list_values[k]] += list_comp_values[k] """ method3=""" llv = [list_list_values[i] for i in list_range_values] lcv = [list_comp_values[i] for i in list_range_values] counts = map(len, llv) indices = np.concatenate(llv) values = np.repeat(lcv, counts) totals, indices_unique = sum_by_group(values, indices) v[indices_unique] += totals """ t1 = Timer(method1,setup=setstr).timeit(100) print t1 t2 = Timer(method2,setup=setstr).timeit(100) print t2 t3 = Timer(method3,setup=setstr).timeit(100) print t3

For a pretty large number of elements in the list:

Method1: (no for loop -jterrace) 1.43 seconds

Method2: (for loop) 4.62 seconds

Method3: (no for loop - bago) 2.99 seconds

For a small number of lists (change Nlists to 10), the for loop is significantly faster than jterrace's solution:

Method1: (no for loop -jterrace) 1.05 seconds

Method2: (for loop) 0.045 seconds

Method3: (no for loop - bago) 0.041 seconds

This is not to knock @jterrace or @bago's solutions, which are quite elegant. Rather it is to point out that often times a simple for loop does not perform that poorly.

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11 Comments

Thank-you so much for your timings as it was exactly what I was wondering. The motivation for my question was that our lists and lists-of-lists are very large (in the millions) and will get larger over time. We use Numpy vectorization extensively and this was the only for-loop remaining in the system.
Very nice, but import itertools should be put in the setup, not the method. 2.89 seconds for Nlists=10 seems fishy.
Also, if you change map to itertools.imap, it might make some difference.
@JoshAdel, nice. I'd be curious to see how my numpy.histogram solution stacks up to the above...
@dbv if the number is in the millions, vectorization might provide significant speedup if you don't run into memory issues. I also think taking a look at cython is a good idea. I've personally had a lot of success with it in the past for getting large speed-ups for things that either don't vectorize well or would have required a large intermediate array that didn't fit into memory.
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Using your example input:

>>> list_list_values = [[3, 6, 7], [5, 7, 11, 25, 99], [8, 45], [4, 7, 8], [0, 1], [21, 31, 41], [9, 11, 22, 33, 44], [17, 19]] >>> list_comp_values = [0.7, 9.8, 1.2, 5, 10, 11.7, 6, 0.2] >>> list_range_values = [1, 3, 5]

First, some generator shenanigans:

>>> indices_weights = ((list_list_values[i], list_comp_values[i]) for i in list_range_values) >>> flat_indices_weights = ((i, weight) for indices, weight in indices_weights for i in indices)

Now we pass the data to numpy. I can't figure out how to produce a rec.array from an iterator, so I had to convert the above generator to a list. Maybe there's a way to avoid that...

>>> i_w = numpy.rec.array(list(flat_indices_weights), dtype=[('i', int), ('weight', float)]) >>> numpy.histogram(i_w['i'], bins=range(0, 100), weights=i_w['weight']) (array([ 0. , 0. , 0. , 0. , 5. , 9.8, 0. , 14.8, 5. , 0. , 0. , 9.8, 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 11.7, 0. , 0. , 0. , 9.8, 0. , 0. , 0. , 0. , 0. , 11.7, 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 11.7, 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 9.8]), array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]))

I had a moment to follow up on JoshAdel's tests with a couple of my own. The fastest solution so far uses Bago's set-up but replaces the sum_by_group function with the built-in histogram function. Here are the numbers I got (updated):

Method1 (jterrace) : 2.65

Method2 (for loop) : 2.25

Method3 (Bago) : 1.14

Method4 (histogram) : 2.82

Method5 (3/4 combo) : 1.07

Note that as implemented here, the first method gives incorrect results according to my test. I didn't have the time to figure out what the problem is. The code for my test is below; it only gently adjusts JoshAdel's original code, but I post it here in full for convenience. (Updated to include Bago's comments and somewhat de-kludged.)

from timeit import Timer setstr="""import numpy as np import itertools import random Nlists = 1000 total_lists = 5000 outsz = 100 maxsublistsz = 100 # create random list of lists list_range_values = random.sample(xrange(total_lists),Nlists) list_list_values = [random.sample(xrange(outsz),np.random.randint(1,maxsublistsz)) for k in xrange(total_lists)] list_comp_values = list(10*np.random.uniform(size=(total_lists,))) v = np.zeros((outsz,)) def indices(start, end): lens = end - start np.cumsum(lens, out=lens) i = np.ones(lens[-1], dtype=int) i[0] = start[0] i[lens[:-1]] += start[1:] i[lens[:-1]] -= end[:-1] np.cumsum(i, out=i) return i def sum_by_group(values, groups): order = np.argsort(groups) groups = groups[order] values = values[order] values.cumsum(out=values) index = np.ones(len(groups), 'bool') index[:-1] = groups[1:] != groups[:-1] values = values[index] groups = groups[index] values[1:] = np.diff(values) return values, groups """ setstr_test = setstr + "\nprint_v = True\n" method1=""" list_list_lens = np.array(map(len, list_list_values)) comp_vals_expanded = np.repeat(list_comp_values, list_list_lens) list_vals_flat = np.fromiter(itertools.chain.from_iterable(list_list_values),dtype=int) list_list_starts = np.concatenate(([0], np.cumsum(list_list_lens)[:-1])) toadd = indices(list_list_starts[list_range_values],(list_list_starts + list_list_lens)[list_range_values]) v[list_vals_flat[toadd]] += comp_vals_expanded[toadd] """ method2=""" for k in list_range_values: v[list_list_values[k]] += list_comp_values[k] """ method3=""" llv = [np.fromiter(list_list_values[i], 'int') for i in list_range_values] lcv = [list_comp_values[i] for i in list_range_values] counts = map(len, llv) indices = np.concatenate(llv) values = np.repeat(lcv, counts) totals, indices_unique = sum_by_group(values, indices) v[indices_unique] += totals """ method4=""" indices_weights = ((list_list_values[i], list_comp_values[i]) for i in list_range_values) flat_indices_weights = ((i, weight) for indices, weight in indices_weights for i in indices) i_w = np.rec.array(list(flat_indices_weights), dtype=[('i', 'i'), ('weight', 'd')]) v += np.histogram(i_w['i'], bins=range(0, outsz + 1), weights=i_w['weight'], new=True)[0] """ method5=""" llv = [np.fromiter(list_list_values[i], 'int') for i in list_range_values] lcv = [list_comp_values[i] for i in list_range_values] counts = map(len, llv) indices = np.concatenate(llv) values = np.repeat(lcv, counts) v += np.histogram(indices, bins=range(0, outsz + 1), weights=values, new=True)[0] """ t1 = Timer(method1,setup=setstr).timeit(100) print t1 t2 = Timer(method2,setup=setstr).timeit(100) print t2 t3 = Timer(method3,setup=setstr).timeit(100) print t3 t4 = Timer(method4,setup=setstr).timeit(100) print t4 t5 = Timer(method5,setup=setstr).timeit(100) print t5 exec(setstr_test + method1 + "\nprint v\n") exec("\nv = np.zeros((outsz,))\n" + method2 + "\nprint v\n") exec("\nv = np.zeros((outsz,))\n" + method3 + "\nprint v\n") exec("\nv = np.zeros((outsz,))\n" + method4 + "\nprint v\n") exec("\nv = np.zeros((outsz,))\n" + method5 + "\nprint v\n")
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3 Comments

Note that to avoid having 98 and 99 in the same bin, you'd have to use bins=range(0, 101) instead.
I changed the setup a little bit, llv = [np.fromiter(list_list_values[i], 'int') for i in list_range_values]. Passing a list of ndarrays to concatenate seems significantly faster than passing a list of lists. The histogram approach is a good idea. Unless the index is very sparse, it's much better if you can avoid having an index on the left side of the assignment.
@Bago, thanks for pointing that out -- it makes a big difference! I've updated the timings and code.
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First, set up the variables you gave:

import numpy as np list_range_values = [1, 3, 5] list_list_values = [[3, 6, 7], [5, 7, 11, 25, 99], [8, 45], [4, 7, 8], [0, 1], [21, 31, 41]] list_comp_values = [0.7, 9.8, 1.2, 5, 10, 11.7] v = np.arange(100, dtype=float)

Next, list_list_values and list_comp_values need to be flattened so they are contiguous:

list_list_lens = np.array(map(len, list_list_values)) comp_vals_expanded = np.repeat(list_comp_values, list_list_lens) import itertools list_vals_flat = np.fromiter(itertools.chain.from_iterable(list_list_values), dtype=int)

Then, the starting indices of each subarray are needed:

list_list_starts = np.concatenate(([0], np.cumsum(list_list_lens)[:-1]))

Now that we have both the starting and ending values, we can use the indices function from this question to get an array of selector indices:

def indices(start, end): lens = end - start np.cumsum(lens, out=lens) i = np.ones(lens[-1], dtype=int) i[0] = start[0] i[lens[:-1]] += start[1:] i[lens[:-1]] -= end[:-1] np.cumsum(i, out=i) return i toadd = indices(list_list_starts[list_range_values], (list_list_starts + list_list_lens)[list_range_values])

Now that we've done all this magic, the array can be added to like this:

v[list_vals_flat[toadd]] += comp_vals_expanded[toadd]
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2 Comments

Thank-you. The results are identical to the for-loop. Your solution is similar to Bago's which a tad cleaner for our needs.
@dbv and @jterrace. Have you guys checked to see if this works when there are repeats in list_vals_flat[toadd]? Unless I'm missing something this method might have a bug.

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