reduce() anomaly?

[Stephen C. Waterbury]

This seems like it ought to work, according to the
description of reduce(), but it doesn't. Is this
a bug, or am I missing something?

Python 2.3.2 (#1, Oct 20 2003, 01:04:35)
[GCC 3.2.2 20030222 (Red Hat Linux 3.2.2-5)] on linux2
Type "help", "copyright" , "credits" or "license" for more information.

d1 = {'a':1}
d2 = {'b':2}
d3 = {'c':3}
l = [d1, d2, d3]
d4 = reduce(lambda x, y: x.update(y), l) Traceback (most recent call last):
File "<stdin>", line 1, in ?
File "<stdin>", line 1, in <lambda>
AttributeError: 'NoneType' object has no attribute 'update' d4 = reduce(lambda x, y: x.update(y), l, {})

Traceback (most recent call last):
File "<stdin>", line 1, in ?
File "<stdin>", line 1, in <lambda>
AttributeError: 'NoneType' object has no attribute 'update'

- Steve.

[Alex Martelli]

Georgy Pruss wrote:

seq=[1,3,4,7]
map( int.__sub__, seq[1:], seq[:-1] ) # nearly twice faster than
....zip.... for long arrays

If this is a race, then let's measure things properly and consider
a few more alternatives, shall we...?

[alex@lancelot xine-lib-1-rc2]$ python a.py
reduce: 100 loops, best of 3: 13.8 msec per loop
zip: 100 loops, best of 3: 18 msec per loop
izip: 100 loops, best of 3: 7.6 msec per loop
w2: 100 loops, best of 3: 7.1 msec per loop
wib: 100 loops, best of 3: 12.7 msec per loop
loop: 100 loops, best of 3: 8.9 msec per loop
map: 100 loops, best of 3: 7.6 msec per loop

itertools.w2 is an experimental addition to itertools which I
doubt I'll be allowed to put in (gaining less than 10% wrt the
more general izip is hardly worth a new itertool, sigh). But,
apart from that, map and izip are head to head, and the plain
good old Python-coded loop is next best...! reduce is slowest.

My code...:
if __name__ != '__main__':
def difs_reduce(seq ):
differences = []
def neighborDiffere nce(left, right, accum=differenc es.append):
accum(right - left)
return right
reduce(neighbor Difference, seq)
return differences

def difs_zip(seq):
return [ b-a for a, b in zip(seq,seq[1:]) ]

import itertools
def difs_izip(seq):
return [ b-a for a, b in itertools.izip( seq,seq[1:]) ]

def difs_w2(seq, wib=itertools.w 2):
return [ b-a for a, b in wib(seq) ]

def window_by_two(i terable):
it = iter(iterable)
last = it.next()
for elem in it:
yield last, elem
last = elem

def difs_wib(seq, wib=window_by_t wo):
return [ b-a for a, b in wib(seq) ]

def difs_loop(seq):
differences = []
it = iter(seq)
a = it.next()
for b in it:
differences.app end(b-a)
a = b
return differences

def difs_map(seq):
return map(int.__sub__ , seq[1:], seq[:-1])

if __name__ == '__main__':
import timeit
bargs = ['-c', '-simport a', '-sx=range(9999)']
funs = 'reduce zip izip w2 wib loop map'.split()
for fun in funs:
args = bargs + ['a.difs_%s(x)' % fun]
print '%8s:' % fun,
timeit.main(arg s)
Alex

[Erik Max Francis]

Alex Martelli wrote:

However, so many of reduce's practical use cases are eaten up by sum,
that reduce is left without real use cases to justify its existence.
Any reduction that doesn't involve summing won't be handled by sum.
Flattening a list of (non-recursive) lists is a good example. reduce is
already in the language; removing an existing, builtin function seems
totally inappropriate given that it's there for a reason and there will
be no replacement.
But comparing plain Python code to a built-in that's almost bereft of
good use cases, and finding the plain Python code _faster_ on such a
regular basis, is IMHO perfectly legitimate.

reduce will be at least as fast as writing an explicit loop.
Potentially more if the function object used is itself a builtin
function.

--
Erik Max Francis && ma*@alcyone.com && http://www.alcyone.com/max/
__ San Jose, CA, USA && 37 20 N 121 53 W && &tSftDotIotE
/ \ A man cannot be comfortable without his own approval.
\__/ Mark Twain

[Alex Martelli]

Erik Max Francis wrote:

Alex Martelli wrote:

However, so many of reduce's practical use cases are eaten up by sum,
that reduce is left without real use cases to justify its existence.
Any reduction that doesn't involve summing won't be handled by sum.
Flattening a list of (non-recursive) lists is a good example. reduce is

If this a good example, what's a bad one?

sum([ ['a list'], ['of', 'non'], ['recursive', 'lists'] ], [])

['a list', 'of', 'non', 'recursive', 'lists']

sum, exactly like reduce(operator .add ... , has bad performance for this
kind of one-level flattening, by the way. A plain loop on .extend is much
better than either (basically, whenever a loop of x+=y has much better
performance than one of x = x + y -- since the latter is what both sum
and reduce(operator .add... are condemned to do -- you should consider
choosing a simple loop if performance has any importance at all).
already in the language; removing an existing, builtin function seems
totally inappropriate given that it's there for a reason and there will
be no replacement.
Existing, builtin functions _will_ be removed in 3.0: Guido is on record
as stating that (at both Europython and OSCON -- I don't recall if he
had already matured that determination at PythonUK time). They
exist for a reason, but when that reason is: "once upon a time, we
thought (perhaps correctly, given the way the rest of the language and
library was at the time) that they were worth having", that's not
sufficient reason to weigh down the language forever with their
not-useful-enough weight. The alternatives to removing those parts that
aren't useful enough any more are, either to stop Python's development
forever, or to make Python _bloated_ with several ways to perform the
same tasks. I much prefer to "lose" the "legacy only real use" built-ins
(presumably to some kind of legacy.py module whence they can easily
be installed to keep some old and venerable piece of code working) than
to choose either of those tragic alternatives.

3.0 is years away, but functions that are clearly being aimed at for
obsolencence then should, IMHO, already be better avoided in new code;
particularly because the obsolescence is due to the existence of better
alternatives. You claim "there will be no replacement", but in fact I have
posted almost a dozen possible replacements for 'reduce' for a case that
was being suggested as a good one for it and _every_ one of them is
better than reduce; I have posted superior replacements for ALL uses of
reduce in the standard library (except those that are testing reduce itself,
but if that's the only good use of reduce -- testing itself -- well, you see
my point...:-). I don't intend to spend much more time pointing out how
reduce can be replaced by better code in real use cases, by the way:-).

But comparing plain Python code to a built-in that's almost bereft of
good use cases, and finding the plain Python code _faster_ on such a
regular basis, is IMHO perfectly legitimate.

reduce will be at least as fast as writing an explicit loop.

You are wrong: see the almost-a-dozen cases I posted to try and demolish
one suggested "good use" of reduce.
Potentially more if the function object used is itself a builtin
function.

In one of the uses of reduce in the standard library, for which I posted
superior replacements today, the function object was int.__mul__ -- builtin
enough for you? Yet I showed how using recursion and memoization instead of
reduce would speed up that case by many, many times.

Another classic example of reduce being hopelessly slow, despite using
a built-in function, is exactly the "flatten a 1-level list" case mentioned
above. Try:
x = reduce(operator .add, listoflists, x)
vs:
for L in listoflists: x.extend(L)
for a sufficiently big listoflists, and you'll see... (the latter if need be
can get another nice little multiplicative speedup by hoisting the x.extend
lookup, but the key issue is O(N**2) reduce vs O(N) loop...).

[alex@lancelot src]$ timeit.py -c -s'xs=[[x] for x in range(999)]' -s'import
operator' 'x=[]' 'x=reduce(opera tor.add, xs, x)'
100 loops, best of 3: 8.7e+03 usec per loop
[alex@lancelot src]$ timeit.py -c -s'xs=[[x] for x in range(999)]' -s'import
operator' 'x=[]' 'for L in xs: x.extend(L)'
1000 loops, best of 3: 860 usec per loop
[alex@lancelot src]$ timeit.py -c -s'xs=[[x] for x in range(999)]' -s'import
operator' 'x=[]; xex=x.extend' 'for L in xs: xex(L)'
1000 loops, best of 3: 560 usec per loop

See what I mean? Already for a mere 999 1-item lists, the plain Python
code is 10 times faster than reduce, and if that's not quite enough and
you want it 15 times faster instead, that's trivial to get, too.
Alex

[Alex Martelli]

JCM wrote:

Alex Martelli <al***@aleax.it > wrote:
...various good points...

if one is in a hurry, recursion and
memoization are obviously preferable:

def facto(n, _memo={1:1}):
try: return _memo[n]
except KeyError:
result = _memo[n] = (n-1) * facto(n-1)
return result ... [alex@lancelot bo]$ timeit.py -c -s'import facs' 'facs.facto(13) '
1000000 loops, best of 3: 1.26 usec per loop

I'm going off topic, but it's really not fair to compare a memoized
function to non-memoized implementations using a "best of 3" timing
test.

The best-of-3 is irrelevant, it's the million loops that help:-).

Of course you can memoize any pure function of hashable args. But
memoizing a recursive implementation of factorial has a nice property,
shared by other int functions implemented recursively in terms of their
values on other ints, such as fibonacci numbers: the memoization you do for
any value _helps_ the speed of computation for other values. This nice
property doesn't apply to non-recursive implementations .

Once you run timeit.py, with its million loops (and the best-of-3, but
that's not crucial:-), this effect disappears. But on smaller tests it is
more easily seen. You can for example define the memoized functions
by a def nested inside another, so each call of the outer function will undo
the memoization, and exercise them that way even with timeit.py. E.g.:

import operator

def wireduce(N=23):
def factorial(x, _memo={0:1, 1:1}):
try: return _memo[x]
except KeyError:
result = _memo[x] = reduce(operator .mul, xrange(2,x+1), 1)
return result
for x in range(N, 0, -1): factorial(x)

def wirecurse(N=23) :
def factorial(x, _memo={0:1, 1:1}):
try: return _memo[x]
except KeyError:
result = _memo[x] = x * factorial(x-1)
return result
for x in range(N, 0, -1): factorial(x)

[alex@lancelot bo]$ timeit.py -c -s'import aa' 'aa.wireduce()'
1000 loops, best of 3: 710 usec per loop
[alex@lancelot bo]$ timeit.py -c -s'import aa' 'aa.wirecurse() '
1000 loops, best of 3: 280 usec per loop
Alex

[Georgy Pruss]

"Alex Martelli" <al***@aleax.it > wrote in message news:Sw******** *************@n ews1.tin.it...

Georgy Pruss wrote:

seq=[1,3,4,7]
map( int.__sub__, seq[1:], seq[:-1] ) # nearly twice faster than
....zip.... for long arrays
If this is a race, then let's measure things properly and consider
a few more alternatives, shall we...?

:) No, it's not a race. I just found the map expression to be clear and elegant.
Fortunatelly, one of the fastest solutions too.

G-:

[alex@lancelot xine-lib-1-rc2]$ python a.py
reduce: 100 loops, best of 3: 13.8 msec per loop
zip: 100 loops, best of 3: 18 msec per loop
izip: 100 loops, best of 3: 7.6 msec per loop
w2: 100 loops, best of 3: 7.1 msec per loop
wib: 100 loops, best of 3: 12.7 msec per loop
loop: 100 loops, best of 3: 8.9 msec per loop
map: 100 loops, best of 3: 7.6 msec per loop

itertools.w2 is an experimental addition to itertools which I
doubt I'll be allowed to put in (gaining less than 10% wrt the
more general izip is hardly worth a new itertool, sigh). But,
apart from that, map and izip are head to head, and the plain
good old Python-coded loop is next best...! reduce is slowest.

My code...:
<...>

Alex

[Terry Reedy]

"Alex Martelli" <al*****@yahoo. com> wrote in message
news:aK******** *************@n ews1.tin.it...

above. Try:
x = reduce(operator .add, listoflists, x)
vs:
for L in listoflists: x.extend(L)
for a sufficiently big listoflists, and you'll see... (the latter if need be can get another nice little multiplicative speedup by hoisting the x.extend lookup, but the key issue is O(N**2) reduce vs O(N) loop...).
Right: however that issue and the possibility of hoisting x.extend
have *nothing* to do with reduce vs. for. For a fair comparison of
the latter pair, try the following, which is algorithmicly equivalent
to your sped-up for loop.

xs=[[i] for i in range(10)]
x=[]
xtend=x.extend
reduce(lambda dum,L: xtend(L), xs, x)
x

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
[timeits snipped]... See what I mean?
That you hate reduce?

I am sure that the O(N) reduce would be similarly faster than an
O(N**2) operator.add for loop: what would *that* mean?
Already for a mere 999 1-item lists, the plain Python
code is 10 times faster than reduce,

No, you have only shown that for N=999, O(N) can be O(N**2)/10, and
that smart programmers who understand that can write better (faster)
code than those who do not.

Terry J. Reedy

PS: for practical rather than didactic programming, I am pretty sure I
would have written a for loop 'reduced' with xtend.

[Dave Benjamin]

In article <dx************ ***********@new s2.tin.it>, Alex Martelli wrote:

Nope -- apply beats it, given that in the last few years apply(f, args) is
best spelled f(*args) ...!-)

Yeah, and speaking of which, where was the debate on explicit vs. implicit
and avoiding Perl-style line-noise syntax-sugaring when that feature was
snuck in? ;)

--
..:[ dave benjamin (ramenboy) -:- www.ramenfest.com -:- www.3dex.com ]:.
: d r i n k i n g l i f e o u t o f t h e c o n t a i n e r :

[Aahz]

In article <sl************ ******@lackingt alent.com>,
Dave Benjamin <ra***@lackingt alent.com> wrote:

In article <dx************ ***********@new s2.tin.it>, Alex Martelli wrote:

Nope -- apply beats it, given that in the last few years apply(f, args) is
best spelled f(*args) ...!-)

Yeah, and speaking of which, where was the debate on explicit vs. implicit
and avoiding Perl-style line-noise syntax-sugaring when that feature was
snuck in? ;)

There wouldn't be any; it's a straightforward integration with the
long-standing ability to use *args and **kwargs when defining a
function.
--
Aahz (aa**@pythoncra ft.com) <*> http://www.pythoncraft.com/

"It is easier to optimize correct code than to correct optimized code."
--Bill Harlan

[Douglas Alan]

Alex Martelli <al*****@yahoo. com> writes:

Existing, builtin functions _will_ be removed in 3.0: Guido is on record
as stating that (at both Europython and OSCON -- I don't recall if he
had already matured that determination at PythonUK time). They
exist for a reason, but when that reason is: "once upon a time, we
thought (perhaps correctly, given the way the rest of the language and
library was at the time) that they were worth having", that's not
sufficient reason to weigh down the language forever with their
not-useful-enough weight. The alternatives to removing those parts that
aren't useful enough any more are, either to stop Python's development
forever, or to make Python _bloated_ with several ways to perform the
same tasks.

I agree: Down with bloat! Get rid of sum() -- it's redundant with
reduce(), which I use all the time, like so:

def longer(x, y):
if len(y) > len(x): return y
else: return x

def longest(seq):
return reduce(longer, seq)

print longest(("abc", "yumyum!", "hello", "goodbye", "?"))

=> yumyum!

|>oug

[Anton Vredegoor]

Alex Martelli <al*****@yahoo. com> wrote:

Of course you can memoize any pure function of hashable args. But
memoizing a recursive implementation of factorial has a nice property,
shared by other int functions implemented recursively in terms of their
values on other ints, such as fibonacci numbers: the memoization you do for
any value _helps_ the speed of computation for other values. This nice
property doesn't apply to non-recursive implementations .

Maybe we need a better example because it is possible to use reduce on
a function which has side effects.

Anton.

class _Memo:
biggest = 1
facdict = {0 : 1, 1 : 1}

def fac(n):
def mymul(x,y):
res = x*y
_Memo.facdict[y] = res
_Memo.biggest = y
return res
def factorial(x):
b = _Memo.biggest
if x > b: return reduce(mymul, xrange(b+1,x+1) , b)
return _Memo.facdict[x]
return factorial(n)

def test():
print fac(5)

if __name__=='__ma in__':
test()