# Is there a list comprehension for this?

Discussion in 'Python' started by liam_herron, Nov 21, 2006.

1. ### liam_herronGuest

Given:
dw = [ 1, -1.1, +1.2 ]

Suppose I want to create a list 'w' that is defined as

w[0] = dw[0],
w[1] = w[0] + dw[1],
w[2] = w[1] + dw[2]

Is there a list comprehension or map expression to do it in one or 2
lines.

liam_herron, Nov 21, 2006

2. ### Tim ChaseGuest

> dw = [ 1, -1.1, +1.2 ]
>
> Suppose I want to create a list 'w' that is defined as
>
> w[0] = dw[0],
> w[1] = w[0] + dw[1],
> w[2] = w[1] + dw[2]
>
> Is there a list comprehension or map expression to do it in one or 2
> lines.

Well, while it's not terribly efficient, you can do something like

w = [sum(dw[:i]) for i in xrange(1,len(dw)+1)]

Or, if you need the efficiencies for larger len(dw) values, you
could do something like

>>> def f(x):

.... i = 0
.... for item in x:
.... i += item
.... yield i
....
>>> list(i for i in f(dw))

[1, -0.10000000000000009, 1.0999999999999999]

Just a few ideas,

-tkc

Tim Chase, Nov 21, 2006

3. ### Mathias PanzenboeckGuest

liam_herron wrote:
> Given:
> dw = [ 1, -1.1, +1.2 ]
>
> Suppose I want to create a list 'w' that is defined as
>
> w[0] = dw[0],
> w[1] = w[0] + dw[1],
> w[2] = w[1] + dw[2]
>
> Is there a list comprehension or map expression to do it in one or 2
> lines.
>

Is this a function where you just want to know a w[n]?

then:

def w(n):
return sum((1 + i * 0.1) * (i % 2 and 1 or -1) for i in xrange(n))

otherwise:

n, w, x = 3, [], 0

for y in ((1 + i * 0.1) * (i % 2 and 1 or -1) for i in xrange(n)):
x += y
w.append(x)

Mathias Panzenboeck, Nov 21, 2006
4. ### Robert KernGuest

liam_herron wrote:
> Given:
> dw = [ 1, -1.1, +1.2 ]
>
> Suppose I want to create a list 'w' that is defined as
>
> w[0] = dw[0],
> w[1] = w[0] + dw[1],
> w[2] = w[1] + dw[2]
>
> Is there a list comprehension or map expression to do it in one or 2
> lines.

One way is to use numpy (numpy.scipy.org):

In [40]: from numpy import cumsum

In [41]: dw = [1, -1.1, +1.2]

In [42]: cumsum(dw)
Out[42]: array([ 1. , -0.1, 1.1])

If you're doing a lot of numerical computing, you'll probably want a number of
other things that numpy provides.

--
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless enigma
an underlying truth."
-- Umberto Eco

Robert Kern, Nov 21, 2006
5. ### Steven D'ApranoGuest

On Tue, 21 Nov 2006 13:19:04 -0800, liam_herron wrote:

>
> Given:
> dw = [ 1, -1.1, +1.2 ]
>
> Suppose I want to create a list 'w' that is defined as
>
> w[0] = dw[0],
> w[1] = w[0] + dw[1],
> w[2] = w[1] + dw[2]
>
> Is there a list comprehension or map expression to do it in one or 2
> lines.

This isn't a list comp and it doesn't need map, but if you
absolutely have to have a one-liner:

w = [dw[0], dw[0] + dw[1], dw[0] + dw[1] + dw[2]]

Obviously that doesn't scale at all to larger lists, but it gives you a
better idea: replace the manual additions with sum().

w = [sum(dw[0:i]) for i in range(1, len(dw))]

but if your dw list is huge, you're spending a lot of time slicing
dw and adding up the same numbers over and over again. (This doesn't
matter if dw is small, but could become expensive if dw is huge.)

Which leads to the next version:

def running_sum(dw):
"""Return a list of the running sums of sequence dw"""
rs = [0]*len(dw)
for i in range(len(dw)):
rs = dw + rs[i-1]
return rs

It isn't a one-liner, but it is clear, the name is self-documenting, it
has a doc-string, you don't have to copy-and-paste code every time you
want to use it, and now that you've defined it once, you can use it as a
one-liner as many times as you like.

>>> running_sum(range(5)):

[0, 1, 3, 6, 10]

--
Steven D'Aprano

Steven D'Aprano, Nov 22, 2006
6. ### John MachinGuest

Steven D'Aprano wrote:

[snip]

> def running_sum(dw):
> """Return a list of the running sums of sequence dw"""
> rs = [0]*len(dw)
> for i in range(len(dw)):
> rs = dw + rs[i-1]

Please explain to the newbies why there is no exception raised when
rs[i-1] is executed for i == 0, and state whether you consider this is
a Good Idea or a Filthy Trick or a Fortunate Accident.

> return rs
>
> It isn't a one-liner, but it is clear, the name is self-documenting, it
> has a doc-string, you don't have to copy-and-paste code every time you
> want to use it, and now that you've defined it once, you can use it as a
> one-liner as many times as you like.
>
> >>> running_sum(range(5)):

> [0, 1, 3, 6, 10]

John Machin, Nov 22, 2006
7. ### Peter OttenGuest

liam_herron wrote:

>
> Given:
> dw = [ 1, -1.1, +1.2 ]
>
> Suppose I want to create a list 'w' that is defined as
>
> w[0] = dw[0],
> w[1] = w[0] + dw[1],
> w[2] = w[1] + dw[2]
>
> Is there a list comprehension or map expression to do it in one or 2
> lines.

>>> from itertools import *
>>> data = [1, -1.1, 1.2]
>>> N = 2
>>> [sum(item) for item in izip(*[chain(repeat(0, i), di) for i, di in

enumerate(tee(data, N))])]
[1, -0.10000000000000009, 0.099999999999999867]

Should work for other values of N, too. No, I'm not serious about it...

Peter

Peter Otten, Nov 22, 2006
8. ### Steven D'ApranoGuest

On Tue, 21 Nov 2006 21:00:02 -0800, John Machin wrote:

> Steven D'Aprano wrote:
>
> [snip]
>
>> def running_sum(dw):
>> """Return a list of the running sums of sequence dw"""
>> rs = [0]*len(dw)
>> for i in range(len(dw)):
>> rs = dw + rs[i-1]

>
> Please explain to the newbies why there is no exception raised when
> rs[i-1] is executed for i == 0, and state whether you consider this is
> a Good Idea or a Filthy Trick or a Fortunate Accident.

Because rs[0-1] is just rs[-1], which fetches the LAST item of the list. I
cunningly initialised the list to all zeroes, so adding zero to the first
term doesn't change the result value.

It is a variation of the sentinel technique, where you add an extra value
to the beginning or end of a list so that you don't need to treat the
first or last item differently. In this specific case, I think it is a
combination of Good Idea and Fortunate Accident, but since the
meaning of list[-1] is both deliberate and well-documented, it is
certainly not a Filthy Trick.

--
Steven.

Steven D'Aprano, Nov 22, 2006
9. ### John MachinGuest

Steven D'Aprano wrote:
> On Tue, 21 Nov 2006 21:00:02 -0800, John Machin wrote:
>
> > Steven D'Aprano wrote:
> >
> > [snip]
> >
> >> def running_sum(dw):
> >> """Return a list of the running sums of sequence dw"""
> >> rs = [0]*len(dw)
> >> for i in range(len(dw)):
> >> rs = dw + rs[i-1]

> >
> > Please explain to the newbies why there is no exception raised when
> > rs[i-1] is executed for i == 0, and state whether you consider this is
> > a Good Idea or a Filthy Trick or a Fortunate Accident.

>
> Because rs[0-1] is just rs[-1], which fetches the LAST item of the list. I
> cunningly initialised the list to all zeroes, so adding zero to the first
> term doesn't change the result value.
>
> It is a variation of the sentinel technique, where you add an extra value
> to the beginning or end of a list so that you don't need to treat the
> first or last item differently. In this specific case, I think it is a
> combination of Good Idea and Fortunate Accident, but since the
> meaning of list[-1] is both deliberate and well-documented, it is
> certainly not a Filthy Trick.
>

Fair enough. But it does make the concerned reader go back a couple of
lines to see why it doesn't run amok. Here's my attempt at a

def running_sum_2(dw):
rs = dw[:1]
for i in xrange(1, len(dw)):
rs.append(dw + rs[-1])
return rs

Cheers,
John

John Machin, Nov 22, 2006
10. ### Steven D'ApranoGuest

On Wed, 22 Nov 2006 02:28:04 -0800, John Machin wrote:

>
> Steven D'Aprano wrote:
>> On Tue, 21 Nov 2006 21:00:02 -0800, John Machin wrote:
>>
>> > Steven D'Aprano wrote:
>> >
>> > [snip]
>> >
>> >> def running_sum(dw):
>> >> """Return a list of the running sums of sequence dw"""
>> >> rs = [0]*len(dw)
>> >> for i in range(len(dw)):
>> >> rs = dw + rs[i-1]
>> >
>> > Please explain to the newbies why there is no exception raised when
>> > rs[i-1] is executed for i == 0, and state whether you consider this is
>> > a Good Idea or a Filthy Trick or a Fortunate Accident.

>>
>> Because rs[0-1] is just rs[-1], which fetches the LAST item of the list. I
>> cunningly initialised the list to all zeroes, so adding zero to the first
>> term doesn't change the result value.
>>
>> It is a variation of the sentinel technique, where you add an extra value
>> to the beginning or end of a list so that you don't need to treat the
>> first or last item differently. In this specific case, I think it is a
>> combination of Good Idea and Fortunate Accident, but since the
>> meaning of list[-1] is both deliberate and well-documented, it is
>> certainly not a Filthy Trick.
>>

>
> Fair enough. But it does make the concerned reader go back a couple of
> lines to see why it doesn't run amok.

Nobody said that every piece of code should be instantly comprehensible
just at a glance. Sometimes you do actually have to think about code to
understand it, even in Python

> Here's my attempt at a
>
> def running_sum_2(dw):
> rs = dw[:1]
> for i in xrange(1, len(dw)):
> rs.append(dw + rs[-1])
> return rs
>

Even with xrange() instead of range, it is a little slower than my version
for largish input lists because you are repeatedly appending to a list.

>>> timeit.Timer("running_sum(L)",

.... "from __main__ import running_sum; L = range(500)").timeit(1000)
0.56354999542236328
>>> timeit.Timer("running_sum_2(L)",

.... "from __main__ import running_sum_2; L = range(500)").timeit(1000)
0.68534302711486816

Although the speed difference disappears (or even reverses) for small
enough lists. Either way, it isn't really a major speed difference --
Python's resizing of lists is very smart.

But why build a list of all the running sums when you probably only need
them one at a time? Here's a generator version that can take any iterable,
not just a sequence:

def running_sum_3(iterable):
sum_ = 0
for x in iterable:
sum_ += x
yield sum_

And it is considerably faster than either of the list-only versions:

>>> timeit.Timer("list(running_sum_3(L))",

.... "from __main__ import running_sum_3; L = range(500)").timeit(1000)
0.33915305137634277

--
Steve.

Steven D'Aprano, Nov 22, 2006
11. ### John MachinGuest

Steven D'Aprano wrote:
> On Wed, 22 Nov 2006 02:28:04 -0800, John Machin wrote:
>
> >
> > Steven D'Aprano wrote:
> >> On Tue, 21 Nov 2006 21:00:02 -0800, John Machin wrote:
> >>
> >> > Steven D'Aprano wrote:
> >> >
> >> > [snip]
> >> >
> >> >> def running_sum(dw):
> >> >> """Return a list of the running sums of sequence dw"""
> >> >> rs = [0]*len(dw)
> >> >> for i in range(len(dw)):
> >> >> rs = dw + rs[i-1]
> >> >
> >> > Please explain to the newbies why there is no exception raised when
> >> > rs[i-1] is executed for i == 0, and state whether you consider this is
> >> > a Good Idea or a Filthy Trick or a Fortunate Accident.
> >>
> >> Because rs[0-1] is just rs[-1], which fetches the LAST item of the list. I
> >> cunningly initialised the list to all zeroes, so adding zero to the first
> >> term doesn't change the result value.
> >>
> >> It is a variation of the sentinel technique, where you add an extra value
> >> to the beginning or end of a list so that you don't need to treat the
> >> first or last item differently. In this specific case, I think it is a
> >> combination of Good Idea and Fortunate Accident, but since the
> >> meaning of list[-1] is both deliberate and well-documented, it is
> >> certainly not a Filthy Trick.
> >>

> >
> > Fair enough. But it does make the concerned reader go back a couple of
> > lines to see why it doesn't run amok.

>
> Nobody said that every piece of code should be instantly comprehensible
> just at a glance.

That's correct. I didn't say it, and nobody else did. You argue ad
extremis, in extremis

My point was merely that it is preferable to be able to understand code
without having to go "OMG!" and then read backwards ...

> Sometimes you do actually have to think about code to
> understand it, even in Python

Correct. However I raised the question explicitly in the context of an
Notwithstandingly, you then mentioned "cunningly" and
"[well-]documented" and now "think"

>
> > Here's my attempt at a
> >
> > def running_sum_2(dw):
> > rs = dw[:1]
> > for i in xrange(1, len(dw)):
> > rs.append(dw + rs[-1])
> > return rs
> >

>

[snip]

>
> Although the speed difference disappears (or even reverses) for small
> enough lists. Either way, it isn't really a major speed difference --

As you say. Perhaps I should have stated in advance how many goalposts
and whether they had a cross-bar or not I was hoping for comments
on the understandibility or otherwise of rs[-1]. My use of xrange was
out of habit; it wasn't intended to provoke the cannonball run.
>
> But why build a list of all the running sums when you probably only need
> them one at a time? Here's a generator version that can take any iterable,
> not just a sequence:
>

.... and whether the cross-bar had a net slung from it

Why? (1) Because that's what the OP was asking for IIRC. (2) Because
some applications (at least back when the storage mechanism was squared
paper) involved cumulative sums of cumulative sums of ... generator

N.B. This is even more fun than discussing cricket with my Pommie
neighbour; keep it up

Best regards,
John

John Machin, Nov 22, 2006