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\section{\module{itertools} ---
Functions creating iterators for efficient looping}
\declaremodule{standard}{itertools}
\modulesynopsis{Functions creating iterators for efficient looping.}
\moduleauthor{Raymond Hettinger}{python@rcn.com}
\sectionauthor{Raymond Hettinger}{python@rcn.com}
\versionadded{2.3}
This module implements a number of iterator building blocks inspired
by constructs from the Haskell and SML programming languages. Each
has been recast in a form suitable for Python.
The module standardizes a core set of fast, memory efficient tools
that are useful by themselves or in combination. Standardization helps
avoid the readability and reliability problems which arise when many
different individuals create their own slightly varying implementations,
each with their own quirks and naming conventions.
The tools are designed to combine readily with one another. This makes
it easy to construct more specialized tools succinctly and efficiently
in pure Python.
For instance, SML provides a tabulation tool: \code{tabulate(f)}
which produces a sequence \code{f(0), f(1), ...}. This toolbox
provides \function{imap()} and \function{count()} which can be combined
to form \code{imap(f, count())} and produce an equivalent result.
Likewise, the functional tools are designed to work well with the
high-speed functions provided by the \refmodule{operator} module.
The module author welcomes suggestions for other basic building blocks
to be added to future versions of the module.
Whether cast in pure python form or compiled code, tools that use iterators
are more memory efficient (and faster) than their list based counterparts.
Adopting the principles of just-in-time manufacturing, they create
data when and where needed instead of consuming memory with the
computer equivalent of ``inventory''.
The performance advantage of iterators becomes more acute as the number
of elements increases -- at some point, lists grow large enough to
severely impact memory cache performance and start running slowly.
\begin{seealso}
\seetext{The Standard ML Basis Library,
\citetitle[http://www.standardml.org/Basis/]
{The Standard ML Basis Library}.}
\seetext{Haskell, A Purely Functional Language,
\citetitle[http://www.haskell.org/definition/]
{Definition of Haskell and the Standard Libraries}.}
\end{seealso}
\subsection{Itertool functions \label{itertools-functions}}
The following module functions all construct and return iterators.
Some provide streams of infinite length, so they should only be accessed
by functions or loops that truncate the stream.
\begin{funcdesc}{chain}{*iterables}
Make an iterator that returns elements from the first iterable until
it is exhausted, then proceeds to the next iterable, until all of the
iterables are exhausted. Used for treating consecutive sequences as
a single sequence. Equivalent to:
\begin{verbatim}
def chain(*iterables):
for it in iterables:
for element in it:
yield element
\end{verbatim}
\end{funcdesc}
\begin{funcdesc}{count}{\optional{n}}
Make an iterator that returns consecutive integers starting with \var{n}.
If not specified \var{n} defaults to zero.
Does not currently support python long integers. Often used as an
argument to \function{imap()} to generate consecutive data points.
Also, used with \function{izip()} to add sequence numbers. Equivalent to:
\begin{verbatim}
def count(n=0):
while True:
yield n
n += 1
\end{verbatim}
Note, \function{count()} does not check for overflow and will return
negative numbers after exceeding \code{sys.maxint}. This behavior
may change in the future.
\end{funcdesc}
\begin{funcdesc}{cycle}{iterable}
Make an iterator returning elements from the iterable and saving a
copy of each. When the iterable is exhausted, return elements from
the saved copy. Repeats indefinitely. Equivalent to:
\begin{verbatim}
def cycle(iterable):
saved = []
for element in iterable:
yield element
saved.append(element)
while saved:
for element in saved:
yield element
\end{verbatim}
Note, this member of the toolkit may require significant
auxiliary storage (depending on the length of the iterable).
\end{funcdesc}
\begin{funcdesc}{dropwhile}{predicate, iterable}
Make an iterator that drops elements from the iterable as long as
the predicate is true; afterwards, returns every element. Note,
the iterator does not produce \emph{any} output until the predicate
is true, so it may have a lengthy start-up time. Equivalent to:
\begin{verbatim}
def dropwhile(predicate, iterable):
iterable = iter(iterable)
for x in iterable:
if not predicate(x):
yield x
break
for x in iterable:
yield x
\end{verbatim}
\end{funcdesc}
\begin{funcdesc}{groupby}{iterable\optional{, key}}
Make an iterator that returns consecutive keys and groups from the
\var{iterable}. The \var{key} is a function computing a key value for each
element. If not specified or is \code{None}, \var{key} defaults to an
identity function and returns the element unchanged. Generally, the
iterable needs to already be sorted on the same key function.
The returned group is itself an iterator that shares the underlying
iterable with \function{groupby()}. Because the source is shared, when
the \function{groupby} object is advanced, the previous group is no
longer visible. So, if that data is needed later, it should be stored
as a list:
\begin{verbatim}
groups = []
uniquekeys = []
for k, g in groupby(data, keyfunc):
groups.append(list(g)) # Store group iterator as a list
uniquekeys.append(k)
\end{verbatim}
\function{groupby()} is equivalent to:
\begin{verbatim}
class groupby(object):
def __init__(self, iterable, key=None):
if key is None:
key = lambda x: x
self.keyfunc = key
self.it = iter(iterable)
self.tgtkey = self.currkey = self.currvalue = xrange(0)
def __iter__(self):
return self
def next(self):
while self.currkey == self.tgtkey:
self.currvalue = self.it.next() # Exit on StopIteration
self.currkey = self.keyfunc(self.currvalue)
self.tgtkey = self.currkey
return (self.currkey, self._grouper(self.tgtkey))
def _grouper(self, tgtkey):
while self.currkey == tgtkey:
yield self.currvalue
self.currvalue = self.it.next() # Exit on StopIteration
self.currkey = self.keyfunc(self.currvalue)
\end{verbatim}
\versionadded{2.4}
\end{funcdesc}
\begin{funcdesc}{ifilter}{predicate, iterable}
Make an iterator that filters elements from iterable returning only
those for which the predicate is \code{True}.
If \var{predicate} is \code{None}, return the items that are true.
Equivalent to:
\begin{verbatim}
def ifilter(predicate, iterable):
if predicate is None:
predicate = bool
for x in iterable:
if predicate(x):
yield x
\end{verbatim}
\end{funcdesc}
\begin{funcdesc}{ifilterfalse}{predicate, iterable}
Make an iterator that filters elements from iterable returning only
those for which the predicate is \code{False}.
If \var{predicate} is \code{None}, return the items that are false.
Equivalent to:
\begin{verbatim}
def ifilterfalse(predicate, iterable):
if predicate is None:
predicate = bool
for x in iterable:
if not predicate(x):
yield x
\end{verbatim}
\end{funcdesc}
\begin{funcdesc}{imap}{function, *iterables}
Make an iterator that computes the function using arguments from
each of the iterables. If \var{function} is set to \code{None}, then
\function{imap()} returns the arguments as a tuple. Like
\function{map()} but stops when the shortest iterable is exhausted
instead of filling in \code{None} for shorter iterables. The reason
for the difference is that infinite iterator arguments are typically
an error for \function{map()} (because the output is fully evaluated)
but represent a common and useful way of supplying arguments to
\function{imap()}.
Equivalent to:
\begin{verbatim}
def imap(function, *iterables):
iterables = map(iter, iterables)
while True:
args = [i.next() for i in iterables]
if function is None:
yield tuple(args)
else:
yield function(*args)
\end{verbatim}
\end{funcdesc}
\begin{funcdesc}{islice}{iterable, \optional{start,} stop \optional{, step}}
Make an iterator that returns selected elements from the iterable.
If \var{start} is non-zero, then elements from the iterable are skipped
until start is reached. Afterward, elements are returned consecutively
unless \var{step} is set higher than one which results in items being
skipped. If \var{stop} is \code{None}, then iteration continues until
the iterator is exhausted, if at all; otherwise, it stops at the specified
position. Unlike regular slicing,
\function{islice()} does not support negative values for \var{start},
\var{stop}, or \var{step}. Can be used to extract related fields
from data where the internal structure has been flattened (for
example, a multi-line report may list a name field on every
third line). Equivalent to:
\begin{verbatim}
def islice(iterable, *args):
s = slice(*args)
it = iter(xrange(s.start or 0, s.stop or sys.maxint, s.step or 1))
nexti = it.next()
for i, element in enumerate(iterable):
if i == nexti:
yield element
nexti = it.next()
\end{verbatim}
If \var{start} is \code{None}, then iteration starts at zero.
If \var{step} is \code{None}, then the step defaults to one.
\versionchanged[accept \code{None} values for default \var{start} and
\var{step}]{2.5}
\end{funcdesc}
\begin{funcdesc}{izip}{*iterables}
Make an iterator that aggregates elements from each of the iterables.
Like \function{zip()} except that it returns an iterator instead of
a list. Used for lock-step iteration over several iterables at a
time. Equivalent to:
\begin{verbatim}
def izip(*iterables):
iterables = map(iter, iterables)
while iterables:
result = [it.next() for it in iterables]
yield tuple(result)
\end{verbatim}
\versionchanged[When no iterables are specified, returns a zero length
iterator instead of raising a \exception{TypeError}
exception]{2.4}
Note, the left-to-right evaluation order of the iterables is guaranteed.
This makes possible an idiom for clustering a data series into n-length
groups using \samp{izip(*[iter(s)]*n)}. For data that doesn't fit
n-length groups exactly, the last tuple can be pre-padded with fill
values using \samp{izip(*[chain(s, [None]*(n-1))]*n)}.
Note, when \function{izip()} is used with unequal length inputs, subsequent
iteration over the longer iterables cannot reliably be continued after
\function{izip()} terminates. Potentially, up to one entry will be missing
from each of the left-over iterables. This occurs because a value is fetched
from each iterator in-turn, but the process ends when one of the iterators
terminates. This leaves the last fetched values in limbo (they cannot be
returned in a final, incomplete tuple and they are cannot be pushed back
into the iterator for retrieval with \code{it.next()}). In general,
\function{izip()} should only be used with unequal length inputs when you
don't care about trailing, unmatched values from the longer iterables.
\end{funcdesc}
\begin{funcdesc}{repeat}{object\optional{, times}}
Make an iterator that returns \var{object} over and over again.
Runs indefinitely unless the \var{times} argument is specified.
Used as argument to \function{imap()} for invariant parameters
to the called function. Also used with \function{izip()} to create
an invariant part of a tuple record. Equivalent to:
\begin{verbatim}
def repeat(object, times=None):
if times is None:
while True:
yield object
else:
for i in xrange(times):
yield object
\end{verbatim}
\end{funcdesc}
\begin{funcdesc}{starmap}{function, iterable}
Make an iterator that computes the function using arguments tuples
obtained from the iterable. Used instead of \function{imap()} when
argument parameters are already grouped in tuples from a single iterable
(the data has been ``pre-zipped''). The difference between
\function{imap()} and \function{starmap()} parallels the distinction
between \code{function(a,b)} and \code{function(*c)}.
Equivalent to:
\begin{verbatim}
def starmap(function, iterable):
iterable = iter(iterable)
while True:
yield function(*iterable.next())
\end{verbatim}
\end{funcdesc}
\begin{funcdesc}{takewhile}{predicate, iterable}
Make an iterator that returns elements from the iterable as long as
the predicate is true. Equivalent to:
\begin{verbatim}
def takewhile(predicate, iterable):
for x in iterable:
if predicate(x):
yield x
else:
break
\end{verbatim}
\end{funcdesc}
\begin{funcdesc}{tee}{iterable\optional{, n=2}}
Return \var{n} independent iterators from a single iterable.
The case where \code{n==2} is equivalent to:
\begin{verbatim}
def tee(iterable):
def gen(next, data={}, cnt=[0]):
for i in count():
if i == cnt[0]:
item = data[i] = next()
cnt[0] += 1
else:
item = data.pop(i)
yield item
it = iter(iterable)
return (gen(it.next), gen(it.next))
\end{verbatim}
Note, once \function{tee()} has made a split, the original \var{iterable}
should not be used anywhere else; otherwise, the \var{iterable} could get
advanced without the tee objects being informed.
Note, this member of the toolkit may require significant auxiliary
storage (depending on how much temporary data needs to be stored).
In general, if one iterator is going to use most or all of the data before
the other iterator, it is faster to use \function{list()} instead of
\function{tee()}.
\versionadded{2.4}
\end{funcdesc}
\subsection{Examples \label{itertools-example}}
The following examples show common uses for each tool and
demonstrate ways they can be combined.
\begin{verbatim}
>>> amounts = [120.15, 764.05, 823.14]
>>> for checknum, amount in izip(count(1200), amounts):
... print 'Check %d is for $%.2f' % (checknum, amount)
...
Check 1200 is for $120.15
Check 1201 is for $764.05
Check 1202 is for $823.14
>>> import operator
>>> for cube in imap(operator.pow, xrange(1,5), repeat(3)):
... print cube
...
1
8
27
64
>>> reportlines = ['EuroPython', 'Roster', '', 'alex', '', 'laura',
'', 'martin', '', 'walter', '', 'mark']
>>> for name in islice(reportlines, 3, None, 2):
... print name.title()
...
Alex
Laura
Martin
Walter
Mark
# Show a dictionary sorted and grouped by value
>>> from operator import itemgetter
>>> d = dict(a=1, b=2, c=1, d=2, e=1, f=2, g=3)
>>> di = sorted(d.iteritems(), key=itemgetter(1))
>>> for k, g in groupby(di, key=itemgetter(1)):
... print k, map(itemgetter(0), g)
...
1 ['a', 'c', 'e']
2 ['b', 'd', 'f']
3 ['g']
# Find runs of consecutive numbers using groupby. The key to the solution
# is differencing with a range so that consecutive numbers all appear in
# same group.
>>> data = [ 1, 4,5,6, 10, 15,16,17,18, 22, 25,26,27,28]
>>> for k, g in groupby(enumerate(data), lambda (i,x):i-x):
... print map(operator.itemgetter(1), g)
...
[1]
[4, 5, 6]
[10]
[15, 16, 17, 18]
[22]
[25, 26, 27, 28]
\end{verbatim}
\subsection{Recipes \label{itertools-recipes}}
This section shows recipes for creating an extended toolset using the
existing itertools as building blocks.
The extended tools offer the same high performance as the underlying
toolset. The superior memory performance is kept by processing elements one
at a time rather than bringing the whole iterable into memory all at once.
Code volume is kept small by linking the tools together in a functional style
which helps eliminate temporary variables. High speed is retained by
preferring ``vectorized'' building blocks over the use of for-loops and
generators which incur interpreter overhead.
\begin{verbatim}
def take(n, seq):
return list(islice(seq, n))
def enumerate(iterable):
return izip(count(), iterable)
def tabulate(function):
"Return function(0), function(1), ..."
return imap(function, count())
def iteritems(mapping):
return izip(mapping.iterkeys(), mapping.itervalues())
def nth(iterable, n):
"Returns the nth item or raise IndexError"
return list(islice(iterable, n, n+1))[0]
def all(seq, pred=None):
"Returns True if pred(x) is true for every element in the iterable"
for elem in ifilterfalse(pred, seq):
return False
return True
def any(seq, pred=None):
"Returns True if pred(x) is true for at least one element in the iterable"
for elem in ifilter(pred, seq):
return True
return False
def no(seq, pred=None):
"Returns True if pred(x) is false for every element in the iterable"
for elem in ifilter(pred, seq):
return False
return True
def quantify(seq, pred=None):
"Count how many times the predicate is true in the sequence"
return sum(imap(pred, seq))
def padnone(seq):
"""Returns the sequence elements and then returns None indefinitely.
Useful for emulating the behavior of the built-in map() function.
"""
return chain(seq, repeat(None))
def ncycles(seq, n):
"Returns the sequence elements n times"
return chain(*repeat(seq, n))
def dotproduct(vec1, vec2):
return sum(imap(operator.mul, vec1, vec2))
def flatten(listOfLists):
return list(chain(*listOfLists))
def repeatfunc(func, times=None, *args):
"""Repeat calls to func with specified arguments.
Example: repeatfunc(random.random)
"""
if times is None:
return starmap(func, repeat(args))
else:
return starmap(func, repeat(args, times))
def pairwise(iterable):
"s -> (s0,s1), (s1,s2), (s2, s3), ..."
a, b = tee(iterable)
try:
b.next()
except StopIteration:
pass
return izip(a, b)
def grouper(n, iterable, padvalue=None):
"grouper(3, 'abcdefg', 'x') --> ('a','b','c'), ('d','e','f'), ('g','x','x')"
return izip(*[chain(iterable, repeat(padvalue, n-1))]*n)
\end{verbatim}
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