How to find the cumulative sum of numbers in a list

Question

time interval    4  6  12    I want to sum up the numbers like  4  4 6  4 6 12  in order to get the list t    4  10  22    I tried the following   t1   time interval 0  t2   time interval 1    t1 t3   time interval 2    t2 print t1  t2  t3     - gt  4 10 22

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Without having to use Numpy  you can loop directly over the array and accumulate the sum along the way  For example   a range 10  i 1 while  i gt 0   amp   i lt 10        a i  a i-1  a i      i i 1 print a   Results in     0  1  3  6  10  15  21  28  36  45

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Somewhat hacky  but seems to work   def cumulative sum l     y    0    def inc n       y 0     n     return y 0    return  inc x  for x in l    I did think that the inner function would be able to modify the y declared in the outer lexical scope  but that didn t work  so we play some nasty hacks with structure modification instead  It is probably more elegant to use a generator

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Try this   accumulate function  along with operator add performs the running addition   import itertools   import operator   result   itertools accumulate  1 2 3 4 5   operator add    list result

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l    1 -1 3  cum list   l  def sum list input list       index   1     for i in input list 1            cum list index    i   input list index-1          index   index   1      return cum list  print sum list l

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I did a bench-mark of the top two answers with Python 3 4 and I found itertools accumulate is faster than numpy cumsum under many circumstances  often much faster  However  as you can see from the comments  this may not always be the case  and it s difficult to exhaustively explore all options   Feel free to add a comment or edit this post if you have further benchmark results of interest    Some timings     For short lists accumulate is about 4 times faster   from timeit import timeit  def sum1 l       from itertools import accumulate     return list accumulate l    def sum2 l       from numpy import cumsum     return list cumsum l    l    1  2  3  4  5   timeit lambda  sum1 l   number 100000    0 4243644131347537 timeit lambda  sum2 l   number 100000    1 7077815784141421   For longer lists accumulate is about 3 times faster   l    1  2  3  4  5  1000 timeit lambda  sum1 l   number 100000    19 174508565105498 timeit lambda  sum2 l   number 100000    61 871223849244416   If the numpy array is not cast to list  accumulate is still about 2 times faster   from timeit import timeit  def sum1 l       from itertools import accumulate     return list accumulate l    def sum2 l       from numpy import cumsum     return cumsum l   l    1  2  3  4  5  1000  print timeit lambda  sum1 l   number 100000     19 18597290944308 print timeit lambda  sum2 l   number 100000     37 759664884768426   If you put the imports outside of the two functions and still return a numpy array  accumulate is still nearly 2 times faster   from timeit import timeit from itertools import accumulate from numpy import cumsum  def sum1 l       return list accumulate l    def sum2 l       return cumsum l   l    1  2  3  4  5  1000  timeit lambda  sum1 l   number 100000    19 042188624851406 timeit lambda  sum2 l   number 100000    35 17324400227517

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lst    4 6 12    sum lst  i 1   for i in xrange len lst      If you are looking for a more efficient solution  bigger lists   a generator could be a good call  or just use numpy if you really care about perf    def gen lst       acu   0     for num in lst          yield num   acu         acu    num  print list gen  4  6  12

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If you re doing much numerical work with arrays like this  I d suggest numpy  which comes with a cumulative sum function cumsum   import numpy as np  a    4 6 12   np cumsum a   array  4  10  22     Numpy is often faster than pure python for this kind of thing  see in comparison to  Ashwini s accumu   In  136   timeit list accumu range 1000    10000 loops  best of 3  161 us per loop  In  137   timeit list accumu xrange 1000    10000 loops  best of 3  147 us per loop  In  138   timeit np cumsum np arange 1000   100000 loops  best of 3  10 1 us per loop   But of course if it s the only place you ll use numpy  it might not be worth having a dependence on it

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You can calculate the cumulative sum list in linear time with a simple for loop   def csum lst       s   lst copy       for i in range 1  len s            s i     s i-1      return s  time interval    4  6  12  print csum time interval       4  10  22    The standard library s itertools accumulate may be a faster alternative  since it s implemented in C    from itertools import accumulate time interval    4  6  12  print list accumulate time interval        4  10  22

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In Python3  To find the cumulative sum of a list where the ith element is the sum of the first i 1 elements from the original list  you may do   a    4   6   12  b      for i in range 0 len a        b append sum a  i 1    print b    OR you may use list comprehension   b    sum a  x 1   for x in range 0 len a      Output    4 10 22

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First  you want a running list of subsequences   subseqs    seq  i  for i in range 1  len seq  1     Then you just call sum on each subsequence   sums    sum subseq  for subseq in subseqs     This isn t the most efficient way to do it  because you re adding all of the prefixes repeatedly  But that probably won t matter for most use cases  and it s easier to understand if you don t have to think of the running totals    If you re using Python 3 2 or newer  you can use itertools accumulate to do it for you   sums   itertools accumulate seq    And if you re using 3 1 or earlier  you can just copy the  equivalent to  source straight out of the docs  except for changing next it  to it next   for 2 5 and earlier

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Try this   result      acc   0 for i in time interval      acc    i     result append acc

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values    4  6  12  total    0 sums         for v in values    total   total   v   sums append total   print  Values     values print  Sums       sums   Running this code gives  Values   4  6  12  Sums     4  10  22

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If You want a pythonic way without numpy working in 2 7 this would be my way of doing it  l    1 2 3 4   d  -1 0  cumsum   d setdefault idx   d idx-1  item  for idx item in enumerate l     now let s try it and test it against all other implementations  import timeit  sys L list range 10000   if sys version info  gt    3  0       reduce   functools reduce     xrange   range   def sum1 l       cumsum        total   0     for v in l          total    v         cumsum append total      return cumsum   def sum2 l       import numpy as np     return list np cumsum l    def sum3 l       return  sum l  i 1   for i in xrange len l     def sum4 l       return reduce lambda c  x  c    c -1    x   l   0   1    def this implementation l        d  -1 0      return   d setdefault idx   d idx-1  item  for idx item in enumerate l       sanity check sum1 L   sum2 L   sum3 L   sum4 L   this implementation L   gt  gt  gt  True        PERFORMANCE TEST timeit timeit  sum1 L    from   main   import sum1 sum2 sum3 sum4 this implementation L   number 100  100   gt  gt  gt  0 001018061637878418  timeit timeit  sum2 L    from   main   import sum1 sum2 sum3 sum4 this implementation L   number 100  100   gt  gt  gt  0 000829620361328125  timeit timeit  sum3 L    from   main   import sum1 sum2 sum3 sum4 this implementation L   number 100  100   gt  gt  gt  0 4606760001182556   timeit timeit  sum4 L    from   main   import sum1 sum2 sum3 sum4 this implementation L   number 100  100   gt  gt  gt  0 18932826995849608  timeit timeit  this implementation L    from   main   import sum1 sum2 sum3 sum4 this implementation L   number 100  100   gt  gt  gt  0 002348129749298096

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Here s another fun solution  This takes advantage of the locals   dict of a comprehension  i e  local variables generated inside the list comprehension scope   gt  gt  gt   locals   setdefault i   elem   locals   get i-1  0    for i  elem       in enumerate time interval    4  10  22   Here s what the locals   looks for each iteration   gt  gt  gt    locals   setdefault i   elem   locals   get i-1  0     locals   copy    1        for i  elem in enumerate time interval       0    lt enumerate at 0x21f21f7fc80 gt    i   0   elem   4  0  4       0    lt enumerate at 0x21f21f7fc80 gt    i   1   elem   6  0  4  1  10       0    lt enumerate at 0x21f21f7fc80 gt    i   2   elem   12  0  4  1  10  2  22    Performance is not terrible for small lists   gt  gt  gt   timeit list accumulate  4  6  12    387 ns    7 53 ns per loop  mean    std  dev  of 7 runs  1000000 loops each    gt  gt  gt   timeit np cumsum  4  6  12   5 31   s    67 8 ns per loop  mean    std  dev  of 7 runs  100000 loops each    gt  gt  gt   timeit  locals   setdefault i   e   locals   get i-1 0    for i e in enumerate time interval   1 57   s    12 ns per loop  mean    std  dev  of 7 runs  1000000 loops each   And obviously falls flat for larger lists   gt  gt  gt  l   list range 1 000 000    gt  gt  gt   timeit list accumulate l   95 1 ms    5 22 ms per loop  mean    std  dev  of 7 runs  10 loops each    gt  gt  gt   timeit np cumsum l  79 3 ms    1 07 ms per loop  mean    std  dev  of 7 runs  10 loops each    gt  gt  gt   timeit np cumsum l  tolist   120 ms    1 23 ms per loop  mean    std  dev  of 7 runs  10 loops each    gt  gt  gt   timeit  locals   setdefault i   e   locals   get i-1  0    for i  e in enumerate l   660 ms    5 14 ms per loop  mean    std  dev  of 7 runs  1 loop each   Even though the method is ugly and not practical  it sure is fun

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A pure python oneliner for cumulative sum    cumsum   lambda X  X  1    cumsum  X 0  X 1     X 2    if X 1   else X   This is a recursive version inspired by recursive cumulative sums  Some explanations    The first term X  1  is a list containing the previous element and is almost the same as  X 0    which would complain for empty lists   The recursive cumsum call in the second term processes the current element  1  and remaining list whose length will be reduced by one  if X 1   is shorter for if len X  gt 1    Test   cumsum  4 6 12     4  10  22   cumsum           And simular for cumulative product   cumprod   lambda X  X  1    cumprod  X 0  X 1     X 2    if X 1   else X   Test   cumprod  4 6 12     4  24  288

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In  42   a    4  6  12   In  43    sum a  i 1   for i in xrange len a    Out 43    4  10  22    This is slighlty faster than the generator method above by  Ashwini for small lists  In  48    timeit list accumu  4 6 12      100000 loops  best of 3  2 63 us per loop  In  49    timeit  sum a  i 1   for i in xrange len a      100000 loops  best of 3  2 46 us per loop   For larger lists  the generator is the way to go for sure        In  50   a   range 1000   In  51    timeit  sum a  i 1   for i in xrange len a      100 loops  best of 3  6 04 ms per loop  In  52    timeit list accumu a     10000 loops  best of 3  162 us per loop

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Behold   a    4  6  12  reduce lambda c  x  c    c -1    x   a   0   1     Will output  as expected     4  10  22

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Assignment expressions from PEP 572  new in Python 3 8  offer yet another way to solve this   time interval    4  6  12   total time   0 cum time    total time    total time   t for t in time interval

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This would be Haskell-style   def wrand vtlg        def helpf lalt lneu             if not lalt                  return helpf lalt 1     lalt 0  lneu 0   lneu          else              lneu reverse               return lneu 1                return helpf vtlg  0

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In Python 2 you can define your own generator function like this   def accumu lis       total   0     for x in lis          total    x         yield total  In  4   list accumu  4 6 12    Out 4    4  10  22    And in Python 3 2  you can use itertools accumulate     In  1   lis    4 6 12   In  2   from itertools import accumulate  In  3   list accumulate lis   Out 3    4  10  22

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There could be many answers for this depending on the length of the list and the performance  One very simple way which I can think without thinking of the performance is this    a    1  2  3  4  a    sum a 0 x 1   for x in range len a  1   1   print a     1  3  6  10   This is by using list comprehension and this may work fairly well it is just that here I am adding over the subarray many times  you could possibly improvise on this and make it simple   Cheers to your endeavor

[python] How to find the cumulative sum of numbers in a list?

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