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Taking sums across indices of a SparseArray efficiently
*To*: mathgroup at smc.vnet.net
*Subject*: [mg95926] Taking sums across indices of a SparseArray efficiently
*From*: "D. Grady" <D.C.Grady at gmail.com>
*Date*: Fri, 30 Jan 2009 05:42:22 -0500 (EST)
Suppose we've got a four-dimensional array:
t = Array[Subscript[w, ##] &, {3, 3, 3, 3}]
If we want to take the sum across one index of this array (which will
reduce its dimension), we can use the Total function:
Dimensions@Total[t, {2}]
{3, 3, 3}
In the problem I'm working on, I've got an array and I need to sum
across the first two dimensions. Using this toy array, I can see that
Total[t,{1,2}] gives me exactly the object that I want. The problem
is that I'm working with a four-dimensional sparse array, and Total
will apparently always try to convert its first argument to a normal
array. This fails because the array is too big to fit in memory:
In[26]:= WAF = Total[W, {1, 2}]; // Timing
During evaluation of In[26]:= SparseArray::ntb: Cannot convert the
sparse array SparseArray[Automatic,{489,489,489,489},0,{<<1>>}] to an
ordinary array because the 57178852641 elements required exceeds the
current size limit. >>
Out[26]= SystemException[SparseArrayNormalLimit,Normal[SparseArray
[<1400152>,{489,489,489,489}]]]
I can roll my own function to do this computation just by sorting
through the ArrayRules:
Timing[
WAF =
SparseArray@(
(#[[1, 1, 3 ;; 4]] -> Total[#[[All, 2]]] &) /@
(SplitBy[#, Drop[First@#, 2] &] &)@
(SortBy[#, Drop[First@#, 2] &] &)@
Most@
ArrayRules@
W)]
{22.1335,SparseArray[<21122>,{489,489}]}
The point is that actually doing the computation isn't particularly
memory or time intensive, but I can't find a simple way to do this
directly using built-in functions like Total. Does anyone know if
there is a way? If there isn't, why not? Thanks a lot!
-Daniel
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