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Re: Efficient function to accumulate a list of

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  Re: Efficient function to accumulate a list of Ray Koopman <koopman@sfu.ca> - 2014-04-08 07:36 +0000

#16747 — Re: Efficient function to accumulate a list of

I found the reference to the undocumented SparseArray option 
that will sum multiple values assigned to the same location. It's
http://forums.wolfram.com/mathgroup/archive/2010/Dec/msg00070.html

In[1]:= SetSystemOptions[
        "SparseArrayOptions" -> {"TreatRepeatedEntries" -> 1}];

In[2]:= 
particles = { {3.6, 7,4}, {3.4, 8,6}, {2.1, 7,4} };
arr = SparseArray[Rest@# -> First@# & /@ particles, {10,10}]

Out[3]= SparseArray[< 2 >,{10,10}]

In[4]:= Normal[arr]

Out[4]= 
{{0,0,0,0,0,0,0,0,0,0},
 {0,0,0,0,0,0,0,0,0,0},
 {0,0,0,0,0,0,0,0,0,0},
 {0,0,0,0,0,0,0,0,0,0},
 {0,0,0,0,0,0,0,0,0,0},
 {0,0,0,0,0,0,0,0,0,0},
 {0,0,0,5.7,0,0,0,0,0,0},
 {0,0,0,0,0,3.4,0,0,0,0},
 {0,0,0,0,0,0,0,0,0,0},
 {0,0,0,0,0,0,0,0,0,0}}

In[5]:= $Version

Out[5]= "6.0 for Mac OS X PowerPC (32-bit) (June 19, 2007)"

----- Ray Koopman <koopman@sfu.ca> wrote:

> In[1]:= 
> particles = { {3.6, 7,4}, {3.4, 8,6}, {2.1, 7,4} };
> arr = SparseArray[Rest@#[[1]] -> Tr@#[[All,1]] & /@ 
>       Last@Reap@Scan[Sow[#,{Rest@#}]&,particles], {10,10}]
> 
> Out[2]= SparseArray[< 2 >,{10,10}]
> 
> In[3]:= Normal[arr]
> 
> Out[3]=
> {{0,0,0,0,0,0,0,0,0,0},
>  {0,0,0,0,0,0,0,0,0,0},
>  {0,0,0,0,0,0,0,0,0,0},
>  {0,0,0,0,0,0,0,0,0,0},
>  {0,0,0,0,0,0,0,0,0,0},
>  {0,0,0,0,0,0,0,0,0,0},
>  {0,0,0,5.7,0,0,0,0,0,0},
>  {0,0,0,0,0,3.4,0,0,0,0},
>  {0,0,0,0,0,0,0,0,0,0},
>  {0,0,0,0,0,0,0,0,0,0}}
>  
>  In[4]:= $Version
> 
> Out[4]= 5.2 for Mac OS X (June 20, 2005)
> 
> With v7+, use GatherBy instead of Reap/Scan/Sow.
> 
> I remember reading somewhere about an undocumented option in SparseArray that will automatically sum multiple values assigned to the same location, but I don't know remember the details.
> 
> ----- julian w francis <julian.w.francis@gmail.com> wrote:
> 
>> Dear all,
>> 
>> I am struggling with how to convert a list of (value, coords) tuples into an array such that the an element in the array should represent the sum of all value elements in that list with matching coords, and zero if no matches, e.g.
>> 
>> { {3.6, 7,4}, {3,4, 8,6}, {2.1, 7,4} }
>> 
>> if it were a 10X10 element array would become all zero's, except element (7,4)->(3.6+2.1) and (8,6)->3.4
>> 
>> I've got some code which does what I want:
>> 
>> ParticleToDensity[particles_] := (
>>   arr = ConstantArray[0, {144, 300}];
>>   For[l = 1, l < NoParticles, l++,
>>    (tp = particles[[l]];
>>     If[tp[[2]] != 0,
>>      arr[[Round[tp[[3]]], Round[tp[[2]]]]] += tp[[1]]]
>>     )];
>>   arr)
>> 
>> So, the argument to the function is a list of "particles", and the first element of this particle is the value in the array I'd like to accumulate, and the next two elements in that particle say where in the array they should be accumulated.
>> 
>> It seems to work, but it is slow. I can see that this isn't really the Mathematica way of doing things, but I'm struggling to think of a better way.
>> 
>> For reference, NoParticles is typically set to something like 10,000, and it takes about 0.1 secs to process on my machine. However this needs to be done frequently, hence I am hoping for a better way.
>> 
>> Any help greatly appreciated.
>> 
>> Thanks,
>> Julian.

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